Palindrome is a word number phrase

A palindrome is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as madam or racecar, the date and time 12/21/33 12:21, and the sentence: «A man, a plan, a canal – Panama». The 19-letter Finnish word saippuakivikauppias (a soapstone vendor), is the longest single-word palindrome in everyday use, while the 12-letter term tattarrattat (from James Joyce in Ulysses) is the longest in English.

The word palindrome was introduced by English poet and writer Henry Peacham in 1638.^[1] The concept of a palindrome can be dated to the 3rd-century BCE, although no examples survive; the first physical examples can be dated to the 1st-century CE with the Latin acrostic word square, the Sator Square (contains both word and sentence palindromes), and the 4th-century Greek Byzantine sentence palindrome nipson anomemata me monan opsin.^[2][3]

Palindrome are also found in music (the table canon and crab canon) and biological structures (most genomes include palindromic gene sequences). In automata theory, the set of all palindromes over an alphabet is a context-free language, but it is not regular.

Etymology[edit]

The word palindrome was introduced by English poet and writer Henry Peacham in 1638.^[1] It is derived from the Greek roots πάλιν ‘again’ and δρóμος ‘way, direction’; a different word is used in Greek, καρκινικός ‘carcinic’ (lit. crab-like) to refer to letter-by-letter reversible writing.^[2][3]

Historical development[edit]

The ancient Greek poet Sotades (3rd-century BC) invented a form of Ionic meter called Sotadic or Sotadean verse, which is sometimes said to have been palindromic,^[4] but no examples survive,^[5] and the exact nature of the readings is unclear.^[6][7][8]

A 1st-century Latin palindrome was found as a graffito at Pompeii. This palindrome, known as the Sator Square, consists of a sentence written in Latin: sator arepo tenet opera rotas ‘The sower Arepo holds with effort the wheels’. It is also an acrostic where the first letters of each word form the first word, the second letters form the second word, and so forth. Hence, it can be arranged into a word square that reads in four different ways: horizontally or vertically from either top left to bottom right or bottom right to top left. Other palindromes found at Pompeii include «Roma-Olina-Milo-Amor», which is also written as an acrostic square.^[9][10] Indeed, composing palindromes was «a pastime of Roman landed gentry».^[11]

Byzantine baptismal fonts were often inscribed with the 4th-century Greek palindrome, ΝΙΨΟΝ ΑΝΟΜΗΜΑΤΑ (or ΑΝΟΜΗΜΑ) ΜΗ ΜΟΝΑΝ ΟΨΙΝ («Nipson anomēmata mē monan opsin«) ‘Wash [your] sin(s), not only [your] face’, attributed to Gregory of Nazianzus;^[5] most notably in the basilica of Hagia Sophia in Constantinople. The inscription is found on fonts in many churches in Western Europe: Orléans (St. Menin’s Abbey); Dulwich College; Nottingham (St. Mary’s); Worlingworth; Harlow; Knapton; London (St Martin, Ludgate); and Hadleigh (Suffolk).^[12]

An 11th-century palindrome with the same square property is the Hebrew palindrome, פרשנו רעבתן שבדבש נתבער ונשרף perashnu: ra`avtan shebad’vash nitba`er venisraf ‘We explained the glutton who is in the honey was burned and incinerated’, credited to Abraham ibn Ezra in 1924,^[13] and referring to the halachic question as to whether a fly landing in honey makes the honey treif (non-kosher).

The palindromic Latin riddle «In girum imus nocte et consumimur igni» ‘we go in a circle at night and are consumed by fire’ describes the behavior of moths. It is likely that this palindrome is from medieval rather than ancient times. The second word, borrowed from Greek, should properly be spelled gyrum.

In English, there are many palindrome words such as eye, madam, and deified, but English writers generally cited Latin and Greek palindromic sentences in the early 19th century;^[14] though John Taylor had coined one in 1614: «Lewd did I live, & evil I did dwel» (with the ampersand being something of a «fudge»^[15]). This is generally considered the first English-language palindrome sentence and was long-reputed, notably by the grammarian James «Hermes» Harris, to be the only one, despite many efforts to find others.^[16][17] (Taylor had also composed two other, «rather indifferent», palindromic lines of poetry: «Deer Madam, Reed», «Deem if I meed».^[4]) Then in 1848, a certain «J.T.R.» coined «Able was I ere I saw Elba», which became famous after it was (implausibly) attributed to Napoleon (alluding to his exile on Elba).^[18][17][19] Other well-known English palindromes are: «A man, a plan, a canal – Panama» (1948),^[20] «Madam, I’m Adam» (1861),^[21] and «Never odd or even».

Types[edit]

Characters, words, or lines[edit]

The most familiar palindromes in English are character-unit palindromes, where the characters read the same backward as forward. Examples are civic, radar, level, rotor, kayak, madam, and refer. The longest common ones are rotator, deified, racecar and reviver; longer examples such as redivider, kinnikinnik and tattarrattat are orders of magnitude rarer.^[22]

There are also word-unit palindromes in which the unit of reversal is the word («Is it crazy how saying sentences backwards creates backwards sentences saying how crazy it is?»). Word-unit palindromes were made popular in the recreational linguistics community by J. A. Lindon in the 1960s. Occasional examples in English were created in the 19th century. Several in French and Latin date to the Middle Ages.^[23]

There are also line-unit palindromes, most often poems. These possess an initial set of lines which, precisely halfway through, is repeated in reverse order, without alteration to word order within each line, and in a way that the second half continues the «story» related in the first half in a way that makes sense, this last being key.^[24]

Sentences and phrases[edit]

Palindromes often consist of a sentence or phrase, e.g., «Mr. Owl ate my metal worm», «Do geese see God?», or «Was it a car or a cat I saw?». Punctuation, capitalization, and spaces are usually ignored. Some, such as «Rats live on no evil star», «Live on time, emit no evil», and «Step on no pets», include the spaces.

Names[edit]

Some names are palindromes, such as the given names Hannah, Ava, Aviva, Anna, Eve, Bob and Otto, or the surnames Harrah, Renner, Salas, and Nenonen.
Lon Nol (1913–1985) was Prime Minister of Cambodia. Nisio Isin is a Japanese novelist and manga writer, whose pseudonym (西尾 維新, Nishio Ishin) is a palindrome when romanized using the Kunrei-shiki or the Nihon-shiki systems, and is often written as NisiOisiN to emphasize this. Some people have changed their name in order to make it palindromic (including as the actor Robert Trebor and rock-vocalist Ola Salo), while others were given a palindromic name at birth (such as the philologist Revilo P. Oliver, the flamenco dancer Sara Baras, the runner Anuța Cătună, the sportswriter Mark Kram and the creator of the Eden Project Tim Smit).

There are also palindromic names in fictional media. «Stanley Yelnats» is the name of the main character in Holes, a 1998 novel and 2003 film. Five of the fictional Pokémon species have palindromic names in English (Eevee, Girafarig, Farigiraf, Ho-Oh, and Alomomola), as does the region Alola.

The 1970s pop band ABBA is a palindrome using the starting letter of the first name of each of the four band members.

Numbers[edit]

The digits of a palindromic number are the same read backwards as forwards, for example, 91019; decimal representation is usually assumed. In recreational mathematics, palindromic numbers with special properties are sought. For example, 191 and 313 are palindromic primes.

Whether Lychrel numbers exist is an unsolved problem in mathematics about whether all numbers become palindromes when they are continuously reversed and added. For example, 56 is not a Lychrel number as 56 + 65 = 121, and 121 is a palindrome. The number 59 becomes a palindrome after three iterations: 59 + 95 = 154; 154 + 451 = 605; 605 + 506 = 1111, so 59 is not a Lychrel number either. Numbers such as 196 are thought to never become palindromes when this reversal process is carried out and are therefore suspected of being Lychrel numbers. If a number is not a Lychrel number, it is called a «delayed palindrome» (56 has a delay of 1 and 59 has a delay of 3). In January 2017 the number 1,999,291,987,030,606,810 was published in OEIS as A281509, and described as «The Largest Known Most Delayed Palindrome», with a delay of 261. Several smaller 261-delay palindromes were published separately as A281508.

Every positive integer can be written as the sum of three palindromic numbers in every number system with base 5 or greater.^[25]

Dates[edit]

A day or timestamp is a palindrome when its digits are the same when reversed. Only the digits are considered in this determination and the component separators (hyphens, slashes, and dots) are ignored. Short digits may be used as in 11/11/11 11:11 or long digits as in 2 February 2020.

A notable palindrome day is this century’s 2 February 2020 because this date is a palindrome regardless of the date format by country (yyyy-mm-dd, dd-mm-yyyy, or mm-dd-yyyy) used in various countries. For this reason, this date has also been termed as a «Universal Palindrome Day».^[26][27] Other universal palindrome days include, almost a millennium previously, 11/11/1111, the future 12/12/2121, and in a millennium 03/03/3030.^[28]

In speech[edit]

A phonetic palindrome is a portion of speech that is identical or roughly identical when reversed. It can arise in context where language is played with, for example in slang dialects like verlan.^[29] In the French language, there is the phrase une Slave valse nue («a Slavic woman waltzes naked»), phonemically /yn slav vals ny/.^[30] John Oswald discussed his experience of phonetic palindromes while working on audio tape versions of the cut-up technique using recorded readings by William S. Burroughs.^[31][32] A list of phonetic palindromes discussed by word puzzle columnist O.V. Michaelsen (Ove Ofteness) include «crew work»/»work crew», «dry yard», «easy», «Funny enough», «Let Bob tell», «new moon», «selfless», «Sorry, Ross», «Talk, Scott», «to boot», «top spot» (also an orthographic palindrome), «Y’all lie», «You’re caught. Talk, Roy», and «You’re damn mad, Roy».^[33]

Longest palindromes[edit]

The longest single-word palindrome in the Oxford English Dictionary is the 12-letter onomatopoeic word tattarrattat, coined by James Joyce in Ulysses (1922) for a knock on the door.^[34][35][36] The Guinness Book of Records gives the title to the 11-letter detartrated, the preterite and past participle of detartrate, a chemical term meaning to remove tartrates. The 9-letter word Rotavator, a trademarked name for an agricultural machine, is listed in dictionaries as being the longest single-word palindrome. The 9-letter term redivider is used by some writers, but appears to be an invented or derived term; only redivide and redivision appear in the Shorter Oxford English Dictionary; the 9-letter word Malayalam, a language of southern India, is also of equal length.

According to Guinness World Records, the Finnish 19-letter word saippuakivikauppias (a soapstone vendor), is the world’s longest palindromic word in everyday use.^[12]

English palindrome sentences of notable length include mathematician Peter Hilton’s «Doc, note: I dissent. A fast never prevents a fatness. I diet on cod»,^[37] and Scottish poet Alastair Reid’s «T. Eliot, top bard, notes putrid tang emanating, is sad; I’d assign it a name: gnat dirt upset on drab pot toilet.»^[38]

In English, two palindromic novels have been published: Satire: Veritas by David Stephens (1980, 58,795 letters), and Dr Awkward & Olson in Oslo by Lawrence Levine (1986, 31,954 words).^[39] Another palindromic English work is a 224-word long poem, «Dammit I’m Mad», written by Demetri Martin.^[40] «Weird Al» Yankovic’s song «Bob» is composed entirely of palindromes.^[41]

Other occurrences[edit]

Classical music[edit]

Joseph Haydn’s Symphony No. 47 in G is nicknamed «the Palindrome». In the third movement, a minuet and trio, the second half of the minuet is the same as the first but backwards, the second half of the ensuing trio similarly reflects the first half, and then the minuet is repeated.

