Quotations with the word idea in

Top 10 idea Quotes

Countries persist in the mistaken idea that human rights are dispensable. At the global level, we must work together towards forging a new momentum on effectuating recognition of human rights.- J BAnd this I believe: that without respect for human rights, we will never know world peace. And this I would fight for: protecting human rights. And this I must fight against: any idea or government which violates human rights. This is what I am and what I am about.- J BIt’s our oneness that gives us the ability to create an idea without a related stimulus. It’s this oneness that separates us from a computer.- Donald Lynn Frost

quotations about ideas

I’ve known people who had fantastic ideas, but who couldn’t get the idea off the ground because they approached everything weakly. They thought that their ideas would somehow take off by themselves, or that just coming up with an idea was enough. Let me tell you something — it’s not enough. It will never be enough. You have to put the idea into action. If you don’t have the motivation and the enthusiasm, your great idea will simply sit on top of your desk or inside your head and go nowhere.

DONALD TRUMP

Trump 101

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The more circumspectly you delay writing down an idea, the more maturely developed it will be on surrendering itself.

WALTER BENJAMIN

Reflections

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America is not just a country, it’s an idea.

BONO

2004 PENN Address

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I can’t understand why people are frightened of new ideas. I’m frightened of the old ones.

JOHN CAGE

Conversing with Cage

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A powerful idea communicates some of its power to the man who contradicts it. Partaking of the universal community of minds, it infiltrates, grafts itself on to, the mind of him who it refutes, among other contiguous ideas, with the aid of which, counter-attacking, he complements and corrects it; so that the final verdict is always to some extent the work of both parties to a discussion.

MARCEL PROUST

Within a Budding Grove

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My weakness has always been to prefer the large intention of an unskilful artist to the trivial intention of an accomplished one: in other words, I am more interested in the high ideas of a feeble executant than in the high execution of a feeble thinker.

THOMAS HARDY

letter, Jul. 8, 1901

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An invasion of armies can be resisted, but not an idea whose time has come.

VICTOR HUGO

Histoire d’un crime

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Wide acceptance of an idea is not proof of its validity.

DAN BROWN

The Lost Symbol

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The difficulty lies not so much in developing new ideas as in escaping from old ones.

JOHN MAYNARD KEYNES

attributed, Engines of Creation

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The problem is that the people with the most ridiculous ideas are always the people who are most certain of them.

BILL MAHER

The Decider, July 21, 2007

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Nothing, believe me, nothing is more satisfying to me personally than getting a great idea and then beatin’ it to death.

DAVID LETTERMAN

Late Night with David Letterman, March 5, 1993

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Man’s mind, once stretched by a new idea, never regains its original dimensions.

OLIVER WENDELL HOLMES

JR., Inspirational Quotes to Motivate

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Everyone sits in the prison of his own ideas; he must burst it open, and that in his youth, and so try to test his ideas on reality.

ALBERT EINSTEIN

Cosmic Religion: With Other Opinions and Aphorisms

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The idea enters the brain from the outside. It rearranges the furniture to make it more to its liking. It finds other Ideas already in residence, and picks fights or forms alliances. The alliances build new structures, to defend themselves against intruders. And then, whenever the opportunity arises, the Idea sends out its shock troops in search of new brains to infect. The successful Idea travels from mind to mind, claiming new territory, mutating as it goes. It’s a jungle out there … many ideas are lost. Only the strongest survive.

BERNARD BECKETT

Genesis

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Ideas are invented only as correctives to the past. Through repeated rectifications of this kind one may hope to disengage an idea that is valid.

GASTON BACHELARD

Fragments of a Poetics of Fire

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Whoso shrinks from ideas ends by having nothing but sensations.

JOHANN WOLFGANG VON GOETHE

The Maxims and Reflections of Goethe

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A man who ain’t got ideas of his own should be mighty careful who he borrows ’em from.

KEN ALSTAD

Savvy Sayin’s

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If those in charge of our society — politicians, corporate executives, and owners of press and television — can dominate our ideas, they will be secure in their power. They will not need soldiers patrolling the streets. We will control ourselves.

HOWARD ZINN

Declarations of Independence: Cross-Examining American Ideology

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We are far more the creatures of our ideas than of our circumstances.

CHRISTIAN NESTELL BOVEE, Intuitions and Summaries of Thought

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One who accepts the general ideas of his time gets along smoothest, but he does the least for progress.

LEWIS F. KORNS

Thoughts

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List of top 100 famous quotes and sayings about idea the word to read and share with friends on your Facebook, Twitter, blogs.

Top 100 Idea The Word Quotes

Idea Quotes (861 quotes)

… I left Caen, where I was living, to go on a geologic excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Eudidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.

Quoted in Sir Roger Penrose, The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics (1990), 541. Science and Method (1908) 51-52, 392.

…an idea is no more an even relatively constant thing than is a feeling or emotion or volitional process. There exist only changing and transient ideational processes; there are no permanent ideas that return again and disappear again.

An Introduction to Psychology (1912)

…travel is more than the seeing of sights; it is a change that goes on, deep and permanent, in the ideas of living.

……

“Le génie n’est qu’une longue patience”, a dit Buffon. Cela est bien incomplet. Le génie, c’est l’impatience dans les idées et la patience dans les faits : une imagination vive et un jugement calme; quelque chose comme un liquide en ébullition dans un vase qui reste toujours froid.
“Genius is just enduring patience,” said Buffon. This is far from complete. Genius is impatience in ideas and patience with the facts: a lively imagination and a calm judgment, rather like a liquid boiling in a cup that remains cold.

In Recueil d’Œuvres de Léo Errera: Botanique Générale (1908), 198. Google translation by Webmaster.

Air Chief Marshal Harris [objecting to a change in strategy recommended by statisticians]: Are we fighting this war with weapons or the slide rule?
Churchill [after puffing on his cigar]: That’s a good idea. Let’s try the slide rule.

During World War II, Britain lost the advantage when enemy U-boats began listening in to the aircraft radar, were forewarned, and would dive. U-boat sinkings fell to zero. Physicist Patrick S. Blackett with his Operational Research colleagues came up with a solution. Concentrate sufficient aircraft in certain areas, causing the subs to dive so frequently their air supply and batteries were exhausted, forcing them to remain on the surface and be vulnerable to attack. The strategy required diverting several squadrons from Bomber Command to Coastal Command. “Bomber” Harris voiced his objection to Churchill, who made the right choice, proved by successful results. As described by R.V. Jones, ‘Churchill and Science’, in Robert Blake and Wm. Roger Louis (eds.), Churchill (1996), 437.

Bernard: Oh, you’re going to zap me with penicillin and pesticides. Spare me that and I’ll spare you the bomb and aerosols. But don’t confuse progress with perfectibility. A great poet is always timely. A great philosopher is an urgent need. There’s no rush for Isaac Newton. We were quite happy with Aristotle’s cosmos. Personally, I preferred it. Fifty-five crystal spheres geared to God’s crankshaft is my idea of a satisfying universe. I can’t think of anything more trivial than the speed of light. Quarks, quasars—big bangs, black holes—who [cares]? How did you people con us out of all that status? All that money? And why are you so pleased with yourselves?
Chloe: Are you against penicillin, Bernard?
Bernard: Don’t feed the animals.

In the play, Acadia (1993), Act 2, Scene 5, 61.

Ce grand ouvrage, toujours plus merveilleux à mesure qu’il est plus connu, nous donne une si grande idée de son ouvrier, que nous en sentons notre esprit accablé d’admiration et de respect.
[The Universe] This great work, always more amazing in proportion as it is better known, raises in us so grand an idea of its Maker, that we find our mind overwhelmed with feelings of wonder and adoration.

Original French and translation in Craufurd Tait Ramage (ed.) Beautiful Thoughts from French and Italian Authors (1866), 119-120.

Clarke’s First Law — Corollary: When, however, the lay public rallies round an idea that is denounced by distinguished but elderly scientists and supports that idea with great fervor and emotion—the distinguished but elderly scientists are then, after all, probably right.

‘Asimov’s Corollary’, Fantasy & Science Fiction (Feb 1977). In collection Quasar, Quasar, Burning Bright (1978), 231.

Il ne fallait jamais faire des expériences pour confirmer ses idées, mais simplement pour les contrôler.
We must never make experiments to confirm our ideas, but simply to control them.

From Introduction à l’étude de la médecine expérimentale (1865), 67-68. Translation from Henry Copley Green, An Introduction to the Study of Experimental Medicine (1957), 38. Bernard footnoted that he had expressed this idea earlier in Leçons sur les propriétés et les altérations des liquides de l’organisme (1859), Première leçon.

Indiana Jones: Archaeology is the search for fact… not truth. If it’s truth you’re looking for, Dr. Tyree’s philosophy class is right down the hall. … So forget any ideas you’ve got about lost cities, exotic travel, and digging up the world. We do not follow maps to buried treasure, and “X” never, ever marks the spot. Seventy percent of all archaeology is done in the library. Research. Reading.

Spoken by actor Harrison Ford as character Indiana Jones in movie, Indiana Jones and the Last Crusade (1989).

Is mihi semper dicendus est inventor, qui primus evuIgaverit, vel saltem cum amicis communicaverit.
I should always call inventor him who first publishes, or at least communicates [the idea] to his friends.

Meditationes Analyticae (1785), ii-iii.

La théorie n’est que l’idée scientifique contrôlée par l’expérience.
A theory is merely a scientific idea controlled by experiment.

Original work in French, Introduction à l’Étude de la Médecine Expérimentale (1865), 40. English translation by Henry Copley Green in An Introduction to the Study of Experimental Medicine (1927, 1957), 26.

Longtemps les objets dont s’occupent les mathématiciens étaient our la pluspart mal définis; on croyait les connaître, parce qu’on se les représentatit avec le sens ou l’imagination; mais on n’en avait qu’une image grossière et non une idée précise sure laquelle le raisonment pût avoir prise.
For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 97.

Ron Hutcheson, a Knight-Ridder reporter: [Mr. President, what are your] personal views [about the theory of] intelligent design?
President George W. Bush: [Laughing. You’re] doing a fine job of dragging me back to the past [days as governor of Texas]. … Then, I said that, first of all, that decision should be made to local school districts, but I felt like both sides ought to be properly taught…”
Hutcheson: Both sides ought to be properly taught?
President: Yes … so people can understand what the debate is about.
Hutcheson: So the answer accepts the validity of “intelligent design” as an alternative to evolution?
President: I think that part of education is to expose people to different schools of thought, and I’m not suggesting—you’re asking me whether or not people ought to be exposed to different ideas, and the answer is yes.
Hutcheson: So we’ve got to give these groups—…
President: [interrupting] Very interesting question, Hutch. [Laughter from other reporters]

From conversation with reporters at the White House (1 Aug 2005), as quoted by Matthew Cooper in ‘Fanning the Controversy Over “Intelligent Design”’, Time (3 Aug 2005). The Time writer stated, “The president has gone farther in questioning the widely-taught theories of evolution and natural selection than any president since Ronald Reagan, who advocated teaching creationism in public schools alongside evolution.” Just a few months later, in the nation’s first case on that point, on 20 Dec 2005, “a federal judge [John E. Jones] ruled it was unconstitutional for a Pennsylvania school district to present intelligent design as an alternative in high school biology courses, because it is a religious viewpoint,” as reported by Laurie Goodstein in ‘Judge Rejects Teaching Intelligent Design’, New York Times (21 Dec 2005). Goodstein also wrote “Judge Jones, a Republican appointed by President Bush, concluded that intelligent design was not science,” and that “the evidence in the trial proved that intelligent design was ‘creationism relabeled.’ The Supreme Court has already ruled that creationism … cannot be taught as science in a public school.”

The Annotated Alice, of course, does tie in with math, because Lewis Carroll was, as you know, a professional mathematician. So it wasn’t really too far afield from recreational math, because the two books are filled with all kinds of mathematical jokes. I was lucky there in that I really didn’t have anything new to say in The Annotated Alice because I just looked over the literature and pulled together everything in the form of footnotes. But it was a lucky idea because that’s been the best seller of all my books.

In Anthony Barcellos, ‘A Conversation with Martin Gardner’, The Two-Year College Mathematics Journal (Sep 1979), 10, No. 4, 241.

Truth then seems to me, in the proper import of the Word, to signifie nothing but the joining or separating of Signs, as the Things signified by them do agree or disagree one with another; which way of joining or separating of Signs, we call Proposition. So that Truth properly belongs only to Propositions: whereof there are two sorts, viz. Mental and Verbal; as there are two sorts of Signs commonly made use of, viz. Ideas and Words.

In ‘Truth in General’, Essay Concerning Human Understanding (1690), book 4, ch. 5, sec. 2, 289.

Une idée anticipée ou une hypothèse est donc le point de départ nécessaire de tout raisonnement expérimental. Sans cela on ne saurait faire aucune investigation ni s’instruire ; on ne pourrait qu’entasser des observations stériles. Si l’on expérimentait sans idée préconçue, on irait à l’aventure; mais d’un autre côté, ainsi que nous l’avons dit ailleurs, si l’on observait avec des idées préconçues, on ferait de mauvaises observations.
An anticipative idea or an hypothesis is, then, the necessary starting point for all experimental reasoning. Without it, we could not make any investigation at all nor learn anything; we could only pile up sterile observations. If we experimented without a preconceived idea, we should move at random.
[Also seen translated as:] A hypothesis is … the obligatory starting point of all experimental reasoning. Without it no investigation would be possible, and one would learn nothing: one could only pile up barren observations. To experiment without a preconceived idea is to wander aimlessly.

Original work in French, Introduction à l’Étude de la Médecine Expérimentale (1865). English translation by Henry Copley Green in An Introduction to the Study of Experimental Medicine (1927, 1957), 32. Alternate translation in Peter Medawar, ‘Hypothesis and Imagination’, collected in The Strange Case of the Spotted Mice and Other Classic Essays on Science (1974), 30.

Wenn sich für ein neues Fossil kein, auf eigenthümliche Eigenschaften desselben hinweisender, Name auffinden lassen Will; als in welchem Falle ich mich bei dem gegenwärtigen zu befinden gestehe; so halte ich es für besser, eine solche Benennung auszuwählen, die an sich gar nichts sagt, und folglich auch zu keinen unrichtigen Begriffen Anlass geben kann. Diesem zufolge will ich den Namen für die gegenwärtige metallische Substanz, gleichergestalt wie bei dem Uranium geschehen, aus der Mythologie, und zwar von den Ursöhnen der Erde, den Titanen, entlehnen, und benenne also dieses neue Metallgeschlecht: Titanium.
Wherefore no name can be found for a new fossil [element] which indicates its peculiar and characteristic properties (in which position I find myself at present), I think it is best to choose such a denomination as means nothing of itself and thus can give no rise to any erroneous ideas. In consequence of this, as I did in the case of Uranium, I shall borrow the name for this metallic substance from mythology, and in particular from the Titans, the first sons of the earth. I therefore call this metallic genus TITANIUM.

Martin Heinrich Klaproth. Original German edition, Beiträge Zur Chemischen Kenntniss Der Mineralkörper (1795), Vol. 1 , 244. English edition, translator not named, Analytical Essays Towards Promoting the Chemical Knowledge of Mineral Substances (1801), Vol. 1, 210. Klaproth’s use of the term fossil associates his knowledge of the metal as from ore samples dug out of a mine.

[About Pierre de Fermat] It cannot be denied that he has had many exceptional ideas, and that he is a highly intelligent man. For my part, however, I have always been taught to take a broad overview of things, in order to be able to deduce from them general rules, which might be applicable elsewhere.

Quoted, without source, in The Grolier Library of Science Biographies (1996), Vol. 3, 191.

[David Harker asked: Dr Pauling, how do you have so many good ideas?]
Well David, I have a lot of ideas and throw away the bad ones.

David Harker was one of Pauling’s students in the 1930s. Quoted in Thomas Hager, Force of Nature: The Life of Linus Pauling (1995), 529.

Science quotes on:  |  Ask (414)  |  Bad (180)  |  Do (1905)  |  Good (894)  |  Lot (151)  |  Throw (43)

[Question: What do you think was the most important physics idea to emerge this year?]
We won’t know for a few years.

Interview with Deborah Solomon, ‘The Science of Second-Guessing’, in New York Times Magazine (12 Dec 2004), 37.

[Recalling Professor Ira Remsen’s remarks (1895) to a group of his graduate students about to go out with their degrees into the world beyond the university:]
He talked to us for an hour on what was ahead of us; cautioned us against giving up the desire to push ahead by continued study and work. He warned us against allowing our present accomplishments to be the high spot in our lives. He urged us not to wait for a brilliant idea before beginning independent research, and emphasized the fact the Lavoisier’s first contribution to chemistry was the analysis of a sample of gypsum. He told us that the fields in which the great masters had worked were still fruitful; the ground had only been scratched and the gleaner could be sure of ample reward.

Quoted in Frederick Hutton Getman, The Life of Ira Remsen (1980), 73.

A bacteriologist is a man whose conversation always starts with the germ of an idea.

Quoted in M. Goran, A Treasury of Science Jokes (1986), 37.

A bad earthquake at once destroys the oldest associations: the world, the very emblem of all that is solid, has moved beneath our feet like a crust over a fluid; one second of time has conveyed to the mind a strange idea of insecurity, which hours of reflection would never have created.

Journal of Researches: Into the Natural History and Geology of the Countries Visited During the Voyage of H.M.S. BeagIe Round the World (1839), ch. XVI, 369.

A casual glance at crystals may lead to the idea that they were pure sports of nature, but this is simply an elegant way of declaring one’s ignorance. With a thoughtful examination of them, we discover laws of arrangement. With the help of these, calculation portrays and links up the observed results. How variable and at the same time how precise and regular are these laws! How simple they are ordinarily, without losing anything of their significance! The theory which has served to develop these laws is based entirely on a fact, whose existence has hitherto been vaguely discerned rather than demonstrated. This fact is that in all minerals which belong to the same species, these little solids, which are the crystal elements and which I call their integrant molecules, have an invariable form, in which the faces lie in the direction of the natural fracture surfaces corresponding to the mechanical division of the crystals. Their angles and dimensions are derived from calculations combined with observation.

Traité de mineralogie … Publié par le conseil des mines (1801), Vol. 1, xiii-iv, trans. Albert V. and Marguerite Carozzi.

A committee is a cul-de-sac down which ideas are lured and then quietly strangled.

As quoted in New Scientist (1973), 60, 424.

A definition is the enclosing a wilderness of idea within a wall of words.

Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 221.

A final proof of our ideas can only be obtained by detailed studies on the alterations produced in the amino acid sequence of a protein by mutations of the type discussed here.

In Nobel Lecture (11 Dec 1962). Collected in Nobel Lectures, Physiology or Medicine 1942-1962 (1964).

A good philosopher is one who does not take ideas seriously.

In ‘Philosophy, Religion, and So Forth’, A Voice Crying in the Wilderness (1989), 1.

A good scientist is a person with original ideas. A good engineer is a person who makes a design that works with as few original ideas as possible. There are no prima donnas in engineering.

In Disturbing the Universe (1979), 114.

A hundred years ago … an engineer, Herbert Spencer, was willing to expound every aspect of life, with an effect on his admiring readers which has not worn off today.
Things do not happen quite in this way nowadays. This, we are told, is an age of specialists. The pursuit of knowledge has become a profession. The time when a man could master several sciences is past. He must now, they say, put all his efforts into one subject. And presumably, he must get all his ideas from this one subject. The world, to be sure, needs men who will follow such a rule with enthusiasm. It needs the greatest numbers of the ablest technicians. But apart from them it also needs men who will converse and think and even work in more than one science and know how to combine or connect them. Such men, I believe, are still to be found today. They are still as glad to exchange ideas as they have been in the past. But we cannot say that our way of life is well-fitted to help them. Why is this?

In ‘The Unification of Biology’, New Scientist (11 Jan 1962), 13, No. 269, 72.

A lot of people ask, “Do you think humans are parasites?” It’s an interesting idea and one worth thinking about. People casually refer to humanity as a virus spreading across the earth. In fact, we do look like some strange kind of bio-film spreading across the landscape. A good metaphor? If the biosphere is our host, we do use it up for our own benefit. We do manipulate it. We alter the flows and fluxes of elements like carbon and nitrogen to benefit ourselves—often at the expense of the biosphere as a whole. If you look at how coral reefs or tropical forests are faring these days, you’ll notice that our host is not doing that well right now. Parasites are very sophisticated; parasites are highly evolved; parasites are very successful, as reflected in their diversity. Humans are not very good parasites. Successful parasites do a very good job of balancing—using up their hosts and keeping them alive. It’s all a question of tuning the adaptation to your particular host. In our case, we have only one host, so we have to be particularly careful.

Talk at Columbia University, ‘The Power of Parasites’.

A man is flying in a hot air balloon and realizes he is lost. He reduces height, spots a man down below and asks,“Excuse me, can you help me? I promised to return the balloon to its owner, but I don’t know where I am.”
The man below says: “You are in a hot air balloon, hovering approximately 350 feet above mean sea level and 30 feet above this field. You are between 40 and 42 degrees north latitude, and between 58 and 60 degrees west longitude.”
“You must be an engineer,” says the balloonist.
“I am,” replies the man.“How did you know?”
“Well,” says the balloonist, “everything you have told me is technically correct, but I have no idea what to make of your information, and the fact is I am still lost.”
The man below says, “You must be a manager.”
“I am,” replies the balloonist,“but how did you know?”
“Well,” says the engineer,“you don’t know where you are, or where you are going. You have made a promise which you have no idea how to keep, and you expect me to solve your problem.The fact is you are in the exact same position you were in before we met, but now it is somehow my fault.”

In Jon Fripp, Michael Fripp and Deborah Fripp, Speaking of Science (2000), 199.

A man with a new idea is a crank until he succeeds.

In ‘Pudd’nhead Wilson’s New Calendar,’ Following the Equator (1897), 297.

A mathematician of the first rank, Laplace quickly revealed himself as only a mediocre administrator; from his first work we saw that we had been deceived. Laplace saw no question from its true point of view; he sought subtleties everywhere; had only doubtful ideas, and finally carried the spirit of the infinitely small into administration.

As quoted in E.T. Bell, Men of Mathematics (1937, 1965), 182. Without citation, except, “As it is often quoted as … Napoleon’s famous estimate of Laplace, of which he is reported to have delivered himself while he was a prisoner at St. Helena.” Laplace had a six-week tenure in the Ministry of the Interior.

A mathematician who can only generalise is like a monkey who can only climb UP a tree. … And a mathematician who can only specialise is like a monkey who can only climb DOWN a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise. … There is, I think, a moral for the teacher. A teacher of traditional mathematics is in danger of becoming a down monkey, and a teacher of modern mathematics an up monkey. The down teacher dishing out one routine problem after another may never get off the ground, never attain any general idea. and the up teacher dishing out one definition after the other may never climb down from his verbiage, may never get down to solid ground, to something of tangible interest for his pupils.

From ‘A Story With A Moral’, Mathematical Gazette (Jun 1973), 57, No. 400, 86-87

A mathematician … has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words.

In A Mathematician’s Apology (1940, 2012), 84.

A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

In A Mathematician’s Apology (1940, reprint with Foreward by C.P. Snow 1992), 84.

A mind exclusively bent upon the idea of utility necessarily narrows the range of the imagination. For it is the imagination which pictures to the inner eye of the investigator the indefinitely extending sphere of the possible,—that region of hypothesis and explanation, of underlying cause and controlling law. The area of suggestion and experiment is thus pushed beyond the actual field of vision.

In ‘The Paradox of Research’, The North American Review (Sep 1908), 188, No. 634, 425.

A mind that is stretched by a new idea can never go back to its original dimensions.

Attributed.

A painter makes patterns with shapes and colours, a poet with words. A painting may embody an “idea,” but the idea is usually commonplace and unimportant. In poetry, ideas count for a good deal more; but, as Housman insisted, the importance of ideas in poetry is habitually exaggerated. … The poverty of ideas seems hardly to affect the beauty of the verbal pattern. A mathematician, on the other hand, has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words.

In A Mathematician’s Apology (1940, 2012), 84-85.

A paradigm is an all-encompassing idea, a model providing a way of looking at the world such that an array of diverse observations is united under one umbrella of belief, and a series of related questions are thus answered. Paradigms provide broad understanding, a certain “comfort level,” the psychological satisfaction associated with a mystery solved. What is important here, and perhaps surprising at first glance, is that a paradigm need not have much to do with reality. It does not have to be factual. It just needs to be satisfying to those whom it serves. For example, all creation myths, including the Judeo-Christian story of Adam and Eve in the Garden of Eden, are certainly paradigms, at least to those who subscribe to the particular faith that generated the myth.

From John Krichter, The Balance of Nature: Ecology’s Enduring Myth (2009), 20.

A professor … may be to produce a perfect mathematical work of art, having every axiom stated, every conclusion drawn with flawless logic, the whole syllabus covered. This sounds excellent, but in practice the result is often that the class does not have the faintest idea of what is going on. … The framework is lacking; students do not know where the subject fits in, and this has a paralyzing effect on the mind.

In A Concrete Approach to Abstract Algebra (1959), 1-2.

A scientific invention consists of six (or some number) ideas, five of which are absurd but which, with the addition of the sixth and enough rearrangement of the combinations, results in something no one has thought of before.

As quoted in Robert Coughlan, ‘Dr. Edward Teller’s Magnificent Obsession’, Life (6 Sep 1954), 66.

A scientific observation is always a committed observation. It confirms or denies one’s preconceptions, one’s first ideas, one’s plan of observation. It shows by demonstration. It structures the phenomenon. It transcends what is close at hand. It reconstructs the real after having reconstructed its representation.

In The New Scientific Spirit (1934).

A scientist can be productive in various ways. One is having the ability to plan and carry out experiments, but the other is having the ability to formulate new ideas, which can be about what experiments can be carried out … by making [the] proper calculations. Individual scientists who are successful in their work are successful for different reasons.

Interview with George B. Kauffman and Laurie M. Kauffman, in ‘Linus Pauling: Reflections’, American Scientist (Nov-Dec 1994), 82, No. 6, 522.

A single idea, if it is right, saves us the labor of an infinity of experiences.

Reflections on America (1958), 97.

A society made up of individuals who were capable of original thought would probably be unendurable. The pressure of ideas would simply drive it frantic.

Minority Report (1956, 2006 reprint), 10.

A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.

In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.

A superficial knowledge of mathematics may lead to the belief that this subject can be taught incidentally, and that exercises akin to counting the petals of flowers or the legs of a grasshopper are mathematical. Such work ignores the fundamental idea out of which quantitative reasoning grows—the equality of magnitudes. It leaves the pupil unaware of that relativity which is the essence of mathematical science. Numerical statements are frequently required in the study of natural history, but to repeat these as a drill upon numbers will scarcely lend charm to these studies, and certainly will not result in mathematical knowledge.

In Primary Arithmetic: First Year, for the Use of Teachers (1897), 26-27.

A surplus of ideas is as dangerous as a drought. The tendency to jump from idea to idea spreads your energy horizontally rather than vertically. As a result you’ll struggle to make progress.

In ‘The Action Method’, Making Ideas Happen (2012).

A very sincere and serious freshman student came to my office with a question that had clearly been troubling him deeply. He said to me, ‘I am a devout Christian and have never had any reason to doubt evolution, an idea that seems both exciting and well documented. But my roommate, a proselytizing evangelical, has been insisting with enormous vigor that I cannot be both a real Christian and an evolutionist. So tell me, can a person believe both in God and in evolution?’ Again, I gulped hard, did my intellectual duty, a nd reassured him that evolution was both true and entirely compatible with Christian belief –a position that I hold sincerely, but still an odd situation for a Jewish agnostic.

……

Accordingly, we find Euler and D’Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsôt has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.

J. C. Maxwell on Louis Poinsôt (1777-1859) in ‘On a Dynamical Top’ (1857). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 1, 248.

Admit for a moment, as a hypothesis, that the Creator had before his mind a projection of the whole life-history of the globe, commencing with any point which the geologist may imagine to have been a fit commencing point, and ending with some unimaginable acme in the indefinitely distant future. He determines to call this idea into actual existence, not at the supposed commencing point, but at some stage or other of its course. It is clear, then, that at the selected stage it appears, exactly as it would have appeared at that moment of its history, if all the preceding eras of its history had been real.

Omphalos: An Attempt to Untie the Geological Knot (1857), 351.

After long reflection in solitude and meditation, I suddenly had the idea, during the year 1923, that the discovery made by Einstein in 1905 should be generalised by extending it to all material particles and notably to electrons.

Preface to his re-edited 1924 Ph.D. Thesis, Recherches sur la théorie des quanta (1963), 4. In Steve Adams, Frontiers (2000), 13.

Again and again in reading even his [William Thomson] most abstract writings one is struck by the tenacity with which physical ideas control in him the mathematical form in which he expressed them. An instance of this is afforded by … an example of a mathematical result that is, in his own words, “not instantly obvious from the analytical form of my solution, but which we immediately see must be the case by thinking of the physical meaning of the result.”

As given in Life of Lord Kelvin (1910), Vol. 2, 1136. The ellipsis gives the reference to the quoted footnote, to a passage in his Mathematical and Physical Papers, Vol. 1, 457. [Note: William Thomson, later became Lord Kelvin. —Webmaster]

All human knowledge begins with intuitions, proceeds from thence to concepts, and ends with ideas.

Critique of Pure Reason (1781, 1787), B 730. As translated by Norman Kemp Smith in Immanuel Kant’s Critique of Pure Reason (1929), 569. Also translated in an epigraph as “All human knowledge thus begins with intuitions, proceeds thence to concepts, and ends with ideas,” in David Hilbert and E.J. Townsend (trans.), ‘Introduction’, Foundations of Geometry (1902), 1, citing Kant, Kritik der reinen Vernunft, Elementarlehre, Part 2, Sec. 2.

All possible truth is practical. To ask whether our conception of chair or table corresponds to the real chair or table apart from the uses to which they may be put, is as utterly meaningless and vain as to inquire whether a musical tone is red or yellow. No other conceivable relation than this between ideas and things can exist. The unknowable is what I cannot react upon. The active part of our nature is not only an essential part of cognition itself, but it always has a voice in determining what shall be believed and what rejected.

The Muscular Perception of Space (1878), 446.

All science as it grows toward perfection becomes mathematical in its ideas.

In An Introduction to Mathematics (1911), 14. This is part of a longer quote that begins, “In modern times the belief that the ultimate explanation…”, on the Alfred North Whitehead Quotes page of this website.

All science requires mathematics.
[Editors’ summary of Bacon’s idea, not Bacon’s wording.]

These are not the exact words of Roger Bacon, but are from an editor’s sub-heading, giving a summary for the topic of Chapter 2, for example, in Roger Bacon and Robert Belle Burke (ed.), Opus Maius (reproduction 2002), Vol. 1, Part 4, 117. Part 4 is devoted to a discourse on Mathematics. In its Chapter 1, as translated, Bacon states that ‘There are four great sciences, without which the other sciences cannot be known nor a knowledge of things secured. … Of these sciences the gate and key is mathematics.’

All that can be said upon the number and nature of elements is, in my opinion, confined to discussions entirely of a metaphysical nature. The subject only furnishes us with indefinite problems, which may be solved in a thousand different ways, not one of which, in all probability, is consistent with nature. I shall therefore only add upon this subject, that if, by the term elements, we mean to express those simple and indivisible atoms of which matter is composed, it is extremely probable we know nothing at all about them; but, if we apply the term elements, or principles of bodies, to express our idea of the last point which analysis is capable of reaching, we must admit, as elements, all the substances into which we are capable, by any means, to reduce bodies by decomposition.

Elements of Chemistry (1790), trans. R. Kerr, Preface, xxiv.

All the different classes of beings which taken together make up the universe are, in the ideas of God who knows distinctly their essential gradations, only so many ordinates of a single curve so closely united that it would be impossible to place others between any two of them, since that would imply disorder and imperfection. Thus men are linked with the animals, these with the plants and these with the fossils which in turn merge with those bodies which our senses and our imagination represent to us as absolutely inanimate. And, since the law of continuity requires that when the essential attributes of one being approximate those of another all the properties of the one must likewise gradually approximate those of the other, it is necessary that all the orders of natural beings form but a single chain, in which the various classes, like so many rings, are so closely linked one to another that it is impossible for the senses or the imagination to determine precisely the point at which one ends and the next begins?all the species which, so to say, lie near the borderlands being equivocal, at endowed with characters which might equally well be assigned to either of the neighboring species. Thus there is nothing monstrous in the existence zoophytes, or plant-animals, as Budaeus calls them; on the contrary, it is wholly in keeping with the order of nature that they should exist. And so great is the force of the principle of continuity, to my thinking, that not only should I not be surprised to hear that such beings had been discovered?creatures which in some of their properties, such as nutrition or reproduction, might pass equally well for animals or for plants, and which thus overturn the current laws based upon the supposition of a perfect and absolute separation of the different orders of coexistent beings which fill the universe;?not only, I say, should I not be surprised to hear that they had been discovered, but, in fact, I am convinced that there must be such creatures, and that natural history will perhaps some day become acquainted with them, when it has further studied that infinity of living things whose small size conceals them for ordinary observation and which are hidden in the bowels of the earth and the depth of the sea.

Lettre Prétendue de M. De Leibnitz, à M. Hermann dont M. Koenig a Cité le Fragment (1753), cxi-cxii, trans. in A. O. Lovejoy, Great Chain of Being: A Study of the History of an Idea (1936), 144-5.

Almost all really new ideas have a certain aspect of foolishness when they are first produced.

In Science and the Modern World (1926, 2011), 60.

Almost everything, which the mathematics of our century has brought forth in the way of original scientific ideas, attaches to the name of Gauss.

In Zahlentheorie, Teil 1 (1901), 43.

Although this may seem a paradox, all exact science is dominated by the idea of approximation. When a man tells you that he knows the exact truth about anything, you are safe in infering that he is an inexact man. Every careful measurement in science is always given with the probable error … every observer admits that he is likely wrong, and knows about how much wrong he is likely to be.

In The Scientific Outlook (1931, 2009), 42.

Although we know nothing of what an atom is, yet we cannot resist forming some idea of a small particle, which represents it to the mind … there is an immensity of facts which justify us in believing that the atoms of matter are in some way endowed or associated with electrical powers, to which they owe their most striking qualities, and amongst them their mutual chemical affinity.
[Summarizing his investigations in electrolysis.]

Experimental Researches in Electricity (1839), section 852. Cited in Laurie M. Brown, Abraham Pais, Brian Pippard, Twentieth Century Physics (1995), Vol. 1, 51.

An honest man, armed with all the knowledge available to us now, could only state that in some sense, the origin of life appears at the moment to be almost a miracle, so many are the conditions which would have had to have been satisfied to get it going. But this should not be taken to imply that there are good reasons to believe that it could not have started on the earth by a perfectly reasonable sequence of fairly ordinary chemical reactions. The plain fact is that the time available was too long, the many microenvironments on the earth’s surface too diverse, the various chemical possibilities too numerous and our own knowledge and imagination too feeble to allow us to be able to unravel exactly how it might or might not have happened such a long time ago, especially as we have no experimental evidence from that era to check our ideas against.

In Life Itself: Its Origin and Nature (1981), 88.

An idea isn’t responsible for the people who believe in it.

Column, ‘The Sun Dial’, New York Sun (1918?). Cited in Bill Swainson, Encarta Book of Quotations (2000), 613.

An idea must not be condemned for being a little shy and incoherent; all new ideas are shy when introduced first among our old ones. We should have patience and see whether the incoherency is likely to wear off or to wear on, in which latter case the sooner we get rid of them the better.

In Samuel Butler and Henry Festing Jones (ed.), ‘Higgledy-Piggledy’, The Note-books of Samuel Butler (1912, 1917), 216-217.

An idea must not be condemned for being a little shy and incoherent; all new ideas are shy when introduced first among our old ones. We should have patience and see whether the incoherency is likely to wear off or to wear on, in which latter case the sooner we get rid of them the better.

Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 216-217.

An important scientific innovation rarely makes its way by gradually winning over and converting its opponents. What does happen is that its opponents gradually die out, and that the growing generation is familiarized with the ideas from the beginning.

Scientific Autobiography and Other Papers, trans. F. Gaynor (1950), 97. Quoted in David L. Hull, Science as a Process (1990), 379.

An invasion of armies can be resisted; an invasion of ideas cannot be resisted.

Histoire d’un Crime (written 1851-52, published 1877), conclusion, chap. 10. Trans. T.H. Joyce and Arthur Locker (1886), 413. From the original French: “On résiste à l’invasion des armées; on ne résiste pas à l’invasion des idées.”

And ye who wish to represent by words the form of man and all the aspects of his membrification, get away from that idea. For the more minutely you describe, the more you will confuse the mind of the reader and the more you will prevent him from a knowledge of the thing described. And so it is necessary to draw and describe.

From Notebooks (AnA, 14v; Cf. QII, 1), as translated by J. Playfair McMurrich, in Leonardo da Vinci the Anatomist (1930), 76, (Institution Publication 411, Carnegie Institution of Washington).

And, notwithstanding a few exceptions, we do undoubtedly find that the most truly eminent men have had not only their affections, but also their intellect, greatly influenced by women. I will go even farther; and I will venture to say that those who have not undergone that influence betray a something incomplete and mutilated. We detect, even in their genius, a certain frigidity of tone; and we look in vain for that burning fire, that gushing and spontaneous nature with which our ideas of genius are indissolubly associated. Therefore, it is, that those who are most anxious that the boundaries of knowledge should be enlarged, ought to be most eager that the influence of women should be increased, in order that every resource of the human mind may be at once and quickly brought into play.

Lecture (19 Mar 1858) at the Royal Institution, ‘The Influence Of Women On The Progress Of Knowledge’, collected in The Miscellaneous and Posthumous Works of Henry Thomas Buckle (1872), Vol. 1, 17. Published in Frazier’s Magazine (Apr 1858).

Any artist or novelist would understand—some of us do not produce their best when directed. We expect the artist, the novelist and the composer to lead solitary lives, often working at home. While a few of these creative individuals exist in institutions or universities, the idea of a majority of established novelists or painters working at the “National Institute for Painting and Fine Art” or a university “Department of Creative Composition” seems mildly amusing. By contrast, alarm greets the idea of a creative scientist working at home. A lone scientist is as unusual as a solitary termite and regarded as irresponsible or worse.

Homage to Gala: The Life of an Independent Scholar (2000), 2.

Applied research generates improvements, not breakthroughs. Great scientific advances spring from pure research. Even scientists renowned for their “useful” applied discoveries often achieved success only when they abandoned their ostensible applied-science goal and allowed their minds to soar—as when Alexander Fleming, “just playing about,” refrained from throwing away green molds that had ruined his experiment, studied them, and discovered penicillin. Or when C. A. Clarke, a physician affiliated with the University of Liverpool, became intrigued in the 1950s by genetically created color patterns that emerged when he cross-bred butterflies as a hobby. His fascination led him—“by the pleasant route of pursuing idle curiosity”—to the successful idea for preventing the sometimes fatal anemia that threatened babies born of a positive-Rhesus-factor father and a negative-Rhesus-factor mother.

In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 214-215.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

In A Mathematician’s Apology (1940, reprint with Foreward by C.P. Snow 1992), 81.

As a scientist and geneticist I started to feel that science would probably soon reach the point where its interference into the life processes would be counterproductive if a properly designed governing policy was not implemented. A heavily overcrowded planet, ninety-five percent urbanized with nuclear energy as the main source of energy and with all aspects of life highly computerized, is not too pleasant a place for human life. The life of any individual soon will be predictable from birth to death. Medicine, able to cure almost everything, will make the load of accumulated defects too heavy in the next two or three centuries. The artificial prolongation of life, which looked like a very bright idea when I started research in aging about twenty-five years ago, has now lost its attractiveness for me. This is because I now know that the aging process is so multiform and complex that the real technology and chemistry of its prevention by artificial interference must be too complex and expensive. It would be the privilege of a few, not the method for the majority. I also was deeply concerned about the fact that most research is now either directly or indirectly related to military projects and objectives for power.

Quoted in ‘Zhores A(leksandrovich) Medvedev’, Contemporary Authors Online, Gale, 2002.

As advertising always convinces the sponsor even more than the public, the scientists have become sold, and remain sold, on the idea that they have the key to the Absolute, and that nothing will do for Mr. Average Citizen but to stuff himself full of electrons.

In Science is a Sacred Cow (1950), 26.

As he [Clifford] spoke he appeared not to be working out a question, but simply telling what he saw. Without any diagram or symbolic aid he described the geometrical conditions on which the solution depended, and they seemed to stand out visibly in space. There were no longer consequences to be deduced, but real and evident facts which only required to be seen. … So whole and complete was his vision that for the time the only strange thing was that anybody should fail to see it in the same way. When one endeavored to call it up again, and not till then, it became clear that the magic of genius had been at work, and that the common sight had been raised to that higher perception by the power that makes and transforms ideas, the conquering and masterful quality of the human mind which Goethe called in one word das Dämonische.

In Leslie Stephen and Frederick Pollock (eds.), Lectures and Essays by William Kingdon Clifford(1879), Vol. 1, Introduction, 4-5.

As ideas are preserved and communicated by means of words, it necessarily follows that we cannot improve the language of any science, without at the same time improving the science itself; neither can we, on the other hand, improve a science without improving the language or nomenclature which belongs to it.

Elements of Chemistry (1790), trans. R. Kerr, Preface, xiv-v.

As science has supplanted its predecessors, so it may hereafter be superseded by some more perfect hypothesis, perhaps by some totally different way of looking at the phenomena—of registering the shadows on the screen—of which we in this generation can form no idea. The advance of knowledge is an infinite progression towards a goal that for ever recedes.

In The Golden Bough: A Study in Magic and Religion (1890, 1900), Vol. 3, 460.

As soon as we got rid of the backroom attitude and brought our apparatus fully into the Department with an inexhaustible supply of living patients with fascinating clinical problems, we were able to get ahead really fast. Any new technique becomes more attractive if its clinical usefulness can be demonstrated without harm, indignity or discomfort to the patient… Anyone who is satisfied with his diagnostic ability and with his surgical results is unlikely to contribute much to the launching of a new medical science. He should first be consumed with a divine discontent with things as they are. It greatly helps, of course, to have the right idea at the right time, and quite good ideas may come, Archimedes fashion, in one’s bath..

As the component parts of all new machines may be said to be old[,] it is a nice discriminating judgment, which discovers that a particular arrangement will produce a new and desired effect. … Therefore, the mechanic should sit down among levers, screws, wedges, wheels, etc. like a poet among the letters of the alphabet, considering them as the exhibition of his thoughts; in which a new arrangement transmits a new idea to the world.

A Treatise on the Improvement of Canal Navigation (1796), preface, x.

As to Science, she has never sought to ally herself to civil power. She has never attempted to throw odium or inflict social ruin on any human being. She has never subjected anyone to mental torment, physical torture, least of all to death, for the purpose of upholding or promoting her ideas. She presents herself unstained by cruelties and crimes. But in the Vatican—we have only to recall the Inquisition—the hands that are now raised in appeals to the Most Merciful are crimsoned. They have been steeped in blood!

History of the Conflict between Religion and Science (1875), xi.

As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid, but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer. But Euclid for children is barbarous.

Electro-Magnetic Theory (1893), Vol. 1, 148. In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 130.

At the end of the book [Zoonomia] he sums up his [Erasmus Darwin] views in the following sentences: “The world has been evolved, not created: it has arisen little by little from a small beginning, and has increased through the activity of the elemental forces embodied in itself, and so has rather grown than come into being at an almighty word.” “What a sublime idea of the infinite might of the great Architect, the Cause of all causes, the Father of all fathers, the Ens Entium! For if we would compare the Infinite, it would surely require a greater Infinite to cause the causes of effects than to produce the effects themselves.”
[This is a restatement, not a verbatim quote of the original words of Erasmus Darwin, who attributed the idea he summarized to David Hume.]

In August Weismann, John Arthur Thomson (trans.), Margaret R. Thomson (trans.) The Evolution Theory (1904), Vol. 1, 17-18. The verbatim form of the quote from Zoonomia, in context, can be seen on the webpage here for Erasmus Darwin. Later authors have quoted from Weismann’s translated book, and given the reworded passage as a direct quote by Erasmus Darwin. Webmaster has found a verbatim form in Zoonomia (1794), but has been unable to find the wording used by Weismann in any primary source by Erasmus Darwin. The rewording is perhaps due to the translation of the quote into German for Weismann’s original book, Vorträge über Descendenztheorie (1902) followed by another translation for the English edition.

At the heart of science is an essential balance between two seemingly contradictory attitudes—an openness to new ideas, no matter how bizarre or counterintuitive they may be, and the most ruthless skeptical scrutiny of all ideas, old and new. This is how deep truths are winnowed from deep nonsense.

The Demon-Haunted World: Science as a Candle in the Dark (1997), 304.

Authority in science exists to be questioned, since heresy is the spring from which new ideas flow.

Address, the Canadian Journalists for Free Expression Awards Banquet, as printed in The Globe and Mail (27 Nov 2004).

Behold the mighty dinosaur,
Famous in prehistoric lore,
Not only for his power and strength
But for his intellectual length.
You will observe by these remains
The creature had two sets of brains—
One in his head (the usual place),
The other at his spinal base.
Thus he could reason ‘A priori’
As well as ‘A posteriori’.
No problem bothered him a bit
He made both head and tail of it.
So wise was he, so wise and solemn,
Each thought filled just a spinal column.
If one brain found the pressure strong
It passed a few ideas along.
If something slipped his forward mind
‘Twas rescued by the one behind.
And if in error he was caught
He had a saving afterthought.
As he thought twice before he spoke
He had no judgment to revoke.
Thus he could think without congestion
Upon both sides of every question.
Oh, gaze upon this model beast
Defunct ten million years at least.

‘The Dinosaur: A Poem’ (1912). In E. H. Colbert (ed.), The Dinosaur Book (1951), 78.

Bombs and pistols do not make a revolution. The sword of revolution is sharpened on the whetting-stone of ideas.

Quoted in India Today (Apr 2008), 33, No 16, as cited on webpage of Dhirubhai Ambani Institute of Information and Communication Technology.

Books have always a secret influence on the understanding; we cannot at pleasure obliterate ideas; he that reads books of science, thogh without any fixed desire of improvement, will grow more knowing…

In Samuel Johnson and W. Jackson Bate (Ed.), ‘,The Adventurer, No. 137, Tuesday, 26 Febraury 1754.’ The Selected Essays from the Rambler, Adventurer, and Idler (1968), 273.

Books won’t stay banned. They won’t burn. Ideas won’t go to jail. In the long run of history, the censor and the inquisitor have always lost. The only sure weapon against bad ideas is better ideas. The source of better ideas is wisdom. The surest path to wisdom is a liberal education.

From Essays on Education. In Alfred Whitney Griswold, 1906-1963: In Memoriam (1964), 24.

But I must confess I am jealous of the term atom; for though it is very easy to talk of atoms, it is very difficult to form a clear idea of their nature, especially when compounded bodies are under consideration.

‘On the Absolute Quantity of Electricity Associated with the Particles or Atoms of Matter,’ (31 Dec 1833), published in Philosophical Transactions (Jan 1834) as part of Series VII. Collected in Experimental Researches in Electricity: Reprinted from the Philosophical Transactions of 1831-1838 (1839), 256.

But in practical affairs, particularly in politics, men are needed who combine human experience and interest in human relations with a knowledge of science and technology. Moreover, they must be men of action and not contemplation. I have the impression that no method of education can produce people with all the qualities required. I am haunted by the idea that this break in human civilization, caused by the discovery of the scientific method, may be irreparable.

My Life & My Views (1968), 57-8.

But in science the credit goes to the man who convinces the world, not to the man to whom the idea first occurs. Not the man who finds a grain of new and precious quality but to him who sows it, reaps it, grinds it and feeds the world on it.

First Galton Lecture before the Eugenics Society’, Eugenics Review, 1914, 6, 9.

But in the heavens we discover by their light, and by their light alone, stars so distant from each other that no material thing can ever have passed from one to another; and yet this light, which is to us the sole evidence of the existence of these distant worlds, tells us also that each of them is built up of molecules of the same kinds as those which we find on earth. A molecule of hydrogen, for example, whether in Sirius or in Arcturus, executes its vibrations in precisely the same time. Each molecule, therefore, throughout the universe, bears impressed on it the stamp of a metric system as distinctly as does the metre of the Archives at Paris, or the double royal cubit of the Temple of Karnac … the exact quantity of each molecule to all others of same kind gives it, as Sir John Herschel has well said, the essential character of a manufactured article and precludes the idea of its being external and self-existent.

‘Molecules’, 1873. In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 375-6.

But nothing of a nature foreign to the duties of my profession [clergyman] engaged my attention while I was at Leeds so much as the, prosecution of my experiments relating to electricity, and especially the doctrine of air. The last I was led into a consequence of inhabiting a house adjoining to a public brewery, where first amused myself with making experiments on fixed air [carbon dioxide] which found ready made in the process of fermentation. When I removed from that house, I was under the necessity making the fixed air for myself; and one experiment leading to another, as I have distinctly and faithfully noted in my various publications on the subject, I by degrees contrived a convenient apparatus for the purpose, but of the cheapest kind. When I began these experiments I knew very little of chemistry, and had in a manner no idea on the subject before I attended a course of chymical lectures delivered in the Academy at Warrington by Dr. Turner of Liverpool. But I have often thought that upon the whole, this circumstance was no disadvantage to me; as in this situation I was led to devise an apparatus and processes of my own, adapted to my peculiar views. Whereas, if I had been previously accustomed to the usual chemical processes, I should not have so easily thought of any other; and without new modes of operation I should hardly have discovered anything materially new.

Memoirs of Dr. Joseph Priestley, in the Year 1795 (1806), Vol. 1, 61-2.

But the idea of science and systematic knowledge is wanting to our whole instruction alike, and not only to that of our business class … In nothing do England and the Continent at the present moment more strikingly differ than in the prominence which is now given to the idea of science there, and the neglect in which this idea still lies here; a neglect so great that we hardly even know the use of the word science in its strict sense, and only employ it in a secondary and incorrect sense.

Schools and Universities on the Continent (1868),278-9.

But the idea that any of the lower animals have been concerned in any way with the origin of man—is not this degrading? Degrading is a term, expressive of a notion of the human mind, and the human mind is liable to prejudices which prevent its notions from being invariably correct. Were we acquainted for the first time with the circumstances attending the production of an individual of our race, we might equally think them degrading, and be eager to deny them, and exclude them from the admitted truths of nature.

By research in pure science I mean research made without any idea of application to industrial matters but solely with the view of extending our knowledge of the Laws of Nature. I will give just one example of the ‘utility’ of this kind of research, one that has been brought into great prominence by the War—I mean the use of X-rays in surgery. Now, not to speak of what is beyond money value, the saving of pain, or, it may be, the life of the wounded, and of bitter grief to those who loved them, the benefit which the state has derived from the restoration of so many to life and limb, able to render services which would otherwise have been lost, is almost incalculable. Now, how was this method discovered? It was not the result of a research in applied science starting to find an improved method of locating bullet wounds. This might have led to improved probes, but we cannot imagine it leading to the discovery of X-rays. No, this method is due to an investigation in pure science, made with the object of discovering what is the nature of Electricity. The experiments which led to this discovery seemed to be as remote from ‘humanistic interest’ —to use a much misappropriated word—as anything that could well be imagined. The apparatus consisted of glass vessels from which the last drops of air had been sucked, and which emitted a weird greenish light when stimulated by formidable looking instruments called induction coils. Near by, perhaps, were great coils of wire and iron built up into electro-magnets. I know well the impression it made on the average spectator, for I have been occupied in experiments of this kind nearly all my life, notwithstanding the advice, given in perfect good faith, by non-scientific visitors to the laboratory, to put that aside and spend my time on something useful.

