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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; and 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 ''parashnuw ra`abtan sheba'dvash nitba'er wenishrap'') by Ibn Ezra, referring to the halachic question as to whether a fly landing in honey makes the honey 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 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.
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 (such as “''civic''” or “''level''” ), a phrase or sentence (“Neil, a trap! Sid is part alien!”, "Was it a rat I saw?") or a longer passage of text (“Sit on a potato pan, Otis.”), even a fragmented sentence ("A man, a plan, a canal: Panama!", "No Roman a moron"). Spaces, punctuation and case are usually ignored, even in terms of abbreviation ("Mr. Owl ate my metal worm").
Three famous English palindromes are “Able was I ere I saw Elba,”[1] “A man, a plan, a canal—Panama!”[2], and “Madam, in Eden I'm Adam,”[3]. 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.) A nickname is Jackson Noskcaj.
Romanian runner Anuta Catuna earned many international titles, including first place womens finish in the 1996 New York City Marathon.
In the book Holes by Louis Sachar, the main protagonist's name (Stanley Yelnats) is a palindrome. A parody of the book in Mad magazine gives the protagonist's name as Johnathan Nahtanhoj.
The supposed lake monster that resides in Okanagan Lake, British Columbia, is named Ogopogo.
Words
Some palindromes use words as units rather than letters. An example is "fall leaves after leaves fall" or "First Ladies rule the State and state the rule: ladies first". The Chinese palindromes described above are most like this type of English palindrome.
Both words and characters
The command "Level madam, level!" is remarkable as not only is it a grammatically correct sentence that is palindromic, but each word in it is also palindromic.
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
Main articles: Palindromic number
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 searched. A palindromic prime is a palindromic number that is a prime number.
Music
Soundgarden's 1992 album Badmotorfinger was released with a second limited edition disc containing the EP Satanoscillatemymetallicsonatas (Satan Oscillate My Metallic Sonatas), or SOMMS for short.
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 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.
On The Fall of Troy's 2007 album, ''Manipulator'', there is a song titled "A Man a Plan a Canal Panama"
"Weird Al" Yankovic's song "Bob", from his 2003 album ''Poodle Hat'', comprises of rhyming palindromes, and parodies the Bob Dylan song ''Subterranean Homesick Blues''.[4]
The song "I Palindrome I", by They Might Be Giants, features palindromic lyrics and imagery. The 27-word bridge is word-symmetrical.
The song "The Divided Sky" by Phish, from the 1988 album ''Junta'', contains a brief musical palindrome near the beginning of the song.
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 civilian overpass on Interstate 94 at 25th Street.
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.
The name of the St. Louis based Indie rock band So Many Dynamos is a palindrome.
The Sigur Rós song "Starálfur", from the 1999 album ''Ágætis byrjun'', contains palindromic string arrangements.
The title track of the 1992 album entitled "UFO Tofu" by Béla Fleck and the Flecktones is said by its composer (Béla Fleck) to be a musical palindrome.
Lutenist/composer Jozef van Wissem has produced two cd's 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).
See also crab canon — in classical music, a canon in which one line of the melody is reversed in time and pitch from the other.
Computer programs
Brian Westley wrote a C program for the 1987 International Obfuscated C Code Contest which is a line-by-line palindrome: http://www.ioccc.org/1987/westley.c
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 = { mutable lol : lol elbatum } ;;
type i = { mutable pop : pop elbatum } ;;
fun erongi lol pop n ->
pop.lol <- let nuf =
erongi;fun erongi lol pop n -> pop.lal ; ignore
n in
erongi ; lol.pop <- n pop lol ignore nuf ; ignore
= fun tel -> 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
The longest palindromic word in the Oxford English Dictionary is ''tattarrattat'', coined by James Joyce in ''Ulysses'' 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.)
''Saippuakivikauppias'', Finnish for "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.
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,[5] running to 17,259 words.[6] The palindrome is an extension of Leigh Mercer's famous palindrome “A man, a plan, a canal—Panama!”2
A palindrome of over 5000 words entitled ''A Gassy Obese Boy's Saga'', composed by Will Thomas[7], forms a narrative that makes some, albeit rambling, sense.
In 1991, Gordon Dow composed a 306 word palindrome entitled ''Dog Sees Ada.''[8]
The poet Graywyvern wrote a 427-line palindromic poem, ''The Angel of Death,'' in 2005.[9]
Two "palindromic novels" appeared, in limited editions, during the 1980s: ''Dr Awkward & Olson in Oslo'' by Lawrence Levine[10] and ''Satire: Veritas'' by David Stephens[11].