The interlude from Alban Berg’s opera Lulu is a palindrome,^[42] as are sections and pieces, in arch form, by many other composers, including James Tenney, and most famously Béla Bartók. George Crumb also used musical palindrome to text paint the Federico García Lorca poem «¿Por qué nací?», the first movement of three in his fourth book of Madrigals. Igor Stravinsky’s final composition, The Owl and the Pussy Cat, is a palindrome.^{[43][unreliable source?]}

The first movement from Constant Lambert’s ballet Horoscope (1938) is entitled «Palindromic Prelude». Lambert claimed that the theme was dictated to him by the ghost of Bernard van Dieren, who had died in 1936.^{[44][unreliable source?]}

British composer Robert Simpson also composed music in the palindrome or based on palindromic themes; the slow movement of his Symphony No. 2 is a palindrome, as is the slow movement of his String Quartet No. 1. His hour-long String Quartet No. 9 consists of thirty-two variations and a fugue on a palindromic theme of Haydn (from the minuet of his Symphony No. 47). All of Simpson’s thirty-two variations are themselves palindromic.

Hin und Zurück («There and Back»: 1927) is an operatic ‘sketch’ (Op. 45a) in one scene by Paul Hindemith, with a German libretto by Marcellus Schiffer. It is essentially a dramatic palindrome. Through the first half, a tragedy unfolds between two lovers, involving jealousy, murder and suicide. Then, in the reversing second half, this is replayed with the lines sung in reverse order to produce a happy ending.

The music of Anton Webern is often palindromic. Webern, who had studied the music of the Renaissance composer Heinrich Isaac, was extremely interested in symmetries in music, be they horizontal or vertical. An example of horizontal or linear symmetry in Webern’s music is the first phrase in the second movement of the symphony, Op. 21. A striking example of vertical symmetry is the second movement of the Piano Variations, Op. 27, in which Webern arranges every pitch of this dodecaphonic work around the central pitch axis of A4. From this, each downward reaching interval is replicated exactly in the opposite direction. For example, a G♯3—13 half-steps down from A4 is replicated as a B♭5—13 half-steps above.

Just as the letters of a verbal palindrome are not reversed, so are the elements of a musical palindrome usually presented in the same form in both halves. Although these elements are usually single notes, palindromes may be made using more complex elements. For example, Karlheinz Stockhausen’s composition Mixtur, originally written in 1964, consists of twenty sections, called «moments», which may be permuted in several different ways, including retrograde presentation, and two versions may be made in a single program. When the composer revised the work in 2003, he prescribed such a palindromic performance, with the twenty moments first played in a «forwards» version, and then «backwards». Each moment, however, is a complex musical unit, and is played in the same direction in each half of the program.^[45] By contrast, Karel Goeyvaerts’s 1953 electronic composition, Nummer 5 (met zuivere tonen) is an exact palindrome: not only does each event in the second half of the piece occur according to an axis of symmetry at the centre of the work, but each event itself is reversed, so that the note attacks in the first half become note decays in the second, and vice versa. It is a perfect example of Goeyvaerts’s aesthetics, the perfect example of the imperfection of perfection.^[46]

In classical music, a crab canon is a canon in which one line of the melody is reversed in time and pitch from the other.
A large-scale musical palindrome covering more than one movement is called «chiastic», referring to the cross-shaped Greek letter «χ» (pronounced /ˈkaɪ/.) This is usually a form of reference to the crucifixion; for example, the Crucifixus movement of Bach’s Mass in B minor. The purpose of such palindromic balancing is to focus the listener on the central movement, much as one would focus on the centre of the cross in the crucifixion. Other examples are found in Bach’s cantata BWV 4, Christ lag in Todes Banden, Handel’s Messiah and Fauré’s Requiem.^[47]

A table canon is a rectangular piece of sheet music intended to be played by two musicians facing each other across a table with the music between them, with one musician viewing the music upside down compared to the other. The result is somewhat like two speakers simultaneously reading the Sator Square from opposite sides, except that it is typically in two-part polyphony rather than in unison.^[48]

Biological structures[edit]

Palindromic motifs are found in most genomes or sets of genetic instructions, palindromic motifs are found. The meaning of palindrome in the context of genetics is slightly different, from the definition used for words and sentences. Since the DNA is formed by two paired strands of nucleotides, and the nucleotides always pair in the same way (Adenine (A) with Thymine (T), Cytosine (C) with Guanine (G)), a (single-stranded) sequence of DNA is said to be a palindrome if it is equal to its complementary sequence read backward. For example, the sequence ACCTAGGT is palindromic because its complement is TGGATCCA, which is equal to the original sequence in reverse complement.

A palindromic DNA sequence may form a hairpin. Palindromic motifs are made by the order of the nucleotides that specify the complex chemicals (proteins) that, as a result of those genetic instructions, the cell is to produce. They have been specially researched in bacterial chromosomes and in the so-called Bacterial Interspersed Mosaic Elements (BIMEs) scattered over them. Recently^[when?] a research genome sequencing project discovered that many of the bases on the Y-chromosome are arranged as palindromes.^[49] A palindrome structure allows the Y-chromosome to repair itself by bending over at the middle if one side is damaged.

It is believed that palindromes are also found in proteins,^[50][51] but their role in the protein function is not clearly known. It has recently^[52] been suggested that the prevalence existence of palindromes in peptides might be related to the prevalence of low-complexity regions in proteins, as palindromes frequently are associated with low-complexity sequences. Their prevalence might also be related to an alpha helical formation propensity of these sequences,^[52] or in formation of proteins/protein complexes.^[53]

Computation theory[edit]

In automata theory, a set of all palindromes in a given alphabet is a typical example of a language that is context-free, but not regular. This means that it is impossible for a computer with a finite amount of memory to reliably test for palindromes. (For practical purposes with modern computers, this limitation would apply only to impractically long letter sequences.)

In addition, the set of palindromes may not be reliably tested by a deterministic pushdown automaton which also means that they are not LR(k)-parsable or LL(k)-parsable. When reading a palindrome from left to right, it is, in essence, impossible to locate the «middle» until the entire word has been read completely.

It is possible to find the longest palindromic substring of a given input string in linear time.^[54][55]

The palindromic density of an infinite word w over an alphabet A is defined to be zero if only finitely many prefixes are palindromes; otherwise, letting the palindromic prefixes be of lengths n_k for k=1,2,… we define the density to be

Among aperiodic words, the largest possible palindromic density is achieved by the Fibonacci word, which has density 1/φ, where φ is the Golden ratio.^[56]

A palstar is a concatenation of palindromic strings, excluding the trivial one-letter palindromes – otherwise all strings would be palstars.^[54]

Notable palindromists[edit]

• Dmitry Avaliani (1938–2003)
• Howard W. Bergerson (1922–2011)
• Hugo Brandt Corstius (1935–2014)
• Simo Frangén (b. 1963)
• Pasi Heikura (b. 1963)
• Velimir Khlebnikov (1885–1922)
• J. A. Lindon (c. 1914–1979)
• Leigh Mercer (1893–1977) best known for devising the palindrome «A man, a plan, a canal: Panama!»
• Georges Perec (1936–1982)
• Mark Saltveit (b. 1961)
• Anthony Etherin (b. 1981)
• Su Hui (poet) (fourth century CE)
• Baby Gramps (active 1964–present)

See also[edit]

• Ambigram
• Anagram
• Ananym
• Anastrophe, different word order
• Antimetabole
• Backmasking
• «Bob» («Weird Al» Yankovic song)
• Chiasmus
• Constrained writing
• Eodermdrome
• «I Palindrome I» by They Might Be Giants
• List of English palindromic phrases
• List of palindromic places
• Mirror writing
• Palindroma, a genus of spiders with palindromic species names
• Palindromic number
• Palindromic polynomial
• Pangram
• Yreka, California for the palindromic Yreka Bakery and Yrella Gallery

References[edit]

Further reading[edit]

• Word Ways: The Journal of Recreational Linguistics. Greenwood Periodicals et al., 1968–. ISSN 0043-7980.
• The Palindromist. Palindromist Press, 1996–.
• Howard W. Bergerson. Palindromes and Anagrams. Dover Publications, 1973. ISBN 978-0486206646.
• Dmitri A.Borgman. Language on Vacation. Charles Scribner’s Sons, 1965. ISBN 978-0006523086
• Stephen J. Chism. From A to Zotamorf: The Dictionary of Palindromes. Word Ways Press, 1992. ISBN 978-0963515209.
• Michael Donner. I Love Me, Vol. I: S. Wordrow’s Palindrome Encyclopedia. Algonquin Books, 1996. ISBN 978-1565121096.

External links[edit]

• Chisholm, Hugh, ed. (1911). «Palindrome» . Encyclopædia Britannica. Vol. 20 (11th ed.). Cambridge University Press. p. 633.
• «Palindromes». Several languages. European Day of Languages (EDL). Celebrated Sep 26

Asked by: Jeremie Gorczany III

Score: 4.6/5
(27 votes)

A palindrome is a word, phrase, number, or sequence of words that reads the same backward as forward. Punctuation and spaces between the words or lettering are allowed.

What makes something a palindrome?

A palindrome is a word, sentence, verse, or even number that reads the same backward or forward. … So, a palindrome is like a word, phrase, or number that “runs back” on itself. This bit of wordplay is not the same thing as when you rearrange the letters of a word or phrase to spell another one. That’s called an anagram.

What are examples of palindromes?

Can a palindrome be one letter?

A palindrome is a word that is spelled the same forward and backward. … We can think of a palindrome as just any sequence of letters that reads the same forward and backward, such as xyzyzyx. We call a sequence of letters a string. So we can say that any string containing just one letter is by default a palindrome.

Can a palindrome be two words?

A palindrome is a word or phrase that reads the same in both directions. … Two-word palindromes include «edit/tide» and «lived/devil».

45 related questions found

A palindrome is a word, phrase, number, or other sequence of units that can be read the same way in either direction, with general allowances for adjustments to punctuation and word dividers.

Composing literature in palindromes is an example of constrained writing. The word «palindrome» was coined from Greek roots palin (πάλιν; «again») and dromos (δρóμος; «way, direction») by English writer Ben Jonson in the 17th century. The actual Greek phrase to describe the phenomenon is karkinikê epigrafê (καρκινικὴ επιγραφή; crab inscription), or simply karkinoi (καρκίνοι; crabs), alluding to the backward movement of crabs, like an inscription that can be read backwards.

History

Palindromes date back at least to 79 AD, as the palindromic Latin word square «Sator Arepo Tenet Opera Rotas» (The sower, Arepo, holds works wheels) was found as a graffito at Herculaneum, buried by ash in that year. This palindrome is remarkable for the fact that it also reproduces itself if one forms a word from the first letters, then the second letters and so forth. Hence, it can be arranged into a word square that reads in four different ways: horizontally or vertically from either top left to bottom right or bottom right to top left.

A palindrome with the same property is the Hebrew palindrome «We explained the glutton who is in the honey was burned and incinerated» (פרשנו רעבתן שבדבש נתבער ונשרף; PRShNW R`BTN ShBDBSh NTB`R WNShRP or parasnu ra`abhtan shebad’vash nitba’er venisraf) by Abraham ibn Ezra, referring to the halachic question as to whether a fly landing in honey makes the honey treif (not kosher).

פ ר ש נ ו
ר ע ב ת ן
ש ב ד ב ש
נ ת ב ע ר
ו נ ש ר ף

Another Latin palindrome, In girum imus nocte et consumimur igni («We go wandering at night and are consumed by fire»—In girum ire is translated as «go wandering» instead of the literal «go in a circle», cf. Italian andare in giro, «go strolling or wandering around»), was said to describe the behavior of moths. It is likely from medieval rather than ancient times.

Byzantine Greeks often inscribed the palindrome «Wash [the] sins not only [the] face» ΝΙΨΟΝ ΑΝΟΜΗΜΑΤΑ ΜΗ ΜΟΝΑΝ ΟΨΙΝ (Nīpson anomēmata mē mōnan ōpsin, note ps is the single Greek letter Ψ, psi) on baptismal fonts. This practice was continued in many English churches. Examples include the font at St. Mary’s Church, Nottingham and also the font in the basilica of St. Sophia, Constantinople, the font of St. Stephen d’Egres, Paris; at St. Menin’s Abbey, Orléans; at Dulwich College; and at the following churches: Worlingworth (Suffolk), Harlow (Essex), Knapton (Norfolk), St Martin, Ludgate (London), and Hadleigh (Suffolk).