In Speech made on behalf of a delegation from the Conjoint Board of Scientific Studies in 1916 to Lord Crewe, then Lord President of the Council. In George Paget Thomson, J. J. Thomson and the Cavendish Laboratory in His Day (1965), 167-8.

By the fruit one judges the tree; the tree of science grows exceedingly slowly; centuries elapse before one can pluck the ripe fruits; even today it is hardly possible for us to shell and appraise the kernel of the teachings that blossomed in the seventeenth century. He who sows cannot therefore judge the worth of the corn. He must have faith in the fruitfulness of the seed in order that he may follow untiringly his chosen furrow when he casts his ideas to the four winds of heaven.

As quoted in Philipp Frank, Modern Science and its Philosophy (1949), 62, which cites Évolution de la Mécanique (1903).

Cat-Ideas and Mouse-Ideas. We can never get rid of mouse-ideas completely, they keep turning up again and again, and nibble, nibble—no matter how often we drive them off. The best way to keep them down is to have a few good strong cat-ideas which will embrace them and ensure their not reappearing till they do so in another shape.

Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 216.

Certain students of genetics inferred that the Mendelian units responsible for the selected character were genes producing only a single effect. This was careless logic. It took a good deal of hammering to get rid of this erroneous idea. As facts accumulated it became evident that each gene produces not a single effect, but in some cases a multitude of effects on the characters of the individual. It is true that in most genetic work only one of these character-effects is selected for study—the one that is most sharply defined and separable from its contrasted character—but in most cases minor differences also are recognizable that are just as much the product of the same gene as is the major effect.

‘The Relation of Genetics to Physiology and Medicine’, Nobel Lecture (4 Jun 1934). In Nobel Lectures, Physiology or Medicine 1922-1941 (1965), 317.

Characteristically skeptical of the idea that living things would faithfully follow mathematical formulas, [Robert Harper] seized upon factors in corn which seemed to blend in the hybrid—rather than be represented by plus or minus signs, and put several seasons into throwing doubt upon the concept of immutable hypothetical units of inheritance concocted to account for selected results.

In ‘Robert Almer Harper’, National Academy Biographical Memoirs (1948), 25, 233-234.

Chemistry has the same quickening and suggestive influence upon the algebraist as a visit to the Royal Academy, or the old masters may be supposed to have on a Browning or a Tennyson. Indeed it seems to me that an exact homology exists between painting and poetry on the one hand and modern chemistry and modern algebra on the other. In poetry and algebra we have the pure idea elaborated and expressed through the vehicle of language, in painting and chemistry the idea enveloped in matter, depending in part on manual processes and the resources of art for its due manifestation.

Attributed.

Common sense … may be thought of as a series of concepts and conceptual schemes which have proved highly satisfactory for the practical uses of mankind. Some of those concepts and conceptual schemes were carried over into science with only a little pruning and whittling and for a long time proved useful. As the recent revolutions in physics indicate, however, many errors can be made by failure to examine carefully just how common sense ideas should be defined in terms of what the experimenter plans to do.

In Science and Common Sense (1951), 32-33.

Concerned to reconstruct past ideas, historians must approach the generation that held them as the anthropologist approaches an alien culture. They must, that is, be prepared at the start to find that natives speak a different language and map experience into different categories from those they themselves bring from home. And they must take as their object the discovery of those categories and the assimilation of the corresponding language.

‘Revisiting Planck’, Historical Studies in the Physical Sciences (1984), 14, 246.

Could Hamlet have been written by a committee, or the “Mona Lisa” painted by a club? Could the New Testament have been composed as a conference report? Creative ideas do not spring from groups. They spring from individuals. The divine spark leaps from the finger of God to the finger of Adam, whether it takes ultimate shape in a law of physics or a law of the land, a poem or a policy, a sonata or a mechanical computer.

Baccalaureate address (9 Jun 1957), Yale University. In In the University Tradition (1957), 156.

Creativity is a double-edged sword. The more ideas we have, the less likely we are to stay loyal to one. So the creative mind ends up jumping from idea to idea, and none of them happen.

In ‘Author Q&A: Art in Action’, Newsweek (7 Jun 2010), 10.

Data isn’t information. … Information, unlike data, is useful. While there’s a gulf between data and information, there’s a wide ocean between information and knowledge. What turns the gears in our brains isn’t information, but ideas, inventions, and inspiration. Knowledge—not information—implies understanding. And beyond knowledge lies what we should be seeking: wisdom.

In High-Tech Heretic: Reflections of a Computer Contrarian (2000), 185-186.

Do not enter upon research unless you can not help it. Ask yourself the “why” of every statement that is made and think out your own answer. If through your thoughtful work you get a worthwhile idea, it will get you. The force of the conviction will compel you to forsake all and seek the relief of your mind in research work.

From Cameron Prize Lecture (1928), delivered before the University of Edinburgh. As quoted in J.B. Collip ‘Frederick Grant Banting, Discoverer of Insulin’, The Scientific Monthly (May 1941), 52, No. 5, 473.

Don’t worry about people stealing an idea. If it’s original, you will have to ram it down their throats.

As quoted, without citation, in Robert Slater, Portraits in Silicon (1987), 88. In reply to a student expressing concern that his own ideas might be stolen before he had published his own thesis. Also seen as “Don’t worry about people stealing your ideas. If your ideas are any good, you’ll have to ram them down people’s throats,” in Eric A. Weiss, A Computer Science Reader: Selections from ABACUS (1988), 404. (The selections were published in the first three-and-a-half years of ABACUS, a quarterly journal for computing professionals.)

During the eighteenth and nineteenth centuries we can see the emergence of a tension that has yet to be resolved, concerning the attitude of scientists towards the usefulness of science. During this time, scientists were careful not to stress too much their relationships with industry or the military. They were seeking autonomy for their activities. On the other hand, to get social support there had to be some perception that the fruits of scientific activity could have useful results. One resolution of this dilemma was to assert that science only contributed at the discovery stage; others, industrialists for example, could apply the results. … Few noted the … obvious paradox of this position; that, if scientists were to be distanced from the ‘evil’ effects of the applications of scientific ideas, so too should they receive no credit for the ‘good’ or socially beneficial, effects of their activities.
Co-author with Philip Gummett (1947- ), -British social scientist

Science, Technology and Society Today (1984), Introduction, 4.

During the school period the student has been mentally bending over his desk; at the University he should stand up and look around. For this reason it is fatal if the first year at the University be frittered away in going over the old work in the old spirit. At school the boy painfully rises from the particular towards glimpses at general ideas; at the University he should start from general ideas and study their applications to concrete cases.

In ‘The Rhythm of Education’, The Aims of Education and Other Essays (1929), 26.

D’you know how embarrassing it is to mention good and evil in a scientific laboratory? Have you any idea? One of the reasons l became a scientist was not to have to think about that kind of thing.

Spoken by character Dr. Malone in His Dark Materials Omnibus (2012), 370.

Edison was by far the most successful and, probably, the last exponent of the purely empirical method of investigation. Everything he achieved was the result of persistent trials and experiments often performed at random but always attesting extraordinary vigor and resource. Starting from a few known elements, he would make their combinations and permutations, tabulate them and run through the whole list, completing test after test with incredible rapidity until he obtained a clue. His mind was dominated by one idea, to leave no stone unturned, to exhaust every possibility.

As quoted in ‘Tesla Says Edison Was an Empiricist’, The New York Times (19 Oct 1931), 25.

Education should form right ideas and right habits.

As quoted, without citation, in ‘What Is Education?’, The Journal of Education (28 Sep 1905), 62, No. 13, 354.

Educators may bring upon themselves unnecessary travail by taking a tactless and unjustifiable position about the relation between scientific and religious narratives. … The point is that profound but contradictory ideas may exist side by side, if they are constructed from different materials and methods and have different purposes. Each tells us something important about where we stand in the universe, and it is foolish to insist that they must despise each other.

In The End of Education: Redefining the Value of School (1995), 107.

Edward [Teller] isn’t the cloistered kind of scientist. He gets his ideas in conversation and develops them by trying them out on people. We were coming back from Europe on the Ile de France and I was standing in the ship’s nightclub when he came up and said, ‘Freddie, I think I have an idea.’ It was something he’d just thought of about magnetohydrodynamics. I was a bachelor then and I’d located several good-looking girls on the ship, but I knew what I had to do, so I disappeared and started working on the calculations. I’d get something finished and start prowling on the deck again when Edward would turn up out of the night and we’d walk the deck together while he talked and I was the brick wall he was bouncing these things off of. By the end of the trip we had a paper. He’d had the ideas, and I’d done some solving of equations. But he insisted that we sign in alphabetical order, which put my name first.

As quoted in Robert Coughlan, ‘Dr. Edward Teller’s Magnificent Obsession’, Life (6 Sep 1954), 61-62.

Engineering is quite different from science. Scientists try to understand nature. Engineers try to make things that do not exist in nature. Engineers stress invention. To embody an invention the engineer must put his idea in concrete terms, and design something that people can use. That something can be a device, a gadget, a material, a method, a computing program, an innovative experiment, a new solution to a problem, or an improvement on what is existing. Since a design has to be concrete, it must have its geometry, dimensions, and characteristic numbers. Almost all engineers working on new designs find that they do not have all the needed information. Most often, they are limited by insufficient scientific knowledge. Thus they study mathematics, physics, chemistry, biology and mechanics. Often they have to add to the sciences relevant to their profession. Thus engineering sciences are born.

Y.C. Fung and P. Tong, Classical and Computational Solid Mechanics (2001), 1.

Environment counts for a great deal. A man’s particular idea may have no chance for growth or encouragement in his community. Real success is denied that man, until he finds a proper environment.

In Orison Swett Marden, ‘Bell Telephone Talk: Hints on Success by Alexander G. Bell’, How They Succeeded: Life Stories of Successful Men Told by Themselves (1901), 39.

Euler could repeat the Aeneid from the beginning to the end, and he could even tell the first and last lines in every page of the edition which he used. In one of his works there is a learned memoir on a question in mechanics, of which, as he himself informs us, a verse of Aeneid gave him the first idea. [“The anchor drops, the rushing keel is staid.”]

In Letters of Euler (1872), Vol. 1, 24.

Even in Europe a change has sensibly taken place in the mind of man. Science has liberated the ideas of those who read and reflect, and the American example has kindled feelings of right in the people. An insurrection has consequently begun of science talents and courage against rank and birth, which have fallen into contempt. It has failed in its first effort, because the mobs of the cities, the instrument used for its accomplishment, debased by ignorance, poverty and vice, could not be restrained to rational action. But the world will soon recover from the panic of this first catastrophe.

Letter to John Adams (Monticello, 1813). In Thomas Jefferson and John P. Foley (ed.), The Jeffersonian Cyclopedia (1900), 49. From Paul Leicester Ford (ed.), The Writings of Thomas Jefferson (1892-99). Vol 4, 439.

Even in the dark times between experimental breakthroughs, there always continues a steady evolution of theoretical ideas, leading almost imperceptibly to changes in previous beliefs.

In Nobel Lecture (8 Dec 1989), ‘Conceptual Foundations of the Unified Theory of Weak and Electromagnetic Interactions.’

Even today I still get letters from young students here and there who say, Why are you people trying to program intelligence? Why don’t you try to find a way to build a nervous system that will just spontaneously create it? Finally I decided that this was either a bad idea or else it would take thousands or millions of neurons to make it work and I couldn’t afford to try to build a machine like that.

As quoted in Jeremy Bernstein, ‘A.I.’, The New Yorker (14 Dec 1981), 57, 70.

Eventually, it becomes hard to take the selections seriously, because we have no idea what factors are taken into consideration, except that somehow, it ends with only white and Asian men receiving the [Nobel] prize.

As quoted in Jesse Emspak, ‘Are the Nobel Prizes Missing Female Scientists?’ (5 Oct 2016), on LiveScience website.

Ever since I was a boy, I’ve been fascinated by crazy science and such things as perpetual motion machines and logical paradoxes. I’ve always enjoyed keeping up with those ideas. I suppose I didn’t get into it seriously until I wrote my first book, Fads and Fallacies in the Name of Science. I was influenced by the Dianetics movement, now called Scientology, which was then promoted by John Campbell in Astounding Science Fiction. I was astonished at how rapidly the thing had become a cult.

In Scot Morris, ‘Interview: Martin Gardner’, Omni, 4, No. 4 (Jan 1982), 68.

Every improvement that is put upon the real estate is the result of an idea in somebody’s head. The skyscraper is another idea; the railroad is another; the telephone and all those things are merely symbols which represent ideas. An andiron, a wash-tub, is the result of an idea that did not exist before.

Speaking to a committee considering a new Copyright Bill (6 Dec 1906). In Mark Twain and William Dean Howells (ed.), Mark Twain’s Speeches? (1910), 320. An andiron is a metal bar, used in a pair, as a stand for logs in a fireplace. The Copyright Bill proposed to give authors, artists and musicians copyright for the term of his life and for 50 years thereafter. John Philip Sousa spoke for the musicians.

Every intellectual revolution which has ever stirred humanity into greatness has been a passionate protest against inert ideas. Then, alas, with pathetic ignorance of human psychology, it has proceeded by some educational scheme to, bind humanity afresh with inert ideas of its own fashioning.

In ‘The Aims of Education’, The Aims of Education and Other Essays (1929), 14.

Every Man being conscious to himself, That he thinks, and that which his Mind is employ’d about whilst thinking, being the Ideas, that are there, ’tis past doubt, that Men have in their Minds several Ideas, such as are those expressed by the words, Whiteness, Hardness, Sweetness, Thinking, Motion, Man, Elephant, Army, Drunkenness, and others: It is in the first place then to be inquired, How he comes by them? I know it is a received Doctrine, That Men have native Ideas, and original Characters stamped upon their Minds, in their very first Being.

An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 2, Chapter 1, Section 1, 104.

Every rule has its limits, and every concept its ambiguities. Most of all is this true in the science of life, where nothing quite corresponds to our ideas; similar ends are reached by varied means, and no causes are simple.

In Internal Factors in Evolution (1965), 13.

Every theoretical physicist who is any good knows six or seven different theoretical representations for exactly the same physics. He knows that they are all equivalent, and that nobody is ever going to be able to decide which one is right at that level, but he keeps them in his head, hoping that they will give him different ideas for guessing.

In The Character of Physical Law (1965, 2001), 168.

Every time you tear a leaf off a calendar, you present a new place for new ideas and progress.

Everyone is a genius at least once a year. The real geniuses simply have their bright ideas closer together.

Aphorisms (1775-1779) trans. Franz H. Mautner and Henry Hatfield. In Fred R. Shapiro and Joseph Epstein, The Yale Book of Quotations (2006), 459:3.

Everyone makes for himself a clear idea of the motion of a point, that is to say, of the motion of a corpuscle which one supposes to be infinitely small, and which one reduces by thought in some way to a mathematical point.

Théorie Nouvelle de la Rotation des Corps (1834). As translated by Charles Thomas Whitley in Outlines of a New Theory of Rotatory Motion (1834), 1.

Everywhere science is enriched by unscientific methods and unscientific results, … the separation of science and non-science is not only artificial but also detrimental to the advancement of knowledge. If we want to understand nature, if we want to master our physical surroundings, then we must use all ideas, all methods, and not just a small selection of them.

Against Method: Outline of an Anarchistic Theory of Knowledge (1975), 305-6.

Evolution… is the most powerful and the most comprehensive idea that has ever arisen on Earth.

‘Education and Humanism’, in Essays of a Humanist (1964), 125.

Exercising the right of occasional suppression and slight modification, it is truly absurd to see how plastic a limited number of observations become, in the hands of men with preconceived ideas.

Meteorographica (1863), 5.

Faced with the admitted difficulty of managing the creative process, we are doubling our efforts to do so. Is this because science has failed to deliver, having given us nothing more than nuclear power, penicillin, space travel, genetic engineering, transistors, and superconductors? Or is it because governments everywhere regard as a reproach activities they cannot advantageously control? They felt that way about the marketplace for goods, but trillions of wasted dollars later, they have come to recognize the efficiency of this self-regulating system. Not so, however, with the marketplace for ideas.

Quoted in Martin Moskovits (ed.), Science and Society, the John C. Polanyi Nobel Lareates Lectures (1995), 8.

Facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world’s data. Theories are structures of ideas that explain and interpret facts. Facts do not go away while scientists debate rival theories for explaining them. Einstein’s theory of gravitation replaced Newton’s, but apples did not suspend themselves in mid-air pending the outcome.

‘Evolution as Fact and Theory’, in Hen’s Teeth and Horse’s Toes (1983, 1994), Chap. 19.

Facts are the materials of science, but all Facts involve Ideas. … we must, for the purposes of science, take care that the Ideas are clear and rigorously applied.

Aphorism 4, ‘Aphorisms Concerning Science’, The Philosophy of the Inductive Sciences (1840), Vol. 1, xxxvii.

Falsity cannot keep an idea from being beautiful; there are certain errors of such ingenuity that one could regret their not ranking among the achievements of the human mind.

Pensées d’un Biologiste (1939). Translated in The Substance of Man (1962), 89.

Finally, I aim at giving denominations to things, as agreeable to truth as possible. I am not ignorant that words, like money, possess an ideal value, and that great danger of confusion may be apprehended from a change of names; in the mean time it cannot be denied that chemistry, like the other sciences, was formerly filled with improper names. In different branches of knowledge, we see those matters long since reformed: why then should chemistry, which examines the real nature of things, still adopt vague names, which suggest false ideas, and favour strongly of ignorance and imposition? Besides, there is little doubt but that many corrections may be made without any inconvenience.

Physical and Chemical Essays (1784), Vol. I, xxxvii.

First, inevitably, the idea, the fantasy, the fairy tale. Then, scientific calculation. Ultimately, fulfillment crowns the dream.

For any one who is pervaded with the sense of causal law in all that happens, who accepts in real earnest the assumption of causality, the idea of a Being who interferes with the sequence of events in the world is absolutely impossible! Neither the religion of fear nor the social-moral religion can have, any hold on him. A God who rewards and punishes is for him unthinkable, because man acts in accordance with an inner and outer necessity, and would, in the eyes of God, be as little responsible as an inanimate object is for the movements which it makes. Science, in consequence, has been accused of undermining morals—but wrongly. The ethical behavior of man is better based on sympathy, education and social relationships, and requires no support from religion. Man’s plight would, indeed, be sad if he had to be kept in order through fear of punishment and hope of rewards after death.

From ‘Religion and Science’, The New York Times Magazine, (9 Nov 1930), 1. Article in full, reprinted in Edward H. Cotton (ed.), Has Science Discovered God? A Symposium of Modern Scientific Opinion (1931), 101. The wording differs significantly from the version collected in ‘Religion And Science’, Ideas And Opinions (1954), 39, giving its source as: “Written expressly for the New York Times Magazine. Appeared there November 9, 1930 (pp. 1-4). The German text was published in the Berliner Tageblatt, November 11, 1930.” This variant form of the quote from the book begins, “The man who is thoroughly convinced of the universal operation of the law of causation….” and is also on the Albert Einstein Quotes page on this website. As for why the difference, Webmaster speculates the book form editor perhaps used a revised translation from Einstein’s German article.

For it is too bad that there are so few who seek the truth and so few who do not follow a mistaken method in philosophy. This is not, however, the place to lament the misery of our century, but to rejoice with you over such beautiful ideas for proving the truth. So I add only, and I promise, that I shall read your book at leisure; for I am certain that I shall find the noblest things in it. And this I shall do the more gladly, because I accepted the view of Copernicus many years ago, and from this standpoint I have discovered from their origins many natural phenomena, which doubtless cannot be explained on the basis of the more commonly accepted hypothesis.

Letter (4 Aug 1597) to Kepler, expressing thanks and interest in the book Kepler sent him. As quoted in translation in Jackson J. Spielvogel, Western Civilization: Alternate Volume: Since 1300 (2010), Vol. 2, 494.

For it is too bad that there are so few who seek the truth and so few who do not follow a mistaken method in philosophy. This is not, however, the place to lament the misery of our century, but to rejoice with you over such beautiful ideas for proving the truth. So I add only, and I promise, that I shall read your book at leisure; for I am certain that I shall find the noblest things in it. And this I shall do the more gladly, because I accepted the view of Copernicus many years ago, and from this standpoint I have discovered from their origins many natural phenomena, which doubtless cannot be explained on the basis of the more commonly accepted hypothesis.

In Letter to Johannes Kepler. As quoted in The Portable Renaissance Reader (1968), 597.

For me, a rocket is only a means—only a method of reaching the depths of space—and not an end in itself… There’s no doubt that it’s very important to have rocket ships since they will help mankind to settle elsewhere in the universe. But what I’m working for is this resettling… The whole idea is to move away from the Earth to settlements in space.

For me, the idea of a creation is not conceivable without invoking the necessity of design. One cannot be exposed to the law and order of the universe without concluding that there must be design and purpose behind it all.

In letter to California State board of Education (14 Sep 1972).

Forests were the first temples of the Divinity, and it is in the forests that men have grasped the first idea of architecture.

F.A. de Chateaubriand and Frederic Shoberl (trans.) The Beauties of Christianity (1813), Vol. 1, 251.

Fortunately I experienced Max Wertheimer’s teaching in Berlin and collaborated for over a decade with Wolfgang Köhler. I need not emphasize my debts to these outstanding personalities. The fundamental ideas of Gestalt theory are the foundation of all our investigations in the field of the will, of affection, and of the personality.

From A Dynamic Theory of Personality. Selected papers (1935), 240.

Fourier’s Theorem … is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics. To mention only sonorous vibrations, the propagation of electric signals along a telegraph wire, and the conduction of heat by the earth’s crust, as subjects in their generality intractable without it, is to give but a feeble idea of its importance.

In William Thomson and Peter Guthrie Tait, Treatise on Natural Philosophy (1867), Vol. 1, 28.

Fractal is a word invented by Mandelbrot to bring together under one heading a large class of objects that have [played] … an historical role … in the development of pure mathematics. A great revolution of ideas separates the classical mathematics of the 19th century from the modern mathematics of the 20th. Classical mathematics had its roots in the regular geometric structures of Euclid and the continuously evolving dynamics of Newton. Modern mathematics began with Cantor’s set theory and Peano’s space-filling curve. Historically, the revolution was forced by the discovery of mathematical structures that did not fit the patterns of Euclid and Newton. These new structures were regarded … as “pathological,” .… as a “gallery of monsters,” akin to the cubist paintings and atonal music that were upsetting established standards of taste in the arts at about the same time. The mathematicians who created the monsters regarded them as important in showing that the world of pure mathematics contains a richness of possibilities going far beyond the simple structures that they saw in Nature. Twentieth-century mathematics flowered in the belief that it had transcended completely the limitations imposed by its natural origins.
Now, as Mandelbrot points out, … Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.

From ‘Characterizing Irregularity’, Science (12 May 1978), 200, No. 4342, 677-678. Quoted in Benoit Mandelbrot, The Fractal Geometry of Nature (1977, 1983), 3-4.

From the age of 13, I was attracted to physics and mathematics. My interest in these subjects derived mostly from popular science books that I read avidly. Early on I was fascinated by theoretical physics and determined to become a theoretical physicist. I had no real idea what that meant, but it seemed incredibly exciting to spend one’s life attempting to find the secrets of the universe by using one’s mind.

From ‘Autobiography’, in Tore Frängsmyr (ed.) Les Prix Nobel. The Nobel Prizes 2004, (2005).

From the intensity of the spots near the centre, we can infer that the protein molecules are relatively dense globular bodies, perhaps joined together by valency bridges, but in any event separated by relatively large spaces which contain water. From the intensity of the more distant spots, it can be inferred that the arrangement of atoms inside the protein molecule is also of a perfectly definite kind, although without the periodicities characterising the fibrous proteins. The observations are compatible with oblate spheroidal molecules of diameters about 25 A. and 35 A., arranged in hexagonal screw-axis. … At this stage, such ideas are merely speculative, but now that a crystalline protein has been made to give X-ray photographs, it is clear that we have the means of checking them and, by examining the structure of all crystalline proteins, arriving at a far more detailed conclusion about protein structure than previous physical or chemical methods have been able to give.

‘X-Ray Photographs of Crystalline Pepsin’, Nature (1934), 133, 795.

From time immemorial, the infinite has stirred men’s emotions more than any other question. Hardly any other idea has stimulated the mind so fruitfully. Yet, no other concept needs clarification more than it does.

In address (4 Jun 1925), at a congress of the Westphalian Mathematical Society in Munster, in honor of Karl Weierstrass. First published in Mathematische Annalen (1926), 95, 161-190. Translated by Erna Putnam and Gerald J. Massey as ‘On the Infinite’, collected in Paul Benacerraf (ed.) Philosophy of Mathematics: Selected Readings (1983), 185. Compare another translation elsewhere on this page, beginning, “The Infinite!…”.

Fundamental progress has to do with the reinterpretation of ideas.

In Science and Philosophy (1948), 228.

Gel’fand amazed me by talking of mathematics as though it were poetry. He once said about a long paper bristling with formulas that it contained the vague beginnings of an idea which could only hint at and which he had never managed to bring out more clearly. I had always thought of mathematics as being much more straightforward: a formula is a formula, and an algebra is an algebra, but Gel’fand found hedgehogs lurking in the rows of his spectral sequences!

In ‘1991 Ruth Lyttle Satter Prize’, Notices of the American Mathematical Society (Mar 1991), 38, No. 3, 186. This is from her acceptance of the 1991 Ruth Lyttle Satter Prize.

Geologists have usually had recourse for the explanation of these changes to the supposition of sundry violent and extraordinary catastrophes, cataclysms, or general revolutions having occurred in the physical state of the earth’s surface.
As the idea imparted by the term Cataclysm, Catastrophe, or Revolution, is extremely vague, and may comprehend any thing you choose to imagine, it answers for the time very well as an explanation; that is, it stops further inquiry. But it also has had the disadvantage of effectually stopping the advance of science, by involving it in obscurity and confusion.

Considerations on Volcanoes (1825), iv.

Geometric writings are not rare in which one would seek in vain for an idea at all novel, for a result which sooner or later might be of service, for anything in fact which might be destined to survive in the science; and one finds instead treatises on trivial problems or investigations on special forms which have absolutely no use, no importance, which have their origin not in the science itself but in the caprice of the author; or one finds applications of known methods which have already been made thousands of times; or generalizations from known results which are so easily made that the knowledge of the latter suffices to give at once the former. Now such work is not merely useless; it is actually harmful because it produces a real incumbrance in the science and an embarrassment for the more serious investigators; and because often it crowds out certain lines of thought which might well have deserved to be studied.

From ‘On Some Recent Tendencies in Geometric Investigations’, Rivista di Matematica (1891), 43. In Bulletin American Mathematical Society (1904), 443.

Great ideas are not charitable.

Le maître de Santiago

Science quotes on:  |  Great (1579)

His [J.J. Sylvester’s] lectures were generally the result of his thought for the preceding day or two, and often were suggested by ideas that came to him while talking. The one great advantage that this method had for his students was that everything was fresh, and we saw, as it were, the very genesis of his ideas. One could not help being inspired by such teaching.

As quoted by Florian Cajori, in Teaching and History of Mathematics in the United States (1890), 267-268.

Hitherto man had to live with the idea of death as an individual; from now onward mankind will have to live with the idea of its death as a species.

As excerpted in Paul S. Burtness, ‘Arthur Koestler (1905-)’, The Contemporary University Reader (1963), 286.

How can a modern anthropologist embark upon a generalization with any hope of arriving at a satisfactory conclusion? By thinking of the organizational ideas that are present in any society as a mathematical pattern.

In Rethinking Anthropology (1961), 2.

How can we have any new ideas or fresh outlooks when 90 per cent of the scientists who have ever lived have still not died?

In Scientific World, 1969.

However much we may enlarge our ideas of the time which has elapsed since the Niagara first began to drain the waters of the upper lakes, we have seen that this period was one only of a series, all belonging to the present zoological epoch; or that in which the living testaceous fauna, whether freshwater or marine, had already come into being. If such events can take place while the zoology of the earth remains almost stationary and unaltered, what ages may not be comprehended in those successive tertiary periods during which the Flora and Fauna of the globe have been almost entirely changed. Yet how subordinate a place in the long calendar of geological chronology do the successive tertiary periods themselves occupy! How much more enormous a duration must we assign to many antecedent revolutions of the earth and its inhabitants! No analogy can be found in the natural world to the immense scale of these divisions of past time, unless we contemplate the celestial spaces which have been measured by the astronomer.

Travels in North America (1845), Vol. 1, 51-2.

Human language is in some ways similar to, but in other ways vastly different from, other kinds of animal communication. We simply have no idea about its evolutionary history, though many people have speculated about its possible origins. There is, for instance, the “bow-bow” theory, that language started from attempts to imitate animal sounds. Or the “ding-dong” theory, that it arose from natural sound-producing responses. Or the “pooh-pooh” theory, that it began with violent outcries and exclamations.
We have no way of knowing whether the kinds of men represented by the earliest fossils could talk or not…
Language does not leave fossils, at least not until it has become written.

Man in Nature (1961), 10.

I am a great believer in the simplicity of things and as you probably know I am inclined to hang on to broad & simple ideas like grim death until evidence is too strong for my tenacity.

Letter to Irving Langmuir (10 Jun 1919). Quoted in Nathan Reingold and Ida H. Reingold, Science in America: A Documentary History 1900-1939 (1981), 354.

I am afraid all we can do is to accept the paradox and try to accommodate ourselves to it, as we have done to so many paradoxes lately in modern physical theories. We shall have to get accustomed to the idea that the change of the quantity R, commonly called the ‘radius of the universe’, and the evolutionary changes of stars and stellar systems are two different processes, going on side by side without any apparent connection between them. After all the ‘universe’ is an hypothesis, like the atom, and must be allowed the freedom to have properties and to do things which would be contradictory and impossible for a finite material structure.

Kosmos (1932), 133.

I am more of a sponge than an inventor. I absorb ideas from every source. I take half-matured schemes for mechanical development and make them practical. I am a sort of middleman between the long-haired and impractical inventor and the hard-headed businessman who measures all things in terms of dollars and cents. My principal business is giving commercial value to the brilliant but misdirected ideas of others.

……

I am not pleading with you to make changes, I am telling you you have got to make them—not because I say so, but because old Father Time will take care of you if you don’t change. Consequently, you need a procurement department for new ideas.

As quoted in book review, T.A. Boyd, ‘Charles F. Kettering: Prophet of Progress’, Science (30 Jan 1959), 256.

I am not yet so lost in lexicography, as to forget that words are the daughters of the earth, and that things are the sons of heaven. Language is only the instrument of science, and words are but the signs of ideas: I wish, however, that the instrument might be less apt to decay, and that signs might be permanent, like the things which they denote.

‘Preface’, A Dictionary of the English Language (1755), Vol. 1.

I ask any one who has adopted the calling of an engineer, how much time he lost when he left school, because he had to devote himself to pursuits which were absolutely novel and strange, and of which he had not obtained the remotest conception from his instructors? He had to familiarize himself with ideas of the course and powers of Nature, to which his attention had never been directed during his school-life, and to learn, for the first time, that a world of facts lies outside and beyond the world of words.

From After-Dinner Speech (Apr 1869) delivered before the Liverpool Philomathic Society, ‘Scientific Education’, collected in Lay Sermons, Addresses, and Reviews (1870), 63. Previously published in Macmillan’s Magazine.

I believe myself to possess a most singular combination of qualities exactly fitted to make me pre-eminently a discoverer of the hidden realities of nature… the belief has been forced upon me…
Firstly: Owing to some peculiarity in my nervous system, I have perceptions of some things, which no one else has… and intuitive perception of… things hidden from eyes, ears, & ordinary senses…
Secondly: my sense reasoning faculties;
Thirdly: my concentration faculty, by which I mean the power not only of throwing my whole energy & existence into whatever I choose, but also of bringing to bear on anyone subject or idea, a vast apparatus from all sorts of apparently irrelevant & extraneous sources…
Well, here I have written what most people would call a remarkably mad letter; & yet certainly one of the most logical, sober-minded, cool, pieces of composition, (I believe), that I ever framed.

Lovelace Papers, Bodleian Library, Oxford University, 42, folio 12 (6 Feb 1841). As quoted and cited in Dorothy Stein (ed.), ‘This First Child of Mine’, Ada: A Life and a Legacy (1985), 86.

I believe scientists have a duty to share the excitement and pleasure of their work with the general public, and I enjoy the challenge of presenting difficult ideas in an understandable way.

From Autobiography in Wilhelm Odelberg (ed.), Les Prix Nobel en 1974/Nobel Lectures (1975)

I believe that in every person is a kind of circuit which resonates to intellectual discovery—and the idea is to make that resonance work

Quoted by Dennis Meredith, in ‘Carl Sagan’s Cosmic Connection and Extraterrestrial Life-Wish’, Science Digest (Jun 1979), 85, 37. Reproduced in Carl Sagan and Tom Head (editor), Conversations With Sagan (2006), 54.

I believe that the useful methods of mathematics are easily to be learned by quite young persons, just as languages are easily learned in youth. What a wondrous philosophy and history underlie the use of almost every word in every language—yet the child learns to use the word unconsciously. No doubt when such a word was first invented it was studied over and lectured upon, just as one might lecture now upon the idea of a rate, or the use of Cartesian co-ordinates, and we may depend upon it that children of the future will use the idea of the calculus, and use squared paper as readily as they now cipher. … When Egyptian and Chaldean philosophers spent years in difficult calculations, which would now be thought easy by young children, doubtless they had the same notions of the depth of their knowledge that Sir William Thomson might now have of his. How is it, then, that Thomson gained his immense knowledge in the time taken by a Chaldean philosopher to acquire a simple knowledge of arithmetic? The reason is plain. Thomson, when a child, was taught in a few years more than all that was known three thousand years ago of the properties of numbers. When it is found essential to a boy’s future that machinery should be given to his brain, it is given to him; he is taught to use it, and his bright memory makes the use of it a second nature to him; but it is not till after-life that he makes a close investigation of what there actually is in his brain which has enabled him to do so much. It is taken because the child has much faith. In after years he will accept nothing without careful consideration. The machinery given to the brain of children is getting more and more complicated as time goes on; but there is really no reason why it should not be taken in as early, and used as readily, as were the axioms of childish education in ancient Chaldea.

In Teaching of Mathematics (1902), 14.

I came to realize that exaggerated concern about what others are doing can be foolish. It can paralyze effort, and stifle a good idea. One finds that in the history of science almost every problem has been worked out by someone else. This should not discourage anyone from pursuing his own path.

From Theodore von Karman and Lee Edson (ed.), The Wind and Beyond: Theodore von Karman, Pioneer in Aviation and Pathfinder in Science (1967).

I cannot face with comfort the idea of life without work; work and the free play of the imagination are for me the same thing, I take no pleasure in anything else.

Letter to Oskar Pfister, 3 Jun 1910. Quoted in H. Meng and E. Freud (eds.), Psycho-Analysis and Faith: The Letters of Sigmund Freud and Oskar Pfister (1963), 146.

I cannot seriously believe in it [quantum theory] because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance [spukhafte Fernwirkungen].

Letter to Max Born (3 Mar 1947). In Born-Einstein Letters (1971), 158.

I confess that Fermat’s Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can easily be set up, which one could neither prove nor disprove. But I have been stimulated by it to bring our again several old ideas for a great extension of the theory of numbers. Of course, this theory belongs to the things where one cannot predict to what extent one will succeed in reaching obscurely hovering distant goals. A happy star must also rule, and my situation and so manifold distracting affairs of course do not permit me to pursue such meditations as in the happy years 1796-1798 when I created the principal topics of my Disquisitiones arithmeticae. But I am convinced that if good fortune should do more than I expect, and make me successful in some advances in that theory, even the Fermat theorem will appear in it only as one of the least interesting corollaries.
In reply to Olbers’ attempt in 1816 to entice him to work on Fermat’s Theorem. The hope Gauss expressed for his success was never realised.

Letter to Heinrich Olbers (21 Mar 1816). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 413.

I could not possibly be of such a nature as I am, and yet have in my mind the idea of a God, if God did not in reality exist.

In Meditations (1641), Part 3. English as given in John Veitch (trans.), ‘Of God: That He Exists’, Meditation III, The Method, Meditations, and Selections from the Principles of Descartes (1880), 132. Also seen translated as, “It is not possible that I could have in myself the idea of God, if God did not truly exist.”

I do not think words alone will solve humanity’s present problems. The sound of bombs drowns out
men’s voices. In times of peace I have great faith in the communication of ideas among thinking men, but today, with brute force dominating so many millions of lives, I fear that the appeal to
man’s intellect is fast becoming virtually meaningless.

In ‘I Am an American’ (22 Jun 1940), Einstein Archives 29-092. Excerpted in David E. Rowe and Robert J. Schulmann, Einstein on Politics: His Private Thoughts and Public Stands on Nationalism, Zionism, War, Peace, and the Bomb (2007), 470. It was during a radio broadcast for the Immigration and Naturalization Service, interviewed by a State Department Official. Einstein spoke following an examination on his application for American citizenship in Trenton, New Jersey. The attack on Pearl Harbor and America’s declaration of war on Japan was still over a year in the future.

I enjoy, and always have enjoyed, disturbing scientists.
[About pioneering with his new ideas.]

As quoted by Neil Shubin in The Universe Within: The Deep History of the Human Body (2013), 113

I feel that to be a director of a laboratory should not be, by definition, a permanent mission. People should have the courage to step down and go back to science. I believe you will never have a good director of a scientific laboratory unless that director knows he is prepared to become a scientist again. … I gave my contribution; I spent five years of my life to work hard for other people’s interest. … It’s time to go back to science again. I have some wonderful ideas, I feel I’m re-born.

From ‘Asking Nature’, collected in Lewis Wolpert and Alison Richards (eds.), Passionate Minds: The Inner World of Scientists (1997), 202.

I find in Geology a never failing interest, as [it] has been remarked, it creates the same gran[d] ideas respecting this world, which Astronomy do[es] for the universe.—We have seen much fine scenery that of the Tropics in its glory & luxuriance, exceeds even the language of Humboldt to describe. A Persian writer could alone do justice to it, & if he succeeded he would in England, be called the ‘grandfather of all liars’.— But I have seen nothing, which more completely astonished me, than the first sight of a Savage; It was a naked Fuegian his long hair blowing about, his face besmeared with paint. There is in their countenances, an expression, which I believe to those who have not seen it, must be inconceivably wild. Standing on a rock he uttered tones & made gesticulations than which, the cries of domestic animals are far more intelligible.

Letter to Charles Whitley, 23 July 1834. In F. Burkhardt and S. Smith (eds.), The Correspondence of Charles Darwin 1821-1836 (1985), Vol. I, 397.

I first met J. Robert Oppenheimer on October 8, 1942, at Berkeley, Calif. There we discussed the theoretical research studies he was engaged in with respect to the physics of the bomb. Our discussions confirmed my previous belief that we should bring all of the widely scattered theoretical work together. … He expressed complete agreement, and it was then that the idea of the prompt establishment of a Los Alamos was conceived.”

In ‘Some Recollections of July 16, 1945’, Bulletin of the Atomic Scientists (Jun 1970), 26, No. 6, 21.

I found the best ideas usually came, not when one was actively striving for them, but when one was in a more relaxed state… I used to take long solitary walks on Sundays, during which I tended to review the current situation in a leisurely way. Such occasions often proved fruitful, even though (or perhaps, because) the primary purpose of the walk was relaxation and not research.

‘Methods in Theoretical Physics’, From A Life of Physics: Evening Lectures at the International Centre for Theoretical Physics, Trieste, Italy. A Special Supplement of the IAEA Bulletin (1968), 24.

I grew up in Japan and Hong Kong and then came to the States. Japan was a huge influence on me because, as a child, I would hear the oxcarts come and collect our sewage at night out of our house from the latrine and then take it off to the farms as fertilizer. And then the food would come back in oxcarts during the day. I always had this sort of “our poop became food” mental model. The idea of “waste equals food” was pretty inculcated, that everything was precious and the systems were coherent and cyclical.

In interview with Kerry A. Dolan, ‘William McDonough On Cradle-to-Cradle Design’, Forbes (4 Aug 2010)

I had an immense advantage over many others dealing with the problem inasmuch as I had no fixed ideas derived from long-established practice to control and bias my mind, and did not suffer from the general belief that whatever is, is right.

In Sir Henry Bessemer, F.R.S.: An Autobiography (1905), 93.

I had gone on a walk on a fine Sabbath afternoon. I had entered the Green [of Glasgow] by the gate at the foot of Charlotte Street—had passed the old washing-house. I was thinking upon the engine at the time, and had gone as far as the herd’s house, when the idea came into my mind that as steam was an elastic body it would rush into a vacuum, and if a communication were made between the cylinder and an exhausted vessel it would rush into it, and might be there condensed without cooling the cylinder. I then saw that I must get rid of the condensed steam and injection water if I used a jet, as in Newcomen’s engine. Two ways of doing this occurred to me. First, the water might be run off by a descending pipe, if an outlet could be got at the depth of 35 or 36 feet, and any air might be extracted by a small pump. The second was to make the pump large enough to extract both water and air. … I had not walked further than the Golf-house when the whole thing was arranged in my mind.
[In Robert Hart’s words, a recollection of the description of Watt’s moment of inspiration, in May 1765, for improving Thomas Newcomen’s steam engine.]

In Robert Hart, ‘Reminiscences of James Watt’ (read 2 Nov 1857), Transactions of the Glasgow Archaeological Society (1859), Vol. 1, 1. Note that these are not the verbatim words of James Watt, but are only a recollection of them by Robert Hart, who is quoting as best he can from memory of a conversation he and his brother had with James Watt that took place over 43 years previously. In his Reminiscences, Hart explains, “I have accordingly thrown together the following brief narrative:— As these meetings took place forty-three years since, many observations that were made at the time may have escaped me at present; yet, when the same subjects are touched on, I have as distinct recollection of his treatment of them as if it were yesterday.”

I had no idea of the worldwide influence of it [the world’s first kidney transplant]. It expanded to other organs, multiple organs.

As quoted by Alvin Powell in ‘A Transplant Makes History’, Harvard Gazette (22 Sep 2011).

I have a good idea every two years. Give me a topic, I will give you the idea!
[Reputed to have been a remark made to the head of his department at Caltech.]

As quoted in Norman K. Glendenning, Our Place in the Universe (2007), 48.

I have always considered my work a joint effort. I was fortunate to have worked on great ideas and with very intelligent people. I may have developed a few equations no one had thought of before but that was nothing unusual—everybody did that.

In interview with Laurel M. Sheppard, ‘An Interview with Mary Ross: First Native American Woman Engineer Aerospace Pioneer Returns to her Native American Roots’, on website of Lash Publications.

I have been driven to assume for some time, especially in relation to the gases, a sort of conducting power for magnetism. Mere space is Zero. One substance being made to occupy a given portion of space will cause more lines of force to pass through that space than before, and another substance will cause less to pass. The former I now call Paramagnetic & the latter are the diamagnetic. The former need not of necessity assume a polarity of particles such as iron has with magnetic, and the latter do not assume any such polarity either direct or reverse. I do not say more to you just now because my own thoughts are only in the act of formation, but this I may say: that the atmosphere has an extraordinary magnetic constitution, & I hope & expect to find in it the cause of the annual & diurnal variations, but keep this to yourself until I have time to see what harvest will spring from my growing ideas.

Letter to William Whewell, 22 Aug 1850. In L. Pearce Williams (ed.), The Selected Correspondence of Michael Faraday (1971), Vol. 2, 589.

I have been especially fortunate for about 50 years in having two memory banks available—whenever I can’t remember something I ask my wife, and thus I am able to draw on this auxiliary memory bank. Moreover, there is a second way In which I get ideas … I listen carefully to what my wife says, and in this way I often get a good idea. I recommend to … young people … that you make a permanent acquisition of an auxiliary memory bank that you can become familiar with and draw upon throughout your lives.

T. Goertzel and B. Goertzel, Linus Pauling (1995), 240.

I have long since come to see that no one deserves either praise or blame for the ideas that come to him, but only for the actions resulting therefrom. Ideas and beliefs are certainly not voluntary acts. They come to us—we hardly know how or whence, and once they have got possession of us we can not reject or change them at will. It is for the common good that the promulgation of ideas should be free—uninfluenced by either praise or blame, reward or punishment. But the actions which result from our ideas may properly be so treated, because it is only by patient thought and work, that new ideas, if good and true, become adopted and utilized; while, if untrue or if not adequately presented to the world, they are rejected or forgotten.

In ‘The Origin of the Theory of Natural Selection’, Popular Science Monthly (1909), 74, 400.

I have mentioned mathematics as a way to settle in the mind a habit of reasoning closely and in train; not that I think it necessary that all men should be deep mathematicians, but that, having got the way of reasoning which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they shall have occasion. For in all sorts of reasoning, every single argument should be managed as a mathematical demonstration; the connection and dependence of ideas should be followed till the mind is brought to the source on which it bottoms, and observes the coherence all along; …

In The Conduct of the Understanding, Sect. 7.

I have never had reason, up to now, to give up the concept which I have always stressed, that nerve cells, instead of working individually, act together, so that we must think that several groups of elements exercise a cumulative effect on the peripheral organs through whole bundles of fibres. It is understood that this concept implies another regarding the opposite action of sensory functions. However opposed it may seem to the popular tendency to individualize the elements, I cannot abandon the idea of a unitary action of the nervous system, without bothering if, by that, I approach old conceptions.

‘The Neuron Doctrine-Theory and Facts’, Nobel Lecture 11 Dec 1906. In Nobel Lectures: Physiology or Medicine 1901-1921 (1967), 216.

I have no trouble publishing in Soviet astrophysical journals, but my work is unacceptable to the American astrophysical journals.
[Referring to the trouble he had with the peer reviewers of Anglo-American astrophysical journals because his ideas often conflicted with the generally accepted or “standard»” theories.]

Quoted in Anthony L. Peratt, ‘Dean of the Plasma Dissidents’, Washington Times, supplement: The World and I (May 1988),197.

I have said that mathematics is the oldest of the sciences; a glance at its more recent history will show that it has the energy of perpetual youth. The output of contributions to the advance of the science during the last century and more has been so enormous that it is difficult to say whether pride in the greatness of achievement in this subject, or despair at his inability to cope with the multiplicity of its detailed developments, should be the dominant feeling of the mathematician. Few people outside of the small circle of mathematical specialists have any idea of the vast growth of mathematical literature. The Royal Society Catalogue contains a list of nearly thirty- nine thousand papers on subjects of Pure Mathematics alone, which have appeared in seven hundred serials during the nineteenth century. This represents only a portion of the total output, the very large number of treatises, dissertations, and monographs published during the century being omitted.

In Presidential Address British Association for the Advancement of Science, Sheffield, Section A,
Nature (1 Sep 1910), 84, 285.

I have the vagary of taking a lively interest in mathematical subjects only where I may anticipate ingenious association of ideas and results recommending themselves by elegance or generality.

Letter to Heinrich Schumacher (17 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.

I have tried to avoid long numerical computations, thereby following Riemann’s postulate that proofs should be given through ideas and not voluminous computations.

In Report on Number Theory (1897). As given in epigraph, without citation, in Eberhard Zeidler and Juergen Quandt (trans.), Nonlinear Functional Analysis and its Applications: IV: Applications to Mathematical Physics (2013), 448.

I have tried to read philosophers of all ages and have found many illuminating ideas but no steady progress toward deeper knowledge and understanding. Science, however, gives me the feeling of steady progress: I am convinced that theoretical physics is actual philosophy. It has revolutionized fundamental concepts, e.g., about space and time (relativity), about causality (quantum theory), and about substance and matter (atomistics), and it has taught us new methods of thinking (complementarity) which are applicable far beyond physics.

My Life & My Views (1968), 48.

I have written many direct and indirect arguments for the Copernican view, but until now I have not dared to publish them, alarmed by the fate of Copernicus himself, our master. He has won for himself undying fame in the eyes of a few, but he has been mocked and hooted at by an infinite multitude (for so large is the number of fools). I would dare to come forward publicly with my ideas if there were more people of your [Johannes Kepler’s] way of thinking. As this is not the case, I shall refrain.

Letter to Kepler (4 Aug 1597). In James Bruce Ross (ed.) and Mary Martin (ed., trans.), ‘Comrades in the Pursuit of Truth’, The Portable Renaissance Reader (1953, 1981), 597-599. As quoted and cited in Merry E. Wiesner, Early Modern Europe, 1450-1789 (2013), 377.

I heard … xenon was a good anesthesia. … I thought, “How can xenon, which doesn’t form any chemical compounds, serve as a general anesthetic? … I lay awake at night for a few minutes before going to sleep, and during the next couple of weeks each night I would think, “…how do anesthetic agents work?» Then I forgot to do it after a while, but I’d trained my unconscious mind to keep this question alive and to call [it] to my consciousness whenever a new idea turned up…. So seven years went by. [One day I] put my feet up on the desk and started reading my mail, and here was a letter from George Jeffrey … an x-ray crystallographer, on his determination of the structure of a hydrate crystal. Immediately I sat up, took my feet off the desk, and said, “I understand anesthesia!” … I spent a year [and] determined the structure of chloroform hydrate, and then I wrote my paper published in June of 1961.

Interview with George B. Kauffman and Laurie M. Kauffman, in ‘Linus Pauling: Reflections’, American Scientist (Nov-Dec 1994), 82, No. 6, 522-523.

I hope you have not murdered too completely your own and my child.
Referring to their independently conceived ideas on the origin of species.

Letter to A. R. Wallace, March 1869. In J. Marchant, Alfred Russel Wallace: Letters and Reminiscences (1916), Vol. 1, 240.

I know that certain minds would regard as audacious the idea of relating the laws which preside over the play of our organs to those laws which govern inanimate bodies; but, although novel, this truth is none the less incontestable. To hold that the phenomena of life are entirely distinct from the general phenomena of nature is to commit a grave error, it is to oppose the continued progress of science.

Leçons sur les Phenomenes Physiques de la Vie (1836-38), Vol. 1, 6. Trans. J. M. D. Olmsted, François Magendie (1944), 203.

I like the scientific spirit—the holding off, the being sure but not too sure, the willingness to surrender ideas when the evidence is against them: this is ultimately fine—it always keeps the way beyond open.

In Horace Traubel, With Walt Whitman in Camden (1906), Vol. 1, 101.

I never really paused for a moment to question the idea that the progressive Spiritualization of Matter—so clearly demonstrated to me by Paleontology—could be anything other, or anything less, than an irreversible process. By its gravitational nature, the Universe, I saw, was falling—falling forwards—in the direction of spirit as upon its stable form. In other words, Matter was not ultra-materialized as I would at first have believed, but was instead metamorphosed in Psyche.

In The Heart of Matter (1978), 27-28.

I ought to say that one of our first joint researches, so far as publication was concerned, had the peculiar effect of freeing me forever from the wiles of college football, and if that is a defect, make the most of it! Dr. Noyes and I conceived an idea on sodium aluminate solutions on the morning of the day of a Princeton-Harvard game (as I recall it) that we had planned to attend. It looked as though a few days’ work on freezing-point determinations and electrical conductivities would answer the question. We could not wait, so we gave up the game and stayed in the laboratory. Our experiments were successful. I think that this was the last game I have ever cared about seeing. I mention this as a warning, because this immunity might attack anyone. I find that I still complainingly wonder at the present position of football in American education.

