Palindrome
A palindrome is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as madam or racecar, the date and time 12/21/33 12:21, and the sentence: "A man, a plan, a canal – Panama". The 19-letter Finnish word saippuakivikauppias (a soapstone vendor), is the longest single-word palindrome in everyday use, while the 12-letter term tattarrattat (from James Joyce in Ulysses) is the longest in English.
The word palindrome was introduced by English poet and writer
Palindromes are also found in music (the
Etymology
The word palindrome was introduced by English poet and writer Henry Peacham in 1638.[1] It is derived from the Greek roots πάλιν 'again' and δρóμος 'way, direction'; a different word is used in Greek, καρκινικός 'carcinic' (lit. crab-like) to refer to letter-by-letter reversible writing.[2][3]
Historical development
The ancient Greek poet Sotades (3rd-century BC) invented a form of Ionic meter called Sotadic or Sotadean 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 at Pompeii. This palindrome, known as the Sator Square, consists of a sentence written in Latin: sator arepo tenet opera rotas 'The sower Arepo holds with effort the wheels'. It is also an acrostic 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 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. Other palindromes found at Pompeii include "Roma-Olina-Milo-Amor", which is also written as an acrostic square.[8][9] Indeed, composing palindromes was "a pastime of Roman landed gentry".[10]
A 12th-century palindrome with the same square property is the
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 spelled gyrum.
In English, there are many palindrome words such as eye, madam, and deified, but English writers generally cited Latin and Greek palindromic sentences in the early 19th century;[14] though John Taylor had coined one in 1614: "Lewd did I live, & evil I did dwel" (with the ampersand being something of a "fudge"[15]). This is generally considered the first English-language palindrome sentence and was long reputed, notably by the grammarian James "Hermes" Harris, to be the only 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 to Napoleon (alluding to his exile on Elba).[18][17][19] Other well-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]
Types
Characters, words, or lines
The most familiar palindromes in English are character-unit palindromes, where the characters read the same backward as forward. Examples are civic, radar, level, rotor, kayak, madam, and refer. The longest common ones are rotator, deified, racecar, and reviver; longer examples such as redivider, kinnikinnik, and tattarrattat 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 the recreational linguistics community by J. A. Lindon in the 1960s. Occasional examples in English were created in the 19th century. Several in French and Latin date to the Middle Ages.[24]
There are also line-unit palindromes, most often poems. 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]
Sentences and phrases
Palindromes often consist of a sentence or phrase, e.g., "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. For more examples, see List of English palindromic phrases.
Names
Some names are palindromes, such as the given names Hannah, Ava, Aviva, Anna, Eve, Bob, and Otto, or the surnames Harrah, Renner, Salas, and Nenonen.
There are also palindromic names in fictional media. "Stanley Yelnats" is the name of the main character in Holes, a 1998 novel and 2003 film. Five of the fictional Pokémon species have palindromic names in English (Eevee, Girafarig, Farigiraf, Ho-Oh, and Alomomola), as does the region Alola.
The 1970s pop band ABBA is a palindrome using the starting letter of the first name of each of the four band members.
Numbers
The digits of a palindromic number are the same read backwards as forwards, for example, 91019; decimal representation is usually assumed. In recreational mathematics, palindromic numbers with special properties are sought. For example, 191 and 313 are palindromic primes.
Whether Lychrel 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 as A281509, and described as "The Largest Known Most Delayed Palindrome", with a delay of 261. Several smaller 261-delay palindromes were published separately as A281508.
Every positive integer can be written as the sum of three palindromic numbers in every number system with base 5 or greater.[26]
Dates
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 in
A notable palindrome day is this century's 2 February 2020 because this date is a palindrome regardless of the
In speech
A phonetic palindrome is a portion of
Longest palindromes
The longest single-word palindrome in the
According to Guinness World Records, the Finnish 19-letter word saippuakivikauppias (a soapstone vendor), is the world's longest palindromic word in everyday use.[12]
English palindrome sentences of notable length include mathematician Peter Hilton's "Doc, note: I dissent. A fast never prevents a fatness. I diet on cod",[38] and Scottish poet Alastair 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), and Dr 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 by Demetri Martin.[41] "Weird Al" Yankovic's song "Bob" is composed entirely of palindromes.[42]
Other occurrences
Classical music
Joseph Haydn's Symphony No. 47 in G is nicknamed "the Palindrome". In the third movement, a minuet and trio, 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.
The interlude from
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.[45]
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.
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 of
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.[46] 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.[47]
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 "chiastic", 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 centre of the cross in the crucifixion. Other examples are found in Bach's cantata BWV 4, Christ lag in Todes Banden, Handel's Messiah and Fauré's Requiem.[48]
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.[49]
Biological structures
Palindromic motifs