Simple Examples for Palindromes

1. Malayalam 2. Amma 3. Appa 4. Madam 5. Racecar 6. WOW 7. civic 8. kayak

Palindromes in ancient Sanskrit

Palindromes of considerable complexity were experimented with in Sanskrit poetry.^[1] Complex palindromes appear in the 19th canto of the 8th-century epic poem śiśupāla-vadha by Magha. It yields the same text if read forwards, backwards, down, up, or diagonally:

sa-
kā-	ya-	sā-	da-	da-	sā-	ya-	kā
ra-	sā-	ha-	vā	vā-	ha-	sā-	ra-
nā-	da-	vā-	da-	da-	vā-	da-	nā.
(nā	da	vā	da	da	vā	da	nā
ra	sā	ha	vā	vā	ha	sā	ra
kā	ya	sā	da	da	sā	ya	kā
sa	kā	ra	nā	nā	ra	kā	sa)

(Note: hyphen indicates continuation of same word.) The last four lines are an inversion of the first four and are not part of the verse. They are included here only so that its properties can be more easily discerned, as the up-and-down reading depends on re-reading the text back up again in each column.

The stanza translates as:

[That army], which relished battle (rasāhavā), contained allies who brought low the bodes and gaits of their various striving enemies (sakāranānārakāsakāyasādadasāyakā), and in it the cries of the best of mounts contended with musical instruments (vāhasāranādavādadavādanā).

The same work (Śiśupāla-vadha) also contains stanzas in which each line is a palindrome, and stanzas that can be read backwards to give a new stanza (semordnilaps). Such stanzas are also found in the earlier work Kirātārjunīya.

This sanskrit poem was written by «nandi-ghanta kavis» in kanda style.

सारस नयना घन जघ

नारचित रतार कलिक हर सार रसा

सार रसारह कलिकर

तारत चिरनाघ जनघ नायनसरसा ! |

Palindromes in Tamil poetry

Palindromes are referred to in Tamil as Maalai Maatru (மாலை மாற்று). The earliest known palindromic verses (11 couplets) occur in the devotional poetry of Shaivism saint Sambandhar who lived around the 7th Century C.E.

The first of these eleven verses runs thus —

யாமாமாநீ யாமாமா யாழீகாமா காணாகா

காணாகாமா காழீயா மாமாயாநீ மாமாயா

It refers to Shiva as the incomparable God, the one who plays the Veena, the beautiful one adorned with snakes, the one who destroyed Kama, whose abode is Sirkazhi, who also appears as Vishnu, and beseeches him (Shiva) to rid the devotee of impurities.

Palindromic verses are also to be found in Madhava Shivagnana Yogi’s Kanchi Puranam (மாதவச்சிவஞானயோகிகள் காஞ்சிப் புராணம்) and Mahavidvaan Meenakshi Sundaram Pillai’s Thirunaagaik kaaronap puranam (மகாவித்துவான் மீனாட்சிசுந்தரம் பிள்ளை திருநாகைக் காரோணப் புராணம்).^[2]

Types

Characters

The most familiar palindromes, in English at least, are character-by-character: The written characters read the same backwards as forwards. Some examples of common palindromic words: civic, radar, level, rotor, kayak, reviver, racecar, redder, madam, toot, boob, pop and noon.

Phrases

Palindromes often consist of a phrase or sentence, e.g.: «Eva, can I stab bats in a cave?», «Mr. Owl ate my metal worm.», «Was it a rat I saw?», «A nut for a jar of tuna», «Ma is as selfless as I am», «Dammit, I’m mad!», and «A Santa lived as a devil at NASA». Punctuation, capitalization, and spacing are usually ignored, although some, such as «Rats live on no evil star» and «Step on no pets», include the spacing.

Famous English palindromes

Some well-known English palindromes are «Able was I ere I saw Elba»,^[3] «A man, a plan, a canal, Panama»,^[4] «Madam, I’m Adam» or «Madam in Eden, I’m Adam», «Doc, note: I dissent. A fast never prevents a fatness. I diet on cod.»^[5] and «Never odd or even.» «Rise to vote sir» was featured in an episode of The Simpsons.

Names

Some people have names that are palindromes. A few common palindrome names are: Maham, Ada, Anna, Bob, Eve, Hannah and Otto. Lon Nol (1913–1985) was Prime Minister of Cambodia. Nisio Isin is a Japanese novelist and manga writer, whose real name (西尾 維新, Nishio Ishin) is a palindrome in Japanese and when romanized using Kunrei-shiki or Nihon-shiki (it is often written as NisiOisiN to emphasize this). Some changed their name in order to be a palindrome (one example is actor Robert Trebor), while others were given a palindromic name at birth (such as philologist Revilo P. Oliver and Korean-American Mike Kim).^[6] Palindromic names are very common in Finland. Examples include Olavi Valo, Emma Lamme, Sanna Rannas, Anni Linna and Asko Oksa. «Stanley Yelnats» is the name of a character in «Holes», a 1998 novel and 2003 film.

Molecular biology

Restriction enzymes recognize a specific sequence of nucleotides and produce a double-stranded cut in the DNA. While recognition sequences vary widely, with lengths between 4 and 8 nucleotides, many of them are palindromic, which correspond to nitrogenous base sequences between complementary strands, which, when read from the 5′ to 3′ direction, are identical sequences.

Numbers

A palindromic number is a number whose digits, with decimal representation usually assumed, are the same read backwards, for example, 5885. They are studied in recreational mathematics where palindromic numbers with special properties are sought. A palindromic prime is a palindromic number that is a prime number.

The continued fraction of is a repeating palindrome when n is an integer.

Dates

Palindromic dates are of interest to recreational mathematicians and numerologists, and sometimes generate comment in the general media.^[7] Whether or not a date is palindromic depends on the style in which it is written. In the mm/dd/yyyy style, the most recently occurring palindromic date was November 2, 2011 (11/02/2011), and the next one will be on February 2, 2020 (02/02/2020). In the dd/mm/yyyy style, 2 January 2010 (01/02/2010) would be one example and the most recent was 11/02/2011 — the 11th day of February, 2011. If a two-digit year is used, the most recent date was November 11, 2011 (11/11/11) and the next will be November 22, 2011 (11/22/11, mm/dd), or 21 November 2012 (21/11/12, dd/mm). Some dates have more than one palindromic form. For example, the date September 29, 1929, can be written as a palindrome 3 ways. Without the year, it’s 9/29. With the year, it is 9/29/29 or 9/29/1929. January 10, 2011 is a four-way palindrome, as 1/10/2011, 1/10/11, I/X/MMXI, or I/X/XI. A date can be a palindrome depending on how is is said. For example, the date October 20, 2010 can be written 10/20/2010 and said as, «Ten, twenty, twenty-ten.»

In Sweden the common date-style is yyyymmdd and a palindrome-date is 20111102

Acoustics

A palindrome in which a recorded phrase of speech sounds the same when it is played backwards was discovered by composer John Oswald in 1974 while he was working on audio tape versions of the cut-up technique using recorded readings by William S. Burroughs. Oswald discovered in repeated instances of Burroughs speaking the phrase «I got» that the recordings still sound like «I got» when played backwards.^[8][9]

In French, a more complex example has been identified with^{[citation needed]} «Une slave valse nue» (a Slavic girl waltzes naked)

Music

Rhythm

The Afro-Cuban rhythm «Cáscara» is a palindrome :

x0xx0x0xx0x0xx0x (where «x» is a hit, «0» is a rest)

Classical music

Joseph Haydn’s Symphony No. 47 in G is nicknamed «the Palindrome». The third movement, minuet and trio is a musical palindrome. This clever piece goes forward twice and backwards twice and arrives back at the same place.

Wolfgang Amadeus Mozart’s Scherzo-Duetto di Mozart is played by one violinist as written and the second with the same music inverted.^[vague]

The interlude from Alban Berg’s opera Lulu is a palindrome, as are sections and pieces, in arch form, by many other composers, including James Tenney, and most famously Béla Bartók. George Crumb also used musical palindrome to text paint the Federico García Lorca poem «¿Por qué nací?», the first movement of three in his fourth book of Madrigals. Igor Stravinsky’s final composition, The Owl and the Pussy Cat, is a palindrome.^{[citation needed]}

The first movement from Constant Lambert’s ballet Horoscope (1938) is titled «Palindromic Prelude». Lambert claimed that the theme was dictated to him by the ghost of Bernard van Dieren, who had died in 1936.^[10]

British composer Robert Simpson also composed music in the palindrome or based on palindromic themes; the slow movement of his Symphony No. 2 is a palindrome, as is the slow movement of his String Quartet No. 1. His hour-long String Quartet No. 9 consists of thirty-two variations and a fugue on a palindromic theme of Haydn (from the minuet of his Symphony No. 47). All of Simpson’s thirty-two variations are themselves palindromic, equating to a remarkable feat in string quartet writing.

The music of Anton Webern is often imbued with palindromes. Webern, who had studied the music of the Renaissance composer Heinrich Isaac, was extremely interested in symmetries in music, be they horizontal or vertical. For one of the most famous examples of horizontal or linear symmetry in Webern’s music, one should look no further than the first phrase in the second movement of the symphony, Op. 21. In one of the most striking examples of vertical symmetry, the second movement of the Piano Variations, Op. 27, Webern arranges every pitch of this dodecaphonic work around the central pitch axis of A4. From this, each downward reaching interval is replicated exactly in the opposite direction. For example, a G♯3—13 half-steps down from A4—is replicated as a B♭5—13 half-steps above.

Just as the letters of a verbal palindrome are not reversed, so are the elements of a musical palindrome usually presented in the same form in both halves. Although these elements are usually single notes, palindromes can be made using more complex elements. For example, Karlheinz Stockhausen’s composition Mixtur, originally written in 1964, consists of twenty sections, called «moments», which may be permuted in several different ways, including retrograde presentation, and two versions may be made in a single program. When the composer revised the work in 2003, he prescribed such a palindromic performance, with the twenty moments first played in a «forwards» version, and then «backwards». Each moment, however, is a complex musical unit, and is played in the same direction in each half of the program.^[11] By contrast, Karel Goeyvaerts’s 1953 electronic composition, Nummer 5 (met zuivere tonen) is an exact palindrome: not only does each event in the second half of the piece occur according to an axis of symmetry at the centre of the work, but each event itself is reversed, so that the note attacks in the first half become note decays in the second, and vice-versa. It is a perfect example of Goeyvaerts’s aesthetics, the perfect example of the imperfection of perfection.^[12]

In classical music, a crab canon is a canon in which one line of the melody is reversed in time and pitch from the other. A large scale musical palindrome covering more than one movement is called «chiasic» referring to the cross shaped Greek letter «χ» (pronounced /ˈkaɪ/.) This is usually a form of reference to the crucifixion for example, the crucifixus section of the Bach B-minor Mass. The purpose of such palindromic balancing is to focus the listener on the central movement much like one would focus on the center of the cross in the crucifixion. Other examples are found in Bach’s Cantata BWV 4, «Christ lag in Todesbanden», Handel’s Messiah and the Fauré Requiem.^[13]

Popular music

Musical content

Hüsker Dü’s concept album Zen Arcade contains the songs «Reoccurring Dreams» and «Dreams Reoccurring», the latter of which appears earlier on the album but is actually the intro of the former song played in reverse. In similar manner, The Stone Roses’ first album contains the songs «Waterfall» and «Don’t Stop», the latter of which is, in essence, the former performed backwards. The 12″ and CD formats of their single Elephant Stone feature the B-side «Full Fathom Five», which is an alternate mix of the title track played in reverse.

The title track of the 1992 album entitled UFO Tofu by Béla Fleck and the Flecktones is said by its composer to be a musical palindrome.