Address upon receiving the Perkin Medal Award, ‘The Big Things in Chemistry’, The Journal of Industrial and Engineering Chemistry (Feb 1921), 13, No. 2, 162-163.

I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary—being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived. And these are the causes that operate in perfect harmony. Each new scientific conception gives occasion to new applications of deductive reasoning; but those applications may be only possible through the methods and the processes which belong to an earlier stage.

Explaining his choice for the exposition in historical order of the topics in A Treatise on Differential Equations (1859), Preface, v-vi.

I respect Kirkpatrick both for his sponges and for his numinous nummulosphere. It is easy to dismiss a crazy theory with laughter that debars any attempt to understand a man’s motivation–and the nummulosphere is a crazy theory. I find that few men of imagination are not worth my attention. Their ideas may be wrong, even foolish, but their methods often repay a close study … The different drummer often beats a fruitful tempo.

……

I see nothing wrong ethically with the idea of correcting single gene defects [through genetic engineering]. But I am concerned about any other kind of intervention, for anything else would be an experiment, [which would] impose our will on future generations [and take unreasonable chances] with their welfare … [Thus] such intervention is beyond the scope of consideration.

in The Second Creation: Dolly and the Age of Biological Control

I shall always feel respect for every one who has written a book, let it be what it may, for I had no idea of the trouble which trying to write common English could cost one—And alas there yet remains the worst part of all correcting the press.

Letter to W. D. Fox, 7 July 1837, referring to his Journal of Researches. In F. Burkhardt and S. Smith (eds), The Correspondence of Charles Darwin 1837-1843 (1986), Vol. 2, 29.

I should rejoice to see … Euclid honourably shelved or buried “deeper than did ever plummet sound” out of the schoolboys’ reach; morphology introduced into the elements of algebra; projection, correlation, and motion accepted as aids to geometry; the mind of the student quickened and elevated and his faith awakened by early initiation into the ruling ideas of polarity, continuity, infinity, and familiarization with the doctrines of the imaginary and inconceivable.

From Presidential Address (1869) to the British Association, Exeter, Section A, collected in Collected Mathematical Papers of Lames Joseph Sylvester (1908), Vol. 2, 657. Also in George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 93. [Note: “plummet sound” refers to ocean depth measurement (sound) from a ship using a line dropped with a weight (plummet). —Webmaster]

I strongly oppose cloning, as do most Americans. We recoil at the idea of growing human beings for spare body parts or creating life for our convenience. And while we must devote enormous energy to conquering disease, it is equally important that we pay attention to the moral concerns raised by the new frontier of human embryo stem cell research. Even the most noble ends do not justify any means.

‘Address to the Nation on Stem Cell Research’, (9 Aug 2001) in Public Papers Of The Presidents Of The United States, George W. Bush, 2001 (2004), Book 2, 955.

I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. Disgusted at my want of success, I went away to spend a few days at the seaside, and thought of entirely different things. One day, as I was walking on the cliff, the idea came to me, again with the same characteristics of conciseness, suddenness, and immediate certainty, that arithmetical transformations of indefinite ternary quadratic forms are identical with those of non-Euclidian geometry.

Science and Method (1908), trans. Francis Maitland (1914), 53-4.

I think a future flight should include a poet, a priest and a philosopher… we might get a much better idea of what we saw.

……

I think all this superstring stuff is crazy and is in the wrong direction. I don’t like that they’re not calculating anything. I don’t like that they don’t check their ideas. I don’t like that for anything that disagrees with an experiment, they cook up an explanation… It doesn’t look right.

Interview published in Paul C.W. Davies and Julian R. Brown (eds.),Superstrings: A Theory of Everything? (1988, 1992), 194.

I think it is not irreligion but a tidiness of mind, which rebels against the idea of permeating scientific research with a religious implication.

Swarthmore Lecture (1929) at Friends’ House, London, printed in Science and the Unseen World (1929), 24-25.

I think it is the general rule that the originator of a new idea is not the most suitable person to develop it, because his fears of something going wrong are really too strong…
At age 69.

The Development of Quantum Theory (1971). In A. Pais, ‘Playing With Equations, the Dirac Way’. Behram N. Kursunoglu (Ed.) and Eugene Paul Wigner (Ed.), Paul Adrien Maurice Dirac: Reminiscences about a Great Physicist (1990), 111.

I think that it is a relatively good approximation to truth—which is much too complicated to allow anything but approximations—that mathematical ideas originate in empirics.

From ‘The Mathematician’, collected in James Roy Newman (ed.), The World of Mathematics (1956), Vol. 4, 2063.

I think that we shall have to get accustomed to the idea that we must not look upon science as a ‘body of knowledge,’ but rather as a system of hypotheses; that is to say, as a system of guesses or anticipations which in principle cannot be justified, but with which we work as long as they stand up to tests, and of which we are never justified in saying that we know they are ‘true’ or ‘more or less certain’ or even ‘probable.’

The Logic of Scientific Discovery (1959), 317.

I wasn’t aware of Chargaff’s rules when he said them, but the effect on me was quite electric because I realized immediately that if you had this sort of scheme that John Griffith was proposing, of adenine being paired with thymine, and guanine being paired with cytosine, then you should get Chargaff’s rules.
I was very excited, but I didn’t actually tell Chargaff because it was something I was doing with John Griffith. There was a sort of musical comedy effect where I forgot what the bases were and I had to go to the library to check, and I went back to John Griffith to find out which places he said. Low and behold, it turned out that John Griffith’s ideas fitted in with Chargaff’s rules!
This was very exciting, and we thought “ah ha!” and we realized—I mean what anyone who is familiar with the history of science ought to realize—that when you have one-to-one ratios, it means things go to together. And how on Earth no one pointed out this simple fact in those years, I don’t know.

From Transcript of documentary by VSM Productions, The DNA Story (1973). As excerpted on web page ‘Chargaff’s Rules’, Linus Pauling and the Race for DNA on website scarc.library.oregonstate.edu

I will ask you to mark again that rather typical feature of the development of our subject; how so much progress depends on the interplay of techniques, discoveries and new ideas, probably in that order of decreasing importance.

I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. That would be claiming too much. But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming-and a little mad. Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings.

In Science and the Modern World (1926), 31.

I would trade all my experimental works for the single idea of the benzene theory.

Quoted by B. L. Lepsius in ‘Hofmann und die Deutsche Chemische Gesellschaft’, Berichte der Deutschen Chemischen Gesellschaft (1918), 51, 51.

I’d climb in the car as it went down the assembly line and introduce myself. Then I’d ask for ideas.
[How, as Ford manager of development for the Taurus car, he sought input from Ford production employees.]

Quoted in Business Week, Issues 3015-3023 (1987). In Robert H. Waterman, The Renewal Factor (1988), 147.

Iconography becomes even more revealing when processes or concepts, rather than objects, must be depicted–for the constraint of a definite ‘thing’ cedes directly to the imagination. How can we draw ‘evolution’ or ‘social organization,’ not to mention the more mundane ‘digestion’ or ‘self-interest,’ without portraying more of a mental structure than a physical reality? If we wish to trace the history of ideas, iconography becomes a candid camera trained upon the scholar’s mind.

……

Ideas are elusive, slippery things. Best to keep a pad of paper and a pencil at your bedside, so you can stab them during the night before they get away.

As quoted, without citation, in Cleophus Jackson, Reprogram Your Mind for Success and Happiness (2001), 150.

Ideas are like stars: You will not succeed in touching them with your hands, but like the seafaring man on the ocean desert of waters, you choose them as your guides, and following them, you reach your destiny.

……

Ideas are the factors that lift civilization. They create revolutions. There is more dynamite in an idea than in many bombs.

In Hialmer Day Gould, New Practical Spelling (1905), 19

Ideas can be willed, and the imagination is their engine.

In The Marketing Imagination (1983, 1986), 127.

Ideas go booming through the world like cannon. Thoughts are mightier than armies.

In Hialmer Day Gould, New Practical Spelling (1905), 19

Ideas pull the trigger, but instinct loads the gun.

Attributed. Widely seen, but without citation. An early example of the aphorism, stated without naming Marquis, is in Southwestern Medicine (Oct 1920). 4, No. 10, 4. If you know the primary source, please contact Webmaster.

Ideas, like ghosts (according to the common notion of a ghost), must be spoken to a little before they will explain themselves.

From Dealings With the Firm of Dombey and Son (1846), Vol. 1, 184.

If an idea presents itself to us, we must not reject it simply because it does not agree with the logical deductions of a reigning theory.

If at first, the idea is not absurd, there is no hope for it.

In Marc J. Madou, Fundamentals of Microfabrication: the Science of Miniaturization (2nd ed., 2002), 535.

If I give you a pfennig, you will be one pfennig richer and I’ll be one pfennig poorer. But if I give you an idea, you will have a new idea, but I shall still have it, too.

……

If I have a thousand ideas a year, and only one turns out to be good, I am satisfied.

As quoted by Linus Pauling in Nobel Prize Acceptance Speech (10 Dec 1963). As reported in Göran Liljestrand (ed.), Les Prix Nobel en 1963, (1964).

If I wished to express the basic principle of my ideas in a somewhat strongly worded sentence, I would say that man, in his bodily development, is a primate fetus that has become sexually mature [einen zur Geschlechsreife gelangten Primatenfetus].

Das Problem der Menschwerdung (1926), 8. Trans. in Stephen Jay Gould, Ontogeny and Phylogeny (1977), 361.

If in a given community unchecked popular rule means unlimited waste and destruction of the natural resources—soil, fertility, waterpower, forests, game, wild-life generally—which by right belong as much to subsequent generations as to the present generation, then it is sure proof that the present generation is not yet really fit for self-control, that it is not yet really fit to exercise the high and responsible privilege of a rule which shall be both by the people and for the people. The term “for the people” must always include the people unborn as well as the people now alive, or the democratic ideal is not realized.

In A Book-Lover’s Holidays in the Open (1916), 319.

If mankind is to profit freely from the small and sporadic crop of the heroically gifted it produces, it will have to cultivate the delicate art of handling ideas. Psychology is now able to tell us with reasonable assurance that the most influential obstacle to freedom of thought and to new ideas is fear; and fear which can with inimitable art disguise itself as caution, or sanity, or reasoned skepticism, or on occasion even as courage.

‘The Commemoration of Great Men’, Hunterian Oration, Royal College of Surgeons (15 Feb 1952) British Medical Journal (20 Feb 1932), 1, 317-20. The Collected Papers of Wilfred Trotter, FRS (1941), 30.

If physical science is dangerous, as I have said, it is dangerous because it necessarily ignores the idea of moral evil; but literature is open to the more grievous imputation of recognizing and understanding it too well.

In ‘Duties of the Church Towards Knowledge’, The Idea of a University Defined and Illustrated (1852, 1873), Discourse 9, 229.

If the national park idea is, as Lord Bryce suggested, the best idea America ever had, wilderness preservation is the highest refinement of that idea.

In magazine article, ‘It All Began with Conservation’, Smithsonian (Apr 1990), 21, No. 1, 34-43. Collected in Wallace Stegner and Page Stegner (ed.), Marking the Sparrow’s Fall: The Making of the American West (1998, 1999), 131.

If the Weismann idea triumphs, it will be in a sense a triumph of fatalism; for, according to it, while we may indefinitely improve the forces of our education and surroundings, and this civilizing nurture will improve the individuals of each generation, its actual effects will not be cumulative as regards the race itself, but only as regards the environment of the race; each new generation must start de novo, receiving no increment of the moral and intellectual advance made during the lifetime of its predecessors. It would follow that one deep, almost instinctive motive for a higher life would be removed if the race were only superficially benefited by its nurture, and the only possible channel of actual improvement were in the selection of the fittest chains of race plasma.

‘The Present Problem of Heredity’, The Atlantic Monthly (1891), 57, 363.

If the world has begun with a single quantum, the notions of space and would altogether fail to have any meaning at the beginning; they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time. I think that such a beginning of the world is far enough from the present order of Nature to be not at all repugnant. It may be difficult to follow up the idea in detail as we are not yet able to count the quantum packets in every case. For example, it may be that an atomic nucleus must be counted as a unique quantum, the atomic number acting as a kind of quantum number. If the future development of quantum theory happens to turn in that direction, we could conceive the beginning of the universe in the form of a unique atom, the atomic weight of which is the total mass of the universe. This highly unstable atom would divide in smaller and smaller atoms by a kind of super-radioactive process.

In a seminal short letter (457 words), ‘The Beginning of the World from the Point of View of Quantum Theory’, Nature (9 May 1931), 127, 706.

If we consider what science already has enabled men to know—the immensity of space, the fantastic philosophy of the stars, the infinite smallness of the composition of atoms, the macrocosm whereby we succeed only in creating outlines and translating a measure into numbers without our minds being able to form any concrete idea of it—we remain astounded by the enormous machinery of the universe.

Address (10 Sep 1934) to the International Congress of Electro-Radio Biology, Venice. In Associated Press, ‘Life a Closed Book, Declares Marconi’, New York Times (11 Sep 1934), 15.

If we define ‘thought collective’ as a community of persons mutually exchanging ideas or maintaining intellectual interaction, we will find by implication that it also provides the special ‘carrier’ for the historical development of any field of thought, as well as for the given stock of knowledge and level of culture. This we have designated thought style.

Genesis and the Development of a Scientific Fact (1935), 39.

If we would indicate an idea … striving to remove the barriers which prejudice and limited views of every kind have erected among men, and to treat all mankind, without reference to religion, nation, or color, as one fraternity, one great community, fitted for the attainment of one object, the unrestrained development of the physical powers. This is the ultimate and highest aim of society.

In Ueber die Kawi-Sprache, Vol. 3, 426. As quoted in Alexander von Humboldt, Cosmos: A Sketch of a Physical Description of the Universe (1850), Vol. 1, 358, as translated by Elise C. Otté.

If you have an idea that you wish your audience to carry away, turn it upside down and inside out, rephrasing it from different angles. Remember that the form in which the thing may appear best to you may not impress half your audience.

Advice to the writer of his first paper for presentation at a scientific meeting. As expressed in quotation marks by Charles Thom in ‘Robert Almer Harper’, National Academy Biographical Memoirs (1948), 25, 233-234. Also, in Thom’s words, “[Harper] added that a miscellaneous audience can not he expected to carry away a lot of separate facts but one good idea, well pictured out, will be remembered by some of them.”

If you want to kill any idea in the world, get a committee working on it.

Science quotes on:  |  Kill (101)  |  Want (498)  |  World (1822)

If, for example, I had some idea, which, as it turned out would, say, be quite wrong, was going off of the tangent, Watson would tell me in no uncertain terms this was nonsense, and vice-versa. If he had some idea I didn’t like and I would say so and this would shake his thinking about it and draw him back again. And in fact, it’s one of the requirements for collaboration of this sort that you must be perfectly candid, one might almost say rude, to the person you are working with. It’s useless, working with somebody who’s either much too junior than yourself, or much too senior, because then politeness creeps in. And this is the end of all real collaboration in science.

As quoted in Robert Olby, The Path to the Double Helix: The Discovery of the Double Helix, (1974, 1994), 316, citing Transcript of BBC TV program, The Prizewinners (1962).

Imagination only rarely leads one to a correct answer, and most of our ideas have to be discarded. Research workers ought not to be afraid of making mistakes provided they correct them in good time.

In The Art of Scientific Investigation (1950), 67.

In 1925 [state legislators] prohibited by law the teaching of evolution in Tennessee. … Anti-evolutionists feared that a scientific idea would undermine religious belief. In the present…, pro-evolutionists fear that a religious idea will undermine scientific belief. The former had insufficient confidence in religion; the latter, insufficient confidence in science.

In Building a Bridge to the 18th Century: How the Past Can Improve Our Future (1999), 167.

In a randomly infinite Universe, any event occurring here and now with finite probability must be occurring simultaneously at an infinite number of other sites in the Universe. It is hard to evaluate this idea any further, but one thing is certain: if it is true then it is certainly not original!

With co-author Frank Tipler, The Anthropic Cosmological Principle (1986).

In all things, therefore, where we have clear evidence from our ideas, and those principles of knowledge I have above mentioned, reason is the proper judge; and revelation, though it may, in consenting with it, confirm its dictates, yet cannot in such cases invalidate its decrees: nor can we be obliged, where we have the clear and evident sentience of reason, to quit it for the contrary opinion, under a pretence that it is matter of faith: which can have no authority against the plain and clear dictates of reason.

in Essay Concerning Human Understanding (1690), book 4, ch. 18, sec. 20.

In an enterprise such as the building of the atomic bomb the difference between ideas, hopes, suggestions and theoretical calculations, and solid numbers based on measurement, is paramount. All the committees, the politicking and the plans would have come to naught if a few unpredictable nuclear cross sections had been different from what they are by a factor of two.

Epigraph in Richard Rhodes, The Making of the Atomic Bomb (1986), 8.

In arranging the bodies in order of their electrical nature, there is formed an electro-chemical system which, in my opinion, is more fit than any other to give an idea of chemistry.

Essai sur le théorie des proportions chimiques (1819). Translated in Henry M. Leicester and Herbert S. Klickstein, A Source Book in Chemistry 1400-1900 (1952), 260.

In design, people like Buckminster Fuller amazed me at the levels at which he could think. He could think molecularly. And he could think at the almost galactic scale. And the idea that somebody could actually talk about molecules and talk about buildings and structures and talk about space just amazed me. As I get older–I’ll be 60 next year–what I’ve discovered is that I find myself in those three realms too.

In interview with Kerry A. Dolan, ‘William McDonough On Cradle-to-Cradle Design’, Forbes (4 Aug 2010)

In Euclid each proposition stands by itself; its connection with others is never indicated; the leading ideas contained in its proof are not stated; general principles do not exist. In modern methods, on the other hand, the greatest importance is attached to the leading thoughts which pervade the whole; and general principles, which bring whole groups of theorems under one aspect, are given rather than separate propositions. The whole tendency is toward generalization. A straight line is considered as given in its entirety, extending both ways to infinity, while Euclid is very careful never to admit anything but finite quantities. The treatment of the infinite is in fact another fundamental difference between the two methods. Euclid avoids it, in modern mathematics it is systematically introduced, for only thus is generality obtained.

In ‘Geometry’, Encyclopedia Britannica (9th edition).

In Europe I have been accused of taking my scientific ideas from the Church. In America I have been called a heretic, because I will not let my church-going friends pat me on the head.

Lecture at a teaching laboratory on Penikese Island, Buzzard’s Bay. Quoted from the lecture notes by David Starr Jordan, Science Sketches (1911), 147.

In every case the awakening touch has been the mathematical spirit, the attempt to count, to measure, or to calculate. What to the poet or the seer may appear to be the very death of all his poetry and all his visions—the cold touch of the calculating mind,—this has proved to be the spell by which knowledge has been born, by which new sciences have been created, and hundreds of definite problems put before the minds and into the hands of diligent students. It is the geometrical figure, the dry algebraical formula, which transforms the vague reasoning of the philosopher into a tangible and manageable conception; which represents, though it does not fully describe, which corresponds to, though it does not explain, the things and processes of nature: this clothes the fruitful, but otherwise indefinite, ideas in such a form that the strict logical methods of thought can be applied, that the human mind can in its inner chamber evolve a train of reasoning the result of which corresponds to the phenomena of the outer world.

In A History of European Thought in the Nineteenth Century (1896), Vol. 1, 314.

In experimenting on the arc, my aim was not so much to add to the large number of isolated facts that had already been discovered, as to form some idea of the bearing of these upon one another, and thus to arrive at a clear conception of what takes place in each part of the arc and carbons at every moment. The attempt to correlate all the known phenomena, and to bind them together into one consistent whole, led to the deduction of new facts, which, when duly tested by experiment, became parts of the growing body, and, themselves, opened up fresh questions, to be answered in their turn by experiment.

In The Electric Arc (1902), Preface, iii. Ayrton described the growth of her published work on the electric arc, from a series of articles in The Electrician in 1895-6, to the full book, which “has attained to its present proportions almost with the growth of an organic body.”

In general, scientific progress calls for no more than the absorption and elaboration of new ideas—and this is a call most scientists are happy to heed.

In Werner Heisenberg and Arnold J. Pomerans (trans.), Physics and Beyond: Encounters and Conversations (1971), 70.

In many places, half-trained people in magnificent laboratories were sitting on sterile ideas like hens sitting on boiled eggs.

In As I Remember Him: The Biography of R.S. (1940), 109. This quote has been used by others to illustrate “that is not at all rare for investigators to adhere to their broken hypotheses, turning a blind eye to contrary evidence,” as in W.I.B. Beveridge, The Art of Scientific Investigation (1957), 48.

In many ways ideas are more important than people — they are much more permanent.

In man’s brain the impressions from outside are not merely registered; they produce concepts and ideas. They are the imprint of the external world upon the human brain. Therefore, it is not surprising that, after a long period of searching and erring, some of the concepts and ideas in human thinking should have come gradually closer to the fundamental laws of the world, that some of our thinking should reveal the true structure of atoms and the true movements of the stars. Nature, in the form of man, begins to recognize itself.

In Knowledge and Wonder (1962).

In modern times the belief that the ultimate explanation of all things was to be found in Newtonian mechanics was an adumbration of the truth that all science, as it grows towards perfection, becomes mathematical in its ideas.

In An Introduction to Mathematics (1911), 13-14. [To suggest, disclose, or outline partially, produces an “adumbration”, which gives only the main facts and not the details. —Webmaster]

In my considered opinion the peer review system, in which proposals rather than proposers are reviewed, is the greatest disaster visited upon the scientific community in this century. No group of peers would have approved my building the 72-inch bubble chamber. Even Ernest Lawrence told me he thought I was making a big mistake. He supported me because he knew my track record was good. I believe that U.S. science could recover from the stultifying effects of decades of misguided peer reviewing if we returned to the tried-and-true method of evaluating experimenters rather than experimental proposals. Many people will say that my ideas are elitist, and I certainly agree. The alternative is the egalitarianism that we now practice and I’ve seen nearly kill basic science in the USSR and in the People’s Republic of China.

Alvarez: Adventures of a Physicist (1987), 200-1.

In no subject is there a rule, compliance with which will lead to new knowledge or better understanding. Skilful observations, ingenious ideas, cunning tricks, daring suggestions, laborious calculations, all these may be required to advance a subject. Occasionally the conventional approach in a subject has to be studiously followed; on other occasions it has to be ruthlessly disregarded. Which of these methods, or in what order they should be employed is generally unpredictable. Analogies drawn from the history of science are frequently claimed to be a guide; but, as with forecasting the next game of roulette, the existence of the best analogy to the present is no guide whatever to the future. The most valuable lesson to be learnt from the history of scientific progress is how misleading and strangling such analogies have been, and how success has come to those who ignored them.

‘Cosmology’, in Arthur Beer (ed.), Vistas in Astronomy (1956), Vol. 2, 1722.

In one of my lectures many years ago I used the phrase “following the trail of light”. The word “light” was not meant in its literal sense, but in the sense of following an intellectual concept or idea to where it might lead. My interest in living things is probably a fundamental motivation for the scientific work in the laboratory, and we created here in Berkeley one of the first and foremost interdisciplinary laboratories in the world.

In autobiography, Following the Trail of Light: A Scientific Odyssey (1992), 134.

In our popular discussions, unwise ideas must have a hearing as well as wise ones, dangerous ideas as well as safe.

……

In our preoccupations with sex, our submission to gods and leaders, our sometimes suicidal commitment to ideas, religions, and trivial details of cultural style, we become the unconscious creators of the social organism’s exploits.

In ‘The Clint Eastwood Conundrum’, The Lucifer Principle: A Scientific Expedition Into the Forces of History (1997), 8.

In our search after the Knowledge of Substances, our want of Ideas, that are suitable to such a way of proceeding, obliges us to a quite different method. We advance not here, as in the other (where our abstract Ideas are real as well as nominal Essences) by contemplating our Ideas, and considering their Relations and Correspondencies; that helps us very little, for the Reasons, and in another place we have at large set down. By which, I think it is evident, that Substances afford Matter of very little general Knowledge; and the bare Contemplation of their abstract Ideas, will carry us but a very little way in the search of Truth and Certainty. What then are we to do for the improvement of our Knowledge in Substantial beings? Here we are to take a quite contrary Course, the want of Ideas of their real essences sends us from our own Thoughts, to the Things themselves, as they exist.

An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 12, Section 9, 644.

In science it is no crime to be wrong, unless you are (inappropriately) laying claim to truth. What matters is that science as a whole is a self-correcting mechanism in which both new and old notions are constantly under scrutiny. In other words, the edifice of scientific knowledge consists simply of a body of observations and ideas that have (so far) proven resistant to attack, and that are thus accepted as working hypotheses about nature.

In The Monkey in the Mirror: Essays on the Science of What Makes Us Human (2003), 9.

In science one must search for ideas. If there are no ideas, there is no science. A knowledge of facts is only valuable in so far as facts conceal ideas: facts without ideas are just the sweepings of the brain and the memory.

Collected Works (1948), Vol.2, 348.

In science the important thing is to modify and change one’s ideas as science advances.

As given by in Bertha McCool, ‘The Development of Embryology’, Bios (Oct 1935), 6, No. 3, 303. Also in Rudolf Franz Flesch, The Art of Clear Thinking (1951), 122. Webmaster has also seen this attributed to Herbert Spencer, but has yet found such examples date only after 1997. If you know the primary source from Bernard, please contact Webmaster.

In science the important thing is to modify and change one’s ideas as science advances.
[Misattributed? See instead Claude Bernard]

Webmaster believes this is a quote by Claude Bernard, for whom examples date back to at least 1935, whereas Webmaster has found attribution to Spencer only as early as 1997. If you know the primary source from either Spencer or Bernard, please contact Webmaster.

In science the primary duty of ideas is to be useful and interesting even more than to be “true.”

Lecture delivered to Anthropological Society of University College, London (25 Jan 1929). Published in ‘The Functions of the Human Skull’, Nature (6 Apr 1929), 123, No. 3101, 533-537. Collected in The Collected Papers of Wilfred Trotter, FRS (1941), 73.

In Science, it is when we take some interest in the great discoverers and their lives that it becomes endurable, and only when we begin to trace the development of ideas that it becomes fascinating.

Quoted in Robert J. Scully, The Demon and the Quantum (2007), 5.

In scientific investigations it is grievously wrong to pander to the public’s impatience for results, or to let them think that for discovery it is necessary only to set up a great manufactory and a system of mass production. If in treatment team work is effective, in research it is the individual who counts first and above all. No great thought has ever sprung from anything but a single mind, suddenly conceiving. Throughout the whole world there has been too violent a forcing of the growth of ideas; too feverish a rush to perform experiments and publish conclusions. A year of vacation for calm detachment with all the individual workers thinking it all over in a desert should be proclaimed.

In Viewless Winds: Being the Recollections and Digressions of an Australian Surgeon (1939), 286.

In the 1920s, there was a dinner at which the physicist Robert W. Wood was asked to respond to a toast … “To physics and metaphysics.” Now by metaphysics was meant something like philosophy—truths that you could get to just by thinking about them. Wood took a second, glanced about him, and answered along these lines: The physicist has an idea, he said. The more he thinks it through, the more sense it makes to him. He goes to the scientific literature, and the more he reads, the more promising the idea seems. Thus prepared, he devises an experiment to test the idea. The experiment is painstaking. Many possibilities are eliminated or taken into account; the accuracy of the measurement is refined. At the end of all this work, the experiment is completed and … the idea is shown to be worthless. The physicist then discards the idea, frees his mind (as I was saying a moment ago) from the clutter of error, and moves on to something else. The difference between physics and metaphysics, Wood concluded, is that the metaphysicist has no laboratory.

In ‘Wonder and Skepticism’, Skeptical Enquirer (Jan-Feb 1995), 19, No. 1.

In the 1940s when I did my natural sciences degree in zoology it was very much laboratory-based. … I was not keen on the idea of spending the rest of my life in the lab. I also don’t think I would have been particularly good at it. I don’t think I have as analytical a mind or the degree of application that one would need to become a first-rate research scientist.

From interview with Michael Bond, ‘It’s a Wonderful Life’, New Scientist (14 Dec 2002), 176, No. 2373, 48.

In the beginning of the year 1800 the illustrious professor [Volta] conceived the idea of forming a long column by piling up, in succession, a disc of copper, a disc of zinc, and a disc of wet cloth, with scrupulous attention to not changing this order. What could be expected beforehand from such a combination? Well, I do not hesitate to say, this apparently inert mass, this bizarre assembly, this pile of so many couples of unequal metals separated by a little liquid is, in the singularity of effect, the most marvellous instrument which men have yet invented, the telescope and the steam engine not excepted.

In François Arago, ‘Bloge for Volta’ (1831), Oeuvres Completes de François Arago (1854), Vol. 1, 219-20.

In the course of normal speaking the inhibitory function of the will is continuously directed to bringing the course of ideas and the articulatory movements into harmony with each other. If the expressive movement which which follows the idea is retarded through mechanical causes, as is the case in writing … such anticipations make their appearance with particular ease.

Folk Psychology (1900)

In the mathematical investigations I have usually employed such methods as present themselves naturally to a physicist. The pure mathematician will complain, and (it must be confessed) sometimes with justice, of deficient rigour. But to this question there are two sides. For, however important it may be to maintain a uniformly high standard in pure mathematics, the physicist may occasionally do well to rest content with arguments which are fairly satisfactory and conclusive from his point of view. To his mind, exercised in a different order of ideas, the more severe procedure of the pure mathematician may appear not more but less demonstrative. And further, in many cases of difficulty to insist upon the highest standard would mean the exclusion of the subject altogether in view of the space that would be required.

In Preface to second edition, The Theory of Sound (1894), Vol. 1, vii.

In the sphere of natural science let us remember that we have always to deal with an insoluble problem. Let us prove keen and honest in attending to anything which is in any way brought to our notice, most of all when it does not fit in with our previous ideas. For it is only thereby that we perceive the problem, which does indeed lie in nature, but still more in man.

In The Maxims and Reflections of Goethe (1906), 183.

In the study of ideas, it is necessary to remember that insistence on hard-headed clarity issues from sentimental feeling, as it were a mist, cloaking the perplexities of fact. Insistence on clarity at all costs is based on sheer superstition as to the mode in which human intelligence functions. Our reasonings grasp at straws for premises and float on gossamers for deductions.

In Adventure of Ideas (1933), 91.

In the year 1902 (while I was attempting to explain to an elementary class in chemistry some of the ideas involved in the periodic law) becoming interested in the new theory of the electron, and combining this idea with those which are implied in the periodic classification, I formed an idea of the inner structure of the atom which, although it contained certain crudities, I have ever since regarded as representing essentially the arrangement of electrons in the atom … In accordance with the idea of Mendeleef, that hydrogen is the first member of a full period, I erroneously assumed helium to have a shell of eight electrons. Regarding the disposition in the positive charge which balanced the electrons in the neutral atom, my ideas were very vague; I believed I inclined at that time toward the idea that the positive charge was also made up of discrete particles, the localization of which determined the localization of the electrons.

Valence and the Structure of Atoms and Molecules (1923), 29-30.

In this great celestial creation, the catastrophy of a world, such as ours, or even the total dissolution of a system of worlds, may possibly be no more to the great Author of Nature, than the most common accident in life with us, and in all probability such final and general Doomsdays may be as frequent there, as even Birthdays or mortality with us upon the earth. This idea has something so cheerful in it, that I know I can never look upon the stars without wondering why the whole world does not become astronomers; and that men endowed with sense and reason should neglect a science they are naturally so much interested in, and so capable of enlarging their understanding, as next to a demonstration must convince them of their immortality, and reconcile them to all those little difficulties incident to human nature, without the least anxiety. All this the vast apparent provision in the starry mansions seem to promise: What ought we then not to do, to preserve our natural birthright to it and to merit such inheritance, which alas we think created all to gratify alone a race of vain-glorious gigantic beings, while they are confined to this world, chained like so many atoms to a grain of sand.

In The Universe and the Stars: Being an Original Theory on the Visible Creation, Founded on the Laws of Nature (1750, 1837), 132.

In this lecture I would like to conclude with … some characteristics [of] gravity … The most impressive fact is that gravity is simple. It is simple to state the principles completely and not have left any vagueness for anybody to change the ideas of the law. It is simple, and therefore it is beautiful. It is simple in its pattern. I do not mean it is simple in its action—the motions of the various planets and the perturbations of one on the other can be quite complicated to work out, and to follow how all those stars in a globular cluster move is quite beyond our ability. It is complicated in its actions, but the basic pattern or the system beneath the whole thing is simple. This is common to all our laws; they all turn out to be simple things, although complex in their actual actions.

In ‘The Law of Gravitation, as Example of Physical Law’, the first of his Messenger Lectures (1964), Cornell University. Collected in The Character of Physical Law (1967), 33-34.

In truth, ideas and principles are independent of men; the application of them and their illustration is man’s duty and merit. The time will come when the author of a view shall be set aside, and the view only taken cognizance of. This will be the millennium of Science.

Notes of hints to Mr Ramsey, Professor of Geology, University College London, 1847. In George Wilson and Archibald Geikie, Memoir of Edward Forbes F.R.S. (1861), 429.

In working out an invention, the most important quality is persistence. Nearly every man who develops an idea works it up to the point where it looks impossible, and then he gets discouraged. That’s not the place to become discouraged, that’s the place to get interested.

As quoted in French Strother, ‘The Modern Profession of Inventing’, World’s Work and Play (Jul 1905), 6, No. 32, 186.

In working out physical problems there should be, in the first place, no pretence of rigorous formalism. The physics will guide the physicist along somehow to useful and important results, by the constant union of physical and geometrical or analytical ideas. The practice of eliminating the physics by reducing a problem to a purely mathematical exercise should be avoided as much as possible. The physics should be carried on right through, to give life and reality to the problem, and to obtain the great assistance which the physics gives to the mathematics.

In Electromagnetic Theory (1892), Vol. 2, 5.

In-depth studies have an influence on general ideas, whereas theories, in turn, in order to maintain themselves, push their spectators to search for new evidence. The mind’s activity that is maintained by the debates about these works, is probably the source of the greatest joys given to man to experience on Earth.

La théorie des glaciers et ses progrès les plus récents. Bibl. universelle de Geneve, (3), Vol. 41, p. 139. Trans. Karin Verrecchia.

Infidels are intellectual discoverers. They sail the unknown seas and find new isles and continents in the infinite realms of thought. An Infidel is one who has found a new fact, who
has an idea of his own, and who in the mental sky has seen another star. He is an intellectual capitalist, and for that reason excites the envy and hatred of the theological pauper.

In ‘The Great Infidels’, The Works of Robert G. Ingersoll (1902), Vol. 3, 309.

Inspiration is the inclination of the spirit to the most lively reception of impressions and to the grasping and exposition of ideas.

(1827). In Aleksandr Sergeevich Pushkin, John Bayley (ed.), Pushkin on Literature (1986), 211.

Intellectual work is an act of creation. It is as if the mental image that is studied over a period of time were to sprout appendages like an ameba—outgrowths that extend in all directions while avoiding one obstacle after another—before interdigitating with related ideas.

From Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), 34.

Inventions and discoveries are of two kinds. The one which we owe to chance, such as those of the mariner’s compass, gunpowder, and in general almost all the discoveries we have made in the arts. The other which we owe to genius: and here we ought to understand by the word discovery, a new combination, or a new relation perceived between certain objects or ideas. A person obtains the title of a man of genius, if the ideas which result from this combination form one grand whole, are fruitful in truths, and are of importance with respect to mankind.

From the original French, “Les inventions ou les découvertes sont de deux espèces. Il en est que nous devons au hazard; telles sont la boussole, la poudre à canon, & généralement presque toutes les découvertes que nous avons faites dans les arts. Il en est d’autres que nous devons au génie: &, par ce mot de découverte, on doit alors entendre une nouvelle combinaison, un rapport nouveau aperçu entre certains objets ou certaines idées. On obtient le titre d’homme de génie, si les idées qui résultent de ce rapport forment un grand ensemble, sont fécondes en vérités & intéressantes pour l’humanité,” in ‘Du Génie’, L’Esprit (1758), Discourse 4, 476. English version from Claude Adrien Helvétius and William Mudford (trans.), ‘Of Genius’, De l’Esprit or, Essays on the Mind and its several Faculties (1759), Essay 4, Chap. 1, 241-242.

Investigators are commonly said to be engaged in a search for the truth. I think they themselves would usually state their aims less pretentiously. What the experimenter is really trying to do is to learn whether facts can be established which will be recognized as facts by others and which will support some theory that in imagination he has projected. But he must be ingenuously honest. He must face facts as they arise in the course of experimental procedure, whether they are favourable to his idea or not. In doing this he must be ready to surrender his theory at any time if the facts are adverse to it.

The Way of an Investigator: A Scientist’s Experiences in Medical Research (1945), 34.

It appears that all that can be, is. The Creator’s hand does not appear to have been opened in order to give existence to a certain determinate number of species, but it seems that it has thrown out all at once a world of relative and non-relative creatures, an infinity of harmonic and contrary combinations and a perpetuity of destructions and replacements. What idea of power is not given us by this spectacle! What feeling of respect for its Author is not inspired in us by this view of the universe!

In ‘Premier Discours: De la Manière d’Étudier et de Traiter l’Histoire naturelle’, Histoire Naturelle, Generale et Particulière, Avec la Description du Cabinet du Roi (1749), Vol. I, 11. Trans. Phillip R. Sloan.

It becomes the urgent duty of mathematicians, therefore, to meditate about the essence of mathematics, its motivations and goals and the ideas that must bind divergent interests together.

In ‘Mathematics in the Modern World’, Scientific American (Sep 1964) 211, No. 3, 42. Collected in Ronald J. Comer and Morris Kline, Mathematics in the Modern World: Readings from Scientific American (1988), 20.

It has often been said that, to make discoveries, one must be ignorant. This opinion, mistaken in itself, nevertheless conceals a truth. It means that it is better to know nothing than to keep in mind fixed ideas based on theories whose confirmation we constantly seek, neglecting meanwhile everything that fails to agree with them.

From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 37.

It is a myth that the success of science in our time is mainly due to the huge amounts of money that have been spent on big machines. What really makes science grow is new ideas, including false ideas.

As quoted by Adam Gopnik, writing about his meeting with Popper at home, in ‘The Porcupine: A Pilgrimage to Popper’ in The New Yorker (1 Apr 2002).

It is a natural inquiry to ask—To what most nearly are these new phenomena [the newly-born science of radioactivity and the spontaneous disintegration of elements] correlated? Is it possible to give, by the help of an analogy to familiar phenomena, any correct idea of the nature of this new phenomenon “Radioactivity”? The answer may surprise those who hold to the adage that there is nothing new under the sun. Frankly, it is not possible, because in these latest developments science has broken fundamentally new ground, and has delved one distinct step further down into the foundations of knowledge.

In The Interpretation of Radium: Being the Substance of Six Free Popular Lectures Delivered at the University of Glasgow (1909, 1912), 2. The original lectures of early 1908, were greatly edited, rearranged and supplemented by the author for the book form.

It is a strange feeling which comes over one as he stands in the centre of the tunnel, and knows that a mighty river is rolling on over his head, and that great ships with their thousands of tons burthen, sail over him. … There is no single work of Art in London (with the exception of St. Paul’s Cathedral) which excites so much curiosity and admiration among foreigners as the Tunnel. Great buildings are common to all parts of Europe, but the world has not such another Tunnel as this. There is something grand in the idea of walking under a broad river—making a pathway dry and secure beneath ships and navies!
[About visiting Brunel’s Thames Tunnel, the first in the world under a navigable waterway.]

What I Saw in London: or, Men and Things in the Great Metropolis (1853), 168-169.

It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.

In On the Study and Difficulties of Mathematics (1898), chap. 1.

It is always better to have no ideas than false ones; to believe nothing than to believe what is wrong.

In Letter (19 Jul 1788) to James Madison. Collected in Thomas Jefferson Randolph, Memoirs, Correspondence, and Private Papers of Thomas Jefferson (1829), Vol. 2, 223.

It is always the case with the best work, that it is misrepresented, and disparaged at first, for it takes a curiously long time for new ideas to become current, and the older men who ought to be capable of taking them in freely, will not do so through prejudice.

From letter reprinted in Journal of Political Economy (Feb 1977), 85, No. 1, back cover, as cited in Stephen M. Stigler, The History of Statistics: The Measurement of Uncertainty Before 1900 (1986), 307. Stigler notes the letter is held by David E. Butler of Nuffield College, Oxford.

It is an irony of fate that I myself have been the recipient of excessive admiration and reverence from my fellow-beings, through no fault, and no merit, of my own. The cause of this may well be the desire, unattainable for many, to understand the few ideas to which I have with my feeble powers attained through ceaseless struggle. I am quite aware that for any organisation to reach its goals, one man must do the thinking and directing and generally bear the responsibility. But the led must not be coerced, they must be able to choose their leader.

In ‘What I Believe’, Forum and Century (1930), 84, 193-194.

It is another property of the human mind that whenever men can form no idea of distant and unknown things, they judge them by what is familiar and at hand.

In The New Science (3rd ed., 1744), Book 1, Para. 122, as translated by Thomas Goddard Bergin and Max Harold Fisch, The New Science of Giambattista Vico (1948, 1984), 60.

It is clear, then, that the idea of a fixed method, or of a fixed theory of rationality, rests on too naive a view of man and his social surroundings. To those who look at the rich material provided by history, and who are not intent on impoverishing it in order to please their lower instincts, their craving for intellectual security in the form of clarity, precision, “objectivity”, “truth”, it will become clear that there is only one principle that can be defended under all circumstances and in all stages of human development. It is the principle: anything goes.

Against Method: Outline of an Anarchistic Theory of Knowledge (1975, 1993), 18-19.

It is difficult to give an idea of the vast extent of modern mathematics. The word “extent” is not the right one: I mean extent crowded with beautiful detail—not an extent of mere uniformity such as an objectless plain, but of a tract of beautiful country seen at first in the distance, but which will bear to be rambled through and studied in every detail of hillside and valley, stream, rock, wood, and flower.

President’s address (1883) to the British Association for the Advancement of Science, in The Collected Mathematical Papers (1895), Vol. 8, xxii.

It is easier to love humanity as a whole than to love one’s neighbor. There may even be a certain antagonism between love of humanity and love of neighbor; a low capacity for getting along with those near us often goes hand in hand with a high receptivity to the idea of the brotherhood of men. About a hundred years ago a Russian landowner by the name of Petrashevsky recorded a remarkable conclusion: “Finding nothing worthy of my attachment either among women or among men, I have vowed myself to the service of mankind.” He became a follower of Fourier, and installed a phalanstery on his estate. The end of the experiment was sad, but what one might perhaps have expected: the peasants—Petrashevsky’s neighbors-burned the phalanstery.

In ‘Brotherhood’, The Ordeal of Change (1963), 91.

It is evident that scientists and philosophers can help each other. For the scientist sometimes wants a new idea, and the philosopher is enlightened as to meanings by the study of the scientific consequences.

From Epilogue to a collection of lectures, ‘The Aim of Philosophy’, Modes of Thought (1938), 235.

It is impossible to devise an experiment without a preconceived idea; devising an experiment, we said, is putting a question; we never conceive a question without an idea which invites an answer. I consider it, therefore, an absolute principle that experiments must always be devised in view of a preconceived idea, no matter if the idea be not very clear nor very well defined.

An Introduction to the Study of Experimental Medicine (1865, translation 1927, 1957), 23.

It is indeed an Opinion strangely prevailing amongst Men, that Houses, Mountains, Rivers, and in a word all sensible Objects have an Existence Natural or Real, distinct from their being perceived by the Understanding. But with how great an Assurance and Acquiescence soever this Principle may be entertained in the World; yet whoever shall find in his Heart to call it in Question, may, if I mistake not, perceive it to involve a manifest Contradiction. For what are the forementioned Objects but the things we perceive by Sense, and what do we perceive besides our own Ideas or Sensations; and is it not plainly repugnant that anyone of these or any Combination of them should exist unperceived?

A Treatise Concerning the Principles of Human Knowledge [first published 1710], (1734),38.

It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.

Quoted in Return to Mathematical Circles H. Eves (Boston 1988).

It is not Cayley’s way to analyze concepts into their ultimate elements. … But he is master of the empirical utilization of the material: in the way he combines it to form a single abstract concept which he generalizes and then subjects to computative tests, in the way the newly acquired data are made to yield at a single stroke the general comprehensive idea to the subsequent numerical verification of which years of labor are devoted. Cayley is thus the natural philosopher among mathematicians.

In Mathematische Annalen, Bd. 46 (1895), 479. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 146.

It is not easy to convey, unless one has experienced it, the dramatic feeling of sudden enlightenment that floods the mind when the right idea finally clinches into place.

In What Mad Pursuit (1988).

It is not of the essence of mathematics to be conversant with the ideas of number and quantity. Whether as a general habit of mind it would be desirable to apply symbolic processes to moral argument, is another question.

An Investigation of the Laws of Thought (1854), 12.

It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.

In Lectures on Science, Philosophy and Art (1908), 32-33.

It is notorious that the same discovery is frequently made simultaneously and quite independently, by different persons. Thus, to speak of only a few cases in late years, the discoveries of photography, of electric telegraphy, and of the planet Neptune through theoretical calculations, have all their rival claimants. It would seem, that discoveries are usually made when the time is ripe for them—that is to say, when the ideas from which they naturally flow are fermenting in the minds of many men.

Hereditary Genius (1869), 192.

It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside. We must, example, use language, and our language is necessarily steeped in preconceived ideas. Only they are unconscious preconceived ideas, which are a thousand times the most dangerous of all.

Science and Hypothesis (1902), trans. W.J.G. (1905), 143.

It is popular to believe that the age of the individual and, above all, of the free individual, is past in science. There are many administrators of science and a large component of the general population who believe that mass attacks can do anything, and even that ideas are obsolete. Behind this drive to the mass attack there are a number of strong psychological motives. Neither the public or the big administrator has too good an understanding of the inner continuity of science, but they both have seen its world-shaking consequences, and they are afraid of it. Both of them wish to decerebrate the scientist, even as the Byzantine State emasculated its civil servants. Moreover, the great administrator who is not sure of his own intellectual level can aggrandize himself only by cutting his scientific employees down to size.

In I am a Mathematician (1956), Epilogue, 363-364.

It is really laughable to see what different ideas are prominent in various naturalists’ minds, when they speak of “species”; in some, resemblance is everything and descent of little weight—in some, resemblance seems to go for nothing, and Creation the reigning idea—in some, descent is the key,—in some, sterility an unfailing test, with others it is not worth a farthing. It all comes, I believe, from trying to define the undefinable.

Letter to J. D. Hooker (24 Dec 1856). In Francis Darwin, The Life and Letters of Charles Darwin (1888), 446.

It is strange, but the longer I live the more I am governed by the feeling of Fatalism, or rather predestination. The feeling or free-will, said to be innate in man, fails me more and more. I feel so deeply that however much I may struggle, I cannot change fate one jot. I am now almost resigned. I work because I feel I am at the worst. I can neither wish nor hope for anything. You have no idea how indifferent I am to everything.

In Letter to Anna Carlotta, collected in Anna Charlotte Leffler, Sonya Kovalevsky: A Biography (1895), 133, as translated by A. De Furuhjelm and A.M. Clive Bayley.

It is the destiny of the sciences, which must necessarily be in the hands of a few, that the utility of their progress should be invisible to the greater part of mankind, especially if those sciences are associated with unobtrusive pursuits. Let a greater facility in using our navigable waters and opening new lines of communication but once exist, simply because at present we know vastly better how to level the ground and construct locks and flood-gates—what does it amount to? The workmen have had their labors lightened, but they themselves have not the least idea of the skill of the geometer who directed them; they have been put in motion nearly as the body is by a soul of which it knows nothing; the rest of the world has even less perception of the genius which presided over the enterprise, and enjoys the success it has attained only with a species of ingratitude.

As quoted in Joseph Henry, ‘Report of the Secretary’, Annual Report of the Board of Regents of the Smithsonian Institution for 1859 (1860), 16-17. Webmaster has not yet been able to locate a primary source for this quote.

It is the lone worker who makes the first advance in a subject: the details may be worked out by a team, but the prime idea is due to the enterprise, thought, and perception of an individual.

In a speech at Edinburgh University (1951). As cited in John Bartlett, Bartlett’s Familiar Quotations (18th ed., 2012), 647.

It is the man of science, eager to have his every opinion regenerated, his every idea rationalised, by drinking at the fountain of fact, and devoting all the energies of his life to the cult of truth, not as he understands it, but as he does not understand it, that ought properly to be called a philosopher. To an earlier age knowledge was power—merely that and nothing more—to us it is life and the summum bonum.

As quoted in Sir Richard Gregory, Discovery: Or, The Spirit and Service of Science (1916), 24.

It is the reciprocity of these appearances—that each party should think the other has contracted—that is so difficult to realise. Here is a paradox beyond even the imagination of Dean Swift. Gulliver regarded the Lilliputians as a race of dwarfs; and the Lilliputians regarded Gulliver as a giant. That is natural. If the Lilliputians had appeared dwarfs to Gulliver, and Gulliver had appeared a dwarf to the Lilliputians—but no! that is too absurd for fiction, and is an idea only to be found in the sober pages of science. …It is not only in space but in time that these strange variations occur. If we observed the aviator carefully we should infer that he was unusually slow in his movements; and events in the conveyance moving with him would be similarly retarded—as though time had forgotten to go on. His cigar lasts twice as long as one of ours. …But here again reciprocity comes in, because in the aviator’s opinion it is we who are travelling at 161,000 miles a second past him; and when he has made all allowances, he finds that it is we who are sluggish. Our cigar lasts twice as long as his.

In Space, Time and Gravitation: An Outline of the General Relativity Theory (1920, 1921), 23-24.

It is therefore through the study of mathematics, and only by it, that one can form a fair and comprehensive idea of what science is. … Any scientific education which does not begin with such a study, necessarily is fundamentally flawed.

From Cours de Philosophie Positive (1830), Vol. 1, 132. Comte believed in a hierarchy of the sciences, ordered by degree of generality and simplicity of their ideas. Mathematics he placed first, followed by astronomy, physics, chemistry, biology, and sociology in the sixth and last place. This quote was included by T.H. Huxley, in ‘The Scientific Aspects of Positivism’, Fortnightly Review (1869), 11, 666-667, in which Huxley strongly disagreed with ranking the abstract discipline of mathematics at the top, since education should begin with the concrete based on investigation by observation, “from the easy to the difficult.” English translation by Webmaster using online resources, from the original French, “C’est donc par l’étude des mathématiques, et seulement par elle, que l’on peut se faire une idée juste et approfondie de ce que c’est qu’une science. … Toute éducation scientifique qui ne commence point par une telle étude pèche donc nécessairement par sa base.”

It is they who hold the secret of the mysterious property of the mind by which error ministers to truth, and truth slowly but irrevocably prevails. Theirs is the logic of discovery, the demonstration of the advance of knowledge and the development of ideas, which as the earthly wants and passions of men remain almost unchanged, are the charter of progress, and the vital spark in history.

Lecture, ‘The Study of History’ (11 Jun 1895) delivered at Cambridge, published as A Lecture on The Study of History (1895), 54-55.

