Definitions

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Palindrome

[pal-in-drohm]

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 (πάλιν; "back") and dromos (δρóμος; "way, direction") by English writer Ben Jonson in the 1600s. The actual Greek phrase to describe the phenomenon is karkinikê epigrafê (καρκινική επιγραφή; crab inscription), or simply karkiniêoi (καρκινιήοι; 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.

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 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" - Ref. 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 face alone" (Medieval Greek: ΝΙΨΟΝΑΝΟΜΗΜΑΤΑΜΗΜΟΝΑΝΟΨΙΝ; Modern: Νίψον ανομήματα μη μόναν όψιν; 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, 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 same word). The up and down reading depends on re-reading the text back up again; the last four lines have been reversed above to clarify this property.

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. Palindromes may consist of a single word (civic, level, racecar, rotator, Malayalam), or a phrase or sentence ("Was it a rat I saw?", "Mr. Owl ate my metal worm", "Sit on a potato pan, Otis", "Neil, a trap! Sid is part alien!", "Go hang a salami I'm a lasagna hog.", "Satan, oscillate my metallic sonatas", "I roamed under it as a tired nude Maori"). Punctuation, case and spacing are usually ignored, although some (such as "Rats live on no evil star") include the spacing.

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 left out, as is often the case.

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).

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.

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.

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.

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.) 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, 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!”, and is effectively just a random list of comma-separated nouns and acronyms, many of which are obscure. Norvig later surpassed his own record with a 17,826-word palindrome created 11 November 2007. 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", the palindromic title written in 1912 (Words at Play: Quips, Quirks & Oddities, 1997) 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.

The "Joke into an area" (2007) by Tadeusz Morawski is the longest palindrome published in Polish. It contains over 33000 letters. The same author wrote the longest palindromic versed poem (2007) containing 4400 letters.

The longest known palindrome in Hebrew, a meaningful palindromic story, was composed by Ghil'ad Zuckermann..

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. It is recently suggested that the prevalence existence of palindromes in peptides might be related to the prevalence of low-complexity regions in proteins, as there is a large chance to observe a palindrome in low-complexity sequences. Their prevalence might be also related to an alpha helical formation propensity of these sequences .

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, heteropalindromes, semi-palindromes, half-palindromes, reversgrams, mynoretehs, reversible anagrams, word reversals, or anadromes. They have also sometimes been called antigrams, 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 instances in English are probably of eight letters, of which examples are:

  • "reporter" / "retroper" (trope v.t chambers' dictionary)
  • " retraped" / "departer" (trape v.i chambers dictionary)
  • rewarder / redrawer
  • stressed / desserts
  • samaroid (resembling a samara) / ''dioramas

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

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 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.

Japanese

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. Other longer examples include and

Chinese

A Chinese word composed of one or more characters, not letters, and in most cases the characters are syllables. 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" ()
  • "I care for everyone, everyone care for me" a dialogue in hong kong movie "He Ain't Heavy, He's My Father" (新難兄難弟) (1993)
  • "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.

Other languages

Some examples in other languages are:

  • Arabic: "كل في فلك" (Each in an orbit...).
  • Bulgarian: "Аз обичам мач и боза" (I like football and boza).
  • Czech: "Kobyla má malý bok" (A mare has a low hip), "Jelenovi pivo nelej" (Do not pour beer for a stag).
  • Danish: "Regninger" (Bills [to pay], accounts), "Tre negre med fane, en af dem er genert" (Three negroes with (a) flag, one of them is shy).
  • German: "Ein Neger mit Gazelle zagt im Regen nie” (A negro with a gazelle never quails in the rain).
  • Dutch: "Nelli plaatst op 'n parterretrap 'n pot staalpillen" (Nelli places a jar of iron pills on the downfloor stairs)
  • Esperanto: "Ora trovo: vortaro" (A golden find: a dictionary).
  • Estonian: "Kuulilennuteetunneliluuk" (The hatch of the tunnel of ballistic trajectory), "Aias sadas saia" (It was raining white bread in the garden)
  • French: "Esope reste ici et se repose" (Aesope stays there and rests), "Elu par cette crapule" (elected by this scoundrel), "Et la marine va venir à Malte" (And the marine will come to Malta).
  • Greek: "Νίψον ανομήματα, μη μόναν όψιν" (Wash the sins, not only the face)
  • Hebrew: "?אבי אל חי שמך למה מלך משיח לא יבא" (Eternal Father be Thy name, why hast the King Messiah not yet come?), "דעו מאביכם כי לא בוש אבוש, שוב אשוב אליכם כי בא מועד" (Know from your forefathers that I will not be embarrassed, I will return to you at the appointed time.)
  • Hungarian: "Kis erek mentén, láp sík ölén odavan a bánya rabja: jaj, Baranyában a vadon élő Kis Pálnét nem keresik!" (Along the small streams and in the flat lap of the moorland gone the prisoner of the mine: oh, nobody looks for Ms. Kis Pál who lived in the woods of Baranya.)
  • Icelandic: "Amma sá afa káfa af ákafa á Samma" ("Grandma saw grandpa touching Sammi intensively")
  • Irish: "A Nóinín, níl an rí anocht ar Ráth Conair, ná linn. In Iona." ("Nettle, the king is neither tonight on Conair's fort, nor with us. In Iona.")
  • Italian: "Autore, ero tua" (Author, I was yours), "I topi non avevano nipoti" (The mice had no grandchildren).
  • Korean: "일요일" (Sunday), "스위스" (Switzerland), "사진사" (Photographer), "시흥시" (Siheung City), "소주 만병만 주소" (Please give me 10,000 bottles of alcohol), "다시 합창합시다" (Let's sing together again).
  • Latin: "Sum summus mus" (I am the greatest mouse), "Si nummi immunis" (If you have money, you will be free {an inscription on the door in a lawyer's office}), "In girum imus nocte et consumimur igni" (We enter the circle at night and are consumed by fire.")
  • Persian: "شو همره بلبل بلب هر مهوش - شکر بترازوی وزارت برکش" (Accompany the nightingale in praising the beauties- You'll get great rewards).
  • Portuguese: "Socorram-me subi no onibus em Marrocos" (Help-me I got in a bus in Morocco).
  • 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).
  • 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: "God apa gavs galna anlag, svag apa dog." (Good ape was given crazy hereditary character, weak ape died), "Ni talar bra latin" (You speak Latin well), "Bor edra gråvita fat i vår garderob?" (Do your grey-white plates live in our wardrobe?), "Dromedaren Alp-Otto planerade mord" (the dromedar Alp-Otto was planning murder).
  • Tagalog: "Nasa bayabasan" (In the guava fields).
  • Tatar: "Ata qadaq ata" (Father throws a nail).
  • Turkish: "Ey Edip, Adana'da pide ye." (Hey! Edip, eat pizza in adana.), "Anasastas, mum satsana." (Anastas, sell candles.)
  • Welsh: "Lladd dafad ddall" (Kill a blind sheep), and "Nawr ydy rwan" (now [southern spelling] is now [northern spelling]).
  • Malay/Indonesian: "Malam" (night), "ini" (this), "ada" (have), "apa" (what), "katak" (also "kodok" in Indonesian) (frog), "masam" (sour).
  • Malayalam/Indian:"Malayalam", "mo-ru tha-ru-mo"

See also

References

External links

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