In 2003, the city of San Diego, California commissioned sculptor Roman DeSalvo and composer Joseph Waters to create a public artwork in the form of a safety railing on the 25th Street overpass at F and 25th Streets. The result, Crab Carillon, is a set of 488 tuned chimes that can be played by pedestrians as they cross the overpass. Each chime is tuned to the note of a melody, composed by Waters. The melody is in the form of a palindrome, to accommodate walking in either direction.^[14]

«Starálfur», from Sigur Rós’s Ágætis byrjun has the strings part palindrome.

The song «You Can Call Me Al» by Paul Simon features a palindromic bass run performed by Bakithi Kumalo.

Lyrics

The song «I Palindrome I», by They Might Be Giants, features palindromic lyrics and imagery. The 27-word bridge is word-symmetrical.

«Weird Al» Yankovic’s song «Bob», from his 2003 album Poodle Hat, consists of rhyming palindromes and parodies the Bob Dylan song «Subterranean Homesick Blues».

Baby Gramps is known for songs where the lyrics are made up of palindromes.

Names and titles

In 1975, the Swedish pop group ABBA had a hit single titled «SOS», a unique occasion in which a song’s title and the name of its recording artist are both palindromes.

The Grateful Dead’s 1969 album Aoxomoxoa is a notable early use of palindrome in the title of a popular music album.

In 1992, the grunge band Soundgarden released an EP called Satanoscillatemymetallicsonatas or SOMMS; the title is a palindrome and puns on the supposed connection between the Devil and heavy metal music.

On Boris and Sunn O)))’s collaborative album «Altar», the vinyl version included a full disc, double-sided bonus track entitled «Satan Oscillate My Metallic Sonatas» (in reference to the Soundgarden EP of the same name), in which the various instruments (mainly guitars) are introduced one at a time on side one, and then fade out in reverse order on side two. Kim Thayil of Soundgarden appears on this track.

The Fall of Troy made a song with the famous palindrome «A Man, A Plan, A Canal, Panama» as the title.

The first and last tracks on Andrew Bird’s album Noble Beast form a palindrome («Oh No» and «On Ho!») and the seventh track is a palindrome in itself: «Ouo». He has also mentioned palindromes in earlier music, giving his songs names like «11:11» «T’N’T» and «Fake Palindromes» (although the last title is not a palindrome itself). He also mentions palindromes in the lyrics of the song «I» and the «I» redux «Imitosis».

«racEcar» by Vitamin Party features a repeating chorus of «A Man, A Plan, A Canal, Panama» (the title itself is palindromic).

«Never Odd or Even», which was to be the title of the first album by Aleka’s Attic, the band formed by the late River Phoenix, is a palindrome.

«If I Had a Hi-Fi», a 2010 cover album by American alternative rock band Nada Surf, is a palindrome.

Miles Davis and Black Sabbath both had albums called «Live Evil». Inversely, Lynch Mob and Diamond Head had albums called «Evil Live».

D.R.U.G.S. has two songs that are palindromes on the self-titled debut album, «Mr. Owl Ate My Metal Worm» and «Laminated E.T. Animal».

The Asian-American teenage Riot Grrrl band Emily’s Sassy Lime’s name is palindromic.

Long palindromes

The longest palindromic word in the Oxford English Dictionary is the onomatopoeic tattarrattat, coined by James Joyce in Ulysses (1922) for a knock on the door. The Guinness Book of Records gives the title to detartrated, the preterit and past participle of detartrate, a chemical term meaning to remove tartrates. Rotavator, a trademarked name for an agricultural machine, is often listed in dictionaries. The term redivider is used by some writers but appears to be an invented or derived term—only redivide and redivision appear in the Shorter Oxford Dictionary. Malayalam, an Indian language, is of equal length.

According to Guiness World Records, the Finnish word saippuakivikauppias (soapstone vendor), a 19 letter word, is claimed to be the world’s longest palindromic word in everyday use. A meaningful derivative from it is saippuakalasalakauppias (soapfish bootlegger). An even longer effort is saippuakuppinippukauppias (soap dish wholesale vendor). Almost equally long is the Estonian word kuulilennuteetunneliluuk (the hatch a bullet flies out of when exiting a tunnel).

In English, two palindromic novels have been published: Satire: Veritas by David Stephens (1980, 58,795 letters), and Dr Awkward & Olson in Oslo by Lawrence Levine (1986, 31,954 words).^[15] In French, Oulipo writer George Perec’s «Grand Palindrome» (1969) is 5,556 letters in length.^[16][17] In Hebrew, Noam Dovev wrote a 303-word, 1111-letter palindromic story called «Do god».^[18]

Biological structures

In most genomes or sets of genetic instructions, palindromic motifs are found. However, the meaning of palindrome in the context of genetics is slightly different from the definition used for words and sentences. Since the DNA is formed by two paired strands of nucleotides, and the nucleotides always pair in the same way (Adenine (A) with Thymine (T), Cytosine (C) with Guanine (G)), a (single-stranded) sequence of DNA is said to be a palindrome if it is equal to its complementary sequence read backwards. For example, the sequence ACCTAGGT is palindromic because its complement is TGGATCCA, which is equal to the original sequence in reverse complement.

A palindromic DNA sequence can form a hairpin. Palindromic motifs are made by the order of the nucleotides that specify the complex chemicals (proteins) that, as a result of those genetic instructions, the cell is to produce. They have been specially researched in bacterial chromosomes and in the so-called Bacterial Interspersed Mosaic Elements (BIMEs) scattered over them. Recently^[when?] a research genome sequencing project discovered that many of the bases on the Y-chromosome are arranged as palindromes.^{[citation needed]} A palindrome structure allows the Y-chromosome to repair itself by bending over at the middle if one side is damaged.

It is believed that palindromes are also found frequently in proteins,^[19][20] but their role in the protein function is not clearly known. It has recently^[21] been suggested that the prevalence existence of palindromes in peptides might be related to the prevalence of low-complexity regions in proteins, as palindromes are frequently associated with low-complexity sequences. Their prevalence might be also related to an alpha helical formation propensity of these sequences,^[21] or in formation of proteins/protein complexes.^[22]

Computation theory

In the automata theory, a set of all palindromes in a given alphabet is a typical example of a language that is context-free, but not regular. This means that it is, in theory, impossible for a computer with a finite amount of memory to reliably test for palindromes. (For practical purposes with modern computers, this limitation would apply only to incredibly long letter-sequences.)

In addition, the set of palindromes cannot be reliably tested by a deterministic pushdown automaton and is not LR(k)-parseable. When reading a palindrome from left-to-right, it is, in essence, impossible to locate the «middle» until the entire word has been read completely.

It is possible to find the longest palindromic substring of a given input string in linear time.^[23][24]

Semordnilap

Semordnilap is a name coined for a word or phrase that spells a different word or phrase backwards. «semordnilap» is itself «palindromes» spelled backwards. According to author O.V. Michaelsen, it was probably coined by logologist Dmitri A. Borgmann and appeared in Oddities and Curiosities, annotated by Martin Gardner, 1961. Semordnilaps are also known as volvograms,^[25] heteropalindromes, semi-palindromes, half-palindromes, reversgrams, mynoretehs, reversible anagrams,^[26] word reversals, or anadromes.^[27] They have also sometimes been called antigrams,^[27] though this term now usually refers to anagrams with opposing meanings.

These words are very useful in constructing palindromic texts; together, each pair forms a palindrome, and they can be added on either side of a shorter palindrome in order to extend it.

The longest single-word English examples contain eight letters:

• stressed / desserts
• samaroid (resembling a samara) / dioramas
• rewarder / redrawer
• departer / retraped (construction based on the fact that verb trape is recorded as an alternative spelling of traipse)^[28]
• reporter / retroper (construction based on the fact that trope is recorded as a verb, meaning «to furnish with tropes»)^[28]

Other examples include:

• was / saw
• god / dog
• gateman / nametag
• enoteca / acetone
• deliver / reviled
• straw / warts
• star / rats
• lived / devil
• live / evil
• diaper / repaid
• smart / trams
• spit / tips
• stop / pots
• bats / stab

The poem Lost Generation is a line-by-line semordnilap. When the lines are read in reverse order, it becomes new poem.

Non-English palindromes

Palindromes in languages that use an alphabetic writing system work in essentially the same way as English palindromes. In languages that use a writing system other than an alphabet (such as Chinese), a palindrome is still a sequence of characters from that writing system that remains the same when reversed, though the characters now represent words rather than letters.

The treatment of diacritics varies. In languages such as Czech and Spanish, letters with diacritics or accents (except tildes) are not given a separate place in the alphabet, and thus preserve the palindrome whether or not the repeated letter has an ornamentation. However, in the Nordic languages, A, Å and Ä/Æ, as well as O and Ö/Ø, are all distinct letters and must be mirrored exactly to be considered a palindrome.

The longest palindrome in the Dutch language, according to the Dutch Guinness Book of World Records, is koortsmeetsysteemstrook, which translates into English as thermometer. The Dutch Wikipedia^[29] states, however, that Hugo Brandt Corstius, in his book, Opperlandse taal- en letterkunde, came up with the longest existing Dutch palindrome—potstalmelkkoortspilstaalplaatslipstrookklemlatstop—which has no definitive meaning, although it consists of legitimate Dutch words.^{[clarification needed]}

See also

• Ambigram
• Anagram
• Antimetabole
• Backmasking
• Constrained writing
• List of palindromic places
• Palindromic number
• Palindromic polynomial
• Pangram
• Phonetic palindrome
• Su Hui (poet)
• Yreka, California for the palindromic Yreka Bakery and Yrella Gallery

References

External links

• Palindromic Baby Names
• List of English Semordnilaps

A palindrome is a word, phrase, number or other sequence of units that can be read the same way in either direction (the adjustment of punctuation and spaces between words is generally permitted). Composing literature in palindromes is an example of constrained writing.
The word «palindrome» was coined from Greek roots palin (Template:Polytonic; «back») and dromos (Template:Polytonic; «way, direction») by English writer Ben Jonson in the 1600s. The actual Greek phrase to describe the phenomenon is karkinikê epigrafê (Template:Polytonic; crab inscription), or simply karkiniêoi (Template:Polytonic; crabs), alluding to the backward movement of crabs, like an inscription which can be read backwards.
Template:TOClimit

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Palindromes date back at least to 79 A.D., as the palindromic Latin word square «Sator Arepo Tenet Opera Rotas» was found as a graffito at Herculaneum, buried by ash in that year. This palindrome is remarkable for the fact that it also reproduces itself if one forms a word from the first letters, then the second letters and so forth. Hence it can be arranged into a word square that reads in four different ways: horizontally or vertically from top left to bottom right orpoertically from bottom right to top left. While some sources translate this as «The sower Arepo holds the wheels at work», translation is problematic as the word arepo is otherwise unknown; the square may have been a coded Christian signifier,^{[citation needed]} with TENET forming a cross.

A palindrome with the same property is the Hebrew palindrome «We explained the glutton who is in the honey was burned and incinerated» (Template:Script/Hebrew; PRShNW R`BTN ShBDBSh NTB`R WNShRP or parasnu ra`avtan sheba’dvash nitba’er venisraf) by Ibn Ezra, referring to the halachic question as to whether a fly landing in honey makes the honey treif.

פ ר ש נ ו
ר ע ב ת ן
ש ב ד ב ש
נ ת ב ע ר
ו נ ש ר ף

Another Latin palindrome, In girum imus nocte et consumimur igni («We go wandering at night and are consumed by fire» — In girum ire is translated as «go wandering» instead of the literal «go in a circle», cf. Italian andare in giro, «go strolling or wandering around»), was said to describe the behavior of moths. It is likely from medieval rather than ancient times.

Byzantine Greeks often inscribed the palindrome «Wash my sins not only my face» (: Template:Polytonic; Modern: Template:Polytonic; Nipson anomēmata mē monan opsin, note ps is the single Greek letter psi (Ψ)) on baptismal fonts. This is round the font at St. Mary’s Church, Nottingham and also the font in the basilica of St. Sophia, Constantinople, the font of St. Stephen d’Egres, Paris; at St. Menin’s Abbey, Orléans; at Dulwich College; and at the following churches: Worlingsworth (Suffolk), Harlow (Essex), Knapton (Norfolk), St Martin, Ludgate (London), and Hadleigh (Suffolk).