It is this mythical, or rather this symbolic, content of the religious traditions which is likely to come into conflict with science. This occurs whenever this religious stock of ideas contains dogmatically fixed statements on subjects which be long in the domain of science. Thus, it is of vital importance for the preservation of true religion that such conflicts be avoided when they arise from subjects which, in fact, are not really essential for the pursuance of the religious aims.

……

It is to geometry that we owe in some sort the source of this discovery [of beryllium]; it is that [science] that furnished the first idea of it, and we may say that without it the knowledge of this new earth would not have been acquired for a long time, since according to the analysis of the emerald by M. Klaproth and that of the beryl by M. Bindheim one would not have thought it possible to recommence this work without the strong analogies or even almost perfect identity that Citizen Haüy found for the geometrical properties between these two stony fossils.

Haüy used the geometry of cleavage to reveal the underlying crystal structure, and thus found the emeral and beryl were geometrically identical. In May Elvira Weeks, The Discovery of the Elements (1934), 153, citing Mellor, Comprehensive Treatise on Inorganic and Theoretical Chemistry (1923), 204-7.

It is very desirable to have a word to express the Availability for work of the heat in a given magazine; a term for that possession, the waste of which is called Dissipation. Unfortunately the excellent word Entropy, which Clausius has introduced in this connexion, is applied by him to the negative of the idea we most naturally wish to express. It would only confuse the student if we were to endeavour to invent another term for our purpose. But the necessity for some such term will be obvious from the beautiful examples which follow. And we take the liberty of using the term Entropy in this altered sense … The entropy of the universe tends continually to zero.

Sketch of Thermodynamics (1868), 100-2.

It is very remarkable that while the words Eternal, Eternity, Forever, are constantly in our mouths, and applied without hesitation, we yet experience considerable difficulty in contemplating any definite term which bears a very large proportion to the brief cycles of our petty chronicles. There are many minds that would not for an instant doubt the God of Nature to have existed from all Eternity, and would yet reject as preposterous the idea of going back a million of years in the History of His Works. Yet what is a million, or a million million, of solar revolutions to an Eternity?

Memoir on the Geology of Central France (1827), 165.

It must be borne in mind that the tragedy of life doesn’t lie in not reaching your goal. The tragedy lies in having no goal to reach. It isn’t a calamity to die with dreams unfulfilled, but it is a calamity not to dream. It is not a disaster to be unable to capture your idea, but it is disaster to have no idea to capture. It is not a disgrace not to reach for the stars, but it is a disgrace to have no stars to reach for. Not failure, but low aim is a sin.

……

It ought … to be understood that no one can be a good physician who has no idea of surgical operations, and that a surgeon is nothing if ignorant of medicine. In a word, one must be familiar with both departments of medicine.

Chirurgia Magna (1296, printed 1479). In Henry Ebenezer Handerson, Gilbertus Anglicus (1918), 77,

It seems to me that the idea of a personal God is an anthropological concept which I cannot take seriously. I also cannot imagine some will or goal outside the human sphere has been cited as a statement that precedes the last three sentences here, but this might have originated in a paraphrase, a transcription error, or a misquotation; it does not appear in any editions of the essay which have thus far been checked.

……

It seems to me what is called for is an exquisite balance between two conflicting needs: the most skeptical scrutiny of all hypotheses that are served up to us and at the same time a great openness to new ideas … If you are only skeptical, then no new ideas make it through to you … On the other hand, if you are open to the point of gullibility and have not an ounce of skeptical sense in you, then you cannot distinguish the useful ideas from the worthless ones.

In ‘The Burden of Skepticism’, Skeptical Inquirer (Fall 1987), 12, No. 1.

It was a reaction from the old idea of “protoplasm”, a name which was a mere repository of ignorance.

Perspectives in Biochemistry (1938). As cited in Max Perutz, I Wish I’d Made You Angry Earlier: Essays on Science, Scientists, and Humanity (1998).

It was during my enchanted days of travel that the idea came to me, which, through the years, has come into my thoughts again and again and always happily—the idea that geology is the music of the earth.

In ‘Prologue’, Conversation with the Earth (1954), 3. As translated by E.B. Garside from Gespräch mit der Erde (1947).

It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule. This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.

In Leibnitz (1884), 44-45. [The first sentence is reworded to better introduce the quotation. —Webmaster]

It was not easy for a person brought up in the ways of classical thermodynamics to come around to the idea that gain of entropy eventually is nothing more nor less than loss of information.

Letter to Irving Langmuir, 5 Aug 1930. Quoted in Nathan Reingold, Science in America: A Documentary History 1900-1939 (1981), 400.

It was not noisy prejudice that caused the work of Mendel to lie dead for thirty years, but the sheer inability of contemporary opinion to distinguish between a new idea and nonsense.

In ‘The Commemoration of Great Men’, British Medical Journal (20 Feb 1932). In The Adelphi (1932), 4, 480, and in The Collected Papers of Wilfred Trotter, FRS (1941), 27.

It wasn’t the finches that put the idea [of natural selection] in Darwin’s head, it was the tortoises. The reason he didn’t use the tortoises [in writing On the Origin of Species] was that, when he got back, he found he didn’t have localities on the tortoise specimens. Here the great god, the greatest naturalist we have records of, made a mistake. His fieldwork wasn’t absolutely perfect.

From interview with Brian Cox and Robert Ince, in ‘A Life Measured in Heartbeats’, New Statesman (21 Dec 2012), 141, No. 5138, 33.

It would be foolish to give credit to Euclid for pangeometrical conceptions; the idea of geometry deifferent from the common-sense one never occurred to his mind. Yet, when he stated the fifth postulate, he stood at the parting of the ways. His subconscious prescience is astounding. There is nothing comperable to it in the whole history of science.

Ancient Science And Modern Civilization (1954, 1959), 28. In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 130.

Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes.

From Théorie Analytique de la Chaleur (1822), Discours Préliminaire, xiv, (Theory of Heat, Introduction), as translated by Alexander Freeman in The Analytical Theory of Heat (1878), 7.

It’s almost a sort of fairy story tale, just what a novelist would write about a discovery.
[Describing how the original idea on the principle of the maser came to him.]

Interview (2 Feb 1991), ‘Creating the Light Fantastic’, Academy of Achievement web site.

It’s becoming clear that in a sense the cosmos provides the only laboratory where sufficiently extreme conditions are ever achieved to test new ideas on particle physics. The energies in the Big Bang were far higher than we can ever achieve on Earth. So by looking at evidence for the Big Bang, and by studying things like neutron stars, we are in effect learning something about fundamental physics.

From editted transcript of BBC Radio 3 interview, collected in Lewis Wolpert and Alison Richards, A Passion For Science (1988), 33.

It’s fine if you as an adult want to run around pretending or claiming that you don’t believe in evolution, but if we educate a generation of people who don’t believe in science, that’s a recipe for disaster. … The main idea in all of biology is evolution. To not teach it to our young people is wrong.

As quoted in Sarah Fecht, ‘Science Guy Bill Nye Explains Why Evolution Belongs in Science Education’, Popular Mechanics (4 Feb 2011).

It’s very dangerous to invent something in our times; ostentatious men of the other world, who are hostile to innovations, roam about angrily. To live in peace, one has to stay away from innovations and new ideas. Innovations, like trees, attract the most destructive lightnings to themselves.

From the play Galileo Galilei (2001) .

I’m convinced that the best solutions are often the ones that are counterintuitive—that challenge conventional thinking—and end in breakthroughs. It is always easier to do things the same old way … why change? To fight this, keep your dissatisfaction index high and break with tradition. Don’t be too quick to accept the way things are being done. Question whether there’s a better way. Very often you will find that once you make this break from the usual way — and incidentally, this is probably the hardest thing to do—and start on a new track your horizon of new thoughts immediately broadens. New ideas flow in like water. Always keep your interests broad — don’t let your mind be stunted by a limited view.

1988

I’m gradually managing to cram my mind more and more full of things. I’ve got this beautiful mind and it’s going to die, and it’ll all be gone. And then I say, not in my case. Every idea I’ve ever had I’ve written down, and it’s all there on paper. And I won’t be gone; it’ll be there.

‘Isaac Asimov Speaks’ with Bill Moyers in The Humanist (Jan/Feb 1989), 49. Reprinted in Carl Howard Freedman (ed.), Conversations with Isaac Asimov (2005), 139.

I’m not afraid of facts, I welcome facts but a congeries of fact is not equivalent to an idea. This is the essential fallacy of the so-called “scientific” mind. People who mistake facts for ideas are incomplete thinkers; they are gossips.

In ‘We Are the Crazy Lady and Other Feisty Feminist Fables,’ in The First Ms. Reader edited by Francine Klagsburn (1972).

I’m quite into the idea of engineering being beautiful.

As quoted in The Wire (2003), 32, dating it as a declaration made “back then” around the 1997 release of the Chiastic Slide album.

I’ve always been inspired by Dr. Martin Luther King, who articulated his Dream of an America where people are judged not by skin color but “by the content of their character.” In the scientific world, people are judged by the content of their ideas. Advances are made with new insights, but the final arbitrator of any point of view are experiments that seek the unbiased truth, not information cherry picked to support a particular point of view.

In letter (1 Feb 2013) to Energy Department employees announcing his decision not to serve a second term.

I’ve tried to make the men around me feel as I do, that we are embarked as pioneers upon a new science and industry in which our problems are so new and unusual that it behooves no one to dismiss any novel idea with the statement, “It can’t be done.”

Start of Boeing’s quote, inscribed on his memorial at the Boeing Developmental Center, Tukwila, WA, as given in Mike Lombardi, ‘Historical Perspective: 50 years at the Leading Edge’, Boeing Frontiers (Aug 2009), 8.

John Dalton was a very singular Man, a quaker by profession & practice: He has none of the manners or ways of the world. A tolerable mathematician He gained his livelihood I believe by teaching the mathematics to young people. He pursued science always with mathematical views. He seemed little attentive to the labours of men except when they countenanced or confirmed his own ideas… He was a very disinterested man, seemed to have no ambition beyond that of being thought a good Philosopher. He was a very coarse Experimenter & almost always found the results he required.—Memory & observation were subordinate qualities in his mind. He followed with ardour analogies & inductions & however his claims to originality may admit of question I have no doubt that he was one of the most original philosophers of his time & one of the most ingenious.

J. Z. Fullmer, ‘Davy’s Sketches of his Contemporaries’, Chymia, 1967, 12, 133-134.

John [H.] Van Vleck, who was a leading young theoretical physicist when I was also a leading young theoretical physicist, said to me one day, “I never have made a contribution to physics that I didn’t get by fiddling with the equations,” and I said, “I’ve never made a contribution that I didn’t get by just having a new idea. Then I would fiddle with the equations to help support the new idea.” Van Vleck was essentially a mathematical physicist, you might say, and I was essentially a person of ideas. I don’t think I’m primarily mathematical. … I have a great curiosity about the nature of the world as a whole, and most of my ideas are qualitative rather than quantitative.

Interview with George B. Kauffman and Laurie M. Kauffman, in ‘Linus Pauling: Reflections’, American Scientist (Nov-Dec 1994), 82, No. 6, 523.

Junior high school seemed like a fine idea when we invented it but it turned out to be an invention of the devil. We’re catching our boys in a net in which they’re socially unprepared. We put them in junior high school with girls who are two years ahead of them. There isn’t a thing they should have to do with girls at this age except growl at them.

As quoted in Frances Glennon, ‘Student and Teacher of Human Ways’, Life (14 Sep 1959), 147.

Just as in the animal and vegetable kingdoms, an individual comes into being, so to speak, grows, remains in being, declines and passes on, will it not be the same for entire species? If our faith did not teach us that animals left the Creator’s hands just as they now appear and, if it were permitted to entertain the slightest doubt as to their beginning and their end, may not a philosopher, left to his own conjectures, suspect that, from time immemorial, animal life had its own constituent elements, scattered and intermingled with the general body of matter, and that it happened when these constituent elements came together because it was possible for them to do so; that the embryo formed from these elements went through innumerable arrangements and developments, successively acquiring movement, feeling, ideas, thought, reflection, consciousness, feelings, emotions, signs, gestures, sounds, articulate sounds, language, laws, arts and sciences; that millions of years passed between each of these developments, and there may be other developments or kinds of growth still to come of which we know nothing; that a stationary point either has been or will be reached; that the embryo either is, or will be, moving away from this point through a process of everlasting decay, during which its faculties will leave it in the same way as they arrived; that it will disappear for ever from nature-or rather, that it will continue to exist there, but in a form and with faculties very different from those it displays at this present point in time? Religion saves us from many deviations, and a good deal of work. Had religion not enlightened us on the origin of the world and the universal system of being, what a multitude of different hypotheses we would have been tempted to take as nature’s secret! Since these hypotheses are all equally wrong, they would all have seemed almost equally plausible. The question of why anything exists is the most awkward that philosophy can raise- and Revelation alone provides the answer.

Thoughts on the Interpretation of Nature and Other Philosophical Works (1753/4), ed. D. Adams (1999), Section LVIII, 75-6.

Just as our eyes need light in order to see, our minds need ideas in order to conceive.

Recherche de la vérité

Keep in mind that new ideas are commonplace, and almost always wrong. Most flashes of insight lead nowhere; statistically, they have a half-life of hours or maybe days. Most experiments to follow up the surviving insights are tedious and consume large amounts of time, only to yield negative or (worse!) ambiguous results.

In Consilience: The Unity of Knowledge (1998, 1999), 60

Knowledge is power.
[Editors’ summary of Bacon’s idea, not Bacon’s wording.]

Bacon’s original text is in Latin, so any quote seen in English is an interpretation by the translator. The dictum, expressed in three words as ‘Knowledge is Power,’ is only seen in notes to the texts made by translators or editors, and is not a direct translation of Bacon’s written words. See, for example, the commentary by F. G. Selby (ed.) in The Advancement of Learning, Book 1, by Francis Bacon (1905), 140; or, the introductory notes by E. A. Abbott (ed.) in Bacon’s Essays (1876), cxxxvii. For the best match in Bacon’s original words, see Novum Organum Aphorism 3: Scientia et potentia humana in idem coincidunt,… or ‘Human knowledge and human power meet in one;…’. The Latin form is in Thomas Fowler (ed.), Bacon’s Novum Organum (2nd Ed., 1878), 188; and this translated form is in Francis Bacon and James Spedding (trans.), The Works of Francis Bacon (1864), Vol. 8, 67.

Language is only the instrument of science, and words are but the signs of ideas.

In ‘Preface to the English Dictionary’, The Works of Samuel Johnson (1810), Vol. 2, 37.

Lecturing after a fashion is easy enough ; teaching is a very different affair. … The transmission of ideas from one mind to another, in a simple unequivocal form, is not always easy ; but in teaching, the object is not merely to convey the idea, but to give a lively and lasting impression; something that should not merely cause the retention of the image, but in such connection as to excite another process, ‘ thought.’

Memoirs of John Abernethy (1854), 253.

Leibnitz believed he saw the image of creation in his binary arithmetic in which he employed only two characters, unity and zero. Since God may be represented by unity, and nothing by zero, he imagined that the Supreme Being might have drawn all things from nothing, just as in the binary arithmetic all numbers are expressed by unity with zero. This idea was so pleasing to Leibnitz, that he communicated it to the Jesuit Grimaldi, President of the Mathematical Board of China, with the hope that this emblem of the creation might convert to Christianity the reigning emperor who was particularly attached to the sciences.

In ‘Essai Philosophique sur les Probabiliés’, Oeuvres (1896), t. 7, 119.

Let us then suppose the Mind to be, as we say, white Paper, void of all Characters, without any Ideas; How comes it to be furnished? Whence comes it by that vast store, which the busy and boundless Fancy of Man has painted on it, with an almost endless variety? Whence has it all the materials of Reason and Knowledge? To this I answer, in one word, from Experience: In that, all our Knowledge is founded; and from that it ultimately derives it self. Our Observation employ’d either about external, sensible Objects; or about the internal Operations of our Minds, perceived and reflected on by our selves, is that, which supplies our Understandings with all the materials of thinking.

In ‘Of Ideas in general, and their Original’, An Essay Concerning Human Understanding (1690), Book 2, Chap. 1, Sec. 2, 37.

Liebig was not a teacher in the ordinary sense of the word. Scientifically productive himself in an unusual degree, and rich in chemical ideas, he imparted the latter to his advanced pupils, to be put by them to experimental proof; he thus brought his pupils gradually to think for themselves, besides showing and explaining to them the methods by which chemical problems might be solved experimentally.

As quoted in G. H. Getman, The Life of Ira Remsen (1980), 18-19.

Like almost every subject of human interest, this one [mathematics] is just as easy or as difficult as we choose to make it. A lifetime may be spent by a philosopher in discussing the truth of the simplest axiom. The simplest fact as to our existence may fill us with such wonder that our minds will remain overwhelmed with wonder all the time. A Scotch ploughman makes a working religion out of a system which appalls a mental philosopher. Some boys of ten years of age study the methods of the differential calculus; other much cleverer boys working at mathematics to the age of nineteen have a difficulty in comprehending the fundamental ideas of the calculus.

In Teaching of Mathematics (1902), 19-20.

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.

As quoted, without citation, in Morris Kline, ‘Logic Versus Pedagogy’, The American Mathematical Monthly (Mar 1970), 77, No. 3, 272.

Logic teaches us that on such and such a road we are sure of not meeting an obstacle; it does not tell us which is the road that leads to the desired end. For this, it is necessary to see the end from afar, and the faculty which teaches us to see is intuition. Without it, the geometrician would be like a writer well up in grammar but destitute of ideas.

……

Look round this universe. What an immense profusion of beings, animated and organized, sensible and active! You admire this prodigious variety and fecundity. But inspect a little more narrowly these living existences, the only beings worth regarding. How hostile and destructive to each other! How insufficient all of them for their own happiness! How contemptible or odious to the spectator! The whole presents nothing but the idea of a blind Nature, inpregnated by a great vivifying principle, and pouring forth from her lap, without discernment or parental care, her maimed and abortive children.

In Dialogues Concerning Natural Religion (1779), 219-220.

M.D.—Make Do.— Quaint idea! … Work for the handicapped … who is handicapped, your patients, or you? Both. Helping the survival of the unfit.… With more to come. What in the world was the solution. Where to find a formula for head and heart too?

Quoted in M.C. Winternitz, ‘Alan Gregg, Physician’, Science (20 Dec 1957), 1279.

Magnetic lines of force convey a far better and purer idea than the phrase magnetic current or magnetic flood: it avoids the assumption of a current or of two currents and also of fluids or a fluid, yet conveys a full and useful pictorial idea to the mind.

Diary Entry for 10 Sep 1854. In Thomas Martin (ed.), Faraday’s Diary: Being the Various Philosophical Notes of Experimental Investigation (1935), Vol. 6, 315.

Man carries the world in his head, the whole astronomy and chemistry suspended in a thought. Because the history of nature is charactered in his brain, therefore he is the prophet and discoverer of her secrets. Every known fact in natural science was divined by the presentiment of somebody, before it was actually verified.

Essay, ‘Nature’, in Ralph Waldo Emerson, Alfred Riggs Ferguson (ed.) and Jean Ferguson Carr (ed.), The Collected Works of Ralph Waldo Emerson, Volume III, Essays: Second Series (1984), 106-107.

Man has never been a particularly modest or self-deprecatory animal, and physical theory bears witness to this no less than many other important activities. The idea that thought is the measure of all things, that there is such a thing as utter logical rigor, that conclusions can be drawn endowed with an inescapable necessity, that mathematics has an absolute validity and controls experience—these are not the ideas of a modest animal. Not only do our theories betray these somewhat bumptious traits of self-appreciation, but especially obvious through them all is the thread of incorrigible optimism so characteristic of human beings.

In The Nature of Physical Theory (1936), 135-136.

Manufacturing is more than just putting parts together. It’s coming up with ideas, testing principles and perfecting the engineering, as well as final assembly.

Epigraph in The Business Book (2014), 286. Need primary source — can you help?

Man’s mind once stretched by a new idea, never regains its original dimension.

……

Math is like love—a simple idea but it can get complicated.

Quoted in Jon Fripp, Michael Fripp, Deborah Fripp Speaking of Science: Notable Quotes on Science, Engineering, and the Environment (2000), 45, and attributed to “R. Drabek” with no further source information. Webmaster wonders if this is a typo for mathematician, Pavel Drábek.

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments.

In ‘Mathematical Problems’, Bulletin American Mathematical Society, 8, 478.

Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be backed up. It’s just that the reliability does not primarily come from mathematicians checking formal arguments; it come from mathematicians thinking carefully and critically about mathematical ideas.

Concerning revision of proofs. In ‘On Proof and Progress in Mathematics’, For the Learning of Mathematics (Feb 1995), 15, No. 1, 33. Reprinted from Bulletin of the American Mathematical Society (1994), 30, No. 2, 170.

Mathematicians create by acts of insight and intuition. Logic then sanctions the conquests of intuition. It is the hygiene that mathematics practices to keep its ideas healthy and strong. Moreover, the whole structure rests fundamentally on uncertain ground, the intuition of humans. Here and there an intuition is scooped out and replaced by a firmly built pillar of thought; however, this pillar is based on some deeper, perhaps less clearly defined, intuition. Though the process of replacing intuitions with precise thoughts does not change the nature of the ground on which mathematics ultimately rests, it does add strength and height to the structure.

In Mathematics in Western Culture (1964), 408.

Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but, we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations into their minds.

Mathematics and art are quite different. We could not publish so many papers that used, repeatedly, the same idea and still command the respect of our colleagues.

As given in essay, Ronald Coifman and Robert S. Strichartz, ‘The School of Antoni Zygmund’, collected in Peter Duren (ed.), A Century of Mathematics in America (1989), 348. The comment was made “after passing through several rooms in a museum filled with the paintings of a rather well-known modem painter”. The authors acknowledge students of Zygmund provided personal recollections to them for the essay in general. Webmaster speculates the quote is from a student recollection, and not necessarily verbatim.

Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.

In ‘Science as an Instrument of Education’, Popular Science Monthly (1897), 253.

Mathematics is often considered a difficult and mysterious science, because of the numerous symbols which it employs. Of course, nothing is more incomprehensible than a symbolism which we do not understand. … But this is not because they are difficult in themselves. On the contrary they have invariably been introduced to make things easy. … [T]he symbolism is invariably an immense simplification. It … represents an analysis of the ideas of the subject and an almost pictorial representation of their relations to each other.

In Introduction to Mathematics (1911), 59-60.

Mathematics is the science of consistency; it is a picture of the universe; as Plato is said to have expressed the idea, “God eternally geometrizes.”

In ‘The Poetry of Mathematics’, The Mathematics Teacher (May 1926), 19, No. 5, 295.

Mathematics is the science which uses easy words for hard ideas.

With co-author James R. Newman, in Mathematics and the Imagination (1940), 4.

Medicine is an incoherent assemblage of incoherent ideas, and is, perhaps, of all the physiological Sciences, that which best shows the caprice of the human mind. What did I say! It is not a Science for a methodical mind. It is a shapeless assemblage of inaccurate ideas, of observations often puerile, of deceptive remedies, and of formulae as fantastically conceived as they are tediously arranged.

Bichat’s General Anatomy, vol. 1, 17. Quoted in Alva Curtis, A Fair Examination and Criticism of All the Medical Systems in Vogue (1855), 1.

Mediocre men often have the most acquired knowledge. It is in the darker. It is in the darker regions of science that great men are recognized; they are marked by ideas which light up phenomena hitherto obscure and carry science forward.

From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (reprint 1999), 42.

Melvin [Calvin]’s marvellous technique for delivering a scientific lecture was unique. His mind must have roamed constantly, especially in planning lectures. His remarkable memory enabled him to formulate a lecture or manuscript with no breaks in the sequence of his thoughts. His lectures usually began hesitatingly, as if he had little idea of how to begin or what to say. This completely disarmed his audiences, who would try to guess what he might have to say. Soon enough, however, his ideas would coalesce, to be delivered like an approaching freight train, reaching a crescendo of information at breakneck speed and leaving his rapt audience nearly overwhelmed.

Co-author with Andrew A. Benson, ‘Melvin Calvin’, Biographical Memoirs of the US National Academy of Science.

Men who have excessive faith in their theories or ideas are not only ill prepared for making discoveries; they also make very poor observations. Of necessity, they observe with a preconceived idea, and when they devise an experiment, they can see, in its results,only a confirmation of their theory. In this way they distort observation and often neglect very important facts because they do not further their aim.

From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 38.

Men who have excessive faith in their theories … make poor observations, because they choose among the results of their experiments only what suits their object, neglecting whatever is unrelated to it and carefully setting aside everything which might tend toward the idea they wish to combat.

From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 38. Note: the ellipsis condenses the quote from two paragraphs, beginning with the same clause as another quote on this web page, beginning, “Men who have excessive faith….”

Mere numbers cannot bring out … the intimate essence of the experiment. This conviction comes naturally when one watches a subject at work. … What things can happen! What reflections, what remarks, what feelings, or, on the other hand, what blind automatism, what absence of ideas! … The experimenter judges what may be going on in [the subject’s] mind, and certainly feels difficulty in expressing all the oscillations of a thought in a simple, brutal number, which can have only a deceptive precision. How, in fact, could it sum up what would need several pages of description!

In La Suggestibilité (1900), 119-20.

Minds think with ideas, not information No amount of data, bandwidth, or processing power can substitute for inspired thought.

In Silicon Snake Oil: Second Thoughts on the Information Highway (1996), 194.

Modern theories did not arise from revolutionary ideas which have been, so to speak, introduced into the exact sciences from without. On the contrary they have forced their way into research which was attempting consistently to carry out the programme of classical physics—they arise out of its very nature. It is for this reason that the beginnings of modern physics cannot be compared with the great upheavals of previous periods like the achievements of Copernicus. Copernicus’s idea was much more an import from outside into the concepts of the science of his time, and therefore caused far more telling changes in science than the ideas of modern physics are creating to-day.

In Philosophical Problems of Nuclear Science: Eight Lectures (1952), 13.

Modern war, even from the consideration of physical welfare, is not creative. Soldiers and civilians alike are supposed to put on mental khaki. … War means the death of that fertile war which consists of the free, restless conflict of ideas. The war which matters is that of the scientist with nature; of the farmer with the tawny desert; of … philosopher against … mob stupidity. Such war is creative. … Inventions that further life and joy; freedom; new knowledge, whether Luther Burbank’s about the breeding of fruits or Einstein’s about relativity; great cathedrals and Beethoven’s music: these modern mechanical war can destroy but never produce. At its most inventive height, war creates the Maxim gun, the submarine, disseminable germs of disease, life-blasting gases. Spiritually and intellectually, modern war is not creative.

From ‘The Stagnation of War’, in Allen D. Hole (ed.) The Messenger of Peace (Nov 1924), 49, No. 11, 162-163.

More about the selection theory: Jerne meant that the Socratic idea of learning was a fitting analogy for ‘the logical basis of the selective theories of antibody formation’: Can the truth (the capability to synthesize an antibody) be learned? If so, it must be assumed not to pre-exist; to be learned, it must be acquired. We are thus confronted with the difficulty to which Socrates calls attention in Meno [ … ] namely, that it makes as little sense to search for what one does not know as to search for what one knows; what one knows, one cannot search for, since one knows it already, and what one does not know, one cannot search for, since one does not even know what to search for. Socrates resolves this difficulty by postulating that learning is nothing but recollection. The truth (the capability to synthesize an antibody) cannot be brought in, but was already inherent.

‘The Natural Selection Theory’, in John Cairns, Gunther S. Stent, and James D. Watson (eds.) Phage and the Origins of Molecular Biology (1966), 301.

Most inventors who have an idea never stop to think whether their invention will be saleable when they get it made. Unless a man has plenty of money to throw away, he will find that making inventions is about the costliest amusement he can find.

As quoted in French Strother, ‘The Modern Profession of Inventing’, World’s Work and Play (Jul 1905), 6, No. 32, 186.

Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone.
Co-authored with Leopold Infeld.

The Evolution of Physics: The Growth of Ideas from the Early Concepts to Relativity and Quanta (1938), 29. Infeld was a Polish physicist (1898-1968).

Most scientists think of science as being a kind of purifying intellectual machinery that leads to honesty, to the withering away of ignorance and wrong ideas, including, provided they are of the atheistic persuasion, those of religion.

In Pamela Weintraub (ed.), ‘E. O. Wilson’, The Omni Interviews (1984), 231.

Most, if not all, of the great ideas of modern mathematics have had their origin in observation. Take, for instance, the arithmetical theory of forms, of which the foundation was laid in the diophantine theorems of Fermat, left without proof by their author, which resisted all efforts of the myriad-minded Euler to reduce to demonstration, and only yielded up their cause of being when turned over in the blow-pipe flame of Gauss’s transcendent genius; or the doctrine of double periodicity, which resulted from the observation of Jacobi of a purely analytical fact of transformation; or Legendre’s law of reciprocity; or Sturm’s theorem about the roots of equations, which, as he informed me with his own lips, stared him in the face in the midst of some mechanical investigations connected (if my memory serves me right) with the motion of compound pendulums; or Huyghen’s method of continued fractions, characterized by Lagrange as one of the principal discoveries of that great mathematician, and to which he appears to have been led by the construction of his Planetary Automaton; or the new algebra, speaking of which one of my predecessors (Mr. Spottiswoode) has said, not without just reason and authority, from this chair, “that it reaches out and indissolubly connects itself each year with fresh branches of mathematics, that the theory of equations has become almost new through it, algebraic geometry transfigured in its light, that the calculus of variations, molecular physics, and mechanics” (he might, if speaking at the present moment, go on to add the theory of elasticity and the development of the integral calculus) “have all felt its influence”.

In ‘A Plea for the Mathematician’, Nature, 1, 238 in Collected Mathematical Papers, Vol. 2, 655-56.

My aim is to argue that the universe can come into existence without intervention, and that there is no need to invoke the idea of a Supreme Being in one of its numerous manifestations.

In The Creation (1981), Preface, vii. As quoted and cited in Karl W. Giberson and Donald A. Yerxa, Species of Origins: America’s Search for a Creation Story (2002), 126 and footnote, 146.

My final remark to young women and men going into experimental science is that they should pay little attention to the speculative physics ideas of my generation. After all, if my generation has any really good speculative ideas, we will be carrying these ideas out ourselves.

‘Reflections on the Discovery of the Tau Lepton’, Nobel Lecture (8 Dec 1995). In Nobel Lectures: Physics 1991-1995 (1997), 193.

My guess is that well over eighty per cent. of the human race goes through life without having a single original thought..

Minority Report (1956, 2006 reprint), 10.

My method consists in allowing the mind to play freely for a very brief period, until a couple or so of ideas have passed through it, and then, while the traces or echoes of those ideas are still lingering in the brain, to turn the attention upon them with a sudden and complete awakening; to arrest, to scrutinise them, and to record their exact appearance… The general impression they have left upon me is like that which many of us have experienced when the basement of our house happens to be under thorough sanitary repairs, and we realise for the first time the complex system of drains and gas and water pipes, flues, bell-wires, and so forth, upon which our comfort depends, but which are usually hidden out of sight, and with whose existence, so long as they acted well, we had never troubled ourselves.

Inquiries into Human Faculty and its Development (1883),185-6.

My profession often gets bad press for a variety of sins, both actual and imagined: arrogance, venality, insensitivity to moral issues about the use of knowledge, pandering to sources of funding with insufficient worry about attendant degradation of values. As an advocate for science, I plead ‘mildly guilty now and then’ to all these charges. Scientists are human beings subject to all the foibles and temptations of ordinary life. Some of us are moral rocks; others are reeds. I like to think (though I have no proof) that we are better, on average, than members of many other callings on a variety of issues central to the practice of good science: willingness to alter received opinion in the face of uncomfortable data, dedication to discovering and publicizing our best and most honest account of nature’s factuality, judgment of colleagues on the might of their ideas rather than the power of their positions.

……

My reflection, when I first made myself master of the central idea of the “Origin”, was, “How extremely stupid not to have thought of that!”

‘On the Reception of the Origin of Species‘. In F. Darwin (ed.), The Life and Letters of Charles Darwin, Including an Autobiographical Chapter (1888), Vol. 2, 197.

My religion consists of a humble admiration of the illimitable superior spirit who reveals himself in the slight details we are able to perceive with our frail and feeble minds. That deeply emotional conviction of the presence of a superior reasoning power, which is revealed in the incomprehensible universe, forms my idea of God.

As quoted in obituary, ‘Einstein Noted as an Iconoclast In Research, Politics and Religion’, The New York Times (19 Apr 1955), 25.

My second fixed idea is the uselessness of men above sixty years of age, and the incalculable benefit it would be in commercial, political, and in professional life, if as a matter of course, men stopped work at this age.

In farewell address, Johns Hopkins University, ‘The Fixed Period’, as quoted in Harvey Cushing, The Life of Sir William Osier (1925), vol. 1, 666. He was reflecting on his own intention to retire (now age 55) because he felt a teacher should have a fixed period of service. The title of his address was from an Anthony Trollope novel The Fixed Period which discussed the retiring of college teachers at age 60.

My view of the matter, for what it is worth, is that there is no such thing as a logical method of having new ideas, or a logical reconstruction of this process. My view may be expressed by saying that every discovery contains an “irrational element,” or “a creative intuition,” in Bergson’s sense. In a similar way Einstein speaks of the “search for those highly universal laws … from which a picture of the world can be obtained by pure deduction. There is no logical path.” he says, “leading to these … laws. They can only be reached by intuition, based upon something like an intellectual love (Einfühlung) of the objects of experience.”

In The Logic of Scientific Discovery: Logik Der Forschung (1959, 2002), 8.

Nearly every subject has a shadow, or imitation. It would, I suppose, be quite possible to teach a deaf and dumb child to play the piano. When it played a wrong note, it would see the frown of its teacher, and try again. But it would obviously have no idea of what it was doing, or why anyone should devote hours to such an extraordinary exercise. It would have learnt an imitation of music. and it would fear the piano exactly as most students fear what is supposed to be mathematics.

In Mathematician’s Delight (1943), 8.

New associations and fresh ideas are more likely to come out of a varied store of memories and experience than out of a collection that is all of one kind.

As quoted, attributed to Taylor, but without further source details, in W.I.B. Beveridge, The Art of Scientific Investigation (1957), 5. Note: the quote is seen incorrectly attributed to Beveridge in Colin McFarland, Experiment! (2012), 103.

New ideas seem like frightening ghosts to people at the beginning; they run away from them for a long time, but they get tired of it in the end!

From the play Galileo Galilei (2001) .

New scientific ideas never spring from a communal body, however organized, but rather from the head of an individually inspired researcher who struggles with his problems in lonely thought and unites all his thought on one single point which is his whole world for the moment.

Address on the 25th anniversary of the Kaiser-Wilhelm Gesellschaft (Jan 1936). Quoted in Surviving the Swastika: Scientific Research in Nazi Germany (1993), 97.

No Geologist worth anything is permanently bound to a desk or laboratory, but the charming notion that true science can only be based on unbiased observation of nature in the raw is mythology. Creative work, in geology and anywhere else, is interaction and synthesis: half-baked ideas from a bar room, rocks in the field, chains of thought from lonely walks, numbers squeezed from rocks in a laboratory, numbers from a calculator riveted to a desk, fancy equipment usually malfunctioning on expensive ships, cheap equipment in the human cranium, arguments before a road cut.

An Urchin in the Storm (1988), 98.

No idea should be suppressed. … And it applies to ideas that look like nonsense. We must not forget that some of the best ideas seemed like nonsense at first. The truth will prevail in the end. Nonsense will fall of its own weight, by a sort of intellectual law of gravitation. If we bat it about, we shall only keep an error in the air a little longer. And a new truth will go into orbit.

In Cecilia Payne-Gaposchkin: An Autobiography and Other Recollections (1996), 233.

No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man’s game. … Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; … [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. … A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.

In A Mathematician’s Apology (1941, reprint with Foreward by C.P. Snow 1992), 70-71.

No one has ever had an idea in a dress suit.

Widely seen, but always without citation, for example, in Obzor (1977), 38, 10. If you know the primary source, please contact Webmaster.

No one must think that Newton’s great creation can be overthrown in any real sense by this [Theory of Relativity] or by any other theory. His clear and wide ideas will for ever retain their significance as the foundation on which our modern conceptions of physics have been built.

In ‘Time, Space, and Gravitation’, The Times (28 Nov 1919). Excerpted in David E. Rowe and Robert J. Schulmann, Einstein on Politics: His Private Thoughts and Public Stands on Nationalism, Zionism, War, Peace, and the Bomb (2007), 104.

No part of Mathematics suffers more from the triviality of its initial presentation to beginners than the great subject of series. Two minor examples of series, namely arithmetic and geometric series, are considered; these examples are important because they are the simplest examples of an important general theory. But the general ideas are never disclosed; and thus the examples, which exemplify nothing, are reduced to silly trivialities.

In An Introduction to Mathematics (1911), 194.

No politics, no committees, no reports, no referees, no interviews – just highly motivated people picked by a few men of good judgment.
[Describing the compelling ideas of Max Perutz on how best to nurture research.]

Quoted in Andrew Jack, «An Acute Talent for Innovation», Financial Times (1 Feb 2009).

No. I have been teaching it all my life, and I do not want to have my ideas upset.

Reply when James Clerk Maxwell’s asked if he would like to see an experimental demonstration of conical refraction. As given in James G. Crowther, The Cavendish Laboratory, 1874-1974 (1974), 9.

Nobody before the Pythagoreans had thought that mathematical relations held the secret of the universe. Twenty-five centuries later, Europe is still blessed and cursed with their heritage. To non-European civilizations, the idea that numbers are the key to both wisdom and power, seems never to have occurred.

In The Sleepwalkers: A History of Man’s Changing Vision of the Universe (1959), Preface, 40.

Nobody can be a good reasoner unless by constant practice he has realised the importance of getting hold of the big ideas and hanging on to them like grim death.

In ‘Presidential Address to the London Branch of the Mathematical Association’, Mathematical Gazette (Mar 1913), 7, No. 104, 92.

Nobody, certainly, will deny that the idea of the existence of an omnipotent, just, and omnibeneficent personal God is able to accord man solace, help, and guidance; also, by virtue of its simplicity it is accessible to the most undeveloped mind. But, on the other hand, there are decisive weaknesses attached to this idea in its elf, which have been painfully felt since the beginning of history. That is, if this being is omnipotent, then every occurrence, including every human action, every human thought, and every human feeling and aspiration is also His work; how is it possible to think of holding men responsible for their deeds and thoughts before such an almighty Being? In giving out punishment and rewards He would to a certain extent be passing judgment on Himself. How can this be combined with the goodness and righteousness ascribed to Him?

……

Non-standard analysis frequently simplifies substantially the proofs, not only of elementary theorems, but also of deep results. This is true, e.g., also for the proof of the existence of invariant subspaces for compact operators, disregarding the improvement of the result; and it is true in an even higher degree in other cases. This state of affairs should prevent a rather common misinterpretation of non-standard analysis, namely the idea that it is some kind of extravagance or fad of mathematical logicians. Nothing could be farther from the truth. Rather, there are good reasons to believe that non-standard analysis, in some version or other, will be the analysis of the future.

In ‘Remark on Non-standard Analysis’ (1974), in S. Feferman (ed.), Kurt Gödel Collected Works: Publications 1938-1974 (1990), Vol. 2, 311.

None of the myriad scientific papers I’d read prepared me for the patience and diligence that go into scientific research. None had prepared me for the acute attention to minutiae that keeps science accurate, and scientific integrity intact. Or for the tedium. … I accepted the idea that finding out you don’t like something can be invaluable.

Recalling undergraduate junior year tropical biology program exploring Costa Rica’s forest jungles. In ‘Concentration Crisis’, Brown Alumni Magazine (Jul-Aug 2007)

Not everything is an idea. Otherwise psychology would contain all the sciences within it or at least it would be the highest judge over all the sciences. Otherwise psychology would rule over logic and mathematics. But nothing would be a greater misunderstanding of mathematics than its subordination to psychology.

In Elmer Daniel Klemke, Essays on Frege (1968), 531.

Not only is science fiction an idea of tremendous import, but it is to be an important factor in making the world a better place to live in, through educating the public to the possibilities of science and the influence of science on life which, even today, are not appreciated byu the man on the street. … If every man, woman, boy and girl, could be induced to read science fiction right along, there would certainly be a great resulting benefit to the community, in that the educational standards of its people would be raised tremendously. Science fiction would make people happier, give them a broader understanding of the world, make tham more tolerant.

Editorial, Science Fiction Week (1930). In Gary Westfahl, Hugo Gernsback and the Century of Science Fiction (2007), 166.

Notable enough, however, are the controversies over the series 1 – 1 + 1 – 1 + 1 – … whose sum was given by Leibniz as 1/2, although others disagree. … Understanding of this question is to be sought in the word “sum”; this idea, if thus conceived—namely, the sum of a series is said to be that quantity to which it is brought closer as more terms of the series are taken—has relevance only for convergent series, and we should in general give up the idea of sum for divergent series.

……

Nothing drives progress like the imagination. The idea precedes the deed. The only exceptions
are accidents and natural selection.

In The Marketing Imagination (1983, 1986), 127.

Nothing in physics seems so hopeful to as the idea that it is possible for a theory to have a high degree of symmetry was hidden from us in everyday life. The physicist’s task is to find this deeper symmetry.

In American Scientist (1977) (as cited in The Atlantic (1984), 254, 81.) As an epigraph in Crystal and Dragon: The Cosmic Dance of Symmetry and Chaos in Nature, Art and Consciousness (1993), 139.

Nothing is known in our profession by guess; and I do not believe, that from the first dawn of medical science to the present moment, a single correct idea has ever emanated from conjecture: it is right therefore, that those who are studying their profession should be aware that there is no short road to knowledge; and that observation on the diseased living, examination of the dead, and experiments upon living animals, are the only sources of true knowledge; and that inductions from these are the sole bases of legitimate theory.

Astley Paston Cooper, Astley Cooper, Bransby Blake Cooper, A Treatise on Dislocations and Fractures of the Joints (1851), 155.

Now Freud may be right or he may be wrong in the place he gives to biology in human fate, but I think we must stop to consider whether this emphasis on biology, whether correct or incorrect, is not so far from being a reactionary idea that it is actually a liberating idea. It proposes to us that culture is not all-powerful. It suggests that there is a residue of human quality beyond the reach of cultural control, and that this residue of human quality, elemental as it may be, serves to bring culture itself under criticism and keeps it from being absolute.

In Freud and the Crisis of our Culture (1955), 48.

Now it came to me: … the independence of the gravitational acceleration from the nature of the falling substance, may be expressed as follows: In a gravitational field (of small spatial extension) things behave as they do in a space free of gravitation. … This happened in 1908. Why were another seven years required for the construction of the general theory of relativity? The main reason lies in the fact that it is not so easy to free oneself from the idea that coordinates must have an immediate metrical meaning.

In Paul Arthur Schilpp, ‘Autobiographical Notes’, Albert Einstein: Philosopher-Scientist (1949), 65-67.

Now the word-symbols of conceptual ideas have passed so long from hand to hand in the service of the understanding, that they have gradually lost all such fanciful reference.

Now this establishment of correspondence between two aggregates and investigation of the propositions that are carried over by the correspondence may be called the central idea of modern mathematics.

In ‘Philosophy of the Pure Sciences’, Lectures and Essays (1901), Vol. 1, 402.

Number, place, and combination … the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.

In Philosophical Magazine (1844), 84, 285; Collected Mathematical Papers, Vol. 1, 91.

Object-oriented programming is an exceptionally bad idea which could only have originated in California.

……

On May 15, 1957 Linus Pauling made an extraordinary speech to the students of Washington University. … It was at this time that the idea of the scientists’ petition against nuclear weapons tests was born. That evening we discussed it at length after dinner at my house and various ones of those present were scribbling and suggesting paragraphs. But it was Linus Pauling himself who contributed the simple prose of the petition that was much superior to any of the suggestions we were making.

Speech, «The 1962 Nobel Peace Prize,» at Unitarian Church, Boulder, Colorado (20 Oct 1963). On Oregon State University Library website.

On two occasions I have been asked [by members of Parliament], “Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?” I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.

In ‘Difference Engine No. 1’, Passages from the Life of a Philosopher (1864), Chap. 5, 59.

One can learn imitation history—kings and dates, but not the slightest idea of the motives behind it all; imitation literature—stacks of notes on Shakespeare’s phrases, and a complete destruction of the power to enjoy Shakespeare.

In Mathematician’s Delight (1943), 8.

One is hard pressed to think of universal customs that man has successfully established on earth. There is one, however, of which he can boast the universal adoption of the Hindu-Arabic numerals to record numbers. In this we perhaps have man’s unique worldwide victory of an idea.

In Mathematical Circles Squared (1972), 13.

One may be a mathematician of the first rank without being able to compute. It is possible to be a great computer without having the slightest idea of mathematics.

In Schriften, Zweiter Teil (1901), 223.

One of Euler’s main recreations was music, and by cultivating it he brought with it all his geometrical spirit; … he rested his serious researches and composed his Essay of a New Theory of Music, published in 1739; a book full of new ideas presented in a new point of view, but that did not have a great success, apparently for the sole reason that it contains too much of geometry for the musician and too much music for the geometer.

From his Eulogy of Leonhard Euler, read at the Imperial Academy of Sciences of Saint Petersburg (23 Oct 1783). Published in ‘Éloge de Léonard Euler, Prononcé en Français par Nicolas Fuss’. Collected in Leonard Euler, Oeuvres Complètes en Français de L. Euler (1839), Vol. 1, xii. From the original French, “Un des principaux délassements d’Euler était la musique, et en la cultivant il y apporta tout son esprit géométrique; … il accordait à ses recherches profondes, il composa son Essai d’une nouvelle théorie de la musique, publié en 1739; ouvrage rempli d’idées neuves ou présentées sous un nouveau point de vue, mais qui n’eut pas un grand succès, apparemment par la seule raison qu’il renferme trop de géométrie pour le musicien et trop de musique pour le géomètre.” English version by Webmaster using Google translate.

One of my complaints is that you’ve got far more scientists than ever before but the pace of discovery has not increased. Why? Because they’re all busy just filling in the details of what they think is the standard story. And the youngsters, the people with different ideas have just as big a fight as ever and normally it takes decades for science to correct itself. But science does correct itself and that’s the reason why science is such a glorious thing for our species.

From transcript of Interview (16 Aug 2007) by Robyn Williams, ‘InConversation’, Australian Broadcasting Corporation.

One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That’s so unlike the true nature of mathematics.

As quoted in L.A. Steen and D.J. Albers (eds.), Teaching Teachers, Teaching Students (1981), 89.

One of the greatest pains to human nature is the pain of a new idea.

In Physics and Politics (1869, 1916), 163.

One of the petty ideas of philosophers is to elaborate a classification, a hierarchy of sciences. They all try it, and they are generally so fond of their favorite scheme that they are prone to attach an absurd importance to it. We must not let ourselves be misled by this. Classifications are always artificial; none more than this, however. There is nothing of value to get out of a classification of science; it dissembles more beauty and order than it can possibly reveal.

In ‘The Teaching of the History of Science’, The Scientific Monthly (Sep 1918), 194.

One of the principal obstacles to the rapid diffusion of a new idea lies in the difficulty of finding suitable expression to convey its essential point to other minds. Words may have to be strained into a new sense, and scientific controversies constantly resolve themselves into differences about the meaning of words. On the other hand, a happy nomenclature has sometimes been more powerful than rigorous logic in allowing a new train of thought to be quickly and generally accepted.

Opening Address to the Annual Meeting of the British Association by Prof. Arthur Schuster, in Nature (4 Aug 1892), 46, 325.

One should guard against inculcating a young man with the idea that success is the aim of life, for a successful man normally receives from his peers an incomparably greater portion than the services he has been able to render them deserve. The value of a man resides in what he gives and not in what he is capable of receiving. The most important motive for study at school, at the university, and in life is the pleasure of working and thereby obtaining results which will serve the community. The most important task for our educators is to awaken and encourage these psychological forces in a young man {or woman}. Such a basis alone can lead to the joy of possessing one of the most precious assets in the world — knowledge or artistic skill.

……

One [idea] was that the Universe started its life a finite time ago in a single huge explosion, and that the present expansion is a relic of the violence of this explosion. This big bang idea seemed to me to be unsatisfactory even before detailed examination showed that it leads to serious difficulties.

In radio talk on the BBC Third Programme, as subsequently printed in the BBC’s The Listener magazine (9 Mar 1950), Vol.43, 420. This was his further use of the term “big bang” that he first expressed in a radio talk on 28 Mar 1949.

One’s ideas must be as broad as Nature if they are to interpret Nature.

Spoken by character, Sherlock Holmes, in A Study in Scarlet (1887), Chap. 5. Collected in Works of Arthur Conan Doyle (1902), Vol. 11, 69.

Only go on working so long as the brain is quite clear. The moment you feel the ideas getting confused leave off and rest, or your penalty will be that you will never learn Mathematics at all!

From letter to Edith Rix with hints for studying (about Mar 1885), in Stuart Dodgson Collingwood, The Life and Letters of Lewis Carroll (1898), 241.

Only when he has published his ideas and findings has the scientist made his contribution, and only when he has thus made it part of the public domain of scholarship can he truly lay claim to it as his own. For his claim resides only in the recognition accorded by peers in the social system of science through reference to his work.

In The Sociology of Science: An Episodic Memoir (1977), 47. As quoted and cited in David A. Kronick, The Literature of the Life Sciences: Reading, Writing, Research (1985), 89. This has been summarized as a paradox “the more freely the scientist gives his intellectual property away, the more securely it becomes his property” by Mengxiong Liu, in ‘The Complexity of Citation Practice: A Review of Citation Studies’, The Journal of Documentation (1993), 49, No. 4, 372.

Ordinarily logic is divided into the examination of ideas, judgments, arguments, and methods. The two latter are generally reduced to judgments, that is, arguments are reduced to apodictic judgments that such and such conclusions follow from such and such premises, and method is reduced to judgments that prescribe the procedure that should be followed in the search for truth.

Ampére expresses how arguments have a logical structure which he expected should be applied to relate scientific theories to experimental evidence. In James R. Hofmann, André-Marie Ampère (1996), 158. Cites Académie des Sciences Ampère Archives, École Normale lecture 15 notes, box 261.

Organization is simply the means by which the acts of ordinary men can be made to add up to extraordinary results. To this idea of progress that does not wait on some lucky break, some chance discovery, or some rare stroke of genius, but instead is achieved through systematic, cumulative effort, the engineer has contributed brilliantly.

In A Professional Guide for Young Engineers (1949, 1967), 36.

Our attention will focus on the institutional context of technological innovation rather than … individual inventors, for the actual course of work that leads to the conception and use of technology always involves a group that has worked for a considerable period of time on the basic idea before success is achieved.

In The Social Context of Innovation: Bureaucrats, Families, and Heroes in the Early Industrial Revolution as Foreseen in Bacon’s New Atlantis (1982, 2003), 3.

Our brains seem to be organised to make random comparisons of the contents of our memories. Daydreaming allows the process to go into free fall. Suddenly, there is a new idea, born with intense excitement. We cannot organise this process but we can distort or even defeat it.
[Commenting that creativity is not a method that can be learnt and taught.]

Quoted in Andrew Jack, «An Acute Talent for Innovation», Financial Times (1 Feb 2009).

Our ideas are only intellectual instruments which we use to break into phenomena; we must change them when they have served their purpose, as we change a blunt lancet that we have used long enough.

