English

Adjective

palindromic

1. of, relating to, or being a palindrome

Derived terms

• palindromic number
• palindromic prime

A palindrome is a word, phrase, number or other sequence of units that has the property of reading the same 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 (; "back") and dromos (; "way, direction") by English writer Ben Jonson in the 1600s. The actual Greek phrase to describe the phenomenon is karkinikê epigrafê (; crab inscription), or simply karkiniêoi (; crabs), alluding to the backward movement of crabs, like an inscription which can be read backwards.

History

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 or horizontally or vertically 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, with TENET forming a cross. For further discussion, see separate article.

A palindrome with the same property is the Hebrew palindrome "We explained the glutton who is in the honey was burned and incinerated" (; PRShW 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 enter the circle at night and are consumed by fire"), 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 face alone" (Medieval Greek: ; Modern: ; 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).

Types

Characters

The most familiar palindromes, in English at least, are character-by-character: the written characters read the same backwards as forwards. Palindromes may consist of a single word (civic, level, racecar, Malayalam), or a phrase or sentence ("Neil, a trap! Sid is part alien!", "Was it a rat I saw?", "Mr. Owl ate my metal worm", "Sit on a potato pan, Otis", "Satan, oscillate my metallic sonatas", "Rats live on no evil star."). Spaces, punctuation and case are usually ignored. Much longer palindromic compositions have been constructed; see "Long palindromes", below.

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 “Madam, in Eden I'm Adam,”. The last example is still palindromic if "in Eden" is omitted; the response is either the one-word palindrome, "Eve," or the more obscure "Name no one man."

Some individuals 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). Fictional names include Stanley Yelnats, the main protagonist in the book Holes by Louis Sachar.

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.

Numbers

A palindromic number is a number where the 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. 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 February 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.

The song "The Divided Sky" by Phish, from the 1988 album Junta, contains a brief musical palindrome near the beginning of the song.

On the 1999 album Ágætis byrjun by Sigur Rós, the song "Starálfur" contains palindromic string arrangements. Their 2005 album Takk... also contains the palindromic songs "Hoppípolla" and "Með Blóðnasir."

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.

Lutenist/composer Jozef van Wissem has produced two CDs consisting of palindrome compositions for lute, electronics, and field recordings made in railway stations and airport lounges. They are entitled Objects in Mirror are Closer than They Appear (BVhaast 0905) and Stations of the Cross (Incunabulum 004).

On his 1999 CD Thrash, Canadian rock soloist Nash the Slash features a track entitled "Theory of the Black Hole". The recording beings with a rhythm track recorded backwards with music and narration played forwards, the song then repeats itself reversed, with the rhythm track playing forwards and the music and narration played backwards.

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. Entitled Crab Carillon, the result 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. The music can be heard on the City of San Diego Public Art Website.

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

The song Bleeding Brain Grow by MC Paul Barman has five palindromes in a row.

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

Computer programs

Brian Westley wrote a C program for the 1987 International Obfuscated C Code Contest which is a line-by-line palindrome.

Up to the type definitions, here is a compilable almost palindrome written in Caml:

type 'a elbatum = 'a ;; type lol = bool ;; type pop = int ;; type b = ;; type i = ;;

fun erongi lol pop n -> pop.lol pop.lol ; ignore n in erongi ; lol.pop lol.pop <- n pop lol ignore nuf ;;

The problem lies in the angle brackets, which are reversed when reading backwards from the end.

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 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 (i.e. someone or something that redivides) 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.)

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, and Kuulilennuteetunneliluuk (bullet flightway tunnel hatch) is the longest palindrome in Estonian.

Palindromic texts

To celebrate the palindromic moment 20:02 02/20 2002, Peter Norvig wrote on that day (20 February 2002) a computer program which produced what may be the world's longest palindromic "sentence", running to 17,259 words. The palindrome is an extension of Leigh Mercer's famous palindrome “A man, a plan, a canal—Panama!”, Norvig also mentions that Gerald M. Berns made a palindromic list of 31,358 words with 119,180 letters, not in the form of a sentence. The palindrome was made in October 2007 with Berns' own rules which limit reuse of words and do not allow proper nouns.

A palindrome of over 5000 words entitled A Gassy Obese Boy's Saga, composed by Will Thomas, forms a narrative that makes some, albeit rambling, sense.

In 1991, Gordon Dow composed a 306 word palindrome entitled Dog Sees Ada.

The poet Graywyvern wrote a 427-line palindromic poem, The Angel of Death, in 2005.

Two "palindromic novels" appeared, in limited editions, during the 1980s: Dr Awkward & Olson in Oslo by Lawrence Levine and Satire: Veritas by David Stephens.

Demetri Martin, a stand-up comedian, wrote a poem titled "Dammit I'm Mad", which is a 223 word palindrome. The poem does not use any made-up words and is grammatically correct..

The "Grand Palindrome" (1969) by novelist Georges Perec is the longest palindrome published in French, with 5,566 letters.

Infinite palindromes in Russian

The Russian language allows infinite palindromes. Here's a sample infinite palindromic dialog:

—Я дядя!

—А я тётя!

—А я дядя!

—А я тётя!

—А я дядя!

...

Transliteration (note that ya and yo are single letters in Russian):

—Ya dyadya!

—A ya tyotya!

—A ya dyadya!

—A ya tyotya!

—A ya dyadya!

...

Translation:

"I'm the uncle!"

"But I'm the aunt!"

"But I'm the uncle!"

"But I'm the aunt!"

"But I'm the uncle!"

...

Another infinite palindrome reads:

Коростели летели, летели, ..., летели лет сорок (Korosteli leteli, leteli, ..., leteli let sorok)

It means, "Landrails have been flying, flying, ..., flying for forty years".

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.

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. 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, but their role in the protein function is not clearly known.

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. 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, As usual in Romanian crosswords, scrabble, and other word games, diacritics in palindromes are often ignored.

• Russian: "Он дивен, палиндром: и ни морд, ни лап не видно" (On diven, palindrom: i ni mord, ni lap ne vidno; It's wonderful, a palindrome: and neither muzzles, nor paws are visible).
• Serbian: "Ana voli Milovana" (Ana loves Milovan)
• Slovenian: "Perica reže raci rep" (Washing woman is cutting the duck's tail); "Ona seksa skesano" (She's having sex with remorse)
• Spanish: "Dábale arroz a la zorra el abad" (The abbott was giving rice to the vixen), "La ruta nos aportó otro paso natural" (The route provided us with another natural passage), "Anita lava la tina" (Anita cleans the bathtub).
• Swedish: "Gnupung" (Gnu scrotum), "Ni talar bra Latin" (You speak Latin well), "Bor edra gråvita fat i vår garderob?" (Do your grey-white plates live in our wardrobe?).
• Tagalog: "Nasa bayabasan" (In the guava fields).
• Tatar: "Ata kadak ata" (Father throws a nail).
• Telugu: "vikatakavi" (comedy poet).
• Turkish: "Anastas kazak satsana" (Anastas, sell a sweater).
• Welsh: "Lladd dafad ddall" (Kill a blind sheep), and "Nawr ydy rwan" (now [southern spelling] is now [northern spelling]).
• Tamil: "Maama" (Maternal uncle), "Paappa" ( a girl child),"Kakka" (Crow),"Kee Kee" (Sound of parrot), "Thaatha" (Grand pa), and "Thelu Meeluthey" (Scorpian returns.

See also

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

References

External links

• Daft Fad, Computer Generated Palindromes
• International Palindromes
• Palindrome of the Day
• The best palindrome