Palindromes in Ancient Sanskrit

Palindromes of considerable complexity were experimented with in Sanskrit poetry. An example which has been called «the most complex and exquisite type of palindrome ever invented»,^[1] appears in the 19th canto of the 8th century epic poem śiśupāla-vadha by Magha. It yields the same text if read forwards, backwards, down, or up:

sa-kA-ra-nA-nA-ra-kA-sa-

kA-ya-sA-da-da-sA-ya-kA

ra-sA-ha-vA vA-ha-sA-ra-

nA-da-vA-da-da-vA-da-nA.

(nA da vA da da vA da nA

ra sA ha vA vA ha sA ra

kA ya sA da da sA ya kA

sa kA ra nA nA ra kA sa)

(note: hyphen indicates continuation of same word). The last four lines are an inversion of the first four and are not part of the verse. They are only included here so that its properties can be more easily discerned, as the up-and-down reading depends on re-reading the text back up again in each column.

The stanza translates as:

[That army], which relished battle (rasAhavA) contained allies who brought low the bodes and gaits of their various striving enemies (sakAranAnArakAsakAyasAdadasAyakA), and in it the cries of the best of mounts contended with musical instruments (vAhasAranAdavAdadavAdanA).

Types

Characters

The most familiar palindromes, in English at least, are character-by-character: the written characters read the same backwards as forwards. Palindromic words exist, for example civic, level, rotator, rotor, kayak, and racecar.

Palindromes often consist of a phrase or sentence («Was it a rat I saw?», «Step on no pets», «Sit on a potato pan, Otis», «Lisa Bonet ate no basil», «Satan, oscillate my metallic sonatas», «I roamed under it as a tired nude Maori»). Punctuation, capitalization, and spacing are usually ignored, although some (such as «Rats live on no evil star») include the spacing.^[2]

The three famous English palindromes are «Able was I ere I saw Elba»^[3] (which is also palindromic with respect to spacing), «A man, a plan, a canal, Panama!”,^[4] and “Madam, I’m Adam”.

Some people have names that are palindromes. Some changed their name in order to be a palindrome (one example is actor Robert Trebor), while others were given a palindromic name at birth (such as Neo-Nazi philologist Revilo Oliver and more than one man named Mike Kim^[5]).

Words

Some palindromes use words as units rather than letters. Examples are «Fall leaves after leaves fall», «First Ladies rule the State and state the rule: ladies first» and «Girl, bathing on Bikini, eyeing boy, sees boy eyeing bikini on bathing girl». The command «Level, madam, level!», composed only of words that are themselves palindromes, is both a character-by-character and a word-by-word palindrome.

Lines

Still other palindromes take the line as the unit. The poem Doppelganger, composed by James A. Lindon, is an example.

The dialogue «Crab Canon» in Douglas Hofstadter’s Gödel, Escher, Bach is nearly a line-by-line palindrome. The second half of the dialog consists, with some very minor changes, of the same lines as the first half, but in reverse order and spoken by the opposite characters (i.e., lines spoken by Achilles in the first half are spoken by the Tortoise in the second, and vice versa). In the middle is a non-symmetrical line spoken by the Crab, who enters and spouts some nonsense, apparently triggering the reversal. The structure is modeled after the musical form known as crab canon, in particular the canon a 2 cancrizans of Johann Sebastian Bach’s The Musical Offering.

Molecular biology

Restriction enzymes recognize a specific sequence of nucleotides and produce a double-stranded cut in the DNA. While recognition sequences vary widely, with lengths between 4 and 8 nucleotides, many of them are palindromic, which correspond to nitrogenous base sequences that read the same backwards and forwards.

Numbers

A palindromic number is a number whose digits, with decimal representation usually assumed, are the same read backwards, for example, 58285. They are studied in recreational mathematics where palindromic numbers with special properties are sought. A palindromic prime is a palindromic number that is a prime number.

Dates

Palindromic dates are of interest to recreational mathematicians and numerologists, and sometimes generate comment in the general media.^[6] Whether or not a date is palindromic depends on the style in which it is written. For example, in the dd/mm/yyyy style, the 20th of February in 2002 (20-02-2002) was palindromic.

Music

Joseph Haydn’s Symphony No.47 in G is nicknamed the Palindrome. The third movement, minuet and trio is a musical palindrome. This clever piece goes forward twice and backwards twice and arrives back at the same place.

The interlude from Alban Berg’s opera Lulu is a palindrome, as are sections and pieces, in arch form, by many other composers, including James Tenney, and most famously Béla Bartók. George Crumb also used musical palindrome to text paint the Federico Garcia Lorca poem «¿Porque nací?», the first movement of three in his fourth book of Madrigals. Igor Stravinsky’s final composition, The Owl and the Pussy Cat, is a palindrome. British composer Robert Simpson also composed music in the palindrome or based on palindromic themes; the slow movement of his Symphony No. 2 is a palindrome, as is the slow movement of his String Quartet No. 1.

The music of Anton Webern is often imbued with palindromes. Webern, who had studied the music of the Renaissance composer Heinrich Issac, was extremely interested in symmetries in music, be they horizontal or vertical. For one of the most famous examples of horizontal or linear symmetry in Webern’s music, one should look no further than the first phrase in the second movement of the Opus 21 Symphony. In one of the most striking examples of vertical symmetry, the second movement of the Opus 27 Piano Variations, Webern arranges every pitch of this dodecaphonic work around the central pitch axis of A4. From this, each downward reaching interval is replicated exactly in the opposite direction. For example, a G-sharp3 – 13 half-steps down from A4 – is replicated as a B-flat5 – 13 half-steps above.

In classical music, a crab canon is a canon in which one line of the melody is reversed in time and pitch from the other.

Hüsker Dü’s concept album Zen Arcade contains the songs «Reoccurring Dreams» and «Dreams Reoccurring,» the latter of which appears earlier on the album but is actually the intro of the former song played in reverse. Similarly, The Stone Roses’ first album contains the songs «Waterfall» and «Don’t Stop,» the latter of which is essentially the former performed backwards.

The title track of the 1992 album entitled UFO Tofu by Béla Fleck and the Flecktones is said by its composer to be a musical palindrome.

In 2003 the city of San Diego, California commissioned sculptor Roman DeSalvo and composer Joseph Waters to create a public artwork in the form of a safety railing on the 25th Street overpass at F and 25th Streets. The result,Crab Carillon, is a set of 488 tuned chimes that can be played by pedestrians as they cross the overpass. Each chime is tuned to the note of a melody, composed by Waters. The melody is in the form of a palindrome, to accommodate walking in either direction.City of San Diego Public Art website.

The song «I Palindrome I», by They Might Be Giants, features palindromic lyrics and imagery. The 27-word bridge is word-symmetrical.

«Weird Al» Yankovic’s song «Bob», from his 2003 album Poodle Hat, consists of rhyming palindromes and parodies the Bob Dylan song Subterranean Homesick Blues.

The 2007 re-release of Yoko Ono’s song «No, No, No» is credited simply to «Ono», making the artist–title combination a palindrome.

Baby Gramps is known for songs where the lyrics are made up of palindromes.

The Fall of Troy made a song with the famous palindrome «A Man, A Plan, A Canal, Panama» as title.

The first and last tracks on Andrew Bird’s album Noble Beast form a palindrome («Oh No» and «On Ho!») and the seventh track is a palindrome in itself «Ouo». He has also mentioned palindromes in earlier music, giving his songs names like «11:11» «T’N’T» and «Fake Palindromes» (although the last title is not a palindrome itself). He also mentions palindromes in the lyrics of the song «I» and the «I» redux «Imitosis».

Starálfur, from Sigur Rós’s Ágætis byrjun has the strings part palindrome.

Acoustic

A palindrome in which a recorded phrase of speech sounds the same when it is played backwards was discovered by composer John Oswald in 1974 while he was working on audio tape versions of the cut-up technique using recorded readings by William S. Burroughs. Oswald discovered in repeated instances of Burroughs speaking the phrase «I got» that the recordings still sound like «I got» when played backwards.^[7][8]

Long palindromes

Single words

The longest palindromic word in the Oxford English Dictionary is the onomatopoeic tattarrattat, coined by James Joyce in Ulysses (1922) for a knock on the door. The Guinness Book of Records gives the title to detartrated, the past tense of detartrate, a somewhat contrived chemical term meaning to remove tartrates. Rotavator, a trademarked name for an agricultural machine, is often listed in dictionaries. The term redivider is used by some writers but appears to be an invented term — only redivide and redivision appear in the Shorter Oxford Dictionary. Malayalam, an Indian language, is of equal length (strictly, this name should be spelt either Malayaalam or Malayālam, as the next to last vowel is long). Another aspect of the word «malayalam» is that it stays a letter palindrome if it is written in any phonetic script like devanagari.

The Finnish word saippuakivikauppias (soap-stone vendor) is claimed to be the world’s longest palindromic word in everyday use. A meaningful derivative from it is saippuakalasalakauppias (soapfish bootlegger). An even longer effort is saippuakuppinippukauppias (soapdish batch seller). Koortsmeetsysteemstrook (fever measuring system strip) is probably the longest palindrome in Dutch.

Biological structures

In most genomes or sets of genetic instructions, palindromic motifs are found. However, the meaning of palindrome in the context of genetics is slightly different from the definition used for words and sentences. Since the DNA is formed by two paired strands of nucleotides, and the nucleotides always pair in the same way (Adenine (A) with Thymine (T), Cytosine (C) with Guanine (G)), a (single-stranded) sequence of DNA is said to be a palindrome if it is equal to its complementary sequence read backwards. For example, the sequence ACCTAGGT is palindromic because its complement is TGGATCCA, which is equal to the original sequence in reverse complement.

A palindromic DNA sequence can form a hairpin. Palindromic motifs are made by the order of the nucleotides that specify the complex chemicals (proteins) which, as a result of those genetic instructions, the cell is to produce. They have been specially researched in bacterial chromosomes and in the so-called Bacterial Interspersed Mosaic Elements (BIMEs) scattered over them. Recently a research genome sequencing project discovered that many of the bases on the Y chromosome are arranged as palindromes.^{[citation needed]} A palindrome structure allows the Y chromosome to repair itself by bending over at the middle if one side is damaged.

It is believed that palindromes are also found frequently in proteins,^[9][10] but their role in the protein function is not clearly known. It is recently ^[11] suggested that the prevalence existence of palindromes in peptides might be related to the prevalence of low-complexity regions in proteins, as palindromes are frequently associated with low-complexity sequences. Their prevalence might be also related to an alpha helical formation propensity of these sequences^[11], or in formation of protein/protein complexes ^[12].

Computation theory

In the automata theory, a set of all palindromes in a given alphabet is a typical example of a language which is context-free, but not regular. This means that it is theoretically impossible for a computer with a finite amount of memory to reliably test for palindromes. (For practical purposes with modern computers, this limitation would only apply to incredibly long letter-sequences.)

Additionally, the set of palindromes cannot be reliably tested by a deterministic pushdown automaton and is not LR(k) parseable. When reading a palindrome from left-to-right, it is essentially impossible to locate the “middle” until the entire word has been read.

Semordnilaps

Semordnilap is a name coined for a word or phrase that spells a different word or phrase backwards. «Semordnilap» is itself «palindromes» spelled backwards. According to author O.V. Michaelsen, it was probably coined by logologist Dmitri A. Borgmann and appeared in Oddities and Curiosities, annotated by Martin Gardner, 1961. Semordnilaps are also known as volvograms,^[13] heteropalindromes, semi-palindromes, half-palindromes, reversgrams, mynoretehs, reversible anagrams,^[14] word reversals, or anadromes.^[15] They have also sometimes been called antigrams,^[15] though this term now usually refers to anagrams with opposing meanings.

These words are very useful in constructing palindromes; together, each pair forms a palindrome, and they can be added on either side of a shorter palindrome in order to extend it.