In An Introduction to the Study of Experimental Medicine (1865).

Our ideas … are for the most part like bad sixpences and we spend our lives in trying to pass them on one another.

Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 216.

Our knowledge is composed not of facts, but of the relations which facts and ideas bear to themselves and to each other; and real knowledge consists not in an acquaintance with facts, which only makes a pedant, but in the use of facts, which makes a philosopher.

Lecture (19 Mar 1858) at the Royal Institution, ‘The Influence Of Women On The Progress Of Knowledge’, collected in The Miscellaneous and Posthumous Works of Henry Thomas Buckle (1872), Vol. 1, 4. Published in Frazier’s Magazine (Apr 1858).

Our new idea is simple: to build a physics valid for all coordinate systems.

Our problem is that the climate crisis hatched in our laps at a moment in history when political and social conditions were uniquely hostile to a problem of this nature and magnitude—that moment being the tail end of the go-go ’80s, the blastoff point for the crusade to spread deregulated capitalism around the world. Climate change is a collective problem demanding collective action the likes of which humanity has never actually accomplished. Yet it entered mainstream consciousness in the midst of an ideological war being waged on the very idea of the collective sphere.

In ‘The Change Within: The Obstacles We Face Are Not Just External’, The Nation (12 May 2014).

Our Science comes to be at once a history of the ideas, the customs, and the deeds of mankind. From these three we shall derive the principles of the history of human nature, which we shall show to be the principles of universal history, which principles it seems hitherto to have lacked.

From The New Science (1744), Chap. 2, para 368, as translated in Thomas Goddard Bergin and Max Harold Fisch (eds.), The New Science of Giambattista Vico (1970), 73.

Our science is a drop, our ignorance a sea. Whatever else be certain, this at least is certain—that the world of our present natural knowledge is enveloped in a larger world of some sort of whose residual properties we at present can frame no positive idea.

In Address to Harvard Young Men’s Christian Association, ‘Is Life Worth Living?’, collected in The Will to Believe and other Essays in Popular Philosophy, (1897, 2006), 54. Published earlier in International Journal of Ethics (Oct 1895).

Our ultimate end must be precisely what Dr. Pauling says, peace based on agreement, upon understanding, on universally agreed and enforced law. I think this is a wonderful idea, but peace based on force buys us the necessary time, and in this time we can work for better understanding, for closer collaboration.

From debate (20 Feb 1958) between Linus Pauling and Edward Teller on WQED-TV, San Francisco. Transcript published as Fallout and Disarmament: The Pauling-Teller Debate (1958). Reprinted in ‘Fallout and Disarmament: A Debate between Linus Pauling and Edward Teller’, Daedalus (Spring 1958), 87, No. 2, 160.

Outside the practice of science itself, scientists have sometimes been the greatest offenders in adhering to dogmatic ideas against all the evidence.

Science and the Human Imagination: Aspects of the History and Logic of Physical Science (1955).

People see the wrongness in an idea much quicker that the rightness.

Science quotes on:  |  Error (333)  |  People (1012)  |  See (1082)

People who are unused to learning, learn little, and that slowly, while those more accustomed do much more and do it more easily. The same thing also happens in connection with research. Those who are altogether unfamiliar with this become blinded and bewildered as soon as their minds begin to work: they readily withdraw from the inquiry, in a state of mental fatigue and exhaustion, much like people who attempt to race without having been trained. He, on the other hand, who is accustomed to research, seeks and penetrates everywhere mentally, passing constantly from one topic to another; nor does he ever give up his investigation; he pursues it not merely for a matter of days, but throughout his whole life. Also by transferring his mind to other ideas which are yet not foreign to the questions at issue, he persists till he reaches the solution.

‘On Paralysis’. Quoted in A. J. Brock, Greek Medicine: Being Extracts Illustrative of Medical Writers from Hippocrates to Galen (1929), 185.

People will accept your idea much more readily if you tell them Benjamin Franklin said it first

In Dr. N Sreedharan, Quotations of Wit and Wisdom (2007), 35.

Perhaps it is better in this present world of ours that a revolutionary idea or invention instead of being helped and patted be hampered and ill-treated in its adolescence—by want of means, by selfish interest, pedantry, stupidity and ignorance; that it be attacked and stifled; that it pass through bitter trials and tribulations, through the heartless strife of commercial existence. … So all that was great in the past was ridiculed, condemned, combatted, suppressed—only to emerge all the more powerfully, all the more triumphantly from the struggle.

‘The Transmission of Electrical Energy Without Wires As a Means for Furthering Peace’, Electrical World and Engineer (7 Jan 1905), 24. Reproduced in John T. Ratzlaff, editor, Tesla Said (1984), 86. Also reprinted in Nikola Tesla, Miscellaneous Writings (2007), 58.

Plants, generally speaking, meet the impact of the terrestrial environment head on, although of course they in turn modify the physical environment by adventitious group activity. The individual plant cannot select its habitat; its location is largely determined by the vagaries of the dispersal of seeds or spores and is thus profoundly affected by chance. Because of their mobility and their capacity for acceptance or rejection terrestrial animals, in contrast, can and do actively seek out and utilize the facets of the environment that allow their physiological capacities to function adequately. This means that an animal by its behavior can fit the environment to its physiology by selecting situations in which its physiological capacities can cope with physical conditions. If one accepts this idea, it follows that there is no such thing as The Environment, for there exist as many different terrestrial environments as there are species of animals.

From ‘The role of physiology in the distribution of terrestrial vertebrates’, collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 84.

Poor teaching leads to the inevitable idea that the subject [mathematics] is only adapted to peculiar minds, when it is the one universal science and the one whose four ground-rules are taught us almost in infancy and reappear in the motions of the universe.

In Mathematical Teaching (1907), 19.

Possible ideas and thoughts are vast in number. A distinct word for every distinct idea and thought would require a vast vocabulary. The problem in language is to express many ideas and thoughts with comparatively few words.

In Introduction to the Study of Indian Languages: With Words, Phrases and Sentences to be Collected (1880), 55.

Preconceived ideas are like searchlights which illumine the path of experimenter and serve him as a guide to interrogate nature. They become a danger only if he transforms them into fixed ideas – this is why I should like to see these profound words inscribed on the threshold of all the temples of science: “The greatest derangement of the mind is to believe in something because one wishes it to be so.”

Speech (8 Jul 1876), to the French Academy of Medicine. As translated in René J. Dubos, Louis Pasteur, Free Lance of Science (1950, 1986), 376. Date of speech identified in Maurice B. Strauss, Familiar Medical Quotations (1968), 502.

Profound thoughts arise only in debate, with a possibility of counterargument, only when there is a possibility of expressing not only correct ideas but also dubious ideas.

In Progress, Coexistence, and Intellectual Freedom (1968).

Progress in science depends on new techniques, new discoveries and new ideas, probably in that order.

Psychoanalytic theory is the most stupendous intellectual confidence trick of the twentieth century and a terminal product as well—something akin to a dinosaur or zeppelin in the history of ideas, a vast structure of radically unsound design and with no posterity.

‘Victims of Psychiatry’, The New York Review of Books (23 Jan 1975), 21. Cited in David E. Stannard, Shrinking History: On Freud and the Failure of Psychohistory (1980), 150.

Psychology appeared to be a jungle of confusing, conflicting, and arbitrary concepts. These pre-scientific theories doubtless contained insights which still surpass in refinement those depended upon by psychiatrists or psychologists today. But who knows, among the many brilliant ideas offered, which are the true ones? Some will claim that the statements of one theorist are correct, but others will favour the views of another. Then there is no objective way of sorting out the truth except through scientific research.

From The Scientific Analysis of Personality (1965), 14.

Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.

In letter (1 May 1935), Letters to the Editor, ‘The Late Emmy Noether: Professor Einstein Writes in Appreciation of a Fellow-Mathematician’, New York Times (4 May 1935), 12.

Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.

In Presidential Address British Association for the Advancement of Science, Section A (1890), Nature, 42, 466.

Quite often, when an idea that could be helpful presents itself, we do not appreciate it, for it is so inconspicuous. The expert has, perhaps, no more ideas than the inexperienced, but appreciates more what he has and uses it better.

How to Solve it: A New Aspect of Mathematical Method (1957), 223.

Realizing how often ingenious speculation in the complex biological world has led nowhere and how often the real advances in biology as well as in chemistry, physics and astronomy have kept within the bounds of mechanistic interpretation, we geneticists should rejoice, even with our noses on the grindstone (which means both eyes on the objectives), that we have at command an additional means of testing whatever original ideas pop into our heads.

‘The Rise of Genetics’, Science (1932), 1969, 264.

Reason must approach nature with the view, indeed, of receiving information from it, not, however, in the character of a pupil, who listens to all that his master chooses to tell him, but in that of a judge, who compels the witnesses to reply to those questions which he himself thinks fit to propose. To this single idea must the revolution be ascribed, by which, after groping in the dark for so many centuries, natural science was at length conducted into the path of certain progress.

Critique of Pure Reason, translated by J.M.D. Meiklejohn (1855), Preface to the Second Edition, xxvii.

Research in neurophysiology is much more like paddling a small canoe on a mountain river. The river which is fed by many distant springs carries you along all right though often in a peculiar direction. You have to paddle quite hard to keep afloat. And sooner or later some of your ideas are upset and are carried downstream like an upturned canoe.

From Speech (10 Dec 1963) at the Nobel Banquet in Stockholm, Sweden. Collected inGöran Liljestrand (ed.), Les Prix Nobel en 1963, (1964).

Researchers keep identifying new species, but they have no idea about the life cycle of a given species or its other hosts. They cut open an animal and find a new species. Where did it come from? What effect does it have on its host? What is its next host? They don’t know and they don’t have time to find out, because there are too many other species waiting to be discovered and described.

Talk at Columbia University, ‘The Power of Parasites.’

Science asks no questions about the ontological pedigree or a priori character of a theory, but is content to judge it by its performance; and it is thus that a knowledge of nature, having all the certainty which the senses are competent to inspire, has been attained—a knowledge which maintains a strict neutrality toward all philosophical systems and concerns itself not with the genesis or a priori grounds of ideas.

Originally published in North American Review (1865). ‘The Philosophy of Herbert Spencer,’ repr. In Philosophical Writings of Chauncey Wright (1963), p. 8.

Science can tell you how to clone a tyrannosaurus rex. Humanities can tell you why this might be a bad idea.

On poster for humanities relevancy produced by the College of Humanities, University of Utah.

Science fiction is the most important literature in the history of the world, because it’s the history of ideas, the history of our civilization birthing itself; Science fiction is central to everything we’ve ever done, and people who make fun of science fiction writers don’t know what they’’re talking about

……

Science is a cemetery of dead ideas, even though life may issue from them.

Tragic Sense of Life (1913), translated by John Ernest Crawford Flitch (1954), 90.

Science quotes on:  |  Life (1830)

Science is a speculative enterprise. The validity of a new idea and the significance of a new experimental finding are to be measured by the consequences—consequences in terms of other ideas and other experiments. Thus conceived, science is not a quest for certainty; it is rather a quest which is successful only to the degree that it is continuous.

In Science and Common Sense (1951), 25-26.

Science is organized knowledge. Wisdom is organized life.
[Author Will Durant’s summary of Kant’s ideas; not a direct translation of Kant’s own words.]

Although often seen, these are (almost certainly) not Kant’s own words. While explaining Kant’s ideas, this are the words used by Will Durant in ‘Kant and German Idealism: Transcendental Analytic’, The Story of Philosophy (1924, 1938), 295-296. The first sentence, “Science is organized knowledge,” was first stated by Herbert Spencer in 1854 (see Science Quotes by Herbert Spencer.) On the webside of quoteinvestigator.com, which pinpoints Durant as the origin of the quote, it is further explained that Kant’s writing style used complicated expression that makes it rare to find intelligible direct quotes of Kant’s own words.

Science is really in the business of disproving current models or changing them to conform to new information. In essence, we are constantly proving our latest ideas wrong.

John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren’t There More Happy People?: Smart Quotes for Dumb Times (2009), 274.

Science is the best idea humans have ever had. The more people who embrace that idea, the better.

In interview with Brian Anthony Hernandez, ‘Bill Nye: “When Rush Limbaugh Says I’m Not a Scientist, I’m Charmed”’ (31 May 2013) on mashable.com web site.

Science requires an almost complete openness to all ideas. On the other hand, it requires the most rigorous and uncompromising skepticism.

In article, ‘Wonder and Skepticism’, Skeptical Inquirer (Jan/Feb 1995), 19, No. 1.

Science … has no consideration for ultimate purposes, any more than Nature has, but just as the latter occasionally achieves things of the greatest suitableness without intending to do so, so also true science, as the imitator of nature in ideas, will occasionally and in many ways further the usefulness and welfare of man,—but also without intending to do so.

Human, All Too Human (1878), Vol. 1, 58. Quoted in Willard Huntington Wright, What Nietzsche Taught (1915), 57.

Scientific findings do not threaten anyone (except to the extent that Homo sapiens may prove incapable of controlling what science makes possible). But what is critical to understand is that our species (or, for that matter, God) is not in the least diminished by the idea that we emerged thanks to the processes of evolution.

In The Monkey in the Mirror: Essays on the Science of What Makes Us Human (2003), 55.

Scientific research is based on the idea that everything that takes place is determined by laws of nature, and therefore this holds for the actions of people. For this reason, a research scientist will hardly be inclined to believe that events could be influenced by a prayer, i.e. by a wish addressed to a supernatural Being.
However, it must be admitted that our actual knowledge of these laws is only imperfect and fragmentary, so that, actually, the belief in the existence of basic all-embracing laws in Nature also rests on a sort of faith. All the same this faith has been largely justified so far by the success of scientific research.

Letter (24 Jan 1936) replying to a a letter (19 Jan 1936) asking if scientists pray, from a child in the sixth grade in a Sunday School in New York City. In Albert Einstein, Helen Dukas (ed.) and Banesh Hoffmann (ed.), Albert Einstein, The Human Side (1981), 32-33.

Scientists constantly get clobbered with the idea that we spent 27 billion dollars on the Apollo programs, and are asked “What more do you want?” We didn’t spend it; it was done for political reasons. … Apollo was a response to the Bay of Pigs fiasco and to the successful orbital flight of Yuri Gagarin. President Kennedy’s objective was not to find out the origin of the moon by the end of the decade; rather it was to put a man on the moon and bring him back, and we did that.

Quoted by Dennis Meredith, in ‘Carl Sagan’s Cosmic Connection and Extraterrestrial Life-Wish’, Science Digest (Jun 1979), 85, 38 & 89. Reproduced in Carl Sagan and Tom Head, Conversations With Sagan (2006), 55-56.

Secondly, the study of mathematics would show them the necessity there is in reasoning, to separate all the distinct ideas, and to see the habitudes that all those concerned in the present inquiry have to one another, and to lay by those which relate not to the proposition in hand, and wholly to leave them out of the reckoning. This is that which, in other respects besides quantity is absolutely requisite to just reasoning, though in them it is not so easily observed and so carefully practised. In those parts of knowledge where it is thought demonstration has nothing to do, men reason as it were in a lump; and if upon a summary and confused view, or upon a partial consideration, they can raise the appearance of a probability, they usually rest content; especially if it be in a dispute where every little straw is laid hold on, and everything that can but be drawn in any way to give color to the argument is advanced with ostentation. But that mind is not in a posture to find truth that does not distinctly take all the parts asunder, and, omitting what is not at all to the point, draws a conclusion from the result of all the particulars which in any way influence it.

In Conduct of the Understanding, Sect. 7.

Segregationalists will even argue that God was the first segregationalist. “Red birds and blue birds don’t fly together”, they contend. … They turn to some pseudo-scientific writing and argue that the Negro’s brain is smaller than the white man’s brain. They do not know, or they refuse to know that the idea of an inferior or superior race has been refuted by the best evidence of the science of anthropology. Great anthropologists, like Ruth Benedict, Margaret Mead, and Melville J. Herskovits, agree that, although there may be inferior and superior individuals within all races, there is no superior or inferior race. And segregationalists refuse to acknowledge that there are four types of blood, and these four types are found within every racial group.

‘Love in Action’, Strength To Love (1963, 1981), 45-46.

Sexual instinct—as emotion, idea, and impulse—is a function of the cerebral cortex. Thus far no definite region of the cortex has been proved to be exclusively the seat of sexual sensations and impulses.

Psychopathia Sexualis: With Special Reference to Contrary Sexual Instinct: A Medico-Legal Study (1886), trans. Charles Gilbert Chaddock (1892), 24.

Since 1849 I have studied incessantly, under all its aspects, a question which was already in my mind [since 1832. I confess that my scheme is still a mere dream, and I do not shut my eyes to the fact that so long as I alone believe it to be possible, it is virtually impossible. … The scheme in question is the cutting of a canal through the Isthmus of Suez. This has been thought of from the earliest historical times, and for that very reason is looked upon as impracticable. Geographical dictionaries inform us indeed that the project would have been executed long ago but for insurmountable obstacles. [On his inspiration for the Suez Canal.]

Letter to M.S.A. Ruyssenaers, Consul-General for Holland in Egypt, from Paris (8 Jul 1852), seeking support. Collected in Ferdinand de Lesseps, The Suez Canal: Letters and Documents Descriptive of Its Rise and Progress in 1854-1856 (1876), 2.

Since it is necessary for specific ideas to have definite and consequently as far as possible selected terms, I have proposed to call substances of similar composition and dissimilar properties isomeric, from the Greek ίσομερης (composed of equal parts).

Jahrebericht (1832). As translated in Henry M. Leicester and Herbert S. Klickstein, A Source Book in Chemistry 1400-1900 (1952), 265.

Since Pawlow [Pavlov] and his pupils have succeeded in causing the secretion of saliva in the dog by means of optic and acoustic signals, it no longer seems strange to us that what the philosopher terms an ‘idea’ is a process which can cause chemical changes in the body.

The Mechanistic Conception of Life (1912), 63.

So far as modern science is concerned, we have to abandon completely the idea that by going into the realm of the small we shall reach the ultimate foundations of the universe. I believe we can abandon this idea without any regret. The universe is infinite in all directions, not only above us in the large but also below us in the small. If we start from our human scale of existence and explore the content of the universe further and further, we finally arrive, both in the large and in the small, at misty distances where first our senses and then even our concepts fail us.

To the German Society of Scientists and Physicists, Braunschweig, Germany (Sep 1896). As quoted in Anton Z. Capri, Quips, Quotes, and Quanta: An Anecdotal History of Physics (2011), 20. Wiechert was reporting his measurement of the mass of the moving particles in a cathode ray beam (electrons).

So long as a man remains a gregarious and sociable being, he cannot cut himself off from the gratification of the instinct of imparting what he is learning, of propagating through others the ideas and impressions seething in his own brain, without stunting and atrophying his moral nature and drying up the surest sources of his future intellectual replenishment.

In Address (22 Feb 1877) for Commemoration Day at Johns Hopkins University. Published as a pamphlet, and reprinted in The Collected Mathematical Papers of James Joseph Sylvester: (1870-1883) (1909), Vol. 3, 77.

So long as new ideas are created, sales will continue to reach new highs.

In Forbes (1946), 57, 46.

Some ideas are better than others. The machinery for distinguishing them is an essential tool in dealing with the world and especially in dealing with the future. And it is precisely the mix of these two modes of thought [skeptical scrutiny and openness to new ideas] that is central to the success of science.

In ‘The Burden of Skepticism’, Skeptical Inquirer (Fall 1987), 12, No. 1.

Some of Feynman’s ideas about cosmology have a modern ring. A good example is his attitude toward the origin of matter. The idea of continuous matter creation in the steady state cosmology does not seriously offend him (and he notes … that the big bang cosmology has a problem just as bad, to explain where all the matter came from in the beginning). … He emphasizes that the total energy of the universe could really be zero, and that matter creation is possible because the rest energy of the matter is actually canceled by its gravitational potential energy. “It is exciting to think that it costs nothing to create a new particle, …”

In John Preskill and Kip S. Thorne, ‘Foreword to Feynman Lectures on Gravitation’ (15 May 1995). Feynman delivered his lectures in 1962–63.

Some people say they cannot understand a million million. Those people cannot understand that twice two makes four. That is the way I put it to people who talk to me about the incomprehensibility of such large numbers. I say finitude is incomprehensible, the infinite in the universe is comprehensible. Now apply a little logic to this. Is the negation of infinitude incomprehensible? What would you think of a universe in which you could travel one, ten, or a thousand miles, or even to California, and then find it comes to an end? Can you suppose an end of matter or an end of space? The idea is incomprehensible. Even if you were to go millions and millions of miles the idea of coming to an end is incomprehensible. You can understand one thousand per second as easily as you can understand one per second. You can go from one to ten, and then times ten and then to a thousand without taxing your understanding, and then you can go on to a thousand million and a million million. You can all understand it.

In ‘The Wave Theory of Light’ (1884), Popular Lectures and Addresses (1891), Vol. 1, 322.

Some scientists find, or so it seems, that they get their best ideas when smoking; others by drinking coffee or whisky. Thus there is no reason why I should not admit that some may get their ideas by observing, or by repeating observations.

Realism and the Aim of Science (1983), 36.

Some writers, rejecting the idea which science had reached, that reefs of rocks could be due in any way to “animalcules,” have talked of electrical forces, the first and last appeal of ignorance.

In Corals and Coral Islands (1879), 17.

Sometimes an idea hangs on, not because it is good, or even seductive, but because it has been around a long time, or constantly repeated. If one wants to verify something written in the newspaper, should one buy 100 more copies of the paper to check it?

As quoted Gordon Younger Craig and John Hewett Hull, James Hutton: Present and Future (1999), 21

Sometimes progress is slow. But then there does come a time when a lot of people accept a new idea and see ways in which it can be exploited. And because of the larger number of workers in the field, progress becomes rapid. That is what happened with the study of protein structure.

From interview with Neil A. Campbell, in ‘Crossing the Boundaries of Science’, BioScience (Dec 1986), 36, No. 11, 739.

Strictly speaking, the idea of a scientific poem is probably as nonsensical as that of a poetic science.

Aphorism 61 from Selected Aphorisms from the Lyceum (1797-1800). In Friedrich Schlegel, translated by Ernst Behler and Roman Struc, Dialogue on Poetry and Literary Aphorisms (trans. 1968), 155.

Such biological ideas as the “survival of the fittest,” whatever their doubtful value in natural science, are utterly useless in attempting to understand society … The life of a man in society, while it is incidentally a biological fact, has characteristics that are not reducible to biology and must be explained in the distinctive terms of a cultural analysis … the physical well-being of men is a result of their social organization and not vice versa … Social improvement is a product of advances in technology and social organization, not of breeding or selective elimination … Judgments as to the value of competition between men or enterprises or nations must be based upon social and not allegedly biological consequences; and … there is nothing in nature or a naturalistic philosophy of life to make impossible the acceptance of moral sanctions that can be employed for the common good.

Social Darwinism in American Thought 1860-1915 (1945), 176.

Such is the tendency of the human mind to speculation, that on the least idea of an analogy between a few phenomena, it leaps forward, as it were, to a cause or law, to the temporary neglect of all the rest; so that, in fact, almost all our principal inductions must be regarded as a series of ascents and descents, and of conclusions from a few cases, verified by trial on many.

In A Preliminary Discourse on the Study of Natural Philosophy (1830), 164-165.

Such propositions are therefore called Eternal Truths, not because they are Eternal Truths, not because they are External Propositions actually formed, and antecedent to the Understanding, that at any time makes them; nor because they are imprinted on the Mind from any patterns, that are any where out of the mind, and existed before: But because, being once made, about abstract Ideas, so as to be true, they will, whenever they can be supposed to be made again at any time, past or to come, by a Mind having those Ideas, always actually be true. For names being supposed to stand perpetually for the same ideas, and the same ideas having immutably the same habitudes one to another, Propositions concerning any abstract Ideas that are once true, must needs be eternal Verities.

An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 11, Section 14, 638-9.

Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection.

Symmetry (1952), 5.

Taken over the centuries, scientific ideas have exerted a force on our civilization fully as great as the more tangible practical applications of scientific research.

From ‘The History of Science and the Teaching of Science’, collected in I.B. Cohen and F.G. Watson(eds.), General Education in Science (1952), 72.

That deeply emotional conviction of the presence of a superior reasoning power, which is revealed in the incomprehensible universe, forms my idea of God.

……

That the great majority of those who leave school should have some idea of the kind of evidence required to substantiate given types of belief does not seem unreasonable. Nor is it absurd to expect that they should go forth with a lively interest in the ways in which knowledge is improved and a marked distaste for all conclusions reached in disharmony with the methods of scientific inquiry.

Address to Section L, Education, of the American Association for the Advancement of Science, at Boston (1909), ‘Science as Subject-Matter and as Method’. Published in Science (28 Jan 1910), N.S. Vol. 31, No. 787, 126.

That was the beginning, and the idea seemed so obvious to me and so elegant that I fell deeply in love with it. And, like falling in love with a woman, it is only possible if you do not know much about her, so you cannot see her faults. The faults will become apparent later, but after the love is strong enough to hold you to her. So, I was held to this theory, in spite of all difficulties, by my youthful enthusiasm.

Expressing how his work on quantum electrodynamics began with an original idea. In his Nobel Prize Lecture (11 Dec 1965), ‘The Development of the Space-Time View of Quantum Electrodynamics’. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 157.

That which the sciences can add to the privileges of the human race has never been more marked than at the present moment. … The air seems to become as accessible to him as the waters…. The name of Montgolfier, the names of those hardy navigators of the new element, will live through time; but who among us, on seeing these superb experiments, has not felt his soul elevated, his ideas expanded, his mind enlarged?

As quoted by François Arago, in a biography of Bailly, read to the Academy of Sciences (26 Feb 1844), as translated by William Henry Smyth, Baden Powell and Robert Grant, published in ‘Bailly’, Biographies of Distinguished Scientific Men (1859), Vol. 1, 124.

The arithmetization of mathematics … which began with Weierstrass … had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics. These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought. But how can we avoid the use of human language? The … symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.

In Tobias Dantzig and Joseph Mazur (ed.), Number: The Language of Science (1930, ed. by Joseph Mazur 2007), 99.

The Ideas of primary Qualities of Bodies, are Resemblances of them, and their Patterns do really exist in the Bodies themselves; but the Ideas, produced in us by these Secondary Qualities, have no resemblance of them at all. There is nothing like our Ideas, existing in the Bodies themselves. They are in Bodies, we denominate from them, only a Power to produce those Sensations in us: And what is Sweet, Blue or Warm in Idea, is but the certain Bulk, Figure, and Motion of the insensible parts in the Bodies themselves, which we call so.

An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 2, Chapter 8, Section 15, 137.

The Qualities then that are in Bodies rightly considered, are of Three sorts.
First, the Bulk, Figure, Number, Situation, and Motion, or Rest of their solid Parts; those are in them, whether we perceive them or no; and when they are of that size, that we can discover them, we have by these an Idea of the thing, as it is in it self, as is plain in artificial things. These I call primary Qualities.
Secondly, The Power that is in any Body, by Reason of its insensible primary Qualities, to operate after a peculiar manner on any of our Senses, and thereby produce in us the different Ideas of several Colours, Sounds, Smells, Tastes, etc. These are usually called sensible Qualities.
Thirdly, The Power that is in any Body, by Reason of the particular Constitution of its primary Qualities, to make such a change in the Bulk, Figure, Texture, and Motion of another Body, as to make it operate on our Senses, differently from what it did before. Thus the Sun has a Power to make Wax white, and Fire to make Lead fluid. These are usually called Powers.

An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 2, Chapter 8, Section 23, 140-1.

The “British Association for the Promotion of Science,” … is almost necessary for the purposes of science. The periodical assemblage of persons, pursuing the same or différent branches of knowledge, always produces an excitement which is favourable to the development of new ideas; whilst the long period of repose which succeeds, is advantageous for the prosecution of the reasonings or the experiments then suggested; and the récurrence of the meeting in the succeeding year, will stimulate the activity of the inquirer, by the hope of being then enabled to produce the successful result of his labours.

In ‘Future Prospects’, On the Economy of Machinery and Manufactures (1st ed., 1832), chap. 32, 274. Note: The British Association for the Advancement of Science held its first meeting at York in 1831, the year before the first publication of this book in 1832.

The advancement of science is slow; it is effected only by virtue of hard work and perseverance. And when a result is attained, should we not in recognition connect it with the efforts of those who have preceded us, who have struggled and suffered in advance? Is it not truly a duty to recall the difficulties which they vanquished, the thoughts which guided them; and how men of different nations, ideas, positions, and characters, moved solely by the love of science, have bequeathed to us the unsolved problem? Should not the last comer recall the researches of his predecessors while adding in his turn his contribution of intelligence and of labor? Here is an intellectual collaboration consecrated entirely to the search for truth, and which continues from century to century.
[Respecting how the work of prior researchers had enabled his isolation of fluorine.]

Proceedings of the Royal Institution (1897). In Annual Report of the Board of Regents of the Smithsonian Institution to July 1897 (1898), 262.

The aim of medicine is to prevent disease and prolong life, the ideal of medicine is to eliminate the need of a physician.

Concluding remark from address, ‘The Aims and Ideals of the American Medical Association’, collected in Proceedings of the 66th Annual Meeting of the National Education Association of the United States (1928), 163.

The amoeba had the architectural ideas of R. Buckminster Fuller before there was anyone around capable of having an idea.

In The Center of Life: A Natural History of the Cell (1977), 16.

The anxious precision of modern mathematics is necessary for accuracy, … it is necessary for research. It makes for clearness of thought and for fertility in trying new combinations of ideas. When the initial statements are vague and slipshod, at every subsequent stage of thought, common sense has to step in to limit applications and to explain meanings. Now in creative thought common sense is a bad master. Its sole criterion for judgment is that the new ideas shall look like the old ones, in other words it can only act by suppressing originality.

In Introduction to Mathematics (1911), 157.

The apodictic quality of mathematical thought, the certainty and correctness of its conclusions, are due, not to a special mode of ratiocination, but to the character of the concepts with which it deals. What is that distinctive characteristic? I answer: precision, sharpness, completeness,* of definition. But how comes your mathematician by such completeness? There is no mysterious trick involved; some ideas admit of such precision, others do not; and the mathematician is one who deals with those that do.

In ‘The Universe and Beyond’, Hibbert Journal (1904-1905), 3, 309. An editorial footnote indicates “precision, sharpness, completeness” — i.e., in terms of the absolutely clear and indefinable.

The Archetypal idea was manifested in the flesh, under divers such modifications, upon this planet, long prior to the existence of those animal species that actually exemplify it. To what natural laws or secondary causes the orderly succession and progression of such organic phaenomena may have been committed we as yet are ignorant. But if, without derogation of the Divine power, we may conceive the existence of such ministers, and personify them by the term ‘Nature,’ we learn from the past history of our globe that she has advanced with slow and stately steps, guided by the archetypal light, amidst the wreck of worlds, from the first embodiment of the Vertebrate idea under its old Ichthyic vestment, until it became arrayed in the glorious garb of the Human form.

On the Nature of Limbs (1849), 86.

The art of reasoning consists in getting hold of the subject at the right end, of seizing on the few general ideas that illuminate the whole, and of persistently organizing all subsidiary facts round them.

In ‘Presidential Address to the London Branch of the Mathematical Association’, Mathematical Gazette (Mar 1913), 7, No. 104, 92.

The basic idea is to shove all fundamental difficulties onto the neutron and to do quantum mechanics in the nucleus.

Letter to Niels Bohr, 20 Jun 1932. Quoted in David C. Cassidy, Uncertainty: The Life and Science of Werner Heisenberg (1992), 292.

The basic ideas and simplest facts of set-theoretic topology are needed in the most diverse areas of mathematics; the concepts of topological and metric spaces, of compactness, the properties of continuous functions and the like are often indispensable.

As co-author with H. Hopf, Topologie I (1935), 23. As quoted, translated and cited in Reinhold Remmert, Theory of Complex Functions (1991), 9-10. From the original German, “Die Grundbegriffe und die einfachsten Tatsachen aus der mengentheoretischen Topologie braucht man in sehr verschiedenen Gebieten der Mathematik; die Begriffe des topologischen und des metrischen Raumes, der Kompaktheit, die Eigenschaften stetiger Abbildungen u. dgl. sind oft unentbehrlich.”

The belief that mathematics, because it is abstract, because it is static and cold and gray, is detached from life, is a mistaken belief. Mathematics, even in its purest and most abstract estate, is not detached from life. It is just the ideal handling of the problems of life, as sculpture may idealize a human figure or as poetry or painting may idealize a figure or a scene. Mathematics is precisely the ideal handling of the problems of life, and the central ideas of the science, the great concepts about which its stately doctrines have been built up, are precisely the chief ideas with which life must always deal and which, as it tumbles and rolls about them through time and space, give it its interests and problems, and its order and rationality. That such is the case a few indications will suffice to show. The mathematical concepts of constant and variable are represented familiarly in life by the notions of fixedness and change. The concept of equation or that of an equational system, imposing restriction upon variability, is matched in life by the concept of natural and spiritual law, giving order to what were else chaotic change and providing partial freedom in lieu of none at all. What is known in mathematics under the name of limit is everywhere present in life in the guise of some ideal, some excellence high-dwelling among the rocks, an “ever flying perfect” as Emerson calls it, unto which we may approximate nearer and nearer, but which we can never quite attain, save in aspiration. The supreme concept of functionality finds its correlate in life in the all-pervasive sense of interdependence and mutual determination among the elements of the world. What is known in mathematics as transformation—that is, lawful transfer of attention, serving to match in orderly fashion the things of one system with those of another—is conceived in life as a process of transmutation by which, in the flux of the world, the content of the present has come out of the past and in its turn, in ceasing to be, gives birth to its successor, as the boy is father to the man and as things, in general, become what they are not. The mathematical concept of invariance and that of infinitude, especially the imposing doctrines that explain their meanings and bear their names—What are they but mathematicizations of that which has ever been the chief of life’s hopes and dreams, of that which has ever been the object of its deepest passion and of its dominant enterprise, I mean the finding of the worth that abides, the finding of permanence in the midst of change, and the discovery of a presence, in what has seemed to be a finite world, of being that is infinite? It is needless further to multiply examples of a correlation that is so abounding and complete as indeed to suggest a doubt whether it be juster to view mathematics as the abstract idealization of life than to regard life as the concrete realization of mathematics.

In ‘The Humanization of Teaching of Mathematics’, Science, New Series, 35, 645-46.

The best part of working at a university is the students. They come in fresh, enthusiastic, open to ideas, unscarred by the battles of life. They don’t realize it, but they’re the recipients of the best our society can offer. If a mind is ever free to be creative, that’s the time. They come in believing textbooks are authoritative but eventually they figure out that textbooks and professors don’t know everything, and then they start to think on their own. Then, I begin learning from them.

As quoted in autobiography of Stephen Chu in Gösta Ekspong (ed.), Nobel Lectures: Physics 1996-2000 (2002), 120.

The best scientist is open to experience and begins with romance— the idea that anything is possible.

……

The best way to have a good idea is to have lots of ideas.

Lilless McPherson Shilling and Linda K. Fuller, Dictionary of Quotations in Communications (1997), 112. Although widely quoted in these words, Webmaster has not yet found the primary source. If you know the primary source, please contact Webmaster.

Science quotes on:  |  Best (464)  |  Good (894)  |  Lot (151)  |  Way (1214)

The Big Idea that had been developed in the seventeenth century … is now known as the scientific method. It says that the way to proceed when investigating how the world works is to first carry out experiments and/or make observations of the natural world. Then, develop hypotheses to explain these observations, and (crucially) use the hypothesis to make predictions about the future outcome of future experiments and/or observations. After comparing the results of those new observations with the predictions of the hypotheses, discard those hypotheses which make false predictions, and retain (at least, for the time being) any hypothesis that makes accurate predictions, elevating it to the status of a theory. Note that a theory can never be proved right. The best that can be said is that it has passed all the tests applied so far.

In The Fellowship: the Story of a Revolution (2005), 275.

The body of the Earth, large, sluggish and inapt for motion, is not to be disturbed by movement (especially three movements), any more than the Aetherial Lights [stars] are to be shifted, so that such ideas are opposed both to physical principles and to the authority of the Holy Writ which many time: confirms the stability of the Earth (as we shall discuss more fully elsewhere).

De Mundi Aetherei Recentioribus Phaenomenis (On Recent Phenomena in the Aetherial World) (1588). Quoted in M. Boas Hall, The Scientific Renaissance 1450-1630 (1962), 115.

The books of the great scientists are gathering dust on the shelves of learned libraries. … While the artist’s communication is linked forever with its original form, that of the scientist is modified, amplified, fused with the ideas and results of others and melts into the stream of knowledge and ideas which forms our culture. The scientist has in common with the artist only this: that he can find no better retreat from the world than his work and also no stronger link with the world than his work.

From Nobel Lecture (10 Dec 1969), ‘A Physicist’s Renewed Look at Biology – Twenty Years Later.’ in Nobel Lectures, Physiology or Medicine 1963-1970 (1972), 409.

The chances for favorable serendipity are increased if one studies an animal that is not one of the common laboratory species. Atypical animals, or preparations, force one to use non-standard approaches and non-standard techniques, and even to think nonstandard ideas. My own preference is to seek out species which show some extreme of adaptation. Such organisms often force one to abandon standard methods and standard points of view. Almost inevitably they lead one to ask new questions, and most importantly in trying to comprehend their special and often unusual adaptations one often serendipitously stumbles upon new insights.

In ‘Scientific innovation and creativity: a zoologist’s point of view’, American Zoologist (1982), 22, 234.

The chemist works along his own brilliant line of discovery and exposition; the astronomer has his special field to explore; the geologist has a well-defined sphere to occupy. It is manifest, however, that not one of these men can tell the whole tale, and make a complete story of creation. Another man is wanted. A man who, though not necessarily going into formal science, sees the whole idea, and speaks of it in its unity. This man is the theologian. He is not a chemist, an astronomer, a geologist, a botanist——he is more: he speaks of circles, not of segments; of principles, not of facts; of causes and purposes rather than of effects and appearances. Not that the latter are excluded from his study, but that they are so wisely included in it as to be put in their proper places.

In The People’s Bible: Discourses Upon Holy Scripture: Vol. 1. Genesis (1885), 120.

The child asks, “What is the moon, and why does it shine?” “What is this water and where does it run?” “What is this wind?” “What makes the waves of the sea?” “Where does this animal live, and what is the use of this plant?” And if not snubbed and stunted by being told not to ask foolish questions, there is no limit to the intellectual craving of a young child; nor any bounds to the slow, but solid, accretion of knowledge and development of the thinking faculty in this way. To all such questions, answers which are necessarily incomplete, though true as far as they go, may be given by any teacher whose ideas represent real knowledge and not mere book learning; and a panoramic view of Nature, accompanied by a strong infusion of the scientific habit of mind, may thus be placed within the reach of every child of nine or ten.

In ‘Scientific Education’, Lay Sermons, Addresses, and Reviews (1870), 71.
https://books.google.com/books?id=13cJAAAAIAAJ
Thomas Henry Huxley — 1870

The Chinese are clearly inculcating the idea that science is exciting and important, and that’s why they, as a whole—they’re graduating four times as many engineers as we are, and that’s just happened over the last 20 years.

NPR Radio interview, Morning Edition, (29 Apr 2005). In Lisa Rogak (ed.) The Impatient Optimist: Bill Gates in his Words (2012), 32.

The complexity of contemporary biology has led to an extreme specialization, which has inevitably been followed by a breakdown in communication between disciplines. Partly as a result of this, the members of each specialty tend to feel that their own work is fundamental and that the work of other groups, although sometimes technically ingenious, is trivial or at best only peripheral to an understanding of truly basic problems and issues. There is a familiar resolution to this problem but it is sometimes difficulty to accept emotionally. This is the idea that there are a number of levels of biological integration and that each level offers problems and insights that are unique to it; further, that each level finds its explanations of mechanism in the levels below, and its significances in the levels above it.

From ‘Interaction of physiology and behavior under natural conditions’, collected in R.I. Bowman (ed.), The Galapagos (1966), 39.

The computer takes up where psychoanalysis left off. It takes the ideas of a decentered self and makes it more concrete by modeling mind as a multiprocessing machine.

The Second Self, ch. 9 (1984). Turkle was on the faculty of the Massachusetts Institute of Technology’s program in Science, Technology and Society.

The cure for a fallacious argument is a better argument, not the suppression of ideas.

The Demon Haunted World: Science as a Candle in the Dark (1997), 429.

The desire to fly after the fashion of the birds is an idea handed down to us by our ancestors who, in their grueling travels across trackless lands in prehistoric times, looked enviously on the birds soaring freely through space, at full speed, above all obstacles, on the infinite highway of the air.

In The Papers of Wilbur and Orville Wright: Including the Chanute-Wright Letters (1953), 934.

The dexterous management of terms and being able to fend and prove with them, I know has and does pass in the world for a great part of learning; but it is learning distinct from knowledge, for knowledge consists only in perceiving the habitudes and relations of ideas one to another, which is done without words; the intervention of sounds helps nothing to it. And hence we see that there is least use of distinction where there is most knowledge: I mean in mathematics, where men have determined ideas with known names to them; and so, there being no room for equivocations, there is no need of distinctions.

In Conduct of the Understanding, Sect. 31.

The difficulties connected with my criterion of demarcation (D) are important, but must not be exaggerated. It is vague, since it is a methodological rule, and since the demarcation between science and nonscience is vague. But it is more than sharp enough to make a distinction between many physical theories on the one hand, and metaphysical theories, such as psychoanalysis, or Marxism (in its present form), on the other. This is, of course, one of my main theses; and nobody who has not understood it can be said to have understood my theory.
The situation with Marxism is, incidentally, very different from that with psychoanalysis. Marxism was once a scientific theory: it predicted that capitalism would lead to increasing misery and, through a more or less mild revolution, to socialism; it predicted that this would happen first in the technically highest developed countries; and it predicted that the technical evolution of the ‘means of production’ would lead to social, political, and ideological developments, rather than the other way round.
But the (so-called) socialist revolution came first in one of the technically backward countries. And instead of the means of production producing a new ideology, it was Lenin’s and Stalin’s ideology that Russia must push forward with its industrialization (‘Socialism is dictatorship of the proletariat plus electrification’) which promoted the new development of the means of production.
Thus one might say that Marxism was once a science, but one which was refuted by some of the facts which happened to clash with its predictions (I have here mentioned just a few of these facts).
However, Marxism is no longer a science; for it broke the methodological rule that we must accept falsification, and it immunized itself against the most blatant refutations of its predictions. Ever since then, it can be described only as nonscience—as a metaphysical dream, if you like, married to a cruel reality.
Psychoanalysis is a very different case. It is an interesting psychological metaphysics (and no doubt there is some truth in it, as there is so often in metaphysical ideas), but it never was a science. There may be lots of people who are Freudian or Adlerian cases: Freud himself was clearly a Freudian case, and Adler an Adlerian case. But what prevents their theories from being scientific in the sense here described is, very simply, that they do not exclude any physically possible human behaviour. Whatever anybody may do is, in principle, explicable in Freudian or Adlerian terms. (Adler’s break with Freud was more Adlerian than Freudian, but Freud never looked on it as a refutation of his theory.)
The point is very clear. Neither Freud nor Adler excludes any particular person’s acting in any particular way, whatever the outward circumstances. Whether a man sacrificed his life to rescue a drowning, child (a case of sublimation) or whether he murdered the child by drowning him (a case of repression) could not possibly be predicted or excluded by Freud’s theory; the theory was compatible with everything that could happen—even without any special immunization treatment.
Thus while Marxism became non-scientific by its adoption of an immunizing strategy, psychoanalysis was immune to start with, and remained so. In contrast, most physical theories are pretty free of immunizing tactics and highly falsifiable to start with. As a rule, they exclude an infinity of conceivable possibilities.

‘The Problem of Demarcation’ (1974). Collected in David Miller (ed.) Popper Selections (1985), 127-128.

The difficulty lies, not in the new ideas, but in escaping the old ones, which ramify, for those brought up as most of us have been, into every corner of our minds.

In Engines of Creation by K. Eric Drexler (1987).

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.

In Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving (1981). As cited, with no more details, in Yi Ma, An Invitation to 3-D Vision (2004), 228.

The energy produced by the breaking down of the atom is a very poor kind of thing. Anyone who expects a source of power from transformation of these atoms is talking moonshine. … We hope in the next few years to get some idea of what these atoms are, how they are made, and the way they are worked.

Address at Leicester (11 Sep 1933), reported in The Times (12 Sep 1933). Also cited as ‘Atom Powered World Absurd, Scientists Told: Lord Rutherford Scoffs at Theory of Harnessing Energy in Laboratories’, New York Herald Tribune (12 Sep 1933), in Jacqueline D. Spears and Dean Zollman, The Fascination of Physics, (1985), 508.

The engineer is concerned to travel from the abstract to the concrete. He begins with an idea and ends with an object. He journeys from theory to practice. The scientist’s job is the precise opposite. He explores nature with his telescopes or microscopes, or much more sophisticated techniques, and feeds into a computer what he finds or sees in an attempt to define mathematically its significance and relationships. He travels from the real to the symbolic, from the concrete to the abstract. The scientist and the engineer are the mirror image of each other.

In The Development of Design (1981), 19-20.

The enthusiasm of Sylvester for his own work, which manifests itself here as always, indicates one of his characteristic qualities: a high degree of subjectivity in his productions and publications. Sylvester was so fully possessed by the matter which for the time being engaged his attention, that it appeared to him and was designated by him as the summit of all that is important, remarkable and full of future promise. It would excite his phantasy and power of imagination in even a greater measure than his power of reflection, so much so that he could never marshal the ability to master his subject-matter, much less to present it in an orderly manner.
Considering that he was also somewhat of a poet, it will be easier to overlook the poetic flights which pervade his writing, often bombastic, sometimes furnishing apt illustrations; more damaging is the complete lack of form and orderliness of his publications and their sketchlike character, … which must be accredited at least as much to lack of objectivity as to a superfluity of ideas. Again, the text is permeated with associated emotional expressions, bizarre utterances and paradoxes and is everywhere accompanied by notes, which constitute an essential part of Sylvester’s method of presentation, embodying relations, whether proximate or remote, which momentarily suggested themselves. These notes, full of inspiration and occasional flashes of genius, are the more stimulating owing to their incompleteness. But none of his works manifest a desire to penetrate the subject from all sides and to allow it to mature; each mere surmise, conceptions which arose during publication, immature thoughts and even errors were ushered into publicity at the moment of their inception, with utmost carelessness, and always with complete unfamiliarity of the literature of the subject. Nowhere is there the least trace of self-criticism. No one can be expected to read the treatises entire, for in the form in which they are available they fail to give a clear view of the matter under contemplation.
Sylvester’s was not a harmoniously gifted or well-balanced mind, but rather an instinctively active and creative mind, free from egotism. His reasoning moved in generalizations, was frequently influenced by analysis and at times was guided even by mystical numerical relations. His reasoning consists less frequently of pure intelligible conclusions than of inductions, or rather conjectures incited by individual observations and verifications. In this he was guided by an algebraic sense, developed through long occupation with processes of forms, and this led him luckily to general fundamental truths which in some instances remain veiled. His lack of system is here offset by the advantage of freedom from purely mechanical logical activity.
The exponents of his essential characteristics are an intuitive talent and a faculty of invention to which we owe a series of ideas of lasting value and bearing the germs of fruitful methods. To no one more fittingly than to Sylvester can be applied one of the mottos of the Philosophic Magazine:
“Admiratio generat quaestionem, quaestio investigationem investigatio inventionem.”

In Mathematische Annalen (1898), 50, 155-160. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 176-178.

The experience was more fulfilling than I could have ever imagined. I have a newfound sense of wonder seeing the Earth and stars from such an incredible perspective. Certainly, through my training I was prepared for the technical aspects, but I had no idea that I would be flooded with such amazement and joy after seeing my first sunrise and sunset from space.

……

In Impossibility: The Limits of Science and the Science of Limits (1999), 11.

The fear of meeting the opposition of envy, or the illiberality of ignorance is, no doubt, the frequent cause of preventing many ingenious men from ushering opinions into the world which deviate from common practice. Hence for want of energy, the young idea is shackled with timidity and a useful thought is buried in the impenetrable gloom of eternal oblivion.

A Treatise on the Improvement of Canal Navigation (1796), preface, ix.

The field of scientific abstraction encompasses independent kingdoms of ideas and of experiments and within these, rulers whose fame outlasts the centuries. But they are not the only kings in science. He also is a king who guides the spirit of his contemporaries by knowledge and creative work, by teaching and research in the field of applied science, and who conquers for science provinces which have only been raided by craftsmen.

While president of the German Chemical Society, making memorial remarks dedicated to the deceased Professor Lunge (Jan 1923). As quoted in Richard Willstätter, Arthur Stoll (ed. of the original German) and Lilli S. Hornig (trans.), From My Life: The Memoirs of Richard Willstätter (1958), 174-175.

The first acquaintance which most people have with mathematics is through arithmetic. That two and two make four is usually taken as the type of a simple mathematical proposition which everyone will have heard of. … The first noticeable fact about arithmetic is that it applies to everything, to tastes and to sounds, to apples and to angels, to the ideas of the mind and to the bones of the body.

In An Introduction to Mathematics (1911), 9.

The first concept of continental drift first came to me as far back as 1910, when considering the map of the world, under the direct impression produced by the congruence of the coast lines on either side of the Atlantic. At first I did not pay attention to the ideas because I regarded it as improbable. In the fall of 1911, I came quite accidentally upon a synoptic report in which I learned for the first time of palaeontological evidence for a former land bridge between Brazil and Africa. As a result I undertook a cursory examination of relevant research in the fields of geology and palaeontology, and this provided immediately such weighty corroboration that a conviction of the fundamental soundness of the idea took root in my mind.

In The Origins of Continents and Oceans (4th ed. 1929), trans. John Biram (1966), 1.

The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you get a bright idea.

In How to Solve It: A New Aspect of Mathematical Method (2004), 172.

The first step in wisdom is to know the things themselves; this notion consists in having a true idea of the objects; objects are distinguished and known by classifying them methodically and giving them appropriate names. Therefore, classification and name-giving will be the foundation of our science.

Systema Naturae (1735), trans. M. S. J. Engel-Ledeboer and H. Engel (1964), 19.

The fun in science lies not in discovering facts, but in discovering new ways of thinking about them. The test which we apply to these ideas is this—do they enable us to fit the facts to each other, and see that more and more of them can be explained by fewer and fewer fundamental laws.

In concluding paragraph of essay, ‘The Atom’, collected in A Short History of Science (1951, 1959), 124. This essay was broadcast earlier (17 Mar 1950), by Bragg, on BBC Home Service radio ‘For the Schools: Talks for Sixth Forms: The History of Science’. It was fifteenth in a series of sixteen talks. The book publishes the original scripts, with a note that “Each author has been free to revise his Talk for publication, but the original spoken version has been retained with only slight variations.” Webmaster has, as yet, not confirmed if the quote in the book varied from the exact words broadcast.

The fundamental idea of these pylons, or great archways, is based on a method of construction peculiar to me, of which the principle consists in giving to the edges of the pyramid a curve of such a nature that this pyramid shall be capable of resisting the force of the wind without necessitating the junction of the edges by diagonals as is usually done.

Writing of his tower after its completion in 1889. As quoted (translated) in ‘Eiffel’s Monument His Famous Tower’, New York Times (6 Jan 1924), X8.

