Palindrome

"Palindromes" redirects here. For the film, see Palindromes (film).

A palindrome is a word, phrase, number, or other sequence of symbols or elements, whose meaning may be interpreted the same way in either forward or reverse direction.

Composing literature in palindromes is an example of constrained writing. The word "palindrome" was coined from the Greek roots palin ([πάλιν] Error: {{Lang}}: text has italic markup (help); "again") and dromos ([δρóμος] Error: {{Lang}}: text has italic markup (help); "way, direction") by the English writer Ben Jonson in the 17th century. The Greek phrase to describe the phenomenon is karkinikê epigrafê ([καρκινικὴ επιγραφή] Error: {{Lang}}: text has italic markup (help); "crab inscription"), or simply karkinoi ([καρκίνοι] Error: {{Lang}}: text has italic markup (help); "crabs"), alluding to the movement of crabs, such as an inscription that may be read backwards.

History

The Sator Square.

Palindromes date back at least to 79 AD, as a palindrome was found as a graffito at Herculaneum, a city buried by ash in that year. This palindrome, called the Sator Square, consists of a sentence written in Latin: "Sator Arepo Tenet Opera Rotas" ("The sower Arepo holds works wheels"). It is remarkable for the fact that 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. As such, they can be referred to as palindromatic.

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 (non-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 which "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 that this palindrome is 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", engraving "ps" with 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).

Palindromes in The Quran

1 - And Magnify your Lord (Mudathir 74:3)

ر ب ك ف ك ب ر → ﻭرﺑﻚ ﻓﻜﺒﺮ  

Wa Rabbaka Fa Kabbir.

Focus only on the consonants in the Arabic language: R, B, K, f, K, B, R. And your Lord magnify (so magnify your Lord).

2 - They all float -each- in an Orbit. (Yasin 36:40)

ك ﻝ ف ﻱ ف ﻝ ك → ﻭﻛﻞ ﻓﻲ ﻓﻟﻚ ﻳﺴﺒﺤﻮﻥ  

Wa Kullun Fi Falakin Yasbahoon.

K, L, F, y, F, L, K.

See the letters Orbitting/floating around the letter ‘Ya’. In this verse God (Allah) is speaking about how the sun and the moon are in orbit. Notice the letters in red, brown and green. They are all floating around the letter in orange. The next word begins with the letter 'Ya' (of Yasbah, in singular form), which is referring to floating (Tasbeeh is from the same root). The letters are floating around one another, since the concept being discussed is orbit.

Palindromes in ancient Sanskrit

Palindromes of considerable complexity were experimented with in Sanskrit poetry. Complex palindromes appear in the 19th canto of the 8th-century epic poem Śiśupāla-vadha by Magha. It yields the same text if read forward, backward, down, up, or diagonally:

sa-	ka-	ra-	na-	na-	ra-	ka-	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: a hyphen indicates a 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 may 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 may be read backward 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 the 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 in Mahavidvaan Meenakshi Sundaram Pillai's Thirunaagaik Kaaronap Puranam (மகாவித்துவான் மீனாட்சிசுந்தரம் பிள்ளை திருநாகைக் காரோணப் புராணம்).

Types

Character, word, or line unit

The most familiar palindromes, in English at least, are character-by-character: The written characters read the same backward as forward. Some examples of common palindromic words: civic, radar, level, rotor, kayak, reviver, racecar, redder, madam, malayalam, and refer. There are also palindromes where the unit of reversal is the word ("So patient a doctor to doctor a patient so") or line (as in the poem "Doppelganger" by J.A. Lindon). These are referred to as "word-unit palindromes" and "line-unit palindromes" respectively. Word-unit palindromes were popularized in the recreational linguistics community by J.A. Lindon in the 1960s, but occasional examples in English are found from at least the 19th century, and several in French and Latin date to the Middle Ages.

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 car or a cat I saw?", "A nut for a jar of tuna", "Do geese see God?", "Ma is as selfless as I am", "On a clover, if alive erupts a vast pure evil, a fire volcano." "Dammit, I'm mad!", "A Toyota's a Toyota", "Go hang a salami, I'm a lasagna hog", 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", "A man, a plan, a canal - Panama!", "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" and "Never odd or even". "Rise to vote, sir" was featured in an episode of The Simpsons. Another relatively famous palindrome is the word "racecar" which is one of the few palindromes consisting of only one word.