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.
Longest palindromes in Polish
Stanisław Barańczak, a Polish poet and translator created a ''Mega-Palindromader'' which is based on symmetry by letters. This work in Polish is composed of 4 introductory small palindromes (as the author called them, 'fanfares') and the main 2,501-letter palindrome. This was bettered by Prof. Tadeusz Morawski, Polish palindrome enthusiast and author, who published two longer palindromes in his 2005 book ''Gór ech chce róg''. In June 2006, Prof. Morawski announced he has created a record-breaking 33,000-letter palindrome, published on his webpage [1], gaining some coverage in national press.
Longest palindrome in French
The "Grand Palindrome" (1969) [2] by novelist Georges Perec is the longest palindrome published in French, with 5 566 letters, which is the result of the palindromic multiplication 11
★ 232
★ 11.
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.
Computation theory
In 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.
The following Context-free grammar produces all palindromes for the alphabet {a,b}:
:S → a | b | aSa | bSb | (empty)
Even though this grammar is not ambiguous, it is not parseable by any LR(k) parser either. Essentially, given an incomplete string that begins a palindrome, it is impossible to identify the “middle”, unless the entire palindrome is present. To illustrate, suppose that a palindrome begins with
:“madamim...”.
There is not enough information to determine whether the string ends with
:“…adam” or
:“...imadam”, or
:“...xyzzyxmimadam”, etc..
It turns out that palindromes cannot be accepted by any deterministic pushdown automaton[3]. The following non-deterministic pushdown automaton accepts palindromes for the alphabet {a,b}. The non-determinism is reflected in the choice of transitions from state 0. This choice essentially represents finding the “middle” of the palindrome.
:Start state: 0
:Accept state: 2
| State | Input | Stack | Action | NextState |
|---|---|---|---|---|
| 0 | a | A, B, or empty | push A | 0 |
| 0 | b | A, B, or empty | push B | 0 |
| 0 | a | A, B, or empty | none | 1 |
| 0 | b | A, B, or empty | none | 1 |
| 0 | a | A, B, or empty | push A | 1 |
| 0 | b | A, B, or empty | push B | 1 |
| 0 | end | empty | none | 2 |
| 1 | a | A | pop | 1 |
| 1 | b | B | pop | 1 |
| 1 | end | empty | none | 2 |
A proof that palindromes are not regular uses the Pumping Lemma:
For any positive integer ''p'', consider the palindrome ''w'' = a''p''ba''p''. For example, for ''p'' = 3, we have ''w'' = “aaabaaa”.
Consider all partitionings of this word
''w'' = ''xyz'', such that |''y''| > 0 and |''xy''| <= ''p''.
For example, for ''p'' = 3, we must consider the possibilities:
:''x'' = “”, ''y'' = “a”, ''z'' = “aabaaa”
:''x'' = “”, ''y'' = “aa”, ''z'' = “abaaa”
:''x'' = “”, ''y'' = “aaa”, ''z'' = “baaa”
:''x'' = “a”, ''y'' = “a”, ''z'' = “aabaaa”
:''x'' = “a”, ''y'' = “aa”, ''z'' = “abaaa”
:''x'' = “aa”, ''y'' = “a”, ''z'' = “baaa”
If palindromes were a regular language, then for one of these partionings ''xyiz'' will also be a palindrome for any ''i''. Here, we will show that for any such partitioning, ''i'' = 0, results in ''xyiz'' being a non-palindrome.
Since |''xy''| ≤ ''p'', ''x'' and ''y'' together must be entirely within the first set of a’s. Since |''y''| > 0, the ''y'' section must contain at least one of these a’s. Thus, deleting the ''y'' section will result in deletion of at least one a from the left side, resulting in a non-palindrome.
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 heteropalindromes, semi-palindromes, half-palindromes, reversgrams, mynoretehs, reversible anagrams [4], word reversals, or anadromes [5]. They have also sometimes been called antigrams [6], though this term now usually refers to anagrams with opposing meanings.
The longest single-word instances in English are probably of eight letters, of which examples are:
★ ''stressed'' / ''desserts''
★ ''samaroid'' (resembling a samara) / ''dioramas
Other examples include:
★ ''deliver'' / ''reviled''
★ ''straw'' / ''warts''
★ ''star'' / ''rats''
★ ''god'' / ''dog''
★ ''lived'' / ''devil''
★ ''diaper'' / ''repaid''
★ ''war'' / ''raw''
An emirp is a prime that becomes a different prime when the decimal digits are read backwards.