The future does not belong to those who are content with today, apathetic toward common problems and their fellow man alike, timid and fearful in the face of bold projects and new ideas. Rather, it will belong to those who can blend passion, reason and courage in a personal commitment to the great enterprises and ideals of American society.

……

The game of chess has always fascinated mathematicians, and there is reason to suppose that the possession of great powers of playing that game is in many features very much like the possession of great mathematical ability. There are the different pieces to learn, the pawns, the knights, the bishops, the castles, and the queen and king. The board possesses certain possible combinations of squares, as in rows, diagonals, etc. The pieces are subject to certain rules by which their motions are governed, and there are other rules governing the players. … One has only to increase the number of pieces, to enlarge the field of the board, and to produce new rules which are to govern either the pieces or the player, to have a pretty good idea of what mathematics consists.

In Book review, ‘What is Mathematics?’, Bulletin American Mathematical Society (May 1912), 18, 386-387.

The general knowledge of our author [Leonhard Euler] was more extensive than could well be expected, in one who had pursued, with such unremitting ardor, mathematics and astronomy as his favorite studies. He had made a very considerable progress in medical, botanical, and chemical science. What was still more extraordinary, he was an excellent scholar, and possessed in a high degree what is generally called erudition. He had attentively read the most eminent writers of ancient Rome; the civil and literary history of all ages and all nations was familiar to him; and foreigners, who were only acquainted with his works, were astonished to find in the conversation of a man, whose long life seemed solely occupied in mathematical and physical researches and discoveries, such an extensive acquaintance with the most interesting branches of literature. In this respect, no doubt, he was much indebted to an uncommon memory, which seemed to retain every idea that was conveyed to it, either from reading or from meditation.

In Philosophical and Mathematical Dictionary (1815), 493-494.

The goddess of learning is fabled to have sprung full-grown from the brain of Zeus, but it is seldom that a scientific conception is born in its final form, or owns a single parent. More often it is the product of a series of minds, each in turn modifying the ideas of those that came before, and providing material for those that came after. The electron is no exception.

‘Electronic Waves’, Nobel Lecture (7 Jun 1938). Nobel Lectures: Physics 1922-1941 (1998), 397.

The great object of all knowledge is to enlarge and purify the soul, to fill the mind with noble contemplations, to furnish a refined pleasure, and to lead our feeble reason from the works of nature up to its great Author and Sustainer. Considering this as the ultimate end of science, no branch of it can surely claim precedence of Astronomy. No other science furnishes such a palpable embodiment of the abstractions which lie at the foundation of our intellectual system; the great ideas of time, and space, and extension, and magnitude, and number, and motion, and power. How grand the conception of the ages on ages required for several of the secular equations of the solar system; of distances from which the light of a fixed star would not reach us in twenty millions of years, of magnitudes compared with which the earth is but a foot-ball; of starry hosts—suns like our own—numberless as the sands on the shore; of worlds and systems shooting through the infinite spaces.

Oration at Inauguration of the Dudley Astronomical Observatory, Albany (28 Jul 1856). Text published as The Uses of Astronomy (1856), 36.

The great object, in trying to understand history, political, religious, literary, or scientific, is to get behind men, and to grasp ideas.

In Letters of Lord Acton to Mary Gladstone (1904), 99.

The great thing [about Kant’s philosophy] was to form the idea that this one thing—mind or world—may well be capable of other forms of appearance that we cannot grasp and that do not imply the notions of space and time. This means an imposing liberation from our inveterate prejudice.

……

The great upheavals which precede changes of civilisation, such as the fall of the Roman Empire and the founding of the Arabian Empire, for example, seem to have been determined mainly by considerable political transformations, invasions, or the overthrow of dynasties. But … most often, the real cause is … a profound modification in the ideas of the peoples. … The memorable events of history are the visible effects of the invisible changes of human thought. … The present epoch is one of these critical moments in which the thought of mankind is undergoing a process of transformation.

From Psychologie des Foules (1895), Introduction, 1-2. English text in The Crowd: A Study of the Popular Mind (1897), Introduction, xiii-xiv, tweaked by Webmaster. Original French text: “Les grands bouleversements qui précèdent les changements de civilisations, tels que la chute de l’Empire romain et la fondation de l’Empire arabe par exemple semblent … déterminés surtout par des transformations politiques considérables: invasions de peuples ou renversements de dynasties. Mais … se trouve le plus souvent, comme cause réelle, une modification profonde dans les peuples. … Les événements mémorables de l’histoire sont les effets visibles des invisibles changements de la pensée des hommes. … L’époque actuelle constitue un de ces moments critiques où la pensée des hommes est en voie de se transformer.”

The greatest spiritual revolutionary Western history, Saint Francis, proposed what he thought was an alternative Christian view of nature and man’s relation to it: he tried to substitute the idea of the equality of creatures, including man, for the idea of man’s limitless rule of creation. He failed. Both our present science and our present technology are so tinctured with orthodox Christian arrogance toward nature that no solution for our ecologic crisis can be expected from them alone. Since the roots of our trouble are so largely religious, the remedy must also be essentially religious, whether we call it that or not. We must rethink and refeel our nature and destiny. The profoundly religious, but heretical, sense of the primitive Franciscans for the spiritual autonomy of all parts of nature may point a direction. I propose Francis as a patron saint for ecologists.

In The Historical Roots of our Ecologic Crisis (1967), 1207.

The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church, which had been maintained through the Middle Ages, had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science “more geometrico.”

In Space,Time, Matter, translated by Henry Leopold Brose (1952), 1.

The Historic Method may be described as the comparison of the forms of an idea, or a usage, or a belief, at any given time, with the earlier forms from which they were evolved, or the later forms into which they were developed and the establishment from such a comparison, of an ascending and descending order among the facts. It consists in the explanation of existing parts in the frame of society by connecting them with corresponding parts in some earlier frame; in the identification of present forms in the past, and past forms in the present. Its main process is the detection of corresponding customs, opinions, laws, beliefs, among different communities, and a grouping of them into general classes with reference to some one common feature. It is a certain way of seeking answers to various questions of origin, resting on the same general doctrine of evolution, applied to moral and social forms, as that which is being applied with so much ingenuity to the series of organic matter.

On Compromise (1874), 22-3.

The history of acceptance of new theories frequently shows the following steps: At first the new idea is treated as pure nonsense, not worth looking at. Then comes a time when a multitude of contradictory objections are raised, such as: the new theory is too fancy, or merely a new terminology; it is not fruitful, or simply wrong. Finally a state is reached when everyone seems to claim that he had always followed this theory. This usually marks the last state before general acceptance.

In ‘Field Theory and the Phase Space’, collected in Melvin Herman Marx, Psychological Theory: Contemporary Readings (1951), 299.

The History of Evolution is the real source of light in the investigation of organic bodies. It is applicable at every step, and all our ideas of the correlation of organic bodies will be swayed by our knowledge of the history of evolution. To carry the proof of it into all branches of research would be an almost endless task. (1828)

Quoted as an epigraph to Chap. 3, in Ernst Haeckel, The Evolution of Man, (1886), Vol 1, 48.

The history of science gives us the materials of an evolution of human intellect, so one could look in the history of the arts and of literature for the story of the evolution of human sensibility. The history of science is a history of ideas; just so the history of art could be considered as a history of man’s dreams.

In ‘The History of Science’, The Monist (July 1916), 26, No. 3, 342.

The history of science has proved that fundamental research is the lifeblood of individual progress and that the ideas that lead to spectacular advances spring from it.

In J. Edwin Holmström, Records and Research in Engineering and Industrial Science (1956), 7.

The history of science is accomplishing an endless purification of scientific facts and ideas.

In ‘The History of Science’, The Monist (July 1916), 26, No. 3, 350.

The history of science, like the history of all human ideas, is a history of irresponsible dreams, of obstinacy, and of error. But science is one of the very few human activities—perhaps the only one—in which errors are systematically criticized and fairly often, in time, corrected. This is why we can say that, in science, we often learn from our mistakes, and why we can speak clearly and sensibly about making progress there. In most other fields of human endeavour there is change, but rarely progress … And in most fields we do not even know how to evaluate change.

From Conjectures and Refutations: The Growth of Scientific Knowledge (1963), 216. Reproduced in Karl Popper, Truth, Rationality and the Growth of Scientific Knowledge (1979), 9.

The history of semiconductor physics is not one of grand heroic theories, but one of painstaking intelligent labor. Not strokes of genius producing lofty edifices, but great ingenuity and endless undulation of hope and despair. Not sweeping generalizations, but careful judgment of the border between perseverance and obstinacy. Thus the history of solid-state physics in general, and of semiconductors in particular, is not so much about great men and women and their glorious deeds, as about the unsung heroes of thousands of clever ideas and skillful experiments—reflection of an age of organization rather than of individuality.

‘Selected Topics from the History of Semiconductor Physics and Its Applications’, in Lillian Hoddeson et al. (eds.), Out of the Crystal Maze (1992), 474.

The history of the word sankhyā shows the intimate connection which has existed for more than 3000 years in the Indian mind between ‘adequate knowledge’ and ‘number.’ As we interpret it, the fundamental aim of statistics is to give determinate and adequate knowledge of reality with the help of numbers and numerical analysis. The ancient Indian word Sankhyā embodies the same idea, and this is why we have chosen this name for the Indian Journal of Statistics.

Editorial, Vol. 1, Part 1, in the new statistics journal of the Indian Statistical Institute, Sankhayā (1933). Also reprinted in Sankhyā: The Indian Journal of Statistics (Feb 2003), 65, No. 1, xii.

The History of the World is nothing but the development of the Idea of Freedom.

From Vorlesungen über die philosophie der weltgeschichte (1837), as translated from the Third German Edition by J. Sibree (1857), in The Philosophy of History (1857, 1861), 476.

The human mind treats a new idea the way the body treats a strange protein; it rejects it.

The Art of the Soluble (1967). Quoted in Colin J. Sanderson, Understanding Genes and GMOs (2007), 1.

The idea of a method that contains firm, unchanging, and absolutely binding principles for conducting the business of science meets considerable difficulty when confronted with the results of historical research. We find, then, that there is not a single rule, however plausible, and however firmly grounded in epistemology, that is not violated at some time or another.

Against Method: Outline of an Anarchistic Theory of Knowledge (1975, 1993), 14.

The idea of achieving security through national armament is, at the present state of military technique, a disastrous illusion.

……

The idea of an atom has been so constantly associated with incredible assumptions of infinite strength, absolute rigidity, mystical actions at a distance, and individuality, that chemists and many other reasonable naturalists of modern times, losing all patience with it, have dismissed it to the realms of metaphysics, and made it smaller than ‘anything we can conceive.’ But if atoms are inconceivably small, why are not all chemical actions infinitely swift? Chemistry is powerless to deal with this question, and many others of paramount importance, if barred by the hardness of its fundamental assumptions, from contemplating the atom as a real portion of matter occupying a finite space, and forming not an immeasurably small constituent of any palpable body.

Sir William Thomson and Peter Guthrie Tait, A Treatise on Natural Philosophy (1883), Vol. I, Part 2, 495.

The idea of an indivisible, ultimate atom is inconceivable by the lay mind. If we can conceive of an idea of the atom at all, we can conceive it as capable of being cut in half; indeed, we cannot conceive it at all unless we so conceive it. The only true atom, the only thing which we cannot subdivide and cut in half, is the universe. We cannot cut a bit off the universe and put it somewhere else. Therefore the universe is a true atom and, indeed, is the smallest piece of indivisible matter which our minds can conceive; and they cannot conceive it any more than they can the indivisible, ultimate atom.

Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 58.

The idea of atomic energy is illusionary but it has taken so powerful a hold on the minds, that although I have preached against it for twenty-five years, there are still some who believe it to be realizable.

Quoted in ‘Tesla, 75, Predicts New Power Source’, New York Times (5 Jul 1931), Section 2, 1.

The idea of making a fault a subject of study and not an object to be merely determined has been the most important step in the course of my methods of observation. If I have obtained some new results it is to this that I owe it.

‘Notice sur les Travaux Scientifiques de Marcel Bertrand’ (1894). In Geological Society of London, The Quarterly Journal of the Geological Society of London (May 1908), 64, li.

The idea of wilderness needs no defense, it only needs defenders.

In ‘Shadows from the Big Woods’, The Journey Home: Some Words in Defense of the American West (1977), 229.

The idea of winning a doctor’s degree gradually assumed the aspect of a great moral struggle, and the moral fight possessed immense attraction for me.

In Pioneer Work in Opening the Medical Profession to Women (1895), 29.

The idea that aptitude for mathematics is rarer than aptitude for other subjects is merely an illusion which is caused by belated or neglected beginners.

In ‘Umriss pädagogischer Vorlesungen’, Werke [Kehrbach] (1902), Bd. 10, 101. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 74.

The idea that memory is linear is nonsense. What we have in our heads is a collection of frames. As to time itself—can it be linear when all these snatches of other presents exist at once in your mind? A very elusive and tricky concept, time.»

Interview with Sarah Crown, in The Guardian (25 Jul 2009).

The idea that our natural resources were inexhaustible still obtained, and there was as yet no real knowledge of their extent and condition. The relation of the conservation of natural resources to the problems of National welfare and National efficiency had not yet dawned on the public mind. The reclamation of arid public lands in the West was still a matter for private enterprise alone; and our magnificent river system, with its superb possibilities for public usefulness, was dealt with by the National Government not as a unit, but as a disconnected series of pork-barrel problems, whose only real interest was in their effect on the re-election or defeat of a Congressman here and there —a theory which, I regret to say, still obtains.

The Works of Theodore Roosevelt. Vol. 20: Theodore Roosevelt, An Autobiography (1926), 386.

The idea that something in food might be of advantage to patients with pernicious anemia was in my mind in 1912, when I was a house officer at the Massachusetts General Hospital…. Ever since my student days, when I had the opportunity, in my father’s wards at the Massachusetts General Hospital, … I have taken a deep interest in this disease. … Prolonged observation permitted me to become acquainted with the multiple variations and many aspects of the disease, and to realize that from a few cases it was difficult to determine the effect of therapeutic procedures.

From Nobel Prize Lecture (12 Dec 1934), collected in Nobel Lectures, Physiology or Medicine 1922-1941 (1965).

The idea that the bumps or depressions on a man’s head indicate the presence or absence of certain moral characteristics in his mental equipment is one of the absurdities developed from studies in this field that has long since been discarded by science. The ideas of the phrenologist Gall, however ridiculous they may now seem in the light of a century’s progress, were nevertheless destined to become metamorphosed into the modern principles of cerebral localization.

From ‘Looking for «The Face Within the Face» in Man’, in the New York Times, 4 Mar 1906, SM page 3.

The idea that the universe is running down comes from a simple observation about machines. Every machine consumes more energy than it renders.

In The Ascent of Man (1973).

The idea that time may vary from place to place is a difficult one, but it is the idea Einstein used, and it is correct—believe it or not.

……

The idea that we shall be welcomed as new members into the galactic community is as unlikely as the idea that the oyster will be welcomed as a new member into the human community. We’re probably not even edible.

In Joseph Silk, The Infinite Cosmos: Questions from the Frontiers of Cosmology (2006), 199.

The ideas that are basic to [my work] often bear witness to my amazement and wonder at the laws of nature which operate in the world around us.

In M.C. Escher: The Graphic Work (1978), 8.

The ideas which these sciences, Geometry, Theoretical Arithmetic and Algebra involve extend to all objects and changes which we observe in the external world; and hence the consideration of mathematical relations forms a large portion of many of the sciences which treat of the phenomena and laws of external nature, as Astronomy, Optics, and Mechanics. Such sciences are hence often termed Mixed Mathematics, the relations of space and number being, in these branches of knowledge, combined with principles collected from special observation; while Geometry, Algebra, and the like subjects, which involve no result of experience, are called Pure Mathematics.

In The Philosophy of the Inductive Sciences (1868), Part 1, Bk. 2, chap. 1, sect. 4.

The impossibility of separating the nomenclature of a science from the science itself, is owing to this, that every branch of physical science must consist of three things; the series of facts which are the objects of the science, the ideas which represent these facts, and the words by which these ideas are expressed. Like three impressions of the same seal, the word ought to produce the idea, and the idea to be a picture of the fact.

Elements of Chemistry (1790), trans. R. Kerr, Preface, xiv.

The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.

Address in memory of Karl Weierstrass. As quoted in Journal of the University of Bombay (1933), 2, 201. Also in Tobias Dantzig, Number: The Language of Science (1937), 237. Also partially quoted as epigraph in in James Roy Newman, The World of Mathematics (1956), Vol. 3, 1593. which dates the address as 1921. Another translation for perhaps the same address (‘On the Infinite’), in honor of Weierstrass, dates it as 4 Jun 1925, in Paul Benacerraf (ed.) Philosophy of Mathematics (1983), 183. See this alternate version elsewhere on this page, beginning, “From time immemorial…”.

The intensity and quantity of polemical literature on scientific problems frequently varies inversely as the number of direct observations on which the discussions are based: the number and variety of theories concerning a subject thus often form a coefficient of our ignorance. Beyond the superficial observations, direct and indirect, made by geologists, not extending below about one two-hundredth of the Earth’s radius, we have to trust to the deductions of mathematicians for our ideas regarding the interior of the Earth; and they have provided us successively with every permutation and combination possible of the three physical states of matter—solid, liquid, and gaseous.

‘Address delivered by the President of Section [Geology] at Sydney (Friday, Aug 21), Report of the Eighty-Fourth Meeting of the British Association for the Advancement of Science: Australia 1914, 1915, 345.

The invention of the differential calculus marks a crisis in the history of mathematics. The progress of science is divided between periods characterized by a slow accumulation of ideas and periods, when, owing to the new material for thought thus patiently collected, some genius by the invention of a new method or a new point of view, suddenly transforms the whole subject on to a higher level.

In An Introduction to Mathematics (1911), 217. Whitehead continued by quoting the poet, Percy Shelley, who compared the slow accumulation of thoughts leading to an avalanche following the laying down of a great truth. See the poetic quote beginning, “The sun-awakened avalanche…” on the Percy Shelley Quotations page.

The invention of the scientific method and science is, I’m sure we’ll all agree, the most powerful intellectual idea, the most powerful framework for thinking and investigating and understanding and challenging the world around us that there is, and it rests on the premise that any idea is there to be attacked. If it withstands the attack then it lives to fight another day and if it doesn’t withstand the attack then down it goes. Religion doesn’t seem to work like that.

From impromptu speech at a Cambridge conference (1998). Quoted in Richard Dawkins, A Devil’s Chaplain: Reflections on Hope, Lies, Science, and Love (2004), 168. In Douglas Adams, The Salmon of Doubt: Hitchhiking the Galaxy One Last Time (2002), 141.

The invention of what we may call primary or fundamental notation has been but little indebted to analogy, evidently owing to the small extent of ideas in which comparison can be made useful. But at the same time analogy should be attended to, even if for no other reason than that, by making the invention of notation an art, the exertion of individual caprice ceases to be allowable. Nothing is more easy than the invention of notation, and nothing of worse example and consequence than the confusion of mathematical expressions by unknown symbols. If new notation be advisable, permanently or temporarily, it should carry with it some mark of distinction from that which is already in use, unless it be a demonstrable extension of the latter.

In ‘Calculus of Functions’, Encyclopaedia of Pure Mathematics (1847), Addition to Article 26, 388.

The inventor is a man who looks upon the world and is not contented with things as they are. He wants to improve whatever he sees, he wants to benefit the world; he is haunted by an idea. The spirit of invention possesses him, seeking materialization.

From Speech to the Patent Congress (1891) in Washington, D.C., as quoted in Jean Lesage, ‘Alexander Graham Bell Museum: Tribute to Genius’, The National Geographic Magazine (Aug 1956), 110, No. 2, 232. The article notes that this statement is “prominently displayed near the foyer” of the Canadian museum opened that month to memorialize Bell, in Baddeck, Nova Scotia.

The iron labor of conscious logical reasoning demands great perseverance and great caution; it moves on but slowly, and is rarely illuminated by brilliant flashes of genius. It knows little of that facility with which the most varied instances come thronging into the memory of the philologist or historian. Rather is it an essential condition of the methodical progress of mathematical reasoning that the mind should remain concentrated on a single point, undisturbed alike by collateral ideas on the one hand, and by wishes and hopes on the other, and moving on steadily in the direction it has deliberately chosen.

In Ueber das Verhältniss der Naturwissenschaften zur Gesammtheit der Wissenschaft, Vorträge und Reden (1896), Bd. 1, 178.

The late Mr. David Hume, in his posthumous works, places the powers of generation much above those of our boasted reason; and adds, that reason can only make a machine, as a clock or a ship, but the power of generation makes the maker of the machine; … he concludes, that the world itself might have been generated, rather than created; that is, it might have been gradually produced from very small beginnings, increasing by the activity of its inherent principles, rather than by a sudden evolution of the whole by the Almighty fiat.—What a magnificent idea of the infinite power of THE GREAT ARCHITECT! THE CAUSE OF CAUSES! PARENT OF PARENTS! ENS ENTIUM!
For if we may compare infinities, it would seem to require a greater infinity of power to cause the causes of effects, than to cause the effects themselves.

‘Generation’, Zoonomia (1794), Vol. 1, 509. Note that this passage was restated in a 1904 translation of a book by August Weismann. That rewording was given in quotation marks and attributed to Erasumus Darwin without reference to David Hume. In the reworded form, it is seen in a number of later works as a direct quote made by Erasmus Darwin. For that restated form see the webpage for August Weismann. Webmaster has checked the quotation on this webpage in the original Zoonomia, and is the only verbatim form found so far.

The leading idea which is present in all our [geological] researches, and which accompanies every fresh observation, the sound of which to the ear of the student of Nature seems echoed from every part of her works, is—Time!—Time!—Time!

The Geology and Extinct Volcanoes of Central France (2nd ed., 1858), 208-9.

The losses of the natural world are our loss, their silence silences something within the human mind. Human language is lit with animal life: we play cats-cradle or have hare-brained ideas; we speak of badgering, or outfoxing someone; to squirrel something away and to ferret it out. … When our experience of the wild world shrinks, we no longer fathom the depths of our own words; language loses its lustre and vividness.

In ‘Fifty Years On, the Silence of Rachel Carson’s Spring Consumes Us’, The Guardian (25 Sep 2012),

The major religions on the Earth contradict each other left and right. You can’t all be correct. And what if all of you are wrong? It’s a possibility, you know. You must care about the truth, right? Well, the way to winnow through all the differing contentions is to be skeptical. I’m not any more skeptical about your religious beliefs than I am about every new scientific idea I hear about. But in my line of work, they’re called hypotheses, not inspiration and not revelation.

Contact (1997), 162.

The man who is thoroughly convinced of the universal operation of the law of causation cannot for a moment entertain the idea of a being who interferes in the course of events–provided, of course, that he takes the hypothesis of causality really seriously. He has no use for the religion of fear and equally little for social or moral religion. A God who rewards and punishes is inconceivable to him for the simple reason that a man’s actions are determined by necessity, external and internal, so that in God’s eyes he cannot be responsible, any more than an inanimate object is responsible for the motions it undergoes. Science has therefore been charged with undermining morality, but the charge is unjust. A man’s ethical behavior should be based effectually on sympathy, education, and social ties and needs; no religious basis is necessary. Man would indeed be in a poor way if he had to be restrained by fear of punishment and hopes of reward after death.

From ‘Religion And Science’, as collected in Ideas And Opinions (1954), 39, given its source as: “Written expressly for the New York Times Magazine. Appeared there November 9, 1930 (pp. 1-4). The German text was published in the Berliner Tageblatt, November 11, 1930.” The NYT Magazine article in full, is reprinted in Edward H. Cotton (ed.), Has Science Discovered God? A Symposium of Modern Scientific Opinion (1931), 101. This original version directly from the magazine has significantly different wording, beginning, “For anyone who is pervaded with the sense of causal law….” See this alternate form on the Albert Einstein Quotes page on this website. As for why the difference, Webmaster speculates the book form editor perhaps used a revised translation from Einstein’s German article.

The mathematician is entirely free, within the limits of his imagination, to construct what worlds he pleases. What he is to imagine is a matter for his own caprice; he is not thereby discovering the fundamental principles of the universe nor becoming acquainted with the ideas of God. If he can find, in experience, sets of entities which obey the same logical scheme as his mathematical entities, then he has applied his mathematics to the external world; he has created a branch of science.

Aspects of Science: Second Series (1926), 92.

The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way.

In A Mathematician’s Apology (1940, reprint with Foreward by C.P. Snow 1992), 85.

The mathematicians are well acquainted with the difference between pure science, which has only to do with ideas, and the application of its laws to the use of life, in which they are constrained to submit to the imperfections of matter and the influence of accidents.

In Samuel Johnson and W. Jackson Bate (Ed.), ‘,The Rambler, No. 14, Saturday, 5 May 1750.’ The Selected Essays from the Rambler, Adventurer, and Idler (1968), 40.

The mechanical world view is a testimonial to three men: Francis Bacon, Rene Descartes, and Isaac Newton. After 300 years we are still living off their ideas.

In Jeremy Rifkin and Ted Howard, Entropy: Into the Greenhouse World (1980), 19.

The members of the department became like the Athenians who, according to the Apostle Paul, “spent their time in nothing else, but either to tell or to hear some new thing.” Anyone who thought he had a bright idea rushed out to try it out on a colleague. Groups of two or more could be seen every day in offices, before blackboards or even in corridors, arguing vehemently about these ‘brain storms.’ It is doubtful whether any paper ever emerged for publication that had not run the gauntlet of such criticism. The whole department thus became far greater than the sum of its individual members.

Obituary of Gilbert Newton Lewis, Biographical Memoirs of the National Academy of Science (1958), 31, 212.

The mental process by which hypotheses are suggested is obscure. Ordinarily they flash into consciousness without premonition, and it would he easy to ascribe them to a mysterious intuition or creative faculty; but this would contravene one of the broadest generalizations of modern psychology. Just as in the domain of matter nothing is created from nothing, just as in the domain of life there is no spontaneous generation, so in the domain of mind there are no ideas which do not owe their existence to antecedent ideas which stand in the relation of parent to child.

In Address (11 Dec 1895) as President of the Geological Society, ‘The Origin of Hypotheses, illustrated by the Discussion of a Topographical Problem’, printed as Presidential Address of Grove Karl Gilbert (1896), 4. Also collected in Science (1896), 3, 2.

The mighty steam-engine has its germ in the simple boiler in which the peasant prepares his food. The huge ship is but the expansion of the floating leaf freighted with its cargo of atmospheric dust; and the flying balloon is but the infant’s soap-bubble lightly laden and overgrown. But the Telescope, even in its most elementary form, embodies a novel and gigantic idea, without an analogue in nature, and without a prototype in experience

Stories of Inventors and Discoverers in Science and the Useful Arts (1860), 145.

The mind likes a strange idea as little as the body likes a strange protein and resists it with similar energy. It would not perhaps be too fanciful to say that a new idea is the most quickly acting antigen known to science. If we watch ourselves honestly we shall often find that we have begun to argue against a new idea even before it has been completely stated.

In The Collected Papers of Wilfred Trotter, FRS (1941), 186. This is seen in several places attributed to W.I.B. Beveridge. However,it appears in his The Art of Scientific Investigation (1950), 109, where it is clearly shown as a quote from Wilfred Trotter, with a footnote citing the source as Collected Papers. (The quote has been removed from the Beveridge page on this web site 29 Jun 2015.)

The moment after, I began to respire 20 quarts of unmingled nitrous oxide. A thrilling, extending from the chest to the extremities, was almost immediately produced. I felt a sense of tangible extension highly pleasurable in every limb; my visible impressions were dazzling, and apparently magnified, I heard distinctly every sound in the room and was perfectly aware of my situation. By degrees, as the pleasurable sensations increased, I last all connection with external things; trains of vivid visible images rapidly passed through my mind, and were connected with words in such a manner, as to produce perceptions perfectly novel. I existed in a world of newly connected and newly modified ideas. I theorised—I imagined that I made discoveries. When I was awakened from this semi-delirious trance by Dr. Kinglake, who took the bag from my mouth, indignation and pride were the first feelings produced by the sight of the persons about me. My emotions were enthusiastic and sublime; and for a minute I walked round the room, perfectly regardless of what was said to me. As I recovered my former state of mind, I felt an inclination to communicate the discoveries I had made during the experiment. I endeavoured to recall the ideas, they were feeble and indistinct; one collection of terms, however, presented itself: and with the most intense belief and prophetic manner, I exclaimed to Dr Kinglake, ‘Nothing exists but thoughts!—the universe is composed of impressions, ideas, pleasures and pains!‘

Researches, Chemical and Philosophical (1800), in J. Davy (ed.), The Collected Works of Sir Humphry Davy (1839-40), Vol 3, 289-90.

The more an idea is developed, the more concise becomes its expression: the more a tree is pruned, the better is the fruit.

Collected in J. de Finod (ed., trans.) A Thousand Flashes of French Wit, Wisdom, and Wickedness (1880), 66, printed citation showing “Alfred Bougeart”. Webmaster has not yet found the primary source for this quote, but has found books with the author name printed on the title page as sometimes Bougeart, others as Bougeard, but references therein to «other books by» have some of the same titles in common. If you know the primary source of this quote, please contact Webmaster.

The most consequential change in man’s view of the world, of living nature and of himself came with the introduction, over a period of some 100 years beginning only in the 18th century, of the idea of change itself, of change over periods of time: in a word, of evolution.

‘Evolution’, Scientific American (Jul 1978), 239:1, 47.

The most important thing accomplished by the ultimate discovery of the 3° K radiation background (Penzias and Wilson, 1965) was to force all of us to take seriously the idea that there was an early universe.

In The First Three Minutes: A Modern View of the Origin of the Universe (1977, 1993), 131-132. (As first printed, the degree symbol was included with the unit K.)

The most powerful antigen in human biology is a new idea.

Saying.

The most powerful factors in the world are clear ideas in the minds of energetic men of good will.

In Outline of Science (1922), Vol. 1, 180.

The national park idea, the best idea we ever had, was inevitable as soon as Americans learned to confront the wild continent not with fear and cupidity but with delight, wonder, and awe.

In Wallace Stegner and Page Stegner (ed.), ‘The Best Idea We Ever Had’, Marking the Sparrow’s Fall: The Making of the American West (1998, 1999), 137.

The nervous system is the most complex and delicate instrument on our planet, by means of which relations, connections are established between the numerous parts of the organism, as well as between the organism, as a highly complex system, and the innumerable, external influences. If the closing and opening of electric current is now regarded as an ordinary technical device, why should there be any objection to the idea that the same principle acts in this wonderful instrument? On this basis the constant connection between the external agent and the response of the organism, which it evokes, can be rightly called an unconditioned reflex, and the temporary connection—a conditioned reflex.

The Conditioned Reflex (1935), 249.

The night before Easter Sunday of that year (1920) I awoke, turned on the light, and jotted down a few notes on a tiny slip of thin paper. Then I fell asleep again. It occurred to me at six o’clock in the morning that during the night I had written down something most important, but I was unable to decipher the scrawl. The next night, at three o’clock, the idea returned. It was the design of an experiment to determine whether the hypothesis of chemical transmission that I had uttered seventeen years ago was correct. I got up immediately, went to the laboratory, and performed a simple experiment on a frog heart according to the nocturnal design. I have to describe this experiment briefly since its results became the foundation of the theory of chemical transmission of the nervous impulse. The hearts of two frogs were isolated, the first with its nerves, the second without. Both hearts were attached to Straub cannulas filled with a little Ringer solution. The vagus nerve of the first heart was stimulated for a few minutes. Then the Ringer solution that had been in the first heart during the stimulation of the vagus was transferred to the second heart. It slowed and its beats diminished just as if its vagus had been stimulated. Similarly, when the accelerator nerve was stimulated and the Ringer from this period transferred, the second heart speeded up and its beats increased. These results unequivocally proved that the nerves do not influence the heart directly but liberate from their terminals specific chemical substances which, in their turn, cause the well-known modifications of the function of the heart characteristic of the stimulation of its nerves.

‘An Autobiographic Sketch’, Perspectives in Biology and Medicine (1960), 4, 17.

The object of psychology is to give us a totally different idea of the things we know best.

Tel quel (1943). In Bill Swainson and Anne H. Soukhanov. Encarta Book of Quotations (2000), 951.

The only thing harder to understand than a law of statistical origin would be a law that is not of statistical origin, for then there would be no way for it—or its progenitor principles—to come into being. On the other hand, when we view each of the laws of physics—and no laws are more magnificent in scope or better tested—as at bottom statistical in character, then we are at last able to forego the idea of a law that endures from everlasting to everlasting.

In ‘Law without Law’ (1979), in John Archibald Wheeler and Wojciech Hubert Zurek (eds.), Quantum Theory and Measurement (1983), 203.

The opinion appears to be gaining ground that this very general conception of functionality, born on mathematical ground, is destined to supersede the narrower notion of causation, traditional in connection with the natural sciences. As an abstract formulation of the idea of determination in its most general sense, the notion of functionality includes and transcends the more special notion of causation as a one-sided determination of future phenomena by means of present conditions; it can be used to express the fact of the subsumption under a general law of past, present, and future alike, in a sequence of phenomena. From this point of view the remark of Huxley that Mathematics “knows nothing of causation” could only be taken to express the whole truth, if by the term “causation” is understood “efficient causation.” The latter notion has, however, in recent times been to an increasing extent regarded as just as irrelevant in the natural sciences as it is in Mathematics; the idea of thorough-going determinancy, in accordance with formal law, being thought to be alone significant in either domain.

In Presidential Address British Association for the Advancement of Science, Sheffield, Section A,
Nature (1 Sep 1910), 84, 290.

The past is a bank where an unlimited number of ideas have been deposited to our credit.

Life and History (1922), 19.

The plain fact is that education is itself a form of propaganda–a deliberate scheme to outfit the pupil, not with the capacity to weigh ideas, but with a simple appetite for gulping ideas readymade. The aim is to make ‘good’ citizens, which is to say, docile and uninquisitive citizens.

……

The present state of the system of nature is evidently a consequence of what it was in the preceding moment, and if we conceive of an intelligence that at a given instant comprehends all the relations of the entities of this universe, it could state the respective position, motions, and general affects of all these entities at any time in the past or future. Physical astronomy, the branch of knowledge that does the greatest honor to the human mind, gives us an idea, albeit imperfect, of what such an intelligence would be. The simplicity of the law by which the celestial bodies move, and the relations of their masses and distances, permit analysis to follow their motions up to a certain point; and in order to determine the state of the system of these great bodies in past or future centuries, it suffices for the mathematician that their position and their velocity be given by observation for any moment in time. Man owes that advantage to the power of the instrument he employs, and to the small number of relations that it embraces in its calculations. But ignorance of the different causes involved in the production of events, as well as their complexity, taken together with the imperfection of analysis, prevents our reaching the same certainty about the vast majority of phenomena. Thus there are things that are uncertain for us, things more or less probable, and we seek to compensate for the impossibility of knowing them by determining their different degrees of likelihood. So it was that we owe to the weakness of the human mind one of the most delicate and ingenious of mathematical theories, the science of chance or probability.

‘Recherches, 1º, sur l’Intégration des Équations Différentielles aux Différences Finies, et sur leur Usage dans la Théorie des Hasards’ (1773, published 1776). In Oeuvres complètes de Laplace, 14 Vols. (1843-1912), Vol. 8, 144-5, trans. Charles Coulston Gillispie, Pierre-Simon Laplace 1749-1827: A Life in Exact Science (1997), 26.

The presentation of mathematics where you start with definitions, for example, is simply wrong. Definitions aren’t the places where things start. Mathematics starts with ideas and general concepts, and then definitions are isolated from concepts. Definitions occur somewhere in the middle of a progression or the development of a mathematical concept. The same thing applies to theorems and other icons of mathematical progress. They occur in the middle of a progression of how we explore the unknown.

Interview for website of the Mathematical Association of America.

The problem [evolution] presented itself to me, and something led me to think of the positive checks described by Malthus in his Essay on Population, a work I had read several years before, and which had made a deep and permanent impression on my mind. These checks—war, disease, famine, and the like—must, it occurred to me, act on animals as well as man. Then I thought of the enormously rapid multiplication of animals, causing these checks to be much more effective in them than in the case of man; and while pondering vaguely on this fact, there suddenly flashed upon me the idea of the survival of the fittest—that the individuals removed by these checks must be on the whole inferior to those that survived. I sketched the draft of my paper … and sent it by the next post to Mr. Darwin.

In ‘Introductory Note to Chapter II in Present Edition’, Natural Selection and Tropical Nature Essays on Descriptive and Theoretical Biology (1891, New ed. 1895), 20.

The purpose of the history of science is to establish the genesis and the development of scientific facts and ideas, taking into account all intellectual exchanges and all influences brought into play by the very progress of civilization. It is indeed a history of civilization considered from its highest point of view. The center of interest is the evolution of science, but general history remains always in the background.

In ‘The History of Science’, The Monist (July 1916), 26, No. 3, 333.

The real problem in speech is not precise language. The problem is clear language. The desire is to have the idea clearly communicated to the other person. [But] precise language is not precise in any sense if you deal with the real objects of the world, and is overly pedantic and quite confusing to use it unless there are some special subtleties which have to be carefully distinguished.

Criticizing “overly pedantic” language in proposed textbooks for a modified arithmetic course for grades 1-8 in California schools. In article, ‘New Textbooks for the ‘New’ Mathematics’, Engineering and Science (Mar 1965), 28, No. 6. Collected in Perfectly Reasonable Deviations from the Beaten Track: The Letters of Richard Feynman (2008), 454. He was writing as a member of the California State Curriculum Committee

The reason I cannot really say that I positively enjoy nature is that I do not quite realize what it is that I enjoy. A work of art, on the other hand, I can grasp. I can — if I may put it this way — find that Archimedian point, and as soon as I have found it, everything is readily clear for me. Then I am able to pursue this one main idea and see how all the details serve to illuminate it.

Søren Kierkegaard, translation by Howard Vincent Hong and Edna Hatlestad Hong Søren Kierkegaard’s Journal and Papers (1834), 50.

The reason why new concepts in any branch of science are hard to grasp is always the same; contemporary scientists try to picture the new concept in terms of ideas which existed before.

In ‘Innovation in Physics’, Scientific American, 1958, 199, 76. Collected in From Eros to Gaia (1993).

The reasoning of mathematicians is founded on certain and infallible principles. Every word they use conveys a determinate idea, and by accurate definitions they excite the same ideas in the mind of the reader that were in the mind of the writer. When they have defined the terms they intend to make use of, they premise a few axioms, or self-evident principles, that every one must assent to as soon as proposed. They then take for granted certain postulates, that no one can deny them, such as, that a right line may be drawn from any given point to another, and from these plain, simple principles they have raised most astonishing speculations, and proved the extent of the human mind to be more spacious and capacious than any other science.

In Diary, Works (1850), Vol. 2, 21.

The reptilian idea of fun
Is to bask all day in the sun.
A physiological barrier,
Discovered by Carrier,
Says they can’t breathe, if they run.

Written about David Carrier’s rule concerning a vertebrate’s breathing when lungs are affected because the rib structure distorts during locomotion. Thus sprawling vertebrates cannot run and breathe at the same time. In sidebar to ‘Respiration, Metabolism, and Locomotion’, History of Life (1991), 177. Carrier’s constraint idea was published in ‘The evolution of locomotor stamina in tetrapods: circumventing a mechanical constraint’ Paleobiology (1987), 13, 326-341.

The result of teaching small parts of a large number of subjects is the passive reception of disconnected ideas, not illuminated with any spark of vitality. Let the main ideas which are introduced into a child’s education be few and important, and let them be thrown into every combination possible.

In The Organisation of Thought: Educational and Scientific (1917), 5.

The role of hypothesis in research can be discussed more effectively if we consider first some examples of discoveries which originated from hypotheses. One of the best illustrations of such a discovery is provided by the story of Christopher Columbus’ voyage; it has many of the features of a classic discovery in science. (a) He was obsessed with an idea—that since the world is round he could reach the Orient by sailing West, (b) the idea was by no means original, but evidently he had obtained some additional evidence from a sailor blown off his course who claimed to have reached land in the west and returned, (c) he met great difficulties in getting someone to provide the money to enable him to test his idea as well as in the actual carrying out of the experimental voyage, (d) when finally he succeeded he did not find the expected new route, but instead found a whole new world, (e) despite all evidence to the contrary he clung to the bitter end to his hypothesis and believed that he had found the route to the Orient, (f) he got little credit or reward during his lifetime and neither he nor others realised the full implications of his discovery, (g) since his time evidence has been brought forward showing that he was by no means the first European to reach America.

The Art of Scientific Investigation (1950), 41.

The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato. I do not mean the systematic scheme of thought which scholars have doubtfully extracted from his writings. I allude to the wealth of general ideas scattered through them.

In Process and Reality (1929), 39.

The same ideas, one must believe, recur in men’s minds not once or twice but again and again.

On the Heavens, 270b, 19-20. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. I, 451.

Science quotes on:  |  Mind (1359)  |  Must (1525)

The sciences are like a beautiful river, of which the course is easy to follow, when it has acquired a certain regularity; but if one wants to go back to the source, one will find it nowhere, because it is everywhere; it is spread so much [as to be] over all the surface of the earth; it is the same if one wants to go back to the origin of the sciences, one will find only obscurity, vague ideas, vicious circles; and one loses oneself in the primitive ideas.

In Essai sur les machines en général (1783), conclusion, as translated in Ivor Grattan-Guinness, Convolutions in French Mathematics, 1800-1840 (1990), Vol. 1, 32.

The scientific man does not aim at an immediate result. He does not expect that his advanced ideas will be readily taken up. His work is like that of the planter—for the future. His duty is to lay the foundation for those who are to come, and point the way.

In ‘The Problem of Increasing Human Energy’, Century Illustrated Monthly Magazine (Jun 1900), 60, 211.

The scientific value of truth is not, however, ultimate or absolute. It rests partly on practical, partly on aesthetic interests. As our ideas are gradually brought into conformity with the facts by the painful process of selection,—for intuition runs equally into truth and into error, and can settle nothing if not controlled by experience,—we gain vastly in our command over our environment. This is the fundamental value of natural science

In The Sense of Beauty: Being the Outlines of Aesthetic Theory (1896), 22.

The scientist values research by the size of its contribution to that huge, logically articulated structure of ideas which is already, though not yet half built, the most glorious accomplishment of mankind.

In The Art of the Soluble (1967), 126. Also ‘Two Conceptions of Science’, collected in The Strange Case of the Spotted Mice and Other Classic Essays on Science (1996), 70.

The senses at first let in particular Ideas, and furnish the yet empty Cabinet: And the Mind by degrees growing familiar with some of them, they are lodged in the Memory, and Names got to them.

An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book I, Chapter 2, Section 15, 55.

The smallest particles of matter were said [by Plato] to be right-angled triangles which, after combining in pairs, … joined together into the regular bodies of solid geometry; cubes, tetrahedrons, octahedrons and icosahedrons. These four bodies were said to be the building blocks of the four elements, earth, fire, air and water … [The] whole thing seemed to be wild speculation. … Even so, I was enthralled by the idea that the smallest particles of matter must reduce to some mathematical form … The most important result of it all, perhaps, was the conviction that, in order to interpret the material world we need to know something about its smallest parts.
[Recalling how as a teenager at school, he found Plato’s Timaeus to be a memorable poetic and beautiful view of atoms.]

In Werner Heisenberg and A.J. Pomerans (trans.) The Physicist’s Conception of Nature (1958), 58-59. Quoted in Jagdish Mehra and Helmut Rechenberg, The Historical Development of Quantum Theory (2001), Vol. 2, 12. Cited in Mauro Dardo, Nobel Laureates and Twentieth-Century Physics (2004), 178.

The so-called Marxian dialectic is simply an effort by third-rate men to give an air of profundity to balderdash. Christianity has gone the same way. There are some sound ideas in it, but its advocates always add a lot of preposterous nonsense. The result is theology.

……

The so-called ‘crank’ may be quite original in his ideas. … Invention, however, in the engineering sense involves originality; but not that alone, if the results are to be of value. There is imagination more or less fertile, but with it a knowledge of what has been done before, carried perhaps by the memory, together with a sense of the present or prospective needs in art or industry. Necessity is not always the mother of invention. It may be prevision.

Address as M.I.T. acting president, to the graduating class (11 Jun 1920). Published in Massachusetts Institute of Technology, Technology Review (Jul 1920), 22, 419-420.

The soft minded man always fears change. He feels security in the status quo and he has an almost morbid fear of the new. For him, the greatest pain is the pain of a new idea.

In Strength to Love (1963, 1977), 15. Compare the earlier quote by Walter Bagehot, “One of the greatest pains to human nature is the pain of a new idea,” in ‘The Age of Discussion’, Physics and Politics (1869, 1916), 163.

The story is told of Lord Kelvin, a famous Scotch physicist of the last century, that after he had given a lecture on atoms and molecules, one of his students came to him with the question, “Professor, what is your idea of the structure of the atom.”
“What,” said Kelvin, “The structure of the atom? Why, don’t you know, the very word ‘atom’ means the thing that can’t be cut. How then can it have a structure?”
“That,” remarked the facetious young man, “shows the disadvantage of knowing Greek.”

As described in ‘Assault on Atoms’ (Read 23 Apr 1931 at Symposium—The Changing World) Proceedings of the American Philosophical Society (1931), 70, No. 3, 219.

The student of mathematics often finds it hard to throw off the uncomfortable feeling that his science, in the person of his pencil, surpasses him in intelligence,—an impression which the great Euler confessed he often could not get rid of. This feeling finds a sort of justification when we reflect that the majority of the ideas we deal with were conceived by others, often centuries ago. In a great measure it is really the intelligence of other people that confronts us in science.

In Popular Scientific Lectures (1910), 196.

The study of mathematics is apt to commence in disappointment. The important applications of the science, the theoretical interest of its ideas, and the logical rigour of its methods all generate the expectation of a speedy introduction to processes of interest. We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet’s father, this great science eludes the efforts of our mental weapons to grasp it.

Opening to An Introduction to Mathematics (1911), 7.

The study of the radio-active substances and of the discharge of electricity through gases has supplied very strong experimental evidence in support of the fundamental ideas of the existing atomic theory. It has also indicated that the atom itself is not the smallest unit of matter, but is a complicated structure made up of a number of smaller bodies.

In Radio-activity (1905), 1.

The study of … simple cases would, I think, often be of advantage even to students whose mathematical attainments are sufficient to enable them to follow the solution of the more general cases. For in these simple cases the absence of analytical difficulties allows attention to be more easily concentrated on the physical aspects of the question, and thus gives the student a more vivid idea and a more manageable grasp of the subject than he would be likely to attain if he merely regarded electrical phenomena through a cloud of analytical symbols.

Elements of the Mathematical Theory of Electricity and Magnetism (189S), v-vi.

The suppression of uncomfortable ideas may be common in religion or in politics, but it is not the path to knowledge; it has no in the endeavor of science. We do not know in advance who will discover fundamental insights.

In Cosmos (1985), 74.

The task of physiological psychology remains the same in the analysis of ideas that it was in the investigation of sensations: to act as mediator between the neighbouring sciences of physiology and psychology.

The technologies which have had the most profound effects on human life are usually simple. A good example of a simple technology with profound historical consequences is hay. Nobody knows who invented hay, the idea of cutting grass in the autumn and storing it in large enough quantities to keep horses and cows alive through the winter. All we know is that the technology of hay was unknown to the Roman Empire but was known to every village of medieval Europe. Like many other crucially important technologies, hay emerged anonymously during the so-called Dark Ages. According to the Hay Theory of History, the invention of hay was the decisive event which moved the center of gravity of urban civilization from the Mediterranean basin to Northern and Western Europe. The Roman Empire did not need hay because in a Mediterranean climate the grass grows well enough in winter for animals to graze. North of the Alps, great cities dependent on horses and oxen for motive power could not exist without hay. So it was hay that allowed populations to grow and civilizations to flourish among the forests of Northern Europe. Hay moved the greatness of Rome to Paris and London, and later to Berlin and Moscow and New York. … Great inventions like hay and printing, whatever their immediate social costs may be, result in a permanent expansion of our horizons, a lasting acquisition of new territory for human bodies and minds to cultivate.

Infinite In All Directions (1988, 2004), 135. The book is a revised version of a series of the Gifford Lectures under the title ‘In Praise of Diversity’, given at Aberdeen, Scotland.

The test of a first-rate intelligence is the ability to hold two opposed ideas in mind at the same time and still retain the ability to function.

The Crack-Up (1936, 1993), 69.

The theoretical idea … does not arise apart from and independent of experience; nor can it be derived from experience by a purely logical procedure. It is produced by a creative act. Once a theoretical idea has been acquired, one does well to hold fast to it until it leads to an untenable conclusion.

‘On the Generalized Theory of Gravitation’, Scientific American (Apr 1950). Collected in David H. Levy (ed.), The Scientific American Book of the Cosmos (2000), 14.

The theory of numbers is particularly liable to the accusation that some of its problems are the wrong sort of questions to ask. I do not myself think the danger is serious; either a reasonable amount of concentration leads to new ideas or methods of obvious interest, or else one just leaves the problem alone. “Perfect numbers” certainly never did any good, but then they never did any particular harm.

In A Mathematician’s Miscellany (1953). Reissued as Béla Bollobás (ed.), Littlewood’s Miscellany (1986), 74.

The truly scientific mind is altogether unafraid of the new, and while having no mercy for ideas which have served their turn or shown their uselessness, it will not grudge to any unfamiliar conception its moment of full and friendly attention, hoping to expand rather than to minimize what small core of usefulness it may happen to contain.

In ‘Observation and Experiment and Their Use in the Medical Sciences’, British Medical Journal (1930), 2, 129-34. As cited in Edward J. Huth and T.J. Murray, Medicine in Quotations: Views of Health and Disease Through the Ages (2006), 357 and 512.

The universe is merely a fleeting idea in God’s mind—a pretty uncomfortable thought, particularly if you’ve just made a down payment on a house.

In Getting Even (1971), 33.

The universe is of the nature of a thought or sensation in a universal Mind… To put the conclusion crudely—the stuff of the world is mind-stuff. As is often the way with crude statements, I shall have to explain that by “mind” I do not exactly mean mind and by “stuff” I do not at all mean stuff. Still that is about as near as we can get to the idea in a simple phrase. The mind-stuff of the world is something more general than our individual conscious minds; but we may think of its nature as not altogether foreign to feelings in our consciousness… Having granted this, the mental activity of the part of world constituting ourselves occasions no great surprise; it is known to us by direct self-knowledge, and we do not explain it away as something other than we know it to be—or rather, it knows itself to be.

From Gifford Lecture, Edinburgh, (1927), ‘Reality’, collected in The Nature of the Physical World (1928), 276.

The value of fundamental research does not lie only in the ideas it produces. There is more to it. It affects the whole intellectual life of a nation by determining its way of thinking and the standards by which actions and intellectual production are judged. If science is highly regarded and if the importance of being concerned with the most up-to-date problems of fundamental research is recognized, then a spiritual climate is created which influences the other activities. An atmosphere of creativity is established which penetrates every cultural frontier. Applied sciences and technology are forced to adjust themselves to the highest intellectual standards which are developed in the basic sciences. This influence works in many ways: some fundamental students go into industry; the techniques which are applied to meet the stringent requirements of fundamental research serve to create new technological methods. The style, the scale, and the level of scientific and technical work are determined in pure research; that is what attracts productive people and what brings scientists to those countries where science is at the highest level. Fundamental research sets the standards of modern scientific thought; it creates the intellectual climate in which our modern civilization flourishes. It pumps the lifeblood of idea and inventiveness not only into the technological laboratories and factories, but into every cultural activity of our time. The case for generous support for pure and fundamental science is as simple as that.

