Apalindrome (/ˈpæl.ɪn.droʊm) is a word,number, phrase, or other sequence of symbols that reads the same backwards as forwards, such asmadam orracecar, the date "22/02/2022" and the sentence: "A man, a plan, a canal –Panama". The 19-letterFinnish wordsaippuakivikauppias (asoapstone vendor) is the longest single-word palindrome in everyday use, while the 12-letter termtattarrattat (fromJames Joyce inUlysses) is the longest in English.
The wordpalindrome was introduced by English poet and writerHenry Peacham in 1638.[1] The concept of a palindrome can be dated to the 3rd-century BCE, although no examples survive. The earliest known examples are the 1st-century CE Latinacrosticword square, theSator Square (which contains both word and sentence palindromes), and the 4th-century Greek Byzantine sentence palindromenipson anomemata me monan opsin.[2][3]
The wordpalindrome was introduced by English poet and writerHenry Peacham in 1638.[1] It is derived from the Greek rootsπάλιν 'again' andδρóμος 'way, direction'; a different word is used in Greek, καρκινικός 'carcinic' (lit.crab-like) to refer to letter-by-letter reversible writing.[2][3]
The ancient Greek poetSotades (3rd-century BC) invented a form ofIonic meter called Sotadic orSotadean verse, which is sometimes said to have been palindromic,[4] since it is sometimes possible to make a sotadean line by reversing a dactylic hexameter.[5][6][7]
A 1st-century Latin palindrome was found as a graffito atPompeii. This palindrome, known as theSator Square, consists of a sentence written in Latin:sator arepo tenet opera rotas 'The sower Arepo holds with effort the wheels'. It is also anacrostic 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 aword 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-Olim-Milo-Amor", which is also written as an acrostic square.[8][9] Indeed, composing palindromes was "a pastime of Roman landed gentry".[10]
Nipson anomēmata mē monan opsin palindrome, on a font atSt Martin, Ludgate
A 12th-century palindrome with the same square property is theHebrew palindrome,פרשנו רעבתן שבדבש נתבער ונשרףperashnu: ra`avtan shebad'vash nitba`er venisraf 'We explained the glutton who is in the honey was burned and incinerated', credited in 1924 to the medieval Jewish philosopherAbraham ibn Ezra,[13][unreliable fringe source?] and referring to thehalachic question as to whether a fly landing in honey makes the honeytreif (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 spelledgyrum.
In English, there are many palindromewords such aseye,madam, anddeified, but English writers generally cited Latin and Greek palindromic sentences in the early 19th century;[14] thoughJohn Taylor had coined one in 1614: "Lewd did I live, & evil I did dwel" (with theampersand being something of a "fudge"[15]). This is generally considered the first English-language palindrome sentence and was long reputed, notably by the grammarianJames "Hermes" Harris, to be theonly 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 toNapoleon (alluding to his exile on Elba).[18][17][19] Otherwell-known English palindromes are: "A man, a plan, a canal – Panama" (1948),[20] "Madam, I'm Adam" (1861),[21] and "Never odd or even" (1930).[22]
The most familiar palindromes in English are character-unit palindromes, where the characters read the same backward as forward. Examples arecivic,radar,level,rotor,kayak,madam, andrefer. The longest common ones arerotator, deified, racecar, andreviver; longer examples such asredivider,kinnikinnik, andtattarrattat are orders of magnitude rarer.[23]
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 therecreational linguistics community byJ. A. Lindon in the 1960s. Occasional examples in English were created in the 19th century. Several in French and Latin date to theMiddle Ages.[24]
There are also line-unit palindromes, most oftenpoems. 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.[25]
Example
Initial order
Reversed order
We can save the world I cannot believe that The world is doomed
The world is doomed I cannot believe that We can save the world
Palindromes often consist of a sentence or phrase, e.g., "A man, a plan, a canal, Panama", "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.
Some names are palindromes, such as thegiven names Hannah, Ava, Aviva, Anna, Eve, Bob, and Otto, or thesurnames Harrah, Renner, Salas, and Nenonen.Lon Nol (1913–1985) was Prime Minister of Cambodia.Nisio Isin is a Japanese novelist andmanga writer, whose pseudonym (西尾 維新,Nishio Ishin) is a palindrome when romanized using theKunrei-shiki or theNihon-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 actorRobert Trebor and rock-vocalistOla Salo), while others were given a palindromic name at birth (such as the philologistRevilo P. Oliver, the flamenco dancerSara Baras, the runnerAnuța Cătună, the creator of theEden ProjectTim Smit, and the Mexican racing driverNoel León).
There are also palindromic names in fictional media. "Stanley Yelnats" is the name of the main character inHoles, a 1998 novel and2003 film. Five of the fictionalPokémonspecies have palindromic names in English (Eevee, Girafarig, Farigiraf, Ho-Oh, and Alomomola), as does the region Alola.