Foreign language palindromes
In languages that use a writing system other than an alphabet, a palindrome is still a sequence of characters from that writing system that remains the same when reversed.
Japanese palindromes, called kaibun, rely on the hiragana syllabary. An example is the word . The Japanese syllabary makes it possible to construct very long palindromes.
A Chinese word is a character, and is not composed of letters or syllables. Therefore, any Chinese word itself is a trivial palindrome. Chinese palindromes have to be phrases or sentences and are much more easy to construct than in languages written with an alphabet. Some examples of this are:
★ "I love mother, mother loves me" ()
★ "Shanghai's tap water comes from the sea" ())
★ "Sheung Shui residents live above the water" ().
Palindromic poetry () was a literary genre in classical Chinese literature. The "forward reading" and the "backward reading" of such a poem would be similar but not exactly the same in meaning. Although called "palindromic", these poems are often not palindromes in the normal English sense of the word. They do not necessarily have symmetry of characters or sound, but merely need to make sense when read in either direction (and would probably be better referred to as Semordnilaps). The following example was composed during the Song Dynasty:
枯眼望遙山隔水，往來曾見幾心知。壺空怕酌一杯酒，筆下難成和韻詩。迷路阻人離別久，訊音無雁寄回遲。孤燈夜守長寥寂，夫憶妻兮父憶兒。
The "forward reading" of the last sentence is about husband missing wife and father missing son, while the "backward reading" is about son missing father and wife missing husband.
Some examples in other languages are:
★ Brazilian Portuguese: "Socorram-me, subi no onibus em Marrocos" (Help me, I took a bus in Morocco).
★ Bulgarian: ''Az obicham mach i boza'' (Аз обичам мач и боза; "I like football and a drink", note ''ch'' is the single Bulgarian letter che (Ч)), ''Nasila zakaraha svinete ni v sahara! - kaza Lisan'' (Насила закараха свинете ни в Сахара! - каза Лисан; "They took our pigs to Sahara - said Lisan").
★ Czech: "Kobyla má malý bok" (A mare has a low hip), "Jelenovi pivo nelej" (Do not pour beer for a stag).
★ German: "Ein Neger mit Gazelle zagt im Regen nie” (A negro with a gazelle never quails in the rain).
★ Finnish: "Innostunut sonni" (an excited bull), "Saippuakivikauppias" (a lye salesman). The latter is also the longest palindromic word in the world with a real meaning.
★ Lithuanian: "Sėdėk užu kėdės” (Sit behind the chair).
★ Spanish: "Dábale arroz a la zorra el abad" (The abbott gave rice to the fox), "La ruta nos aportó otro paso natural" (The route provided us with another natural passage).
★ Swedish: "Ni talar bra Latin" (You speak Latin well), "Bor edra gråvita fat i vår garderob?" (Do your grey-white plates live in our wardrobe?).
★ Welsh: "Lladd dafad ddall" (Kill a blind sheep).
In languages such as Czech and Spanish, letters with diacritics or accents 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 Swedish 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.
See also
★ Ambigram
★ Anagram
★ Backmasking
★ List of palindromic places
★ Phonetic palindrome
References
1. Honoring the first exile of Napoleon
2. By Leigh Mercer, published in ''Notes and Queries,'' 13 Nov. 1948, according to ''The Yale Book of Quotations,'' F. R. Shapiro, ed. (2006, ISBN 0-300-10798-6). The "man" may refer to Theodore Roosevelt or Ferdinand Lesseps, both instrumental in the realization of the Panama Canal.
3. A reference to the creation story in the Bible.
4. http://www.seeklyrics.com/lyrics/Weird-Al-Yankovic/Bob.html
5. In a strict grammatical sense, this is not a sentence, but a noun phrase.
6. Palindrome, program, and discussion online.
7. Will Thomas's page, palindrome reproduced at http://www.palindromelist.com/longest.htm.
8. http://www.growndodo.com/wordplay/palindromes/dogseesada.html.
9. Available online and in the author's printed collection ''sedna''.
10. Self-published, St Augustine, Florida.
11. Word Ways Monographs, also here and here.
External links
★ Daft Fad, Computer Generated Palindromes
★ International Palindromes
★ Palindrome of the Day
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