In ‘Why Pure Science?’ in Bulletin of the Atomic Scientists, 1965.

The vitality of thought is in adventure. Idea’s won’t keep. Something must be done about them. When the idea is new, its custodians have fervour, live for it, and, if need be, die for it. Their inheritors receive the idea, perhaps now strong and successful, but without inheriting the fervour; so the idea settles down to a comfortable middle age, turns senile, and dies.

In Alfred North Whitehead and Lucien Price (ed.), Dialogues of Alfred North Whitehead (1954, 1977), 100.

The Wegener hypothesis has been so stimulating and has such fundamental implications in geology as to merit respectful and sympathetic interest from every geologist. Some striking arguments in his favor have been advanced, and it would be foolhardy indeed to reject any concept that offers a possible key to the solution of profound problems in the Earth’s history.
Published while geologists remained sceptical of Alfred Wegener’s idea of Continental Drift, Though unconvinced, he published these thoughts suggesting that critics should be at least be open-minded. His patience was proven justified when two decades later, the theory of plate tectonics provided a mechanism for the motion of the continents.

Some Thoughts on the Evidence for Continental Drift (1944).

The White medullary Substance of the Brain is also the immediate Instrument, by which Ideas are presented to the Mind: Or, in other Words, whatever Changes are made in this Substance, corresponding Changes are made in our Ideas; and vice versa.

Observations on Man, His Frame, His Duty, and His Expectations (1749), part 1, 8.

The whole inherent pride of human nature revolts at the idea that the lord of the creation is to be treated like any other natural object. No sooner does the naturalist discover the resemblance of some higher mammals, such as the ape, to man, than there is a general outcry against the presumptuous audacity that ventures to touch man in his inmost sanctuary. The whole fraternity of philosophers, who have never seen monkeys except in zoological gardens, at once mount the high horse, and appeal to the mind, the soul, to reason, to consciousness, and to all the rest of the innate faculties of man, as they are refracted in their own philosophical prisms.

From Carl Vogt and James Hunt (ed.), Lectures on Man: His Place in Creation, and in the History of the Earth (1861), 10.

The whole question of imagination in science is often misunderstood by people in other disciplines. They try to test our imagination in the following way. They say, “Here is a picture of some people in a situation. What do you imagine will happen next?” When we say, “I can’t imagine,” they may think we have a weak imagination. They overlook the fact that whatever we are allowed to imagine in science must be consistent with everything else we know; that the electric fields and the waves we talk about are not just some happy thoughts which we are free to make as we wish, but ideas which must be consistent with all the laws of physics we know. We can’t allow ourselves to seriously imagine things which are obviously in contradiction to the laws of nature. And so our kind of imagination is quite a difficult game. One has to have the imagination to think of something that has never been seen before, never been heard of before. At the same time the thoughts are restricted in a strait jacket, so to speak, limited by the conditions that come from our knowledge of the way nature really is. The problem of creating something which is new, but which is consistent with everything which has been seen before, is one of extreme difficulty

In The Feynman Lectures in Physics (1964), Vol. 2, Lecture 20, p.20-10 to p.20-11.

The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite hierarchy and absolute evidence of the truths with which it is concerned, these, and such like, are the surest grounds of the title of mathematics to human regard, and would remain unimpeached and unimpaired were the plan of the universe unrolled like a map at our feet, and the mind of man qualified to take in the whole scheme of creation at a glance.

In Presidential Address to British Association (19 Aug 1869), ‘A Plea for the Mathematician’, published in Nature (6 Jan 1870), 1, 262. Collected in Collected Mathematical Papers (1908), Vol. 2, 659.

The worth of a new idea is invariably determined, not by the degree of its intuitiveness—which incidentally, is to a major extent a matter of experience and habit—but by the scope and accuracy of the individual laws to the discovery of which it eventually leads.

In Scientific Autobiography and Other Papers (1968), 109-110.

The Wright Brothers created the single greatest cultural force since the invention of writing. The airplane became the first World Wide Web, bringing people, languages, ideas, and values together.

……

The ‘mad idea’ which will lie at the basis of a future fundamental physical theory will come from a realization that physical meaning has some mathematical form not previously associated with reality. From this point of view the problem of the ‘mad idea’ is the problem of choosing, not of generating, the right idea. One should not understand that too literally. In the 1960s it was said (in a certain connection) that the most important discovery of recent years in physics was the complex numbers. The author [Yuri Manin] has something like that in mind.

Mathematics and Physics (1981), Foreward. Reprinted in Mathematics as Metaphor: Selected Essays of Yuri I. Manin (2007), 90.

The “seriousness” of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.

In A Mathematician’s Apology (1940, 2012), 89.

Then I had shown, in the same place, what the structure of the nerves and muscles of the human body would have to be in order for the animal spirits in the body to have the power to move its members, as one sees when heads, soon after they have been cut off, still move and bite the ground even though they are no longer alive; what changes must be made in the brain to cause waking, sleep and dreams; how light, sounds, odours, tastes, warmth and all the other qualities of external objects can impress different ideas on it through the senses; how hunger, thirst, and the other internal passions can also send their ideas there; what part of the brain should be taken as “the common sense”, where these ideas are received; what should be taken as the memory, which stores the ideas, and as the imagination, which can vary them in different ways and compose new ones and, by the same means, distribute the animal spirits to the muscles, cause the limbs of the body to move in as many different ways as our own bodies can move without the will directing them, depending on the objects that are present to the senses and the internal passions in the body. This will not seem strange to those who know how many different automata or moving machines can be devised by human ingenuity, by using only very few pieces in comparison with the larger number of bones, muscles, nerves, arteries, veins and all the other parts in the body of every animal. They will think of this body like a machine which, having been made by the hand of God, is incomparably better structured than any machine that could be invented by human beings, and contains many more admirable movements.

Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 5, 39-40.

There are also two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible: truths of fact are contingent and their opposite is possible. When a truth is necessary, reason can be found by analysis, resolving it into more simple ideas and truths, until we come to those which are primary.

The Monadology and Other Philosophical Writings (1714), trans. Robert Latta (1898), 235-6.

There are many hypotheses in science which are wrong. That’s perfectly all right; they’re the aperture to finding out what’s right. Science is a self-correcting process. To be accepted, new ideas must survive the most rigorous standards of evidence and scrutiny.

Quoted in Donald R. Prothero and Carl Dennis Buell, Evolution: What the Fossils Say and Why it Matters (2007), 3.

There are things out there that are very simple and you never think would work. … Wikipedia is one of those that it would never occur to me that something like that would work. … But it does work. … People who have taken fairly simple ideas, … at a certain scale and after they gain a certain amount of momentum, they can really take off and work. And that’s really an amazing thing.

Guest Lecture, UC Berkeley, ‘Search Engines, Technology, and Business’ (3 Oct 2005). At 1:13 in the YouTube video.

There are three creative ideas which, each in its turn, have been central to science. They are the idea of order, the idea of causes, and the idea of chance.

From The Common Sense of Science (1951), 145.

There are three ruling ideas, three so to say, spheres of thought, which pervade the whole body of mathematical science, to some one or other of which, or to two or all three of them combined, every mathematical truth admits of being referred; these are the three cardinal notions, of Number, Space and Order.
Arithmetic has for its object the properties of number in the abstract. In algebra, viewed as a science of operations, order is the predominating idea. The business of geometry is with the evolution of the properties of space, or of bodies viewed as existing in space.

In ‘A Probationary Lecture on Geometry, York British Association Report (1844), Part 2; Collected Mathematical Papers, Vol. 2, 5.

There are young people who constantly come to tell me: you, too, are making Op Art. I haven’t the slightest idea what that is, Op Art. I’ve been doing this work for thirty years now.

As quoted, without citation, on the mcescher.com website.

There are, at present, fundamental problems in theoretical physics … the solution of which … will presumably require a more drastic revision of our fundmental concepts than any that have gone before. Quite likely, these changes will be so great that it will be beyond the power of human intelligence to get the necessary new ideas by direct attempts to formulate the experimental data in mathematical terms. The theoretical worker in the future will, therefore, have to proceed in a more direct way. The most powerful method of advance that can be suggested at present is to employ all the resources of pure mathematics in attempts to perfect and generalize the mathematical formalism that forms the existing basis of theoretical physics, and after each success in this direction, to try to interpret the new mathematical features in terms of physical entities.
At age 28.

Proceedings of the Royal Society (1931), A133, 60. In A. Pais, ‘Playing With Equations, the Dirac Way’. Behram N. Kursunoglu (Ed.) and Eugene Paul Wigner (Ed.), Paul Adrien Maurice Dirac: Reminiscences about a Great Physicist (1990), 109.

There is a noble vision of the great Castle of Mathematics, towering somewhere in the Platonic World of Ideas, which we humbly and devotedly discover (rather than invent). The greatest mathematicians manage to grasp outlines of the Grand Design, but even those to whom only a pattern on a small kitchen tile is revealed, can be blissfully happy. … Mathematics is a proto-text whose existence is only postulated but which nevertheless underlies all corrupted and fragmentary copies we are bound to deal with. The identity of the writer of this proto-text (or of the builder of the Castle) is anybody’s guess. …

In ‘Mathematical Knowledge: Internal, Social, and Cultural Aspects’, Mathematics As Metaphor: Selected Essays (2007), 4.

There is always the danger in scientific work that some word or phrase will be used by different authors to express so many ideas and surmises that, unless redefined, it loses all real significance.

‘Valence and Tautomerism’, Journal of the American Chemical Society (1913), 35, 1448.

There is in the chemist a form of thought by which all ideas become visible in the mind as strains of an imagined piece of music. This form of thought is developed in Faraday in the highest degree, whence it arises that to one who is not acquainted with this method of thinking, his scientific works seem barren and dry, and merely a series of researches strung together, while his oral discourse when he teaches or explains is intellectual, elegant, and of wonderful clearness.

Autobiography, 257-358. Quoted in William H. Brock, Justus Von Liebig (2002), 9.

There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.

From ‘The Power of Words’, collected in Siân Miles (ed.), Simone Weil: An Anthology (2000), 222-223.

There is no royal road to learning. But it is equally an error to confine attention to technical processes, excluding consideration of general ideas. Here lies the road to pedantry.

In An Introduction to Mathematics (1911), 8.

There is no science which does not spring from pre-existing knowledge, and no certain and definite idea which has not derived its origin from the senses.

In Willis (trans.) and Alex Bowie (trans.), ‘The First Anatomical Disquisition on the Circulation of the Blood, Addressed to Jo. Riolan’, On the Motion of the Heart and Blood in Animals (1889), 93.

There is no substitute for honest, thorough, scientific effort to get correct data (no matter how much of it clashes with preconceived ideas). There is no substitute for actually reaching a correct claim of reasoning. Poor data and good reasoning give poor results. Good data and poor reasoning give poor results. Poor data and poor reasoning give rotten results.

In ‘Right Answers—A Short Guide for Obtaining Them,’ Computers and Automation, September 1969.

There is now a feeling that the pieces of physics are falling into place, not because of any single revolutionary idea or because of the efforts of any one physicist, but because of a flowering of many seeds of theory, most of them planted long ago.

In ‘The Forces of Nature’, Bulletin of the American Academy of Arts and Sciences (Jan 1976), 29:4, 14.

There is one thing stronger than all the armies in the world; and that is an idea whose time has come.

The Nation, 15 April 1943.

There is thus a possibility that the ancient dream of philosophers to connect all Nature with the properties of whole numbers will some day be realized. To do so physics will have to develop a long way to establish the details of how the correspondence is to be made. One hint for this development seems pretty obvious, namely, the study of whole numbers in modern mathematics is inextricably bound up with the theory of functions of a complex variable, which theory we have already seen has a good chance of forming the basis of the physics of the future. The working out of this idea would lead to a connection between atomic theory and cosmology.

From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), ‘The Relation Between Mathematics And Physics’, printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 129.

There may be times when what is most needed is, not so much a new discovery or a new idea as a different “slant”; I mean a comparatively slight readjustment in our way of looking at the things and ideas on which attention is already fixed.

In Saving the Appearances (1957), 11.

There must be a marsh in the brains of these men or there would not be so many frogs of wrong ideas gathered in their heads.

From the play Galileo Galilei (2001) .

There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, … the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its solution must be obtained. By the labours of LaGrange, the motions of a disturbed planet are reduced with all their complication and variety to a purely mathematical question. It then ceases to be a physical problem; the disturbed and disturbing planet are alike vanished: the ideas of time and force are at an end; the very elements of the orbit have disappeared, or only exist as arbitrary characters in a mathematical formula

Address to the Mechanics Institute, ‘An Address on the Genius and Discoveries of Sir Isaac Newton’ (1835), excerpted in paper by Luis M. Laita, Luis de Ledesma, Eugenio Roanes-Lozano and
Alberto Brunori, ‘George Boole, a Forerunner of Symbolic Computation’, collected in John A. Campbell and Eugenio Roanes-Lozano (eds.), Artificial Intelligence and Symbolic Computation: International Conference AISC 2000 (2001), 3.

There’s a touch of the priesthood in the academic world, a sense that a scholar should not be distracted by the mundane tasks of day-to-day living. I used to have great stretches of time to work. Now I have research thoughts while making peanut butter and jelly sandwiches. Sure it’s impossible to write down ideas while reading “Curious George” to a two-year-old. On the other hand, as my husband was leaving graduate school for his first job, his thesis advisor told him, “You may wonder how a professor gets any research done when one has to teach, advise students, serve on committees, referee papers, write letters of recommendation, interview prospective faculty. Well, I take long showers.”

In ‘In Her Own Words: Six Mathematicians Comment on Their Lives and Careers: Susan Landau’, Notices of the AMS (Sep 1991), 38, No. 7, 704.

These changes—the more rapid pulse, the deeper breathing, the increase of sugar in the blood, the secretion from the adrenal glands—were very diverse and seemed unrelated. Then, one wakeful night, after a considerable collection of these changes had been disclosed, the idea flashed through my mind that they could be nicely integrated if conceived as bodily preparations for supreme effort in flight or in fighting. Further investigation added to the collection and confirmed the general scheme suggested by the hunch.

The Way of an Investigator: A Scientist’s Experiences in Medical Research (1945), 59-60.

These Disciplines [mathematics] serve to inure and corroborate the Mind to a constant Diligence in Study; to undergo the Trouble of an attentive Meditation, and cheerfully contend with such Difficulties as lie in the Way. They wholly deliver us from a credulous Simplicity, most strongly fortify us against the Vanity of Scepticism, effectually restrain from a rash Presumption, most easily incline us to a due Assent, perfectly subject us to the Government of right Reason, and inspire us with Resolution to wrestle against the unjust Tyranny of false Prejudices. If the Fancy be unstable and fluctuating, it is to be poized by this Ballast, and steadied by this Anchor, if the Wit be blunt it is sharpened upon this Whetstone; if luxuriant it is pared by this Knife; if headstrong it is restrained by this Bridle; and if dull it is rouzed by this Spur. The Steps are guided by no Lamp more clearly through the dark Mazes of Nature, by no Thread more surely through the intricate Labyrinths of Philosophy, nor lastly is the Bottom of Truth sounded more happily by any other Line. I will not mention how plentiful a Stock of Knowledge the Mind is furnished from these, with what wholesome Food it is nourished, and what sincere Pleasure it enjoys. But if I speak farther, I shall neither be the only Person, nor the first, who affirms it; that while the Mind is abstracted and elevated from sensible Matter, distinctly views pure Forms, conceives the Beauty of Ideas, and investigates the Harmony of Proportions; the Manners themselves are sensibly corrected and improved, the Affections composed and rectified, the Fancy calmed and settled, and the Understanding raised and excited to more divine Contemplations. All which I might defend by Authority, and confirm by the Suffrages of the greatest Philosophers.

Prefatory Oration in Mathematical Lectures (1734), xxxi.

They think that differential equations are not reality. Hearing some colleagues speak, it’s as though theoretical physics was just playing house with plastic building blocks. This absurd idea has gained currency, and now people seem to feel that theoretical physicists are little more than dreamers locked away ivory towers. They think our games, our little houses, bear no relation to their everyday worries, their interests, their problems, or their welfare. But I’m going to tell you something, and I want you to take it as a ground rule for this course. From now on I will be filling this board with equations. … And when I’m done, I want you to do the following: look at those numbers, all those little numbers and Greek letters on the board, and repeat to yourselves, “This is reality,” repeat it over and over.

Zig Zag, trans. Lisa Dillman (2008), 63.

They [mathematicians] only take those things into consideration, of which they have clear and distinct ideas, designating them by proper, adequate, and invariable names, and premising only a few axioms which are most noted and certain to investigate their affections and draw conclusions from them, and agreeably laying down a very few hypotheses, such as are in the highest degree consonant with reason and not to be denied by anyone in his right mind. In like manner they assign generations or causes easy to be understood and readily admitted by all, they preserve a most accurate order, every proposition immediately following from what is supposed and proved before, and reject all things howsoever specious and probable which can not be inferred and deduced after the same manner.

In Mathematical Lectures (1734), 65-66.

Thinking is merely the comparing of ideas, discerning relations of likeness and of difference between ideas, and drawing inferences. It is seizing general truths on the basis of clearly apprehended particulars. It is but generalizing and particularizing. Who will deny that a child can deal profitably with sequences of ideas like: How many marbles are 2 marbles and 3 marbles? 2 pencils and 3 pencils? 2 balls and 3 balls? 2 children and 3 children? 2 inches and 3 inches? 2 feet and 3 feet? 2 and 3? Who has not seen the countenance of some little learner light up at the end of such a series of questions with the exclamation, “Why it’s always that way. Isn’t it?” This is the glow of pleasure that the generalizing step always affords him who takes the step himself. This is the genuine life-giving joy which comes from feeling that one can successfully take this step. The reality of such a discovery is as great, and the lasting effect upon the mind of him that makes it is as sure as was that by which the great Newton hit upon the generalization of the law of gravitation. It is through these thrills of discovery that love to learn and intellectual pleasure are begotten and fostered. Good arithmetic teaching abounds in such opportunities.

In Arithmetic in Public Education (1909), 13. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 68.

Thinking must never submit itself, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, if not to facts themselves, because, for it, to submit would be to cease to be.

……

This is what writers mean when they say that the notion of cause involves the idea of necessity. If there be any meaning which confessedly belongs to the term necessity, it is unconditionalness. That which is necessary, that which must be, means that which will be, whatever supposition we may make in regard to all other things.

A System of Logic, Ratiocinative and Inductive (1858), 203.

This therefore is Mathematics:
She reminds you of the invisible forms of the soul;
She gives life to her own discoveries;
She awakens the mind and purifies the intellect;
She brings light to our intrinsic ideas;
She abolishes oblivion and ignorance which are ours by birth…

Quoted in Benjamin Franklin Finkel, Mathematical Association of America, The American Mathematical Monthly (1947), Vol. 54, 425.

This whole period was a golden age of immunology, an age abounding in important synthetic discoveries all over the world, a time we all thought it was good to be alive. We, who were working on these problems, all knew each other and met as often as we could to exchange ideas and hot news from the laboratory.

In Memoir of a Thinking Radish: An Autobiography (1986), 135.

This whole theory of electrostatics constitutes a group of abstract ideas and general propositions, formulated in the clear and precise language of geometry and algebra, and connected with one another by the rules of strict logic. This whole fully satisfies the reason of a French physicist and his taste for clarity, simplicity and order. The same does not hold for the Englishman. These abstract notions of material points, force, line of force, and equipotential surface do not satisfy his need to imagine concrete, material, visible, and tangible things. ‘So long as we cling to this mode of representation,’ says an English physicist, ‘we cannot form a mental representation of the phenomena which are really happening.’ It is to satisfy the need that he goes and creates a model.
The French or German physicist conceives, in the space separating two conductors, abstract lines of force having no thickness or real existence; the English physicist materializes these lines and thickens them to the dimensions of a tube which he will fill with vulcanised rubber. In place of a family of lines of ideal forces, conceivable only by reason, he will have a bundle of elastic strings, visible and tangible, firmly glued at both ends to the surfaces of the two conductors, and, when stretched, trying both to contact and to expand. When the two conductors approach each other, he sees the elastic strings drawing closer together; then he sees each of them bunch up and grow large. Such is the famous model of electrostatic action imagined by Faraday and admired as a work of genius by Maxwell and the whole English school.
The employment of similar mechanical models, recalling by certain more or less rough analogies the particular features of the theory being expounded, is a regular feature of the English treatises on physics. Here is a book* [by Oliver Lodge] intended to expound the modern theories of electricity and to expound a new theory. In it are nothing but strings which move around pulleys, which roll around drums, which go through pearl beads, which carry weights; and tubes which pump water while others swell and contract; toothed wheels which are geared to one another and engage hooks. We thought we were entering the tranquil and neatly ordered abode of reason, but we find ourselves in a factory.
*Footnote: O. Lodge, Les Théories Modernes (Modern Views on Electricity) (1889), 16.

The Aim and Structure of Physical Theory (1906), 2nd edition (1914), trans. Philip P. Wiener (1954), 70-1.

Those intervening ideas, which serve to show the agreement of any two others, are called proofs; and where the agreement or disagreement is by this means plainly and clearly perceived, it is called demonstration; it being shown to the understanding, and the mind made to see that it is so. A quickness in the mind to find out these intermediate ideas, (that shall discover the agreement or disagreement of any other) and to apply them right, is, I suppose, that which is called sagacity.

In An Essay concerning Human Understanding, Bk. 6, chaps. 2, 3.

Those who are unacquainted with the details of scientific investigation have no idea of the amount of labour expended in the determination of those numbers on which important calculations or inferences depend. They have no idea of the patience shown by a Berzelius in determining atomic weights; by a Regnault in determining coefficients of expansion; or by a Joule in determining the mechanical equivalent of heat.

In Sound: A Course of Eight Lectures Delivered at the Royal Institution of Great Britain (1867), 26.

Those who consider James Watt only as a great practical mechanic form a very erroneous idea of his character: he was equally distinguished as a natural philosopher and a chemist, and his inventions demonstrate his profound knowledge of those sciences, and that peculiar characteristic of genius, the union of them for practical application.

As reported in Proceedings of the Public Meeting held at Preemasons’ Hall, on the 18th June, 1824, for Erecting a Monument to the Late James Watt (1824), 8.

Those [scientists] who dislike entertaining contradictory thoughts are unlikely to enrich their science with new ideas.

Attributed. (If you know a primary source, please contact webmaster.)

Thought, looked at from the inside, is not a mechanical succession of ideas, but a cry for ‘more light’.

In The Nature Of Thought Vol. 1 (1921), 459.

Thus ordered thinking arises out of the ordered course of nature in which man finds himself, and this thinking is from the beginning nothing more than the subjective reproduction of the regularity according to the law of natural phenomena. On the other hand, this reproduction is only possible by means of the will that controls the concatenation of ideas.

An Introduction to Psychology (1912)

Time, which measures everything in our idea, and is often deficient to our schemes, is to nature endless and as nothing; it cannot limit that by which alone it had existence; and as the natural course of time, which to us seems infinite, cannot be bounded by any operation that may have an end, the progress of things upon this globe, that is, the course of nature, cannot be limited by time, which must proceed in a continual succession.

‘Theory of the Earth’, Transactions of the Royal Society of Edinburgh (1788), 1, 215.

To appreciate a work of art we need bring with us nothing from life, no knowledge of its ideas and affairs, no familiarity with its emotions. Art transports us from the world of man’s activity to a world of æsthetic exaltation. For a moment we are shut off from human interests; our anticipations and memories are arrested; we are lifted above the stream of life. The pure mathematician rapt in his studies knows a state of mind which I take to be similar, if not identical. He feels an emotion for his speculations which arises from no perceived relation between them and the lives of men, but springs, inhuman or super-human, from the heart of an abstract science. I wonder, sometimes, whether the appreciators of art and of mathematical solutions are not even more closely allied.

In Art (1913), 25.

To be genuinely thoughtful, we must be willing to sustain and protract that state of doubt which is the stimulus to thorough enquiry, so as not to accept an idea or make a positive assertion of a belief, until justifying reasons have been found.

In How We Think (1933), 16.

To bring scientific investigation to a happy end once appropriate methods have been determined, we must hold firmly in mind the goal of the project. The object here is to focus the train of thought on more and more complex and accurate associations between images based on observation and ideas slumbering in the unconscious.

From Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), 33.

To consider the matter aright, reason is nothing but a wonderful and unintelligible instinct in our souls, which carries us along a certain train of ideas, and endows them with particular qualities, according to their particular situations and relations. This instinct, ’tis true, arises from past observation and experience; but can anyone give the ultimate reason, why past experience and observation produces such an effect, any more than why nature alone should produce it?

A Treatise on Human Nature (1739-40), ed. L. A. Selby-Bigge (1888), book 1, part 3, section 16, 179.

To emphasize this opinion that mathematicians would be unwise to accept practical issues as the sole guide or the chief guide in the current of their investigations, … let me take one more instance, by choosing a subject in which the purely mathematical interest is deemed supreme, the theory of functions of a complex variable. That at least is a theory in pure mathematics, initiated in that region, and developed in that region; it is built up in scores of papers, and its plan certainly has not been, and is not now, dominated or guided by considerations of applicability to natural phenomena. Yet what has turned out to be its relation to practical issues? The investigations of Lagrange and others upon the construction of maps appear as a portion of the general property of conformal representation; which is merely the general geometrical method of regarding functional relations in that theory. Again, the interesting and important investigations upon discontinuous two-dimensional fluid motion in hydrodynamics, made in the last twenty years, can all be, and now are all, I believe, deduced from similar considerations by interpreting functional relations between complex variables. In the dynamics of a rotating heavy body, the only substantial extension of our knowledge since the time of Lagrange has accrued from associating the general properties of functions with the discussion of the equations of motion. Further, under the title of conjugate functions, the theory has been applied to various questions in electrostatics, particularly in connection with condensers and electrometers. And, lastly, in the domain of physical astronomy, some of the most conspicuous advances made in the last few years have been achieved by introducing into the discussion the ideas, the principles, the methods, and the results of the theory of functions. … the refined and extremely difficult work of Poincare and others in physical astronomy has been possible only by the use of the most elaborate developments of some purely mathematical subjects, developments which were made without a thought of such applications.

In Presidential Address British Association for the Advancement of Science, Section A, (1897), Nature, 56, 377.

To most … of us, Russia was as mysterious and remote as the other side of the moon and not much more productive when it came to really new ideas or inventions. A common joke of the time [mid 1940s] said that the Russians could not surreptitiously introduce nuclear bombs in suitcases into the United States because they had not yet been able to perfect a suitcase.

In Richard Rhodes, The Making of the Atomic Bomb (1986), 760.

To see the clear, logical ideas gradually being disentangled from vagueness and confusion is vastly more instructive than simply starting with the logical ideas.

In ‘Projective Geometery’, Prelude to Mathematics (1955), 145.

To wage war with Marchand or anyone else again will benefit nobody and bring little profit to science. You consume yourself in this way, you ruin your liver and eventually your nerves with Morrison pills. Imagine the year 1900 when we have disintegrated into carbonic acid, ammonia and water and our bone substance is perhaps once more a constituent of the bones of the dog who defiles our graves. Who will then worry his head as to whether we have lived in peace or anger, who then will know about your scientific disputes and of your sacrifice of health and peace of mind for science? Nobody. But your good ideas and the discoveries you have made, cleansed of all that is extraneous to the subject, will still be known and appreciated for many years to come. But why am I trying to advise the lion to eat sugar.

Letter from Wohler to Liebig (9 Mar 1843). In A. W. Hofmann (ed.), Aus Justus Liebigs und Friedrich Wohlers Briefwechsel (1888), Vol. 1, 224. Trans. Ralph Oesper, The Human Side of Scientists (1975), 205.

Too much openness and you accept every notion, idea, and hypothesis—which is tantamount to knowing nothing. Too much skepticism—especially rejection of new ideas before they are adequately tested—and you’re not only unpleasantly grumpy, but also closed to the advance of science. A judicious mix is what we need.

In ‘Wonder and Skepticism’, Skeptical Enquirer (Jan-Feb 1995), 19, No. 1.

True physics was founded the day when Galileo, rejecting fruitless speculations, conceived the idea … of defining the general form to give to experiments, by assigning for their immediate purpose the measure of all that can be measurable in natural phenomena.

From the original French, “La vraie physique a été fondée le jour où Galilée, rejetant des spéculations depuis si longtemps stériles, a conçu l’idée … de préciser la forme générale à donner aux expériences, en leur assignant pour objet immédiat la mesure de tout ce qui peut être mesurable dans les phénomènes naturels,” in De l’origine et des limites de la correspondance entre l’algèbre et la géométrie (1847), 375. English version by Webmaster using Google translate. This may be the basis of Thomas-Henri Martin describing Galileo’s experimental method , often translated as Measure what is measurable, and make measurable what is not so, from the original French in Galilée: Les droits de la science et la méthode des sciences physiques (1868), 289. Note that in both cases, the words were narrative by the authors, not quoting actual words by Galileo. What the authors wrote was in their own words, and should not be attributed to Galileo with quotation marks.

Truth is a dangerous word to incorporate within the vocabulary of science. It drags with it, in its train, ideas of permanence and immutability that are foreign to the spirit of a study that is essentially an historically changing movement, and that relies so much on practical examination within restricted circumstances. … Truth is an absolute notion that science, which is not concerned with any such permanency, had better leave alone.

In The Universe of Science (1933).

Under certain given circumstances, and only under those circumstances, an agglomeration of men presents new characteristics very different from those of the individuals composing it. The sentiments and ideas of all the persons in the gathering take one and the same direction, and their conscious personality vanishes. A collective mind is formed, doubtless transitory, but presenting very clearly defined characteristics. The gathering has thus become what, in the absence of a better expression, I will call an organized crowd, or, if the term is considered preferable, a psychological crowd. It forms a single being and is subject to the law of the mental unity of crowds.

From Psychologie des Foules (1895), 12. English text in The Crowd: A Study of the Popular Mind (1897), Book 1, Chap. 1, 1-2. The original French text is, “Dans certaines circonstances données, et seulement dans ces circonstances, une agglomération d’hommes possède des caractères nouveaux fort différents de ceux des individus composant cette agglomération. La personnalité consciente s’évanouit, les sentiments et les idées de toutes les unités sont orientés dans une même direction. Il se forme une âme collective, transitoire sans doute, mais présentant des caractères très nets. La collectivité est alors devenue ce que, faute d’une expression meilleure, j’appellerai une foule organisée, ou, si l’on préfère, une foule psychologique. Elle forme un seul être et se trouve soumise à la loi de l’unité mentale des foules.”

Under the… new hypothesis [of Continental Drift] certain geological concepts come to acquire a new significance amounting in a few cases to a complete inversion of principles, and the inquirer will find it necessary to re-orient his ideas. For the first time he will get glimpses… of a pulsating restless earth, all parts of which are in greater or less degree of movement in respect to the axis of rotation, having been so, moreover, throughout geological time. He will have to leave behind him—perhaps reluctantly—the dumbfounding spectacle of the present continental masses, firmly anchored to a plastic foundation yet remaining fixed in space; set thousands of kilometres apart, it may be, yet behaving in almost identical fashion from epoch to epoch and stage to stage like soldiers, at drill; widely stretched in some quarters at various times and astoundingly compressed in others, yet retaining their general shapes, positions and orientations; remote from one another through history, yet showing in their fossil remains common or allied forms of terrestrial life; possessed during certain epochs of climates that may have ranged from glacial to torrid or pluvial to arid, though contrary to meteorological principles when their existing geographical positions are considered -to mention but a few such paradoxes!

Our Wandering Continents: An Hypothesis of Continental Drifting (1937), 3.

Uniform ideas originating among entire peoples unknown to each other must have a common ground of truth.

In The New Science (3rd ed., 1744), Book 1, Para. 144, as translated by Thomas Goddard Bergin and Max Harold Fisch, The New Science of Giambattista Vico (1948), 57.

Von Helmholtz, the great German physicist said that after previous investigation of a problem “in all directions … happy ideas came unexpectedly without effort like an inspiration.” He found that ideas did not come to him when his mind was fatigued or when at the working table, but often in the morning after a night’s rest or during the slow ascent of wooded hills on a sunny day.

In The Art of Scientific Investigation (1950), 69.

Von Neumann gave me an interesting idea: that you don’t have to be responsible for the world that you’re in. So I have developed a very powerful sense of social irresponsibility as a result of Von Neumann’s advice. It’s made me a very happy man ever since.

In ‎’Los Alamos From Below’, “Surely You’re Joking, Mr. Feynman!”: Adventures of a Curious Character (1997, 2010), 132, a collection of stories told to Ralph Leighton and edited by Edward Hutchings.

We are apt to consider that invention is the result of spontaneous action of some heavenborn genius, whose advent we must patiently wait for, but cannot artificially produce. It is unquestionable, however, that education, legal enactments, and general social conditions have a stupendous influence on the development of the originative faculty present in a nation and determine whether it shall be a fountain of new ideas or become simply a purchaser from others of ready-made inventions.

Epigraph, without citation, in Roger Cullisin, Patents, Inventions and the Dynamics of Innovation: A Multidisciplinary Study (2007), ix.

We are just beginning to understand how molecular reaction systems have found a way to “organize themselves”. We know that processes of this nature ultimately led to the life cycle, and that (for the time being?) Man with his central nervous system, i.e. his memory, his mind, and his soul, stands at the end of this development and feels compelled to understand this development. For this purpose he must penetrate into the smallest units of time and space, which also requires new ideas to make these familiar concepts from physics of service in understanding what has, right into our century, appeared to be beyond the confines of space and time.

Answering “Where Now?” as the conclusion of his Nobel Lecture (11 Dec 1967) on ‘Immeasurably Fast Reactions’, published in Nobel Lectures, Chemistry 1963-1970 (1972).

We are not to think that Jupiter has four satellites given him by nature, in order, by revolving round him, to immortalize the name of the Medici, who first had notice of the observation. These are the dreams of idle men, who love ludicrous ideas better than our laborious and industrious correction of the heavens.—Nature abhors so horrible a chaos, and to the truly wise, such vanity is detestable.

From Nodus Gordius, Appendix, as cited in John Elliot Drinkwater Bethune, Life of Galileo Galilei: With Illustrations of the Advancement of Experimental Philosophy (1832), 93.

We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context.

Unterrichtsblätter für Mathematik und Naturwissenschaften (1932), 38, 177-188. As translated by Abe Shenitzer, in ‘Part I. Topology and Abstract Algebra as Two Roads of Mathematical Comprehension’, The American Mathematical Monthly (May 1995), 102, No. 7, 453.

We are told that “Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.” I think no statement could have been made more opposite to the facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activities of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world (to which the inner one in each individual man may, I think, be conceived to stand somewhat in the same relation of correspondence as a shadow to the object from which it is projected, or as the hollow palm of one hand to the closed fist which it grasps of the other), that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of the imagination and invention.

In Presidential Address to British Association, Exeter British Association Report (1869), pp. 1-9, in Collected Mathematical Papers, Vol. 2, 654.

We are too ready to accept others and ourselves as we are and to assume that we are incapable of change. We forget the idea of growth, or we do not take it seriously. There is no good reason why we should not develop and change until the last day we live. Psychoanalysis is one of the most powerful means of helping us to realize this aim.

In ‘Dedication’, American Journal of Psychoanalysis (1942), 35, 99-100. As quoted and cited in Milton M. Berger, Women Beyond Freud: New Concepts Of Feminine Psychology (2013).

We are, perhaps, uniquely among the earth’s creatures, the worrying animal. We worry away our lives, fearing the future, discontent with the present, unable to take in the idea of dying, unable to sit still.

In The Medusa and the Snail: More Notes of a Biology Watcher (1974, 1995), 17.

We do not associate the idea of antiquity with the ocean, nor wonder how it looked a thousand years ago, as we do of the land, for it was equally wild and unfathomable always.

……

We find in the history of ideas mutations which do not seem to correspond to any obvious need, and at first sight appear as mere playful whimsies—such as Apollonius’ work on conic sections, or the non-Euclidean geometries, whose practical value became apparent only later.

In ‘Epilogue’, The Sleepwalkers: A History of Man’s Changing Vision of the Universe (1959), 515.

We greatly want a brief word to express the science of improving stock, which is by no means confined to questions of judicious mating, but which, especially in the case of man, takes cognisance of all influences that tend in however remote a degree to give to the more suitable races or strains of blood a better chance of prevailing speedily over the less suitable than they otherwise would have had. The word eugenics would sufficiently express the idea; it is at least a neater word and a more generalised one than viviculture, which I once ventured to use.
First use of the term Eugenics.

Inquiries into Human Faculty and its Development (1883), 25, footnote.

We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover up all the tracks, to not worry about the blind alleys or describe how you had the wrong idea first, and so on. So there isn’t any place to publish, in a dignified manner, what you actually did in order to get to do the work.

In his Nobel Prize Lecture (11 Dec 1965), ‘The Development of the Space-Time View of Quantum Electrodynamics’. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 155.

We have hitherto considered those Ideas, in the reception whereof, the Mind is only passive, which are those simple ones received from Sensation and Reflection before-mentioned, whereof the Mind cannot make anyone to it self, nor have any Idea which does not wholy consist of them. But as these simple Ideas are observed to exist in several Combinations united together; so the Mind has a power to consider several of them united together, as one Idea; and that not only as they are united in external Objects, but as it self has joined them. Ideas thus made up of several simple ones put together, I call Complex; such as are Beauty, Gratitude, a Man, an Army, the Universe; which tough complicated various simple Ideas, made up of simple ones, yet are, when the Mind pleases, considered each by if self, as one entire thing, and signified by one name.

An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 2, Chapter 12, Section 1, 163-4.

We have little more personal stake in cosmic destiny than do sunflowers or butterflies. The transfiguration of the universe lies some 50 to 100 billion years in the future; snap your fingers twice and you will have consumed a greater fraction of your life than all human history is to such a span. … We owe our lives to universal processes … and as invited guests we might do better to learn about them than to complain about them. If the prospect of a dying universe causes us anguish, it does so only because we can forecast it, and we have as yet not the slightest idea why such forecasts are possible for us. … Why should nature, whether hostile or benign, be in any way intelligible to us? All the mysteries of science are but palace guards to that mystery.

……

We have reason not to be afraid of the machine, for there is always constructive change, the enemy of machines, making them change to fit new conditions.
We suffer not from overproduction but from undercirculation. You have heard of technocracy. I wish I had those fellows for my competitors. I’d like to take the automobile it is said they predicted could be made now that would last fifty years. Even if never used, this automobile would not be worth anything except to a junkman in ten years, because of the changes in men’s tastes and ideas. This desire for change is an inherent quality in human nature, so that the present generation must not try to crystallize the needs of the future ones.
We have been measuring too much in terms of the dollar. What we should do is think in terms of useful materials—things that will be of value to us in our daily life.

In ‘Quotation Marks: Against Technocracy’, New York Times (1 Han 1933), E4.

We have simply arrived too late in the history of the universe to see this primordial simplicity easily … But although the symmetries are hidden from us, we can sense that they are latent in nature, governing everything about us. That’s the most exciting idea I know: that nature is much simpler than it looks. Nothing makes me more hopeful that our generation of human beings may actually hold the key to the universe in our hands—that perhaps in our lifetimes we may be able to tell why all of what we see in this immense universe of galaxies and particles is logically inevitable.

Quoted in Nigel Calder, The Key to the Universe: A Report on the New Physics (1978), 185.

We hence acquire this sublime and interesting idea; that all the calcareous mountains in the world, and all the strata of clay, coal, marl, sand, and iron, which are incumbent on them, are MONUMENTS OF THE PAST FELICITY OF ORGANIZED NATURE!

Phytologia (1800), 560.

We live in a cultural milieu … The idea that culture is our ecological niche is still applicable. The impact and force of natural selection on the human physique are conditioned by the dimensions of culture.

Interview with Pat Shipman, 21 January 1991. Quoted in Erik Trinkaus and Pat Shipman, The Neanderthals: Changing the Image of Mankind (1993), 334.

We live on an obscure hunk of rock and metal circling a humdrum sun, which is on the outskirts of a perfectly ordinary galaxy comprised of 400 billion other suns, which, in turn, is one of some hundred billion galaxies that make up the universe, which, current thinking suggests, is one of a huge number—perhaps an infinite number—of other closed-off universes. From that perspective, the idea that we’re at the center, that we have some cosmic importance, is ludicrous.

From interview with Linda Obst in her article ‘Valentine to Science’, in Interview (Feb 1996). Quoted and cited in Tom Head (ed.), Conversations with Carl Sagan (2006), ix, and cited on p.xix.

We may fondly imagine that we are impartial seekers after truth, but with a few exceptions, to which I know that I do not belong, we are influenced—and sometimes strongly—by our personal bias; and we give our best thoughts to those ideas which we have to defend.

(Said in Boston, 1929.) As quoted by E. Snorrason, ‘Krogh, Schack August Steenberg’, in Charles Coulton Gillispie (ed.), Dictionary of Scientific Biography (1973), Vol 7, 503.

We must remember that all our [models of flying machine] inventions are but developments of crude ideas; that a commercially successful result in a practically unexplored field cannot possibly be got without an enormous amount of unremunerative work. It is the piled-up and recorded experience of many busy brains that has produced the luxurious travelling conveniences of to-day, which in no way astonish us, and there is no good reason for supposing that we shall always be content to keep on the agitated surface of the sea and air, when it is possible to travel in a superior plane, unimpeded by frictional disturbances.

Paper to the Royal Society of New South Wales (4 Jun 1890), as quoted in Octave Chanute, Progress in Flying Machines (1894), 2226.

We must take the abiding spiritual values which inhere in the deep experiences of religion in all ages and give them new expression in terms of the framework which our new knowledge gives us. Science forces religion to deal with new ideas in the theoretical realm and new forces in the practical realm.

Address to Seventh Annual Midsummer Conferences of Ministers and Other Christian Workers, held by Union Theological Seminary, at Columbia University gymnasium (19 Jul 1927), as quoted in ‘Fosdick Sees Bible Outrun by Science’, New York Times (20 Jul 1927), 23.

We need a name for the new replicator, a noun that conveys the idea of a unit of cultural transmission, or a unit of imitation. ‘Mimeme’ comes from a suitable Greek root, but I want a monosyllable that sounds a bit like ‘gene’. I hope my classicist friends will forgive me if I abbreviate mimeme to meme. If it is any consolation, it could alternatively be thought of as being related to ‘memory’, or to the French word même. It should be pronounced to rhyme with ‘cream’.

In The Selfish Gene (1976).

We receive it as a fact, that some minds are so constituted as absolutely to require for their nurture the severe logic of the abstract sciences; that rigorous sequence of ideas which leads from the premises to the conclusion, by a path, arduous and narrow, it may be, and which the youthful reason may find it hard to mount, but where it cannot stray; and on which, if it move at all, it must move onward and upward… . Even for intellects of a different character, whose natural aptitude is for moral evidence and those relations of ideas which are perceived and appreciated by taste, the study of the exact sciences may be recommended as the best protection against the errors into which they are most likely to fall. Although the study of language is in many respects no mean exercise in logic, yet it must be admitted that an eminently practical mind is hardly to be formed without mathematical training.

In Orations and Speeches (1870), Vol. 8, 510.

We see, then, that the disappearance of the conscious personality, the predominance of the unconscious personality, the turning by means of suggestion and contagion of feelings and ideas in an identical direction, the tendency to immediately transform the suggested ideas into acts; these, we see, are the principal characteristics of the individual forming part of a crowd. He is no longer himself, but has become an automaton who has ceased to be guided by his will.

From Psychologie des Foules (1895), 20. English text in The Crowd: A Study of the Popular Mind (1897), Book 1, Chap. 1, 12. Original French text: “Donc, évanouissement de la personnalité consciente, prédominance de la personnalité inconsciente, orientation par voie de suggestion et de contagion des sentiments et des idées dans un même sens, tendance a transformer immédiatement en actes les idée suggérées, tels sont les principaux caractères de l’individu en foule. II n’est plus lui-même, il est devenu un automate que sa volonté ne guide plus.”

We see, then, that the elements of the scientific method are interrelated. Facts are necessary materials; but their working up by experimental reasoning, i.e., by theory, is what establishes and really builds up science. Ideas, given form by facts, embody science. A scientific hypothesis is merely a scientific idea, preconceived or previsioned. A theory is merely a scientific idea controlled by experiment. Reasoning merely gives a form to our ideas, so that everything, first and last, leads back to an idea. The idea is what establishes, as we shall see, the starting point or the primum movens of all scientific reasoning, and it is also the goal in the mind’s aspiration toward the unknown.

From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 26.

We seem to have a compulsion these days to bury time capsules in order to give those people living in the next century or so some idea of what we are like.

……

We seem to think that God speaks by seconding the ideas we’ve already adopted, but God nearly always catches us by surprise…God tends to confound, astonish, and flabbergast.

Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 154

We set out, therefore, with the supposition that an organised body is not produced by a fundamental power which is guided in its operation by a definite idea, but is developed, according to blind laws of necessity, by powers which, like those of inorganic nature, are established by the very existence of matter. As the elementary materials of organic nature are not different from those of the inorganic kingdom, the source of the organic phenomena can only reside in another combination of these materials, whether it be in a peculiar mode of union of the elementary atoms to form atoms of the second order, or in the arrangement of these conglomerate molecules when forming either the separate morphological elementary parts of organisms, or an entire organism.

Mikroskopische Untersuchungen über die Uebereinstimmung in der Struktur und dem Wachsthum der Thiere und Pflanzen (1839). Microscopic Researches into the Accordance in the Structure and Growth of Animals and Plants, trans. Henry Smith (1847), 190-1.

We should remember that there was once a discipline called natural philosophy. Unfortunately, this discipline seems not to exist today. It has been renamed science, but science of today is in danger of losing much of the natural philosophy aspect.
[Pointing out the increasing specialization of science during the century to explain the resistance to his ideas,]

(1986) Quoted in Anthony L. Peratt, ‘Dean of the Plasma Dissidents’, Washington Times, supplement: The World and I (May 1988),192.

We [Frisch and Lise Meitner] walked up and down in the snow, I on skis and she on foot (she said and proved that she could get along just as fast that way), and gradually the idea took shape that this was no chipping or cracking of the nucleus but rather a process to be explained by Bohr’s idea that the nucleus was like a liquid drop; such a drop might elongate and divide itself.

Otto Frisch and John A. Wheeler, ‘The Discovery of Fission’, Physics Today, Nov 1967, 20, 47.

Well, evolution is a theory. It is also a fact. And facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world’s data. Theories are structures of ideas that explain and interpret facts. Facts do not go away while scientists debate rival theories for explaining them. Einstein’s theory of gravitation replaced Newton’s, but apples did not suspend themselves in mid-air pending the outcome. And human beings evolved from apelike ancestors whether they did so by Darwin’s proposed mechanism or by some other, yet to be discovered … Evolutionists make no claim for perpetual truth, though creationists often do (and then attack us for a style of argument that they themselves favor).

‘Evolution as Fact and Theory’, in Hen’s Teeth and Horse’s Toes: Further Reflections in Natural History (1983), 254-255.

What a glorious title, Nature, a veritable stroke of genius to have hit upon. It is more than a cosmos, more than a universe. It includes the seen as well as the unseen, the possible as well as the actual, Nature and Nature’s God, mind and matter. I am lost in admiration of the effulgent blaze of ideas it calls forth.
[Commenting on the title of the journal.]

From ‘History’ web page of NPG, Nature Publishing Group, www.nature.com.

What is peculiar and new to the [19th] century, differentiating it from all its predecessors, is its technology. It was not merely the introduction of some great isolated inventions. It is impossible not to feel that something more than that was involved. … The process of change was slow, unconscious, and unexpected. In the nineteeth century, the process became quick, conscious, and expected. … The whole change has arisen from the new scientific information. Science, conceived not so much in its principles as in its results, is an obvious storehouse of ideas for utilisation. … Also, it is a great mistake to think that the bare scientific idea is the required invention, so that it has only to be picked up and used. An intense period of imaginative design lies between. One element in the new method is just the discovery of how to set about bridging the gap between the scientific ideas, and the ultimate product. It is a process of disciplined attack upon one difficulty after another This discipline of knowledge applies beyond technology to pure science, and beyond science to general scholarship. It represents the change from amateurs to professionals. … But the full self-conscious realisation of the power of professionalism in knowledge in all its departments, and of the way to produce the professionals, and of the importance of knowledge to the advance of technology, and of the methods by which abstract knowledge can be connected with technology, and of the boundless possibilities of technological advance,—the realisation of all these things was first completely attained in the nineteeth century.

In Science and the Modern World (1925, 1997), 96.

What is that we human beings ultimately depend on? We depend on our words. We are suspended in language. Our task is to communicate experience and ideas to others.

Quoted in Aage Petersen, ‘The Philosophy of Niels Bohr’, Bulletin of the Atomic Scientists, 1963, 19, 10.

What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating. … The restricted theory changed our ideas of space and time in a way that may be summarised by stating that the group of transformations to which the space-time continuum is subject must be changed from the Galilean group to the Lorentz group.

From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), ‘The Relation Between Mathematics And Physics’, printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 123.

What of the future of this adventure? What will happen ultimately? We are going along guessing the laws; how many laws are we going to have to guess? I do not know. Some of my colleagues say that this fundamental aspect of our science will go on; but I think there will certainly not be perpetual novelty, say for a thousand years. This thing cannot keep on going so that we are always going to discover more and more new laws … It is like the discovery of America—you only discover it once. The age in which we live is the age in which we are discovering the fundamental laws of nature, and that day will never come again. Of course in the future there will be other interests … but there will not be the same things that we are doing now … There will be a degeneration of ideas, just like the degeneration that great explorers feel is occurring when tourists begin moving in on a territory.

In The Character of Physical Law (1965, 1994), 166.

What renders a problem definite, and what leaves it indefinite, may best be understood from mathematics. The very important idea of solving a problem within limits of error is an element of rational culture, coming from the same source. The art of totalizing fluctuations by curves is capable of being carried, in conception, far beyond the mathematical domain, where it is first learnt. The distinction between laws and co-efficients applies in every department of causation. The theory of Probable Evidence is the mathematical contribution to Logic, and is of paramount importance.

In Education as a Science (1879), 151-152.

What was really great about ‘Star Trek’ when I was growing up as a little girl is not only did they have Lt. Uhura played by Nichelle Nichols as a technical officer—she was African. … At the same time, they had this crew that was composed of people from all around the world and they were working together to learn more about the universe. … So that helped to fuel my whole idea that I could be involved in space exploration as well as in the sciences.

As quoted in ‘Then & Now: Dr. Mae Jemison’ (19 Jun 2005) on CNN web site.

When entering on new ground we must not be afraid to express even risky ideas so as to stimulate research in all directions. As Priestley put it, we must not remain inactive through false modesty based on fear of being mistaken.

From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 164-165.

When I came home not a single acre of Government, state, or private timberland was under systematic forest management anywhere on the most richly timbered of all continents. … When the Gay Nineties began, the common word for our forests was ‘inexhaustible.’ To waste timber was a virtue and not a crime. There would always be plenty of timber. … The lumbermen … regarded forest devastation as normal and second growth as a delusion of fools. … And as for sustained yield, no such idea had ever entered their heads. The few friends the forest had were spoken of, when they were spoken of at all, as impractical theorists, fanatics, or ‘denudatics,’ more or less touched in the head. What talk there was about forest protection was no more to the average American that the buzzing of a mosquito, and just about as irritating.