The 1970s pop bandABBA is a palindrome using the starting letter of the first name of each of the four band members.
The digits of a palindromic number are the same read backwards as forwards, for example, 91019;decimal representation is usually assumed. Inrecreational mathematics, palindromic numbers with special properties are sought. For example, 191 and 313 arepalindromic primes.
WhetherLychrel 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 asA281509, and described as "The Largest Known Most Delayed Palindrome", with a delay of 261. Several smaller 261-delay palindromes were published separately asA281508.
Every positive integer can be written as the sum of three palindromic numbers in every number system with base 5 or greater.[26]
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 in11/11/11 11:11 or long digits as in2 February 2020.
A notable palindrome day is this century's 2 February 2020 because this date is a palindrome regardless of thedate 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".[27][28] Other universal palindrome days include, almost a millennium previously,11/11/1111, the future12/12/2121, and in a millennium03/03/3030.[29]
A phonetic palindrome is a portion ofspeech that is identical or roughly identical when reversed. It can arise in context where language is played with, for example in slang dialects likeverlan.[30] In theFrench language, there is the phraseune Slave valse nue ("a Slavic woman waltzes naked"), phonemically/ynslavvalsny/.[31]John Oswald discussed his experience of phonetic palindromes while working on audio tape versions of thecut-up technique using recorded readings byWilliam S. Burroughs.[32][33] A list of phonetic palindromes discussed byword 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".[34]
The longest single-word palindrome in theOxford English Dictionary is the 12-letteronomatopoeic wordtattarrattat, coined byJames Joyce inUlysses (1922) for a knock on the door.[35][36][37] TheGuinness Book of Records gives the title to the 11-letterdetartrated, thepreterite and past participle ofdetartrate, a chemical term meaning to removetartrates. The 9-letter wordRotavator, a trademarked name for an agricultural machine, is listed in dictionaries as being the longest single-word palindrome. The 9-letter termredivider is used by some writers, but appears to be an invented or derived term; onlyredivide andredivision appear in the Shorter Oxford English Dictionary; the 9-letter wordMalayalam, a language of southern India, is also of equal length.
English palindrome sentences of notable length include mathematicianPeter Hilton's "Doc, note: I dissent. A fast never prevents a fatness. I diet on cod",[38] and Scottish poetAlastair 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."[39]
In English, two palindromic novels have been published:Satire: Veritas by David Stephens (1980, 58,795 letters), andDr Awkward & Olson in Oslo by Lawrence Levine (1986, 31,954 words).[40] Another palindromic English work is a 224-word long poem, "Dammit I'm Mad", written byDemetri Martin.[41]"Weird Al" Yankovic's song "Bob" is composed entirely of palindromes.[42]
Centre part of palindrome in Alban Berg's operaLulu
Joseph Haydn'sSymphony No. 47 in G is nicknamed "the Palindrome". In the third movement, aminuet andtrio, 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.
British composerRobert Simpson also composed music in the palindrome or based on palindromic themes; the slow movement of hisSymphony No. 2 is a palindrome, as is the slow movement of hisString Quartet No. 1. His hour-longString 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 ofAnton Webern is often palindromic. Webern, who had studied the music of the Renaissance composerHeinrich 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 thesymphony, Op. 21. A striking example of vertical symmetry is the second movement of thePiano Variations, Op. 27, in which Webern arranges every pitch of thisdodecaphonic 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 compositionMixtur, originally written in 1964, consists of twenty sections, called "moments", which may bepermuted 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 is a complex musical unit and is played in the same direction in each half of the program.[46] By contrast,Karel Goeyvaerts's 1953 electronic composition,Nummer 5 (met zuivere tonen) is anexact 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.[47]
Inclassical music, acrab canon is acanon 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, theCrucifixus movement of Bach'sMass 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'sMessiah and Fauré'sRequiem.[48]
Atable 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 theSator Square from opposite sides, except that it is typically in two-part polyphony rather than in unison.[49]
Palindromic motifs are found in mostgenomes or sets ofgenetic instructions. The meaning of palindrome in the context of genetics is slightly different, from the definition used for words and sentences. Since theDNA is formed by two paired strands ofnucleotides, and the nucleotides always pair in the same way (Adenine (A) withThymine (T),Cytosine (C) withGuanine (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 sequenceACCTAGGT is palindromic because its complement isTGGATCCA, which is equal to the original sequence in reverse complement.