The longest single-word instance in English is probably stratagem / mega tarts, which consists of nine letters. There are many examples containing eight letters, such as:

• stressed / desserts
• samaroid (resembling a samara) / dioramas
• rewarder / redrawer
• departer / retraped (construction based on the fact that verb trape is recorded as an alternative spelling of traipse^[16])
• reporter / retroper (construction based on the fact that trope is recorded as a verb, meaning «to furnish with tropes»^[16])

Other examples include:

• gateman / nametag
• deliver / reviled
• lamina / animal
• dennis / sinned
• straw / warts
• star / rats
• stop / pots
• snap / pans
• pins / snip
• lived / devil
• diaper / repaid
• smart / trams
• spit / tips
• live / evil
• dog / god
• gut / tug
• maps / spam
• war / raw
• was / saw
• trap / part

Non-English palindromes

Palindromes in languages that use an alphabetic writing system work in essentially the same way as English palindromes. In languages that use a writing system other than an alphabet (such as Chinese), a palindrome is still a sequence of characters from that writing system that remains the same when reversed, though the characters now represent words rather than letters.

The treatment of diacritics varies. In languages such as Czech and Spanish, letters with diacritics or accents (except tildes) are not given a separate place in the alphabet, and thus preserve the palindrome whether or not the repeated letter has an ornamentation. However, in Danish and other Nordic languages, A and A with a ring (Å) are distinct letters and must be mirrored exactly to be considered a true palindrome.

More examples of English palindromes

• Step on no pets.
• Dammit, I’m mad!
• Rise to vote, sir.
• Never odd or even
• If I had a hi-fi
• Yo, banana boy!
• Do geese see God?
• No devil lived on.
• Ah, Satan sees Natasha.
• Lewd did I live & evil I did dwel!
• Was it a car or a cat I saw?
• Are we not drawn onward, we few, drawn onward to new era?
• No lemon, no melon
• Now I see bees, I won.
• Ma is as selfless as I am.
• Nurse, I spy gypsies—run!
• Was it Eliot’s toilet I saw?
• No, sir, away! A papaya war is on!
• Go hang a salami, I’m a lasagna hog.
• I, madam, I made radio! So I dared! Am I mad? Am I?
• Swap God for a janitor, rot in a jar of dog paws.
• Eva, can I see bees in a cave?
• So many dynamos!
• Red rum, sir, is murder.
• Never even

Family

There is a certain warmth provided by palindromes perhaps coming from childhood.
Ironically many family nicknames, particularly in English, are palindromes:
Mom, Dad, Pop, Pap and Sis.
Likewise there are palindromes with a tag like: Momma, Poppa, Poppy, Pappy, Bubba, Nanna, Mamma,
Daddy and Sissa. Abba is the name for God the father.

See also

• Ambigram
• Anagram
• Backmasking
• List of palindromic places
• Phonetic palindrome
• Palindromic number
• Palindromic polynomial
• Reverse spelling
• Aibohphobia

References

External links

• Daft Fad, Computer Generated Palindromes
• List of English Semordnilaps

be-x-old:Паліндром
bg:Палиндром
ca:Palíndrom
cs:Palindrom
da:Palindrom
de:Palindrom
el:Καρκινική επιγραφή
eo:Palindromo
eu:Palindromo
fa:واروخوانه
ko:회문
hr:Obrtaljka
io:Palindromo
id:Palindrom
ia:Palindromo
is:Samhverfa
it:Palindromo
he:פלינדרום
ka:პალინდრომი
la:Palindromus
lb:Palindrom
hu:Palindrom
ml:പാലിന്‍ഡ്രോം
nl:Palindroom
no:Palindrom
nn:Palindrom
sq:Palindromi
simple:Palindrome
sk:Palindróm
sl:Palindrom
sh:Palindromi
fi:Palindromi
sv:Palindrom
uk:Паліндром
fiu-vro:Palindruum’

Template:WH
Template:WS

CONTENTS

Introduction……………………………………………………………..…3

1.The origin and
history of  palindromes…………………………………..5

1.1
Basic principles of palindrome construction………………..…………….5

2.
Linguistic features of palindromes…….……………………………………7

        
 2.1 Types of
palindromes…………………………………………………………………..9

3. Using the palindrome technique in
poetry and prose……………………13

4. Practical part……………………………………………………………15

Conclusion…………………………………………………………….…..17

Literature……………………………………………………………………………………….18

Application……………………………………………………….……….19

INTRODUCTION

A
palindrome is a word, phrase, number, or other sequence of characters which reads
the same backward or forward, such as madam or kayak. Sentence-length
palindromes may be written when allowances are made for adjustments to capital
letters, punctuation, and word dividers, such as «A man, a plan, a canal,
Panama!», «Was it a car or a cat I saw?» or «No ‘x’ in
Nixon».

Actuality: insufficient
knowledge about the linguistic features of the palindrome.

Material
for the study:
palindromes collected in the Internet.

Subject
of research:
linguistic characteristics of English palindrome.

The Objective
of the work is to explore the history of the palindrome, and describe the
features of English palindrome.

To
achieve the set aim I’ve determined the following tasks:

·                  
to
get general information about palindromes

·                  
to
find information about  history of palindromes

·                  
to
learn some facts about the typical palindromes and the common
features of the English language palindrome.

·                  
to
interview the pupils and teachers  of our school

·                  
to
analyze information

·                  
to
create a computer presentation

·                  
to
make a conclusion

The
practical importance:
the materials can be used in English lessons, will help to better understand
the development of modern English, a variety of linguistic and poetic forms.

In
my work I have used the following methods of research:

a.       Theoretical
study

b.      The
observation

c.       The
questionnaire

d.      Interweaving

e.       Generalization

Hypothesis: Not many people
know what a palindrome is and can hardly give any examples of palindrome words
or phrases.

Palindrome
refers to a rare form of poetry where the writing process is associated with
considerable technical difficulties, but the result does not always satisfy the
aesthetic sense [2]. It is most often referred to as experimental poetry
related to the comprehension of the secrets of craft and art of versification.
But along with this interpretation of the palindrome, and there its amazing
popularity in the general reading environment — almost every European would
call one or two palindromes known to them.

Therefore,
the interest to study this curious form — its genesis, history and development
of the theory — is due to the length of the «experiment» of poets
with a palindrome, which has more than two thousand years and still continues
to be considered experimental.

It
is expected that the study of poetry samples and information about palindrome
help to better understand the features of the palindrome as a form and genre,
to clarify its varieties and trace the evolution of the palindrome from its
origins to modern times.

1. The origin and
history of palindromes

It
is known that palindromes first appeared on the vessels, vases and other
objects of the spherical shape, «Inscription-palindrome can be read by
turning the» rotation of the body «in any direction or approaching it
from all sides.» Since antiquity palindromes were placed on the portals of
houses and temples, on fountains and tombstones.

The
origin of the palindrome is caused by the interaction of several equally
important factors. Firstly, the aesthetic sense of mirror symmetry, it is
almost a mathematical expression, not only in numbers and in letters. Secondly,
the aesthetics of the game — the game of the mind, an intellectual exercise in
the highest skill. Palindrome placed in Mystery crafts, famous and subservient
only the initiated, like «The Glass Bead Game» by H. Hesse. The most
logical justification for the emergence of European palindrome is necessary to
consider the variety of forms of writing, which coexisted in the ancient
Mediterranean since the time of Alexander the Great.

1.1Basic
principles of palindrome construction

Depending
on the number of occasions and variations of space, as well as measures match
the forward and reverse reading palindromes are classified according to the
degree of complexity and accuracy. Direct text palindrome, reading, in
accordance with the normal reading direction in the writing (in all types of
the Cyrillic and Latin alphabet — from left to right). The word
«palindrome» was coined from the Greek roots pálin
(«again») and drómos («path guide») British author Ben
Johnson in the 1600s. A classic example is the English palindrome: A man, a
plan, a canal — Panama

History
of palindrome has approximately two thousand years. Its origins are lost at the
turn of the old and the new era. Some tend to date the emergence of the
European palindrome IV century BC, what is said in the article «The oldest
palindrome», prepared based on «Bild der Vissenshaft» German
magazine. Other sources attribute the invention of the Greek poet Sotades palindrome
(Sotadisu), who lived in Alexandria during the reign of Ptolemy Philadelphus in
the III BC. (194, 78).

By
the X-XI centuries palindromes spread first in Italy and then in Western
Europe. From the twelfth and thirteenth centuries information about them,
though rare, appear in the books of poetics and treatises on prosody. This is
due to the opening of the first universities and the formation of a single
European romanized system of education.

By
the XIV century, it is the first appearance in the independent music
palindromic form. This discovery belongs to Guillaume de Machaut (1300-1377) —
famous poet and musician. And the music, and poetry palindromes throughout the
historical period of its existence, regarded as one of the highest
manifestations of technical skill, exquisite «jokes masters» of
poetry and music, designed for the elite connoisseurs.

In
the XIX century known sample palindrome:

«Lewd
did [I] live & Evil did dwel» ( «Obscene I lived, and lived like the
devil») is based on the specular words live — to live and evil — evil, and
goes back to the phrase of the «Our Father» prayer: «deliver us from
the Evil One »(« Deliver us from evil «).

Martin
Gardner cites several English palindromes Bomobo from the book «Literary
curiosities»

L.Mersera:
«! A man, a plan, a canal, — Panama» (Man, plan Canal — Panama!)

and
absurdist palindrome:

«Straw?
No, too stupid a fad. I put soot on warts » (« Straw? No, it’s too stupid a
fad. I smear soot warts «).

Based
on these examples, the XIX century genre «of curious poems» from
textbooks poetics finally moved to the entertainment sections of popular
magazines and as such continues to exist until the XX century. Poetry and magic
alternate jokes and fun [4].

Palindrome
in its broadest sense is not limited to verbal form. Palindrome is possible to
name an object, having a linear or cyclic form of organization, which is given
the symmetry of from beginning to end and from end to beginning.

Palindromes
may have a verse form (split into lines), or written prose — linear, with no
line breaks. Single-palindromes, respectively, do not belong to the verse nor
prose.

‘Live
not on evil

‘Was
it a car or a cat I saw?’

‘Pull
up if I pull up’

‘Some
men interpret nine memos’

‘Not
New York, Roy went on’

Sometimes
palindromic structure is used in the titles of the works: the name of the story
L. Levin (Lawrence Levin) “Dr Awkward & Olson in Oslo”.

The
syllabic structure of palindrome makes authors use the word form, so in English
palindrome there is often lack of the verbal forms and short nouns are used.

2. Linguistic
features of palindromes

Classification
of palindromes on the degree of complexity involves the introduction of the
concept of palindrome axis (palindromic or axis) and the  multiline palindrome.
This axis is an imaginary line extending in the letter or letters between and
separates the palindromic text so that one half of the letters were other
reverse (formed halfpalindromy). The introduction of the «axis»
concept and its visualization lets you see what a palindrome — «poem for
the eyes.»

The
central axis of the palindrome makes explicit the fact that the palindromic
verse text is both the product of special verbal and visual arts.

Quantitatively,
the complexity of the palindrome is determined by the minimum number of spaces
in halfpalindroms. The simplest is a palindrome complexity with the number zero,
one of which contains halfpalindroms occasions and, respectively, spacing. The
simplest example would be a palindrome associated with proper names: Emma
Lamme, Sanna Rannas, Enny Lynne and Asko Oksa.

Palindrome
Lewd did [I] live | Evil did dwel difficult because axis is not in the letter,
and between the letters.