In Breaking New Ground (1947, 1998), 27.

When I read an Italian letter [Saggio by Voltaire] on changes which had occurred on the surface of the earth, published in Paris this year (1746), I believed that these facts were reported by La Loubère. Indeed, they correspond perfectly with the author’s ideas. Petrified fish are according to him merely rare fish thrown away by Roman cooks because they were spoiled; and with respect to shells, he said that they were from the sea of the Levant and brought back by pilgrims from Syria at the time of the crusades. These shells are found today petrified in France, in Italy and in other Christian states. Why did he not add that monkeys transported shells on top of high mountains and to every place where humans cannot live? It would not have harmed his story but made his explanation even more plausible.

In ‘Preuves de la Théorie de la Terre’, Histoire Naturelle, Générale et Particuliere, Avec la Description du Cabinet du Roi (1749), Vol. I, 281. Trans. Albert V. and Marguerite Carozzi.

When I saw the alpha-helix and saw what a beautiful, elegant structure it was, I was thunderstruck and was furious with myself for not having built this, but on the other hand, I wondered, was it really right?
So I cycled home for lunch and was so preoccupied with the turmoil in my mind that didn’t respond to anything. Then I had an idea, so I cycled back to the lab. I realized that I had a horse hair in a drawer. I set it up on the X-ray camera and gave it a two hour exposure, then took the film to the dark room with my heart in my mouth, wondering what it showed, and when I developed it, there was the 1.5 angstrom reflection which I had predicted and which excluded all structures other than the alpha-helix.
So on Monday morning I stormed into my professor’s office, into Bragg’s office and showed him this, and Bragg said, ‘Whatever made you think of that?’ And I said, ‘Because I was so furious with myself for having missed that beautiful structure.’ To which Bragg replied coldly, ‘I wish I had made you angry earlier.’

From transcript of audio of Max Perutz in BBC programme, ‘Lifestory: Linus Pauling’ (1997). On ‘Linus Pauling and the Race for DNA’ webpage ‘I Wish I Had Made You Angry Earlier.’

When one begins to speak of something it sounds plausible, but when we reflect on it we find it false. The initial impression a thing makes on my mind is very important. Taking an overall view of a thing the mind sees every side of it obscurely, which is often of more value than a clear idea of only one side of it.

Aphorism 47 in Notebook D (1773-1775), as translated by R.J. Hollingdale in Aphorisms (1990). Reprinted as The Waste Books (2000), 50-51.

When questioned by Stanislaw Ulam, “Which is more important, ideas or things?” Alfred North Whitehead instantly replied, “Ideas about things.”

As described by Martin Gardner in book review, ‘Adventures Of a Mathematician: The Man Who Invented the H-Bomb’, New York Times (9 May 1976), 201.

When Richard Dawkins first published his idea of a meme, he made it clear he was speaking of “a unit of imitation” … Memes were supposed to be exclusive triumphs of humanity. But memes come in two different kinds—behavioral and verbal. … behavioral memes began brain-hopping long before there were such things as human minds.

In ‘Threading a New Tapestry’, Global Brain: The Evolution of Mass Mind from the Big Bang to the 21st Century (2000), 62.

When the child outgrows the narrow circle of family life … then comes the period of the school, whose object is to initiate him into the technicalities of intercommunication with his fellow-men, and to familiarize him with the ideas that underlie his civilization, and which he must use as tools of thought if he would observe and understand the phases of human life around him; for these … are invisible to the human being who has not the aid of elementary ideas with which to see them.

In Psychologic Foundations of Education: An Attempt to Show the Genesis of the Higher Faculties of the Mind (1907), 265.

When the pioneer in science sets forth the groping feelers of his thought, he must have a vivid, intuitive imagination, for new ideas are not generated by deduction, but by an artistically creative imagination.

In Scientific Autobiography and Other Papers (1968), 109.

When two texts, or two assertions, perhaps two ideas, are in contradiction, be ready to reconcile them rather than cancel one by the other; regard them as two different facets, or two successive stages, of the same reality, a reality convincingly human just because it is too complex.

In Gary William Flake, The Computational Beauty of Nature (2000), 427.

When we mention the end of the world, the idea of some kind of catastrophe always comes to mind.

In Teilhard de Chardin and Sara Appleton-Weber (trans.), The Human Phenomenon (1999, 2003), 196. Originally published in French as Le Phénomene Humain (1955).

When, however, you see the specification, you will see that the fundamental principles are contained therein. I do not, however, claim even the credit of inventing it, as I do not believe a mere description of an idea that has never been reduced to practice—in the strict sense of that phrase—should be dignified with the name invention.‎

Letter (5 Mar 1877) to Alexander Graham Bell. Quoted in The Bell Telephone (1908), 168.

Whenever ideas fail, men invent words.

Martin H. Fischer, Howard Fabing (ed.) and Ray Marr (ed.), Fischerisms (1944).

Whenever we pride ourselves upon finding a newer, stricter way of thought or exposition; whenever we start insisting too hard upon “operationalism” or symbolic logic or any other of these very essential systems of tramlines, we lose something of the ability to think new thoughts. And equally, of course, whenever we rebel against the sterile rigidity of formal thought and exposition and let our ideas run wild, we likewise lose. As I see it, the advances in scientific thought come from a combination of loose and strict thinking, and this combination is the most precious tool of science.

In ‘Culture Contact and Schismogenesis’ (1935), in Steps to an Ecology of Mind: Collected Essays in Anthropology, Psychiatry, Evolution, and Epistemology (1972).

Where do correct ideas come from? Do they drop from the skies? No. They come from social practice, and from it alone; they come from three kinds of social practice, the struggle for production, the class struggle and scientific experiment.

In Where do Correct Ideas Come From? (May 1963). As quoted and cited in Quotations from Chairman Mao Tse-Tung (1966, 1972), 206.

Whereas what knowledge we derive from lectures, reading and conversation, is but the copy of other men’s men’s ideas; that is, the picture of a picture; and ’tis one remove farther from the original.

In Interesting Anecdotes, Memoirs, Allegories, Essays, and Poetical Fragments (1793), Vols 3-4, Vol 4, 72-73.

Wherever we seek to find constancy we discover change. Having looked at the old woodlands in Hutcheson Forest, at Isle Royale, and in the wilderness of the boundary waters, in the land of the moose and the wolf, and having uncovered the histories hidden within the trees and within the muds, we find that nature undisturbed is not constant in form, structure, or proportion, but changes at every scale of time and space. The old idea of a static landscape, like a single musical chord sounded forever, must be abandoned, for such a landscape never existed except in our imagination. Nature undisturbed by human influence seems more like a symphony whose harmonies arise from variation and change over many scales of time and space, changing with individual births and deaths, local disruptions and recoveries, larger scale responses to climate from one glacial age to another, and to the slower alterations of soils, and yet larger variations between glacial ages.

Discordant Harmonies (1990), 62.

While the artist’s communication is linked forever with its original form, that of the scientist is modified, amplified, fused with the ideas and results of others.

In The Eighth Day of Creation by Horace Freeland Judson (1979).

Why, these men would destroy the Bible on evidence that would not convict a habitual criminal of a misdemeanor. They found a tooth in a sand pit in Nebraska with no other bones about it, and from that one tooth decided that it was the remains of the missing link. They have queer ideas about age too. They find a fossil and when they are asked how old it is they say they can’t tell without knowing what rock it was in, and when they are asked how old the rock is they say they can’t tell unless they know how old the fossil is.

In Henry Fairfield Osborn, ‘Osborn States the Case For Evolution’, New York Times (12 Jul 1925), XX1. In fact, the tooth was misidentified as anthropoid by Osborn, who over-zealously proposed Nebraska Man in 1922. This tooth was shortly thereafter found to be that of a peccary (a Pliocene pig) when further bones were found. A retraction was made in 1927, correcting the scientific blunder.

Wise men put their trust in ideas and not in circumstances.

In Lecture, Boston, (Mar 1838). Printed in E. P. Peabody (ed.), Aesthetic Papers (1849). Collected in ‘War’, Complete Works (1883), Vol. 2, 190.

With the growth of knowledge our ideas must from time to time be organised afresh. The change takes place usually in accordance with new maxims as they arise, but it always remains provisional.

In The Maxims and Reflections of Goethe (1906), 186.

Without some idea of oxidation processes, of the chemical structure of food, and of the chemical reactions in digestion, visceral behavior is a blank. And without some understanding of visceral behavior, psychic behavior is up in the air.

From Why We Behave Like Human Beings (1925), xiv.

Without the slightest doubt there is something through which material and spiritual energy hold togehter and are complementary. In the last analysis, somehow or other, there must be a single energy operating in the world. And the first idea that occurs to us is that the ‘soul’ must be as it were the focal point of transformation at which, from all the points of nature, the forces of bodies converge, to become interiorised and sublimated in beauty and truth.

In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 63. Originally published in French as Le Phénomene Humain (1955).

Without tracing back to the Tower of Babel, one can observe that the very idea of building a very tall tower has long haunted human imagination. That kind of victory over the formidable law of gravity that tethers man to the ground has always appeared to him a symbol of the force and the challenges overcome.

From the original French, “Sans remonter à la Tour de Babel, on peut observer que l’idée même de la construction d’une tour de très grande hauteur a depuis longtemps hanté l’imagination des hommes. Celle sorte de victoire sur cette terrible loi de la pesanteur qui attache l’homme au sol lui a toujours paru un symbole de la force et des difficultés vaincues.” First sentences of Chap. 1, in Travaux Scientifiques Exécutés à la Tour de 300 Mètres de 1889 à 1900 (1900), 1. English translation by Webmaster using online resources.

Workers must root out the idea that by keeping the results of their labors to themselves a fortune will be assured to them. Patent fees are so much wasted money. The flying machine of the future will not be born fully fledged and capable of a flight for 1,000 miles or so. Like everything else it must be evolved gradually. The first difficulty is to get a thing that will fly at all. When this is made, a full description should be published as an aid to others. Excellence of design and workmanship will always defy competition.

As quoted in Octave Chanute, Progress in Flying Machines (1894), 218.

Worship the spirit of criticism. If reduced to itself it is not an awakener of ideas or a stimulant to great things, but, without it, everything is fallible; it always has the last word.

Address at the Inauguration of the Pasteur Institute. In René Vallery-Radot, The Life of Pasteur, translated by Mrs. R. L. Devonshire (1919), 443.

Would you have a man reason well, you must use him to it betimes; exercise his mind in observing the connection between ideas, and following them in train. Nothing does this better than mathematics, which therefore, I think should be taught to all who have the time and opportunity, not so much to make them mathematicians, as to make them reasonable creatures; for though we all call ourselves so, because we are born to it if we please, yet we may truly say that nature gives us but the seeds of it, and we are carried no farther than industry and application have carried us.

In Conduct of the Understanding, Sect. 6.

Yes, gentlemen, give me the map of any country, its configuration, its climate, its waters, its winds, and the whole of its physical geography; give me its natural productions, its flora, its zoology, &c., and I pledge myself to tell you, a priori, what will be the quality of man in history:—not accidentally, but necessarily; not at any particular epoch, but in all; in short, —what idea he is called to represent.

Introduction to the History of Philosophy (1832), trans. by Henning Gotfried Linberg, 240.

You can hardly imagine how I am struggling to exert my poetical ideas just now for the discovery of analogies & remote figures respecting the earth, Sun & all sorts of things—for I think it is the true way (corrected by judgement) to work out a discovery.

Letter to C. Schrenbein, 13th Nov, 1845. In Frank A. J. L. James (ed.), The Correspondence of Michael Faraday (1996), Vol. 3, 428.

You cannot force ideas. Successful ideas are the result of slow growth. Ideas do not reach perfection in a day, no matter how much study is put upon them. It is perserverance in the pursuit of studies that is really wanted.

In Orison Swett Marden, ‘Bell Telephone Talk: Hints on Success by Alexander G. Bell’, How They Succeeded: Life Stories of Successful Men Told by Themselves (1901), 34.

You cannot put a rope around the neck of an idea; you cannot put an idea up against a barrack-square wall and riddle it with bullets; you cannot confine it in the strongest prison cell that your slaves could ever build.

Death of Thomas Ashe

You have to have a lot of ideas. First, if you want to make discoveries, it’s a good thing to have good ideas. And second, you have to have a sort of sixth sense—the result of judgment and experience—which ideas are worth following up. I seem to have the first thing, a lot of ideas, and I also seem to have good judgment as to which are the bad ideas that I should just ignore, and the good ones, that I’d better follow up.

As quoted by Nancy Rouchette, The Journal of NIH Research (Jul 1990), 2, 63. Reprinted in Linus Pauling, Barclay Kamb, Linus Pauling: Selected Scientific Papers, Vol. 2, Biomolecular Sciences (2001), 1101.

You may not divide the seamless coat of learning. What education has to impart is an intimate sense for the power of ideas, for the beauty of ideas, and for the structure of ideas, together with a particular body of knowledge which has peculiar reference to the life of the being possessing it.

In ‘The Aims of Education’, The Aims of Education and Other Essays (1929), 23.

You never have an idea of what you might accomplish. All that you do is you pursue a question. And see where it leads.

From video interview on achievement.org website (16 May 1991)

[An appealing problem is] a combination of being fairly concrete—so one can understand concretely examples—and also connecting with a lot of other ideas. For example, you see the analysis in a minimal surface equation, but then you also realize it has connections with other geometric questions that are not just analysis. I am definitely very attracted to the idea that there are a lot of different facets in mathematics and seeing the connections.

From Allyn Jackson, ‘Interview with Karen Uhlenbeck’, part of Celebratio Mathematica on the celebratio.org website.

[An engineer’s] invention causes things to come into existence from ideas, makes world conform to thought; whereas science, by deriving ideas from observation, makes thought conform to existence.

Types of Technology’, Research in Philosophy & Technology (1978), Vol. 1, 244.

[Boswell]: Sir Alexander Dick tells me, that he remembers having a thousand people in a year to dine at his house: that is, reckoning each person as one, each time that he dined there.
[Johnson]: That, Sir, is about three a day.
[Boswell]: How your statement lessens the idea.
[Johnson]: That, Sir, is the good of counting. It brings every thing to a certainty, which before floated in the mind indefinitely.

Entry for Fri 18 Apr 1783. In George Birkbeck-Hill (ed.), Boswell’s Life of Johnson (1934-50), Vol. 4, 204.

[Describing a freshman seminar titled “How the Tabby Cat Got Her Stripes or The Silence of the Genes”:] The big idea we start with is: “How is the genome interpreted, and how are stable decisions that affect gene expression inherited from one cell to the next? This is one of the most competitive areas of molecular biology at the moment, and the students are reading papers that in some instances were published this past year. As a consequence, one of the most common answers I have to give to their questions is, “We just don’t know.”

As quoted by Kitta MacPherson in ‘Exploring Epigenetics: President Shirley Tilghman in the Classroom,’
Princeton University Undergraduate Admission web page accessed 14 Oct 2013.

[Edison’s ideas are] good enough for our transatlantic friends … but unworthy of the attention of practical or scientific men.

Committee set up by the British Parliament to look into the effect of Edison’s work on the incandescent lamp on gas company securities, c. 1878, in Profiles of the Future by Arthur C. Clarke (1974).

[Freud’s] great strength, though sometimes also his weakness, was the quite extraordinary respect he had for the singular fact… When he got hold of a simple but significant fact he would feel, and know, that it was an example of something general or universal, and the idea of collecting statistics on the matter was quite alien to him.

The Life and Work of Sigmund Freud (1953), Vol 1, 96-7.

[Fritz Haber’s] greatness lies in his scientific ideas and in the depth of his searching. The thought, the plan, and the process are more important to him than the completion. The creative process gives him more pleasure than the yield, the finished piece. Success is immaterial. “Doing it was wonderful.” His work is nearly always uneconomical, with the wastefulness of the rich.

In Richard Willstätter, Arthur Stoll (ed. of the original German) and Lilli S. Hornig (trans.), From My Life: The Memoirs of Richard Willstätter (1958), 268.

[Godfrey H. Hardy] personified the popular idea of the absent-minded professor. But those who formed the idea that he was merely an absent-minded professor would receive a shock in conversation, where he displayed amazing vitality on every subject under the sun. … He was interested in the game of chess, but was frankly puzzled by something in its nature which seemed to come into conflict with his mathematical principles.

In ‘Prof. G. H. Hardy: A Mathematician of Genius,’ Obituary The Times.

[Great scientists] are men of bold ideas, but highly critical of their own ideas: they try to find whether their ideas are right by trying first to find whether they are not perhaps wrong. They work with bold conjectures and severe attempts at refuting their own conjectures.

‘The Problem of Demarcation’ (1974). Collected in David Miller (ed.) Popper Selections (1985), 118-119.

[In research on bacteria metabolism] we have indeed much the same position as an observer trying to gain an idea of the life of a household by careful scrutiny of the persons and material arriving or leaving the house; we keep accurate records of the foods and commodities left at the door and patiently examine the contents of the dust-bin and endeavour to deduce from such data the events occurring within the closed doors.

Bacterial Metabolism (1930), Preface. In ‘Obituary Notice: Marjory Stephenson, 1885–1948’, Biochemistry Journal (1950), 46:4, 380.

[In] the evolution of ideas… New ideas are thrown up spontaneously like mutations; the vast majority of them are useless crank theories, the equivalent of biological freaks without survival-value.

In Epilogue, The Sleepwalkers: A History of Man’s Changing Vision of the Universe (1959), 515.

[It] is not the nature of things for any one man to make a sudden, violent discovery; science goes step by step and every man depends on the work of his predecessors. When you hear of a sudden unexpected discovery—a bolt from the blue—you can always be sure that it has grown up by the influence of one man or another, and it is the mutual influence which makes the enormous possibility of scientific advance. Scientists are not dependent on the ideas of a single man, but on the combined wisdom of thousands of men, all thinking of the same problem and each doing his little bit to add to the great structure of knowledge which is gradually being erected.

Concluding remark in Lecture ii (1936) on ‘Forty Years of Physics’, revised and prepared for publication by J.A. Ratcliffe, collected in Needham and Pagel (eds.), Background to Modern Science: Ten Lectures at Cambridge Arranged by the History of Science Committee, (1938), 73-74. Note that the words as prepared for publication may not be verbatim as spoken in the original lecture by the then late Lord Rutherford.

[Luis] Alvarez’s whole approach to physics was that of an entrepreneur, taking big risks by building large new projects in the hope of large rewards, although his pay was academic rather than financial. He had drawn around him a group of young physicists anxious to try out the exciting ideas he was proposing.

As quoted in Walter Sullivan, ‘Luis W. Alvarez, Nobel Physicist Who Explored Atom, Dies at 77: Obituary’, New York Times (2 Sep 1988).

[L]et us not overlook the further great fact, that not only does science underlie sculpture, painting, music, poetry, but that science is itself poetic. The current opinion that science and poetry are opposed is a delusion. … On the contrary science opens up realms of poetry where to the unscientific all is a blank. Those engaged in scientific researches constantly show us that they realize not less vividly, but more vividly, than others, the poetry of their subjects. Whoever will dip into Hugh Miller’s works on geology, or read Mr. Lewes’s “Seaside Studies,” will perceive that science excites poetry rather than extinguishes it. And whoever will contemplate the life of Goethe will see that the poet and the man of science can co-exist in equal activity. Is it not, indeed, an absurd and almost a sacrilegious belief that the more a man studies Nature the less he reveres it? Think you that a drop of water, which to the vulgar eye is but a drop of water, loses anything in the eye of the physicist who knows that its elements are held together by a force which, if suddenly liberated, would produce a flash of lightning? Think you that what is carelessly looked upon by the uninitiated as a mere snow-flake, does not suggest higher associations to one who has seen through a microscope the wondrously varied and elegant forms of snow-crystals? Think you that the rounded rock marked with parallel scratches calls up as much poetry in an ignorant mind as in the mind of a geologist, who knows that over this rock a glacier slid a million years ago? The truth is, that those who have never entered upon scientific pursuits know not a tithe of the poetry by which they are surrounded. Whoever has not in youth collected plants and insects, knows not half the halo of interest which lanes and hedge-rows can assume. Whoever has not sought for fossils, has little idea of the poetical associations that surround the places where imbedded treasures were found. Whoever at the seaside has not had a microscope and aquarium, has yet to learn what the highest pleasures of the seaside are. Sad, indeed, is it to see how men occupy themselves with trivialities, and are indifferent to the grandest phenomena—care not to understand the architecture of the Heavens, but are deeply interested in some contemptible controversy about the intrigues of Mary Queen of Scots!—are learnedly critical over a Greek ode, and pass by without a glance that grand epic written by the finger of God upon the strata of the Earth!

In Education: Intellectual, Moral, and Physical (1889), 82-83.

[N]o scientist likes to be criticized. … But you don’t reply to critics: “Wait a minute, wait a minute; this is a really good idea. I’m very fond of it. It’s done you no harm. Please don’t attack it.” That’s not the way it goes. The hard but just rule is that if the ideas don’t work, you must throw them away. Don’t waste any neurons on what doesn’t work. Devote those neurons to new ideas that better explain the data. Valid criticism is doing you a favor.

In ‘Wonder and Skepticism’, Skeptical Enquirer (Jan-Feb 1995), 19, No. 1.

[Philosopher Lao-tse] is not dogmatic, and he does not go in for big, universal ideas. For instance, I like what he says about failure and success, “Failure is the foundation of success and the means by which it is achieved. Success is the lurking place of failure; but who can tell when the turning point will come?”

As quoted in Robert Coughlan, ‘Dr. Edward Teller’s Magnificent Obsession’, Life (6 Sep 1954), 74.

[Plato] was the first to envisage the idea of timeless existence and to emphasize it—against reason—as a reality, more [real] than our actual experience…

Quoted in Robert J. Scully, The Demon and the Quantum (2007), 3.

[Professor Pauling] confesses that he had harboured the feeling that sooner or later he would be the one to get the DNA structure; and although he was pleased with the double-helix, he ‘rather wished the idea had been his’.

‘The Need to Understand’, New Scientist (1971), 50, 755.

[Richard Drew] always encouraged his people to pursue ideas… He said, “If it’s a dumb idea, you’ll find out. You’ll smack into that brick wall, then you’ll stagger back and see another opportunity that you wouldn’t have seen otherwise.”

As quoted in W. James McNerney Jr., A Century of Innovation: The 3M Story (2002), 68. (Note: The quote is in the words of Art Fry, as a recollection, and not necessarily a verbatim quote as spoken by Drew.)

[Some] philosophers have been of opinion that our immortal part acquires during this life certain habits of action or of sentiment, which become forever indissoluble, continuing after death in a future state of existence … I would apply this ingenious idea to the generation, or production of the embryon, or new animal, which partakes so much of the form and propensities of the parent.

Zoonomia (1794), Vol. 1, 483-4.

[The ancient monuments] were all dwarfs in size and pigmies in spirit beside this mighty Statue of Liberty, and its inspiring thought. Higher than the monument in Trafalgar Square which commemorates the victories of Nelson on the sea; higher than the Column Vendome, which perpetuates the triumphs of Napoleon on the land; higher than the towers of the Brooklyn Bridge, which exhibit the latest and greatest results of science, invention, and industrial progress, this structure rises toward the heavens to illustrate an idea … which inspired the charter in the cabin of the Mayflower and the Declaration of Independence from the Continental Congress.

Speech at unveiling of the Statue of Liberty, New York. In E.S. Werner (ed.), Werner’s Readings and Recitations (1908), 107.

[The toughest part of being in charge is] killing ideas that are great but poorly timed. And delivering tough feedback that’s difficult to hear but that I know will help people—and the team—in the long term.

In Issie Lapowsky, ‘Scott Belsky’, Inc. (Nov 2013), 140. Biography in Context,

[There is an] immense advantage to be gained by ample space and appropriate surroundings in aiding the formation of a just idea of the beauty and interest of each specimen… Nothing detracts so much from the enjoyment … from a visit to a museum as the overcrowding of the specimens exhibited.

Essays on Museums (1898), 33.

[To give insight to statistical information] it occurred to me, that making an appeal to the eye when proportion and magnitude are concerned, is the best and readiest method of conveying a distinct idea.

In The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe (1801), 2.

[To the cultures of Asia and the continent of Africa] it is the Western impact which has stirred up the winds of change and set the processes of modernization in motion. Education brought not only the idea of equality but also another belief which we used to take for granted in the West—the idea of progress, the idea that science and technology can be used to better human conditions. In ancient society, men tended to believe themselves fortunate if tomorrow was not worse than today and anyway, there was little they could do about it.

Lecture at State University of Iowa (6 Apr 1961). In Barbara Ward, The Unity of the Free World (1961), 12.

[T]he idea of protoplasm, which was really a name for our ignorance, [is] only a little less misleading than the expression “Vital force”.

Adventures of a Biologist (1940), 118.

[When I was a child] I grew up in Brooklyn, New York, and I was a street kid. … [T]here was one aspect of that environment that, for some reason, struck me as different, and that was the stars. … I could tell they were lights in the sky, but that wasn’t an explanation. I mean, what were they? Little electric bulbs on long black wires, so you couldn’t see what they were held up by? What were they? … My mother said to me, «Look, we’ve just got you a library card … get out a book and find the answer.” … It was in there. It was stunning. The answer was that the Sun was a star, except very far away. … The dazzling idea of a universe vast beyond imagining swept over me. … I sensed awe.

In ‘Wonder and Skepticism’, Skeptical Enquirer (Jan-Feb 1995), 19, No. 1.

~~[Anecdote]~~ Be less curious about people and more curious about ideas.

Anecdotal response to a reporter’s enquiry. As quoted in Clifton Fadiman and André Bernard, Bartlett’s Book of Anecdotes (2000), 150. As yet, Webmaster has found no primary source for authentication.

~~[Attributed]~~ It is not once nor twice but times without number that the same ideas make their appearance in the world.

As quoted in Thomas L. Heath Manual of Greek Mathematics (1931, 2003), 205. Webmaster has so far found no primary source, and is dubious about authenticity. Can you help?

~~[False Attribution]~~ Sometimes I think we’re alone in the universe, and sometimes I think we’re not. In either case, the idea is quite staggering.

~~[Unverified]~~ I don’t care that they stole my idea. I care that they don’t have any of their own.

Webmaster has not, yet, found an authentic primary source for this quote. Can you help? This has been circulated around the web, copied into books, and never to be found with a citation. It may be misattributed from some other speaker. Or it may be a paraphrase of a longer statement by Tesla. Meanwhile, Webmaster is very dubious, and suggests it is better attributed to Anonymous until a source can be paired with it.

Science quotes on:  |  Care (197)  |  Steal (14)

… just as the astronomer, the physicist, the geologist, or other student of objective science looks about in the world of sense, so, not metaphorically speaking but literally, the mind of the mathematician goes forth in the universe of logic in quest of the things that are there; exploring the heights and depths for facts—ideas, classes, relationships, implications, and the rest; observing the minute and elusive with the powerful microscope of his Infinitesimal Analysis; observing the elusive and vast with the limitless telescope of his Calculus of the Infinite; making guesses regarding the order and internal harmony of the data observed and collocated; testing the hypotheses, not merely by the complete induction peculiar to mathematics, but, like his colleagues of the outer world, resorting also to experimental tests and incomplete induction; frequently finding it necessary, in view of unforeseen disclosures, to abandon one hopeful hypothesis or to transform it by retrenchment or by enlargement:—thus, in his own domain, matching, point for point, the processes, methods and experience familiar to the devotee of natural science.

In Lectures on Science, Philosophy and Art (1908), 26

…there is no prescribed route to follow to arrive at a new idea. You have to make the intuitive leap. But the difference is that once you’ve made the intuitive leap you have to justify it by filling in the intermediate steps. In my case, it often happens that I have an idea, but then I try to fill in the intermediate steps and find that they don’t work, so I have to give it up.

In Michael Harwood, ‘The Universe and Dr. Hawking’, New York Times Magazine (23 Jan 1983), 53.

“Planning” is simply the result of experience read backward and projected into the future. To me the “purposive” action of a beehive is simply the summation and integration of its units, and Natural Selection has put higher and higher premiums on the most “purposeful” integration. It is the same way (to me) in the evolution of the middle ear, the steps in the Cynodonts (clearly shown by me in 1910 and by you later in Oudenodon) make it easier to see how such a wonderful device as the middle ear could arise without any predetermination or human-like planning, and in fact in the good old Darwinian way, if only we admit that as the “twig is bent the tree’s inclined” and that each stage conserves the advantages of its predecessors… The simple idea that planning is only experience read backward and combined by selection in suitable or successful combinations takes the mystery out of Nature and out of men’s minds.

Letter to Robert Broom [1933]. In Ronald Rainger, An Agenda for Antiquity (1991), 238.

“That’s another thing we’ve learned from your Nation,” said Mein Herr, “map-making. But we’ve carried it much further than you. What do you consider the largest map that would be really useful?”
“About six inches to the mile.”
“Only six inches!” exclaimed Mein Herr. “We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all! We actually made a map of the country, on the scale of a mile to the mile!”
“Have you used it much?” I enquired.
“It has never been spread out, yet,” said Mein Herr: “the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well.”

From Sylvie and Bruno Concluded (1893), 169.

Below you will find our collection of inspirational, wise, and humorous
old idea quotes, idea sayings, and idea proverbs, collected over the years from a variety
of sources.

An idea is a concept or mental impression. Very often, ideas are construed as representational images; i.e. images of some object. In other contexts, ideas are taken to be concepts, although abstract concepts do not necessarily appear as images.

Quotes[edit]

• Don’t worry about people stealing an idea. If it’s original, you will have to ram it down their throats.
  • Howard H. Aiken, as quoted in Portraits in Silicon (1987) by Robert Slater
  • Variant: Don’t worry about people stealing your ideas. If your ideas are any good, you’ll have to ram them down people’s throats.
    • As quoted in A Computer Science Reader: Selections from Abacus (1988) by Eric A. Weiss, p. 404.

• Man has always been afraid of anything mysterious, forgetting that the key to the mystery is within himself. One must free oneself from all impeding conditions or circumstances, which are different for everyone. Progress depends upon free will that is directed toward good. The power of good compels even machines to act not for themselves, but for humanity. Thus, Our apparatuses function with Our collaboration. People may laugh, but ideas do rule the world. These words are entered into the Statutes of the Brotherhood.
  • Agni Yoga, Supermundane I, (1938) 2.

• Unknown names, unknown places and unfamiliar words often come to the surface from the depths of consciousness. Scientists call this the subconscious, but they are unaware that communications from space accumulate… and when given an impulse, are transferred to the brain… one should pay heed to such flashes of consciousness… In everyday life one should learn to recognize these messages which always come at the right moment. People complain that they are deprived of lofty Guidance, but such a strong statement is unreasonable. We give much, and it is they who perceive little! Therefore, We remind people to pay more heed to words that spring forth suddenly in the conscious mind. Such words should not be dismissed, but should be carefully applied in life. Many other useful ideas come in a flash, like flying butterflies, but people only brush them aside. We never tire of disseminating useful information, and We advise you to treat it with care, for it will be of use in the Subtle World. Thus, one should develop the particular ability to catch the thoughts of space.
  • Agni Yoga, Supermundane I, (1938) 145.

• Nothing is more dangerous than an idea, when you have only one idea.
  • Propos sur le Religion no. 74 (1938), under the pen name Alain.
  • Alternate translation: “Nothing is more dangerous than an idea, when it’s the only one we have.” IZQuotes (retrieved 10/30/18).

• It is in this realm of ideas that humanity is not a free agent. . . . Once an idea becomes an ideal, humanity can freely reject or accept it, but ideas come from a higher source and are imposed… whether men want them or not. Upon the use made of these ideas (which are in the nature of divine emanations, embodying the divine plan for planetary progress) will depend the rapidity of humanity’s progress, or its retardation for lack of understanding.
  • Alice Bailey, The Destiny of Nations (1949) p 8.

• It’s important not to overstate the benefits of ideas. Quite frankly, I know it’s kind of a romantic notion that you’re just going to have this one brilliant idea and then everything is going to be great. But the fact is that coming up with an idea is the least important part of creating something great. It has to be the right idea and have good taste, but the execution and delivery are what’s key.
  • Sergey Brin. Interviewed by Jemima Kiss for The Guardian (UK) newspaper, ‘Secrets of a nimble giant’, Wednesday 17th June 2009.

• … the best way to think about investments is to be in a room with no one else and just think. And if that doesn’t work — nothing else is going to work. … what you are looking for is some way to get one good idea a year … and then ride it to its full potential. … Wall Street makes its money on activity — you make your money on inactivity.
  • Warren Buffett, (July 3, 2013)»Warren Buffett speaks with Florida University». LeylandPAM, YouTube. (quote at 55:30 of 1:27:35)

• Incredulity doesn’t kill curiosity; it encourages it. Though distrustful of logical chains of ideas, I loved the polyphony of ideas. As long as you don’t believe in them, the collision of two ideas — both false — can create a pleasing interval, a kind of diabolus in musica. I had no respect for some ideas people were willing to stake their lives on, but two or three ideas that I did not respect might still make a nice melody. Or have a good beat, and if it was jazz, all the better.
  • Casaubon, Binah, Foucault’s Pendulum by Umberto Eco, Chapter 7

• But arms – instrumentalities, as President Wilson called them – are not sufficient by themselves. We must add to them the power of ideas. People say we ought not to allow ourselves to be drawn into a theoretical antagonism between Nazidom and democracy; but the antagonism is here now. It is this very conflict of spiritual and moral ideas which gives the free countries a great part of their strength. You see these dictators on their pedestals, surrounded by the bayonets of their soldiers and the truncheons of their police. On all sides they are guarded by masses of armed men, cannons, aeroplanes, fortifications, and the like – they boast and vaunt themselves before the world, yet in their hearts there is unspoken fear. They are afraid of words and thoughts; words spoken abroad, thoughts stirring at home – all the more powerful because forbidden – terrify them. A little mouse of thought appears in the room, and even the mightiest potentates are thrown into panic. They make frantic efforts to bar our thoughts and words; they are afraid of the workings of the human mind. Cannons, airplanes, they can manufacture in large quantities; but how are they to quell the natural promptings of human nature, which after all these centuries of trial and progress has inherited a whole armoury of potent and indestructible knowledge?
  • Winston Churchill, Broadcast to the United States and to London, 16 October 1938

• Fundamental ideas play the most essential role in forming a physical theory. Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning of every physical theory. The ideas must later take the mathematical form of a quantitative theory, to make possible the comparison with experiment.
  • Albert Einstein, The Evolution of Physics (1938) (co-written with Leopold Infeld).

• A man to whom it has been given to bless the world with a great creative idea has no need for the praise of posterity. His very achievement has already conferred a higher boon upon him.
  • Albert Einstein, «Max Planck in Memorium» (1948)

• A new idea comes suddenly and in a rather intuitive way. But intuition is nothing but the outcome of earlier intellectual experience.
  • Albert Einstein, Letter to Dr. H. L. Gordon (May 3, 1949 – AEA 58-217) as quoted in Einstein: His Life and Universe (2007) by Walter Isaacson.

• The key to every man is his thought…. He can only be reformed by showing him a new idea which commands his own.
  • Ralph Waldo Emerson, “Circles,” Essays: First Series, p. 303 (1903).

• The phrase a Russian intellectual is probably most likely to use when talking about the early 1980s is bezvozdushnoye prostranstvo—“airless space.” The era was stuffy like the Russian izba, a log cabin, when its windows are caulked for the winter: it keeps out the cold, but also the fresh air. The windows will not be opened even a crack until well into spring, and as time goes on, smells of people, food, and clothing mix into one mind-numbing undifferentiated smell of gigantic proportions. Something similar had happened to the Russian mind over two generations of Soviet rule. At the time of the October Revolution, the Russian intellectual elite had been both a part of and a partner to the European conversation about God, power, and human life. After fifty years of purges, arrests, and, most damaging, unrelenting pressure on what had become an isolated thought universe, the Russian intellectual landscape was populated by barely articulated ghosts of once vibrant ideas. Even Communist ideology was a shadow of its former self, a set of ritually repeated words that had lost all meaning. Lenin had long ago dispensed with most of what Karl Marx had to say, enshrining a few of his selected ideas as überlaw.
  • Masha Gessen, The Future Is History: How Totalitarianism Reclaimed Russia, (2017)

• Could Hamlet have been written by a committee, or the Mona Lisa painted by a club? Could the New Testament have been composed as a conference report? Creative ideas do not spring from groups. They spring from individuals. The divine spark leaps from the finger of God to the finger of Adam, whether it takes ultimate shape in a law of physics or a law of the land, a poem or a policy, a sonata or a mechanical computer.
  • Alfred Whitney Griswold, baccalaureate address, Yale University, New Haven, Connecticut (9 June 1957) —Congressional Record (11 June 1957), vol. 103, Appendix, p. A4545.

• Books won’t stay banned. They won’t burn. Ideas won’t go to jail. In the long run of history, the censor and the inquisitor have always lost. The only sure weapon against bad ideas is better ideas.
  • Alfred Whitney Griswold, Essays on Education as quoted in The New York Times (24 February 1959).

• Religious ideas, supposedly private matters between man and god, are in practice always political ideas.
  • Christopher Hitchens, The Monarchy: A Critique of Britain’s Favourite Fetish (1990), Chatto Counterblasts

• The real Antichrist is he who turns the wine of an original idea into the water of mediocrity.
  • Eric Hoffer, “Thoughts of Eric Hoffer, Including: ‘Absolute Faith Corrupts Absolutely,’” The New York Times, April 25, 1971, p. 60.

• If it’s a good idea, go ahead and do it. It is much easier to apologize than it is to get permission.
  • Admiral Grace Hopper, as quoted in Built to Learn: The inside story of how Rockwell Collins became a true learning organization (2003) by Cliff Purington, Chris Butler, and Sarah Fister Gale, p. 171.

• A person with imprecise ideas can understand little and be of less help to others.
  • Ignatius of Loyola, Letter to Teresa Rejadell (11 September 1536).

• If nature has made any one thing less susceptible than all others of exclusive property, it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of every one, and the receiver cannot dispossess himself of it. Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me.
  • Thomas Jefferson, Letter to Isaac McPherson (13 August 1813).

• That fellow seems to me to possess but one idea, and that is a wrong one,
  • Samuel Johnson, in Life of Johnson (Boswell), Volume iii, Chapter v (1770).
  • Compare Benjamin Disraeli, Sybil, book 4, chapter 5 (1845):
    • Mr. Kremlin himself was distinguished for ignorance, for he had only one idea,—and that was wrong.

• A man may die, nations may rise and fall, but an idea lives on. Ideas have endurance without death.
  • Remarks Recorded for the Opening of a USIA Transmitter at Greenville, North Carolina (8 February 1963) Audio at JFK Library (01:29 — 01:40) · Text of speech at The American Presidency Project

• The composition of this book has been for the author a long struggle of escape, and so must the reading of it be for most readers if the author’s assault upon them is to be successful,—a struggle of escape from habitual modes of thought and expression. The ideas which are here expressed so laboriously are extremely simple and should be obvious. The difficulty lies, not in the new ideas, but in escaping from the old ones, which ramify, for those brought up as most of us have been, into every corner of our minds.
  • John Maynard Keynes, The General Theory of Employment, Interest and Money, Preface, p. viii (1936).

• The ideas of economists and political philosophers, both when they are right and when they are wrong, are more powerful than is commonly understood. Indeed the world is ruled by little else. Practical men, who believe themselves to be quite exempt from any intellectual influence, are usually the slaves of some defunct economist. Madmen in authority, who hear voices in the air, are distilling their frenzy from some academic scribbler of a few years back. I am sure that the power of vested interests is vastly exaggerated compared with the gradual encroachment of ideas. Not, indeed, immediately, but after a certain interval; for in the field of economic and political philosophy there are not many who are influenced by new theories after they are twenty-five or thirty years of age, so that the ideas which civil servants and politicians and even agitators apply to current events are not likely to be the newest. But, soon or late, it is ideas, not vested interests, which are dangerous for good or evil.
  • John Maynard Keynes, The General Theory of Employment, Interest and Money, Ch. 24 «Concluding Notes» p. 383-384

• Plato was right: ideas rule the world, and, as men’s minds will receive new ideas, laying aside the old and effete, the world will advance: mighty revolutions will spring from them; creeds and even powers will crumble before their onward march crushed by the irresistible force. It will be just as impossible to resist their influx, when the time comes, as to stay the progress of the tide. But all this will come gradually on, and before it comes we have a duty set before us; that of sweeping away as much as possible the dross left to us by our pious forefathers. New ideas have to be planted on clean places, for these ideas touch upon the most momentous subjects.
  • Koot Hoomi, The Mahatma Letters to A. P. Sinnett, Letter VI, p. 24, (1923)

• People don’t understand this: Ideas are important, but they’re not essential. What’s essential and important is the execution of the idea. Everyone has had the experience of seeing a movie and saying, «Hey! That was my idea!» Well, it doesn’t mean anything that you had that idea. There’s no such thing as an original concept. What’s original is the way you re-use ancient concepts.
  • John Landis [1]

• It is of the nature of idea to be communicated: written, spoken, done. The idea is like grass. It craves light, likes crowds, thrives on crossbreeding, grows better for being stepped on.
  • Ursula K. Le Guin, The Dispossessed (1974), Chapter 3, p. 72.

• You can’t crush ideas by suppressing them. You can only crush them by ignoring them. By refusing to think, refusing to change. And that’s precisely what our society is doing!
  • Ursula K. Le Guin, The Dispossessed (1974), Chapter 6, p. 165.

• It’s impossible not to admire a person who devoted his life to his ideas.
  • Gideon Levy, This Biography Makes It Clear: The Founder of the Palestinian Popular Front Was Right (April 15, 2018), Haaretz.

• When people speak of ideas that revolutionize society, they do but express the fact that within the old society, the elements of a new one have been created, and that the dissolution of the old ideas keeps even pace with the dissolution of the old conditions of existence.
  • Karl Marx, Das Manifest der Kommunistischen Partei (The Communist Manifesto) (1848) by Karl Marx and Friedrich Engels, Section 2, paragraph 58.

• The ideas of the ruling class are, in every age, the ruling ideas. … The class which is the dominant material force in society is at the same time its dominant intellectual force. The class which has the means of material production at its disposal has control over the means of mental production, so that in consequence the ideas of those who lack the means of mental production are, in general, subject to it.
  • Karl Marx, German Ideology

• A good idea is something that does not solve just one single problem, but rather can solve multiple problems at once.
  • Shigeru Miyamoto, Interviewed by Eurogamer.net, 31 March 2010.

• Ideas, unlike solid structures, do not perish. They remain immortal, immaterial and everywhere, like all Divine things. Ideas are a golden, savage landscape that we wander unaware, without a map. Be careful: in the last analysis, reality may be exactly what we think it is.
  • Alan Moore, What Is Reality?

• There’s no flesh or blood within this cloak to kill. There’s only an idea. Ideas are bulletproof. Farewell.
  • Alan Moore, V for Vendetta as spoken by «V»

• To me, when we talk about the world, we are talking about our ideas of the world. Our ideas of organisation, our different religions, our different economic systems, our ideas about it are the world. We are heading for a radical revision where you could say we are heading towards the end of the world, but more in the R.E.M. sense than the Revelation sense. That is what apocalypse means – revelation. I could square that with the end of the world, a revelation, a new way of looking at things, something that completely radicalises our notions of the where we were, when we were, what we were, something like that would constitute an end to the world in the kind of abstract – yet very real sense – that I am talking about. A change in the language, a change in the thinking, a change in the music. It wouldn’t take much – one big scientific idea, or artistic idea, one good book, one good painting – who knows – we are at a critical point where the ideas are coming thicker and faster and stranger and stranger than they ever were before. They are realised at a greater speed, everything has become very fluid.
  • Alan Moore De Abaitua interview (1998)

• If you want to have good ideas you must have many ideas. Most of them will be wrong, and what you have to learn is which ones to throw away.
  • Linus Pauling, as quoted by Francis Crick in his presentation «The Impact of Linus Pauling on Molecular Biology» (1995).

• It is terrible to see how a single unclear idea, a single formula without meaning, lurking in a young man’s head, will sometimes act like an obstruction … in an artery, hindering the nutrition of the brain, and condemning its victim to pine away in the fullness of his intellectual vigor and in the midst of intellectual plenty.
  • Charles Sanders Peirce, «How to make our ideas clear,” Popular Science, January 1878.

• The consciousness of a general idea has a certain «unity of the ego» in it, which is identical when it passes from one mind to another. It is, therefore, quite analogous to a person, and indeed, a person is only a particular kind of general idea.
  • Charles Sanders Peirce, «Man’s Glassy Essence» in The Monist, Vol. III, No. 1 (October 1892).

• We are accustomed to speak of ideas as reproduced, as passed from mind to mind, as similar or dissimilar to one another, and, in short, as if they were substantial things; nor can any reasonable objection be raised to such expressions. But taking the word «idea» in the sense of an event in an individual consciousness, it is clear that an idea once past is gone forever, and any supposed recurrence of it is another idea. These two ideas are not present in the same state of consciousness, and therefore cannot possibly be compared.
  • Charles Sanders Peirce, The Law of Mind (1892), First published in The Monist, Vol. II, No. 4 (July 1892), p. 533.

• The best of ideas is hurt by uncritical acceptance and thrives on critical examination.
  • George Pólya, How to Solve It (1945), p. 100 in the 2004 edition.

• New scientific ideas never spring from a communal body, however organized, but rather from the head of an individually inspired researcher who struggles with his problems in lonely thought and unites all his thought on one single point which is his whole world for the moment.
  • Max Planck addressing the 25th anniversary of the Kaiser-Wilhelm Gesellschaft (January 1936), as quoted in Surviving the Swastika: Scientific Research in Nazi Germany (1993) ISBN 0-19-507010-0

• One thing I learnt was never to hoard ideas because either they are not so relevant or they’ve gone stale. Whatever it is, pour them out.
  • Mary Quant, Daily Express, 29th October 2008.

• Historians must break out of the prison of ideas.
  • Dave Renton, Fascism: Theory and Practice. Pluto Press. 1999. p. 29. ISBN 978-0-7453-1470-9.

• Nothing is as difficult as to achieve results in this world if one is filled full of great tolerance and the milk of human kindness. The person who achieves must generally be a one-ideaed individual, concentrated entirely on that one idea, and ruthless in his aspect toward other men and other ideas.
  • Corinne Roosevelt Robinson, My Brother Theodore Roosevelt (1921). New York: Charles Scribner’s Sons, p. 3.

• Ideas are everywhere, but knowledge is rare.
  • Thomas Sowell, Knowledge and Decisions (1980), Ch. 1: The Role of Knowledge

• What is important is not the ideas themselves, but the context in which they operate.
  • Colin Sparks, Fascism in Britain From International Socialism, No. 71, September 1974, pp. 13–28. Transcribed & marked up by Einde O’Callaghan for ETOL. Text online at Marxists Internet Archive.

• In the brain model proposed here, the causal potency of an idea, or an ideal, becomes just as real as that of a molecule, a cell, or a nerve impulse. Ideas cause ideas and help evolve new ideas. They interact with each other and with other mental forces in the same brain, in neighboring brains, and, thanks to global communication, in far distant, foreign brains. And they also interact with the external surroundings to produce, in toto a burstwise advance in evolution that is far beyond anything to hit the evolutionary scene yet, including the emergence of the living cell.
  • Roger Wolcott Sperry, «Mind, Brain and Humanist Values,» New Views on the Nature of Man (1965) ed., John R. Platt, pp. 82-83.

• Ideas are more powerful than guns. We would not let our enemies have guns, why should we let them have ideas?
  • Often attributed to Stalin, there is not a single source which show that Stalin said this at any given time. There is only one source outside the blogosphere which attributes the quote to Stalin, but does not provide any evidence for the attribution. That source is the book Quotations for Public Speakers: A Historical, Literary, and Political Anthology (2001), p. 121 by the USA Ex-senator Robert Torricelli.

• Ideas are like rabbits. You get a couple and learn how to handle them, and pretty soon you have a dozen.
  • John Steinbeck, Interview with Robert van Gelder (April 1947), as quoted in John Steinbeck: A Biography (1994) by Jay Parini.

• “Our ideas” are only partly our ideas. Most of our ideas are abbreviations or residues of the thought of other people, of our teachers (in the broadest sense of the term) and of our teachers’ teachers; they are abbreviations and residues of the thought of the past. These thoughts were once explicit and in the center of consideration and discussion. It may even be presumed that they were once perfectly lucid. By being transmitted to later generations they have possibly been transformed, and there is no certainty that the transformation was effected consciously and with full clarity. … This means that the clarification of our political ideas insensibly changes into and becomes indistinguishable from the history of political ideas.
  • Leo Strauss, What is Political Philosophy? (1959), p. 73

• An idea starts to be interesting when you get scared of taking it to its logical conclusion.
  • Nassim Nicholas Taleb, The Bed of Procrustes: Philosophical and Practical Aphorisms (2010) Preludes, p.3.

• The scientific man does not aim at an immediate result. He does not expect that his advanced ideas will be readily taken up. His work is like that of the planter — for the future. His duty is to lay the foundation for those who are to come, and point the way. He lives and labors and hopes.
  • Nikola Tesla «Radio Power Will Revolutionize the World» in Modern Mechanics and Inventions (July 1934)

• Universal Peace, assuming it to be in the fullest sense realizable, might not require eons for its accomplishment, however probable this may appear, judging from the imperceptibly slow growth of all great reformatory ideas of the past. … Our accepted estimates of the duration of natural metamorphoses, or changes in general, have been thrown in doubt of late. The very foundations of science have been shaken.
  • Nikola Tesla A Means for Furthering Peace (1905)

• To say that everything is idea or that everything is spirit, is the same as saying that everything is matter or that everything is energy, for if everything is idea or spirit, just as my consciousness is, it is not plain why the diamond should not endure for ever, if my consciousness, because it is idea or spirit, endures forever.
  • Miguel de Unamuno, Del Sentimiento Trágico de la Vida (The Tragic Sense of Life), V: The Rationalist Dissolution (1913).

• There is no tyranny in the world more hateful than that of ideas. Ideas bring ideophobia, and the consequence is that people begin to persecute their neighbors in the name of ideas. I loathe and detest all labels, and the only label that I could now tolerate would be that of ideoclast or idea breaker.
  • Miguel de Unamuno, as recalled by Walter Starkie from a conversation he had with Unamuno, as related in the Epilogue of Unamuno.

• We are told to remember the idea, not the man, because a man can fail. He can be caught, he can be killed and forgotten, but 400 years later, an idea can still change the world. I’ve witnessed first hand the power of ideas. I’ve seen people kill in the name of them, and die defending them … but you cannot kiss an idea, cannot touch it, or hold it … ideas do not bleed, they do not feel pain, they do not love… And it is not an idea that I miss, it is a man.
  • Lana & Lilly Wachowski, V for Vendetta based on the comic series by Alan Moore, as spoken by Evey Hammond.

• Beneath this mask there is more than flesh. Beneath this mask there is an idea, Mr. Creedy, and ideas are bulletproof.
  • Lana & Lilly Wachowski, V for Vendetta based on the comic series by Alan Moore, as spoken by «V».

See also[edit]

• Intellectual property

External links[edit]