A palindromicDNA sequence may form ahairpin. Palindromic motifs are made by the order of thenucleotides that specify the complex chemicals (proteins) that, as a result of thosegenetic instructions, thecell is to produce. They have been specially researched inbacterial chromosomes and in the so-called Bacterial Interspersed Mosaic Elements (BIMEs) scattered over them. In 2003, a research genome sequencing project discovered that many of the bases on theY-chromosome are arranged as palindromes.[50] 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,[51][52] but their role in the protein function is not clearly known. It has been suggested in 2008[53] that the prevalent 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 analpha helical formation propensity of these sequences,[53] or in formation of protein/protein complexes.[54]
In addition, the set of palindromes may not be reliably tested by adeterministic pushdown automaton which also means that they are notLR(k)-parsable orLL(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.
Thepalindromic density of an infinite wordw over an alphabetA is defined to be zero if only finitely many prefixes are palindromes; otherwise, letting the palindromic prefixes be of lengthsnk fork=1,2,... we define the density to be
Among aperiodic words, the largest possible palindromic density is achieved by theFibonacci word, which has density 1/φ, where φ is theGolden ratio.[57]
Apalstar is aconcatenation of palindromic strings, excluding the trivial one-letter palindromes – otherwise all strings would be palstars.[55]
February 2, 2020, was the most recent palindromic date which was can perfectly fit to any date formats in 8-digit FIGURES. And it happens very rare in any Millennium. The next of it will occur on December 12, 2121, which will be the last in this 3rd millennium.
3rd Millennium: February 2, 2020, and December 12, 2121.
^abH.B. Wheatley,Of Anagrams: A Monograph Treating of Their History from the Earliest Ages..., London, 1862,p. 9-11Archived 26 March 2023 at theWayback Machine
^Jan Kwapisz,The Paradigm of Simias: Essays on Poetic Eccentricity, p. 62-68
^Alex Preminger, ed.,Princeton Encyclopedia of Poetry and Poetics, 1965,JSTORj.ctt13x0qvn,s.v. 'Sotadean', p. 784
^The Century Dictionary, 1889,s.v. 'Sotadic', p.5:5780. "Sotadic verse... A palindromic verse; so named apparently from some ancient examples of Sotadean verse being palindromic."
^Soclof, Adam (28 December 2011)."Jewish Wordplay".Jewish Telegraphic Agency.Archived from the original on 21 November 2016. Retrieved21 November 2016.
^"Doings in Baltimore".Gazette of the Union, Golden Rule and Odd-fellows' Family Companion.9 (2): 30. 8 July 1848.
^By Leigh Mercer, published inNotes and Queries, 13 November 1948, according toThe Yale Book of Quotations, F. R. Shapiro, ed. (2006,ISBN0-300-10798-6).
^Do you give it up?: A collection of the most amusing conundrums, riddles, etc. of the day, London, 1861,p. 4Archived 7 April 2023 at theWayback Machine
^Mark J. Nelson (7 February 2012)."Word-unit palindromes".Archived from the original on 12 February 2013. Retrieved18 November 2012.
^"Never Odd Or Even, and Other Tricks Words Can Do" by O.V. Michaelsen (Sterling Publishing Company: New York), 2005 p124-7
^Cilleruelo, Javier; Luca, Florian; Baxter, Lewis (19 February 2016). "Every positive integer is a sum of three palindromes".arXiv:1602.06208 [math.NT].
^James Joyce (1982).Ulysses. Editions Artisan Devereaux. pp. 434–.ISBN978-1-936694-38-9....I was just beginning to yawn with nerves thinking he was trying to make a fool of me when I knew his tattarrattat at the door he must ...
^O.A. Booty (1 January 2002).Funny Side of English. Pustak Mahal. pp. 203–.ISBN978-81-223-0799-3.The longest palindromic word in English has 12 letters: tattarrattat. This word, appearing in the Oxford English Dictionary, was invented by James Joyce and used in his book Ulysses (1922), and is an imitation of the sound of someone ...
^Rudolf Frisius,Karlheinz Stockhausen II: Die Werke 1950–1977; Gespräch mit Karlheinz Stockhausen, "Es geht aufwärts" (Mainz, London, Berlin, Madrid, New York, Paris, Prague, Tokyo, Toronto: Schott Musik International, 2008): 164–65.ISBN978-3-7957-0249-6.
^M[orag] J[osephine] Grant,Serial Music, Serial Aesthetics: Compositional Theory in Post-war Europe (Cambridge, U.K.; New York: Cambridge University Press, 2001): 64–65.
^Charton, Shawn E.Jennens vs. Handel: Decoding the Mysteries of Messiah.
^Adamczewski, Boris; Bugeaud, Yann (2010), "8. Transcendence and diophantine approximation", inBerthé, Valérie; Rigo, Michael (eds.),Combinatorics, automata, and number theory, Encyclopedia of Mathematics and its Applications, vol. 135, Cambridge:Cambridge University Press, p. 443,ISBN978-0-521-51597-9,Zbl1271.11073
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