Classification
of palindromes can also be made on the degree of accuracy due to the fact that
the reverse reading — compared to direct — changing place occasions, lost
importance of punctuation and capitalization, as well as permitted deviations
in spelling entries:

Al,
sign it, Lover! … Revolting, Isla (palindromic song was composed by Edward
Benbow)

First,
palindromes can be divided into accurate and inaccurate. The exact reverse
palindrome when read with absolute literal identity preserved spaces and
places: Madam I’m Adam. The highest degree of precision, or palindrome absolute
style, requires a complete coincidence occasions and absolute literal identity
rakohoda. To this end, the recording is often used only lowercase letters.
Strict style palindrome allows freedom in the gaps (and therefore takes into
account one-pointedness of punctuation), uppercase and lowercase letters;
excluded also carry the words between the lines, palindromes and single-letter
strings. Simply furnished written, for example, a palindrome:

Able
was I ere I saw Elba («I was strong, until I saw Elba.»)

It
is said that in drafting shifters tried his hand and Napoleon himself. Anyway,
he attributed this remarkable recognition in English.

Freestyle
allows palindrome (in varying degrees) the inaccuracy, single-letter strings,
hyphenation and doubling of letters. For example, ‘Niagara o roar again’

Recently
created cross-language palindromes and werewolves. The words of different
languages ​​may be recorded in a single transliteration, such as a dialogue.

Currency.
But you love? Or be palindrome, implying interchanged letters of different
languages ​​with similar phonetics, for example,

Crack
in the «Insert». ( «Insert» — key on the keyboard)

«User!»
— Dreams.

Yes
pop music! (Yes — yes)

Ball
on the forehead. (Ball [Ball] — ball)

Mile
— lim. (Lim = limit — limit)

Fire
— the sheriff. (Fire — the fire)

And
love was calling. (Love [Love] — love)

BEND,
King! (King — King)

Chimera
— remix. (Remix — remix)

In
English literature, despite no inversion of the English language, but thanks to
the advanced analytic, verbal palindrome has a much broader operation: Darling,
my love / Is great, so great; / <…> / Great, so great is / Love, my
darling (J.A.Lindon).

This
example shows that a palindrome is written from two sides, rather than from the
beginning to the end.

Superpalindrom
— this consists of the letters of the text passage, in which location in the
square table is the same sequence of letters when reading the following 4 ways:

1)
in lines from left to right and top to bottom;

2)
from top to bottom in columns and left to right;

3)
in rows from right to left and bottom to top;

4)
rows from the bottom up and from right to left.

2.1 Types of
palindromes

Characters

The
most familiar palindromes, in English at least, are character-by-character: the
written characters read the same backwards as forwards. Some examples of
palindromic words: civic, radar, level, rotator, rotor,
kayak, reviver, racecar, and redder.

Phrases

Palindromes often
consist of a phrase or sentence («Go hang a salami I’m a lasagna
hog.», «Was it a rat I saw?», «Step on no pets»,
«Sit on a potato pan, Otis», «Lisa Bonet ate no
basil», «Satan, oscillate my metallic sonatas», «I roamed
under it as a tired nude Maori,»  or the
exclamation «Dammit, I’m mad!»). Punctuation, capitalization, and
spacing are usually ignored, although some (such as «Rats live on no evil
star») include the spacing.  

Famous
quotations

Three
famous English palindromes are «Able was I ere I saw Elba» which is
also palindromic with respect to spacing), «A man, a plan, a canal,
Panama!», and

A
possible, also palindromic reply is, «Name no one man.»

Names

Some people have
names that are palindromes. Lon Nol (1913-1985) was Prime Minister of Cambodia.
Nisio Isin is a
Japanese novelist and manga writer, whose real name (西尾 維新, Nishio
Ishin) is a palindrome  when romanized using Kunrei-shiki or Nihon-shiki (it is often
written as NisiOisiN to emphasize this). Some changed their name in order to be
a palindrome (one example is actor Robert Trebor), while others
were given a palindromic name at birth (such as philologist Revilo P. Oliver and
Korean-American Mike Kim) [9].

Words

Some
palindromes use words as units rather than letters. Examples are «Fall
leaves after leaves fall», «First Ladies rule the State and state the
rule: ladies first» and «Girl, bathing on Bikini, eyeing boy, sees
boy eyeing bikini on bathing girl». The command «Level, madam, level!
, composed only of words that are themselves palindromes, is both a
character-by-character and a word-by-word palindrome.

Lines

Still
other palindromes take the line as the unit. The poem Doppelgänger,
composed by James A. Lindon, is an example.

The
dialogue «Crab Canon» in Douglas Hofstadter‘s Gödel,
Escher, Bach is nearly a line-by-line palindrome. The
second half of the dialog consists, with some very minor changes, of the same
lines as the first half, but in reverse order and spoken by the opposite
characters (i.e., lines spoken by Achilles in the first half are spoken by the
Tortoise in the second, and vice versa). In the middle is a non-symmetrical
line spoken by the Crab, who enters and spouts some nonsense, apparently
triggering the reversal. The structure is modeled after the musical form known
as crab canon, in
particular the canon a 2 cancrizans of Johann Sebastian
Bach‘s
The
Musical Offering.

Molecular
biology

Main
article: Palindromic
sequence

Restriction
enzymes recognize a specific sequence of nucleotides and
produce a double-stranded cut in the DNA. While recognition sequences vary
widely, with lengths between 4 and 8 nucleotides, many of them are palindromic,
which correspond to nitrogenous base sequences between complementary strands,
which, when read from the 5′ to 3′ direction, are identical sequences.

Numbers

Main
article: Palindromic number

A
palindromic number is a number whose digits, with decimal representation usually assumed,
are the same read backwards, for example, 58285. They are studied in recreational
mathematics where palindromic numbers with special properties are
sought. A palindromic prime is a palindromic
number that is a prime number.

Dates

Palindromic
dates are of interest to recreational mathematicians and numerologists, and sometimes
generate comment in the general media.^[6] Whether or not a
date is palindromic depends on the style in which it is written. In the mm/dd/yyyy
style, the most recently occurring palindromic date was January 2nd, 2010
(01/02/2010), and the next one will be on November 2nd, 2011 (11/02/2011).  While in
the dd/mm/yyyy style, the 1st of February, 2010 (01/02/2010) would be
one example. Some dates have more than one palindromic form. For example, the
date September 29, 1929, can be written as a palindrome 3 ways. Without the
year, it’s 9/29. With the year, it is 9/29/29 or 9/29/1929.

Acoustics

A
palindrome in which a recorded phrase of speech sounds the same when it is
played backwards was discovered by composer John
Oswald
in 1974 while he was working on audio tape versions of the cut-up technique using
recorded readings by William S.
Burroughs. Oswald discovered in repeated instances of Burroughs
speaking the phrase «I got» that the recordings still sound like
«I got» when played backwards.

Music

Classical
music

Joseph Haydn‘s Symphony
No. 47
in G is nicknamed «the Palindrome». The third movement, minuet and trio is a musical palindrome. This
clever piece goes forward twice and backwards twice and arrives back at the
same place.

W.A. Mozart‘s
Scherzo-Duetto di Mozart is played by one violinist as written and the second
with the same music inverted.

The
interlude from Alban Berg‘s opera Lulu is a palindrome, as are sections
and pieces, in arch form, by many other
composers, including James Tenney, and most
famously Béla Bartók. George Crumb also used musical
palindrome to text paint the Federico Garcia
Lorca
poem «¿Porque nací?», the first movement of three in his fourth book
of Madrigals. Igor Stravinsky‘s final composition,
The Owl and the Pussy Cat, is a palindrome.

The
first movement from Constant Lambert‘s ballet Horoscope (1938) is titled
«Palindromic Prelude». Lambert claimed that the theme was dictated to
him by the ghost of Bernard van Dieren, who had died in
1936.^[9]

British
composer Robert
Simpson also composed music in the palindrome or based on
palindromic themes; the slow movement of his Symphony
No. 2
is a palindrome, as is the slow movement of his String Quartet No. 1. His
hour-long String
Quartet No. 9 consists of thirty-two variations and a
fugue on a palindromic theme of Haydn (from the minuet of his Symphony No. 47).
All of Simpson’s thirty-two variations are themselves palindromic, equating to
a remarkable feat in string quartet writing.

In
classical music, a crab canon is a canon in which one line of the melody is
reversed in time and pitch from the other.

The
longest palindromic song was composed by Edward Benbow in November 1987, she
begins Al words, sign it, Lover! and ends with the revolting, Isla. The
composition consists of 100,000 words.

3. Using palindrome
technique in poetry and prose

Palindromes
are willingly used in visual poetry, thereby creating the so-called videopalindroms
— visual poetry, based on the technique of the palindrome. Such structures are
created by recording of the text on the closed line (generally a circle), resulting
in a cyclodrome. Cyclodrome reads the same in both directions at the beginning
of the end splice; while a physical copy of the initial letters of the forward
and reverse reading can be different. For example, the longest English word
palindrome TATTARRATTAT, which is recorded in the Oxford dictionary [10.

A
more complex view of the palindrome (verbal and non-alpha) is a poem written by
this principle: first line to the last, as well as from the last to the first
verses is read the same way. The verses below, written by James Lyndon (James
A. Lindon). From the first line to the last, as well as from the last to the
first verses are read the same way. They were first published in a book by Dmitry
Borgman «Beyond Language»:

Entering
the lonely house with my wife

I
saw him for the first time

Peering
furtively from behind a bush —

Blackness
that moved,

A
shape amid the shadows,

A
momentary glimpse of gleaming eyes

Revealed
in the ragged moon.

A
closer look (he seemed to turn) might have

Put
him to flight forever —

I
dared not

(For
reasons that I failed to understand),

Though
I knew I should act at once.

I
puzzled over it, hiding alone,

Watching
the woman as she neared the gate.

He
came, and I saw him crouching

Night
after night.

Night
after night

He
came, and I saw him crouching,

Watching
the woman as she neared the gate.

I
puzzled over it, hiding alone —

Though
I knew I should act at once,

For
reasons that I failed to understand

I
dared not

Put
him to flight forever.

A
closer look (he seemed to turn) might have

Revealed
in the ragged moon

A
momentary glimpse of gleaming eyes

A
shape amid the shadows,

Blackness
that moved.

Peering
furtively from behind a bush,

I
saw him, for the first time

Entering
the lonely house with my wife.

(James
A. Lindon) [10].

Palindrome
technique used literary figures not only in poetry but in stories. In this
regard, two well-known story in the English language — Dr Awkward & Olson
in Oslo (Okvard Dr. Olson and Oslo), which Levin (Lawrence Levin) wrote in
1986, consists of 31 954 words, and Veritas (1980) the pen Deaida Stevens
(David Stephens), — 58 795 words.

In
2002 the longest palindrome in English was generated. It consists of 17 259
words. However, this palindrome can be called such only conditionally, since it
is not logically related to the text. It’s just a collection of words,
separated by commas.

4. Practical Part

A
key limitation of this research is that this phenomenon though being rather old
isn’t widely spread and there hasn’t been much professional research done on
it. However, taking into account most previous studies I’ve carried out a
survey among 200 pupils and 20 teachers of our school asking them the following
questions: Do you know what is a palindrome? If “yes”—can you give any
examples?

Out
of 200 pupils who were interviewed only 18 know what a palindrome is. 6 people
gave examples in Russian language. One girl mentioned the fact that her surname
is a palindrome: “Казак”.

The
percentage of teachers who gave positive answers on both questions is higher:
40 % (8 teachers):

As
you can see the number of people who don’t know about palindromes dominates. My
preliminary finding is that I have proved the hypothesis of the work: Not many people
know what a palindrome is and can hardly give any examples of palindrome words
or phrases.

CONCLUSION

The
idea of the palindrome is closely associated with the material and corporeal
aspect of verbal signification. Animal images are used for symbolizing the
palindromic processes of regression and circularity: the crab or cancer, and
the snake biting its own tail. Likewise, the mirror metaphor has been applied
to palindrome structures. Largely a visual phenomenon, the palindrome
epitomizes the spatiality of language and scripture, something indicated
already on the metaphorological plane of classical terminology: «running
back again» (palindromos), «stepping back» –a temporal motion in
space. Allowing for reversibility of the linear discourse, the palindrome
represents the very idea of transformation and metamorphosis. Palindromic
reversion is a device for breaking up the linearity of speech and, by
implication, the irreversibility of time. Irreversibility «themantises
itself in the palindrome form by eating itself up» (a quotation from Oskar
Pastior, the outstanding contemporary German palindrome poet). Sequentiality
and causality of time and space are annihilated in the palindromic motion.
Thus, the palindrome can be conceived of as a chronotope of revolution.
(‘chrono-topos’: time-space) [5].