Names

Some people have names that are palindromes. Included are given names (Ada, Anna, Bob, Aviva), surnames (Harrah, Renner, Salas) or both (Eve, Hannah, Maham, 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 when romanized using the Kunrei-shiki or the Nihon-shiki systems. (It is often written as NisiOisiN to emphasize this). Some persons have changed their name in order to make of it a palindrome (one example is actor Robert Trebor), while others were given a palindromic name at birth (such as the philologist Revilo P. Oliver).

Palindromic names are very common in Finland. Examples include Olavi Valo, Emma Lamme, Sanna Rannas, Anni Linna and Asko Oksa.

There are also palindromic names in fictional media. "Stanley Yelnats" is the name of a character in Holes, a 1998 novel and 2003 film. Four of the fictional Pokémon species have palindromic names in English (Eevee, Girafarig, Ho-Oh, and Alomomola).

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 of 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 backward, 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, for example, 191 and 313.

The continued fraction of ${\sqrt {n}}+\lfloor {\sqrt {n}}\rfloor$ is a repeating palindrome when $n$ is an integer.

Acoustics

A palindrome in which a recorded phrase of speech sounds the same when it is played backward 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 backward.

In France, a more complex example has been identified with "Une slave valse nue" (a Slavic girl waltzes naked).

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. The second half of the piece is the same as the first but backwards.

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.

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.

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.

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. 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.

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 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 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.

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.

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 a 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 backward. 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 may 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.

The strings part in "Starálfur", from the album Ágætis byrjun by Sigur Rós, is a 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 is a style parody the Bob Dylan song "Subterranean Homesick Blues". There is an accompanying video for the song which also parodies Dylan's video. Yankovic shows all of the palindromes on cue cards as they are being sung.

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 entitled, "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 a 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 such as "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.

In 2012, the American band Liars released an LP called WIXIW.

The German electronic trio To Rococo Rot is also a palindrome.

Comics

Watchmen #5, "Fearful Symmetry", the first page mirrors the last (in terms of frame disposition), with the following pages mirroring each other before the center-spread is (broadly) symmetrical in layout.

"NogegoN", Volume 3 of Les Terres creuses, by Luc et François Schuiten, Les Humanoïdes Associés, (1990) : each frame has its mirror image.

Television

Disney's Phineas and Ferb frequently alludes to palendromes, including the once-mentioned character Professor Ross E. Forp. Danville, the setting locale is also said to have a "Palendrome Road".

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 preterite 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.

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). In French, Oulipo writer George Perec's "Grand Palindrome" (1969) is 5,556 letters in length. In Hebrew, Noam Dovev wrote a 717-word, 2,662 letter palindromic story called, "Name sold, I'd lose man".

Biological structures

Main article: Palindromic sequence

Palindrome of DNA structure
A: Palindrome, B: Loop, C: Stem

In most genomes or sets of genetic instructions, palindromic motifs are found. The meaning of palindrome in the context of genetics is slightly different, however, 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 a research genome sequencing project discovered that many of the bases on the Y-chromosome are arranged as palindromes. 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 frequently are also found in proteins, but their role in the protein function is not clearly known. It has recently 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, or in formation of proteins/protein complexes.

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 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.

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

$d_{P}(w)=\left({\limsup _{k\rightarrow \infty }{\frac {n_{k+1}}{n_{k}}}}\right)^{-1}\ .$

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.

A palstar is a composition of palindromic strings.

Semordnilap

Semordnilap is a name coined for a word or phrase that spells a different word or phrase backward. "semordnilap" is itself "palindromes" spelled backward. According to logologist Dmitri A. Borgmann, the word was coined by Martin Gardner in Oddities and Curiosities of Words and Literature. Semordnilaps are also known as volvograms, heteropalindromes, semi-palindromes, half-palindromes, reversgrams, mynoretehs, reversible anagrams, word reversals, or anadromes. They have also sometimes been called antigrams, though now, this term usually refers to anagrams with opposing meanings.

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

The longest single-word English examples contain eight letters, such as "stressed" ("desserts") and "dioramas" ("samaroid", resembling a samara). Other shorter examples include "deliver" ("reviled") and "swap" ("paws").

Non-English palindromes

According to Guinness 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).

The longest palindrome in the Dutch language, according to the Dutch Guinness Book of World Records, is koortsmeetsysteemstrook, which translates into English as thermometer (for measuring fevers).

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

External links

• List of palindromes from Princeton Lexical Database.