This
report examines the different types of palindromes, regularities of their
structure, their  classification.

The
result is a dictionary of palindromes (see. Appendix ) which can be applied to
the English lessons.

This
phenomenon in language, though not new, but is very interesting and original. A
combination of different styles of speech, word creation, the importance of
each word, and at the same time a limited set of sounds and syllables create
magic words. Determination of palindromes is a very difficult  task, but if you
are lucky enough to create a successful and, most importantly, not devoid of
meaning small masterpiece, it is destined to live long, as an exemplary
representative of this wonderful genre. Some poets-experimenters write
palindromes entire poems — palindromony — this is the top of the skill. It is extremely
difficult to write  rhymed palindromony. Palindromes are not usually considered
in terms of their truth — but only in terms of their form [8]. Their form is
symmetrical, and therefore sacred. I plan to continue studying palindromic
structures and their linguistic features in comparison of 2 or 3 languages.

LITERATURE

1.    
English
Russian dictionary of genetic terms. Arefiev VA Lisovenko LA, Moscow. VNIRO,
1995

2.    
Baranov
AN, Dobrovolsky DO, Mikhailov MN, Parshin PB, Romanov OI English-Russian and
Russian-English dictionary of linguistics and semiotics. T. 1. M., 1996.

3.    
Bubnov
AV Language palindrome. Kursk, 1996

4.      [Donner M.] I
Love Me, Vol. I / S.Wordrow Palindrome Encyclopedia. Chapel Hill, North
Carolina,  1996.

5.    
Bergerson
H.W. Palindromes and Anagrams. N.Y., 1973.

6.     Crystal D.
Language play. [London], 1998.

7.     E. Greber
Palindromon B Revolutio // Russian Literature XLIII. 1998 S. 159CH203.

8.     Palindrome // The
Oxford Companion to English Literature / Compiled and edited by sir Paul
Harvey. Oxford, 1967. P. 610.

9.     http://www.languages-study.com/guinness-2.html

10. http://palindromist.org/chronotype

11. http://www.screen.ru/vadvad/Vadvad/Arp/Skld.htm

Appendix

Dictionary
palindromes

A
nut for a jar of tuna — Орех для фляги тунца.

Able
was I ere I saw Elba — Я был силён, пока не увидел Эльбу

Ada
— Ада

Anna
—Анна

Asko
Oksa – Аско Окса

Bob
— Боб

Civic
— гражданский

Dad
— папа

Dammit, I‘m mad!  — Черт
возьми я безумен!

Deed
— дело

Dr
Awkward – доктор Оквард (название рассказа)

Emma
Lamme – Эмма Лэйм

Enny
Lynne- Энни Лин

Eve
— Ева

Hannah
– Ханна

Kayak
— каяк

Level
— уровень

Live not on evil – Жизнь не
в зле

Ma
is as selfless as i am. — Мама так же самоотверженна, как я.

Madam,
I’m Adam  — Мадам, я Адам

Malayalam
— малаялам

Mom
– мама

Net
ewe ten (поймать в сеть овцу десять)

Niagara
o roar again – Ниагара ревет снова

Noon
— полдень

Not
New York, Roy went on – Рой был не в Нью Йорке

Nun
— монархия

Olson
in Oslo – Олсон в Осло (название рассказа)

Otto
— Отто

Peep
— пищать

Pull
up if I pull up – остановитесь, если я остановлюсь

Racecar
— гоночный автомобиль

Radar
— радар

Rats
live on no evil star. — Крысы не живут ни на какой злой звезде.

Redder
– более красный

Reviver
— оживитель

Rotor
— ротор

Sagas
— саги

Sanna
Rannas – Санна Раннас

Sator
arepo tenet opera rotas — Сеятель Арепо держит колеса в деле    
 

Shahs
– шахи

Solos
— соло

Some
men interpret nine memos – Несколько мужчин объясняют девять записок

Step
time emit pets (Время шага выпустить домашних животных)

Tattarrattat
– звук открывающейся двери, звук барабана

Tenet
 — принцип

Was
it a car or a cat I saw? – Это была машина или я увидел кота?

Was
it a rat I saw? — Действительно ли это была крыса, которую я видел?

Yay
– ура

Палиндромы
– биязы

Ball
в лоб

Fire
– шериф

User!
– грезю

Yes
 попсе

А
love звала

Гни,
King

Миля
– lim

Тресни в Insert

Химера – remix

Some famous names as fine palindrome examples:

•                   
Lon Nol was a  was Prime Minister of
Cambodia

•                   
Nisio Isin was a Japanese novelist

•                   
Robert Trebor was an actor

Stanley Yelnats is a character of  a movie Holes

Names of Places in Palindrome Style

•                   
Notton, Yorkshire, England

•                   
Kanakanak (Alaska)

•                   
Neuquen (Argentina)

•                   
Yreka Bakery (Yreka, California)

•                   
Madoko Dam, Zimbabwe

•                   
Renner (South Dakota)

•                   
Semmes (Alabama)

•                   
Caraparac, Peru

•                   
Allagalla, Sri Lanka

•                   
Glenelg (cities in Ontario, Maryland, and
Australia)

•                   
Vellev, Denmark

•                   
Capac (Michigan)

•                   
Lon Nol (Vietnam)

•                   
Tassat, France

•                   
Navan (Ireland)

•                   
Elleyelle, Nigeria

•                   
Akka, Morocco

•                   
Tumut (Australia)

•                   
Ward Draw (South Dakota)

•                   
Ruppur, Bangladesh

•                   
Oruro, Bolivia

•                   
Kivik, Sweden

•                   
Sajas, France

•                   
Wassamassaw (South Carolina)

•                   
Hattah, Australia

Names of Girls& Boys with Palindromes

•                   
Elle

•                   
Hannah

•                   
Anna

•                   
Ava

•                   
Ada

•                   
Emme

•                   
Ara

•                   
Asa

•                   
Bob

•                   
Natan

•                   
Kerek

•                   
Nitin

•                   
Siris

•                   
Nissin

Palindromic Names of Twins

•                   
Nadia & Aidan

•                   
Lexa & Axel

•                   
Nella & Allen

•                   
Kira & Arik

•                   
Nala & Alan

Palindromic Phrases & Sentences

•                   
Dammit, I’m mad!

•                   
Wonder if Sununu’s fired now.

•                   
Don’t nod.

•                   
Dog God.

•                   
Borrow or rob?

•                   
Evil rats on no star live.

•                   
Evil olive

•                   
I’m a fool; aloof am I.

•                   
Let Omro open one poor motel.

•                   
A new order began, a more Roman age bred Rowena.

•                   
Murder for a jar of red rum.

•                   
Satan, oscillate my metallic sonatas!

•                   
Did Hannah see bees? Hannah did.

•                   
Live, O Devil, revel ever! Live! Do evil!

•                   
Ma is as selfless as I am.

•                   
Must sell at tallest sum.

•                   
Cigar? Toss it in a can. It is so tragic.

•                   
Lay a wallaby baby ball away, Al.

•                   
See, slave, I demonstrate yet arts no medieval
sees.

•                   
Madam, I’m Adam.

•                   
Denim axes examined.

•                   
Naomi, did I moan?

•                   
May a moody baby doom a yam.

•                   
A dog, a plan, a canal: pagoda.

•                   
Desserts, I stressed!

•                   
No, Mel Gibson is a casino’s big lemon.

•                   
Eva, can I stab bats in a cave?

•                   
Stack cats.

•                   
Poor Dan is in a droop.

•                   
Golf? No sir, prefer prison-flog.

•                   
Draw, O coward!

•                   
No cab, no tuna nut on bacon.

•                   
Ten animals I slam in a net.

•                   
Meet animals; laminate ’em.

•                   
Never odd or even.

•                   
No lemon, no melon.

•                   
Party boobytrap.

•                   
Tino dump mud on it.

•                   
Rise to vote, sir.

•                   
Stella won no wallets.

•                   
Won’t lovers revolt now?

•                   
Was it a car or a cat I saw?

•                   
So many dynamos!

•                   
Let O’Hara gain an inn in a Niagara hotel.

•                   
Reviled did I live, said I, as evil I did
deliver.

•                   
Ma is a nun, as I am.

•                   
A nut for a jar of tuna.

•                   
Wonton? Not now.

•                   
Lay a wallaby baby ball away, Al.

•                   
No, Mel Gibson is a casino’s big lemon.

•                   
Gate man sees name, garage man sees name tag.

•                   
Drab as a fool, aloof as a bard.

•                   
Draw pupil’s lip upward.

•                   
Anne, I vote more cars race Rome to Vienna.

•                   
As I pee, sir, I see Pisa!

•                   
Dennis and Edna sinned.

•                   
Go deliver a dare, vile dog!

•                   
A Santa at Nasa.

•                   
Draw nine men inward.

•                   
Acrobats stab orca.

•                   
Do geese see God?

•                   
Zeus was deified, saw Suez.

•                   
Are we not drawn onward, we few, drawn onward to
new era?

•                   
Camp Mac

•                   
Evil, a sin, is alive.

•                   
Devil never even lived.

•                   
No, it never propagates if I set a gap or
prevention

•                   
Emu love volume.

•                   
No, I save on final perusal — a sure plan if no
evasion.

•                   
God saw I was dog.

•                   
No, Sir, panic is a basic in a prison.

•                   
He did, eh?

•                   
Hey, Roy! Am I mayor? Yeh!

•                   
I’m a pup, am I?

•                   
Oh, cameras are macho.

•                   
In words, alas, drown I.

•                   
Laid at a dial.

•                   
Sh…Tom sees moths.

•                   
Lid off a daffodil.

•                   
No, tie it on.

•                   
Seven eves.

•                   
Marge,lets send a sadness telegram.

•                   
My gym.

•                   
Name now one man.

•                   
Was it Eliot’s toilet I saw?

•                   
Pull up, Eva, we’re here! Wave! Pull up!

•                   
Oprah deified Harpo.

•                   
Niagara, eh? I hear again!

•                   
O Geronimo, no minor ego.

•                   
Pass mom’s sap.

•                   
Some men interpret nine memos.

•                   
Rail delivers reviled liar

•                   
Salt an atlas.

•                   
Too bad I hid a boot.

•                   
Won’t I panic in a pit now?

•                   
Selim’s tired — no wonder, it’s miles!

•                   
Yo bro! Free beer for boy!

•                   
Was it a bar or a bat I saw?

•                   
Too hot to hoot.

•                   
Yawn a more Roman way.

•                   
Star comedy by Democrats.

•                   
Now I draw an award. I won!

By Vishal Basumatary
in
Hackerrank
—
Jul 29, 2020

A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward or forward.(Wikipedia)

---

Given a string , print Yes if it is a palindrome, print No otherwise.

Constraints

• will consist at most  lower case english letters.

Sample Input

madam

Sample Output

Yes

Solution in java8

Approach 1.

import java.io.*;
import java.util.*;

public class Solution {

    public static void main(String[] args) {
        
        Scanner sc=new Scanner(System.in);
        String A=sc.next();
        
        
        if(A.equalsIgnoreCase(new StringBuffer(A).reverse().toString()))
            System.out.println("Yes");
        else
            System.out.println("No");
        
    }
}

---

Approach 2.

import java.io.*;
import java.util.*;

public class Solution {

    public static void main(String[] args) {
        
        Scanner sc=new Scanner(System.in);
        String A=sc.next();
        /* Enter your code here. Print output to STDOUT. */
        String rev = "";
        for(int i=A.length()-1;i>=0;i--)
            rev+=A.charAt(i);
        if(rev.equals(A))
            System.out.println("Yes");
        else
                    System.out.println("No");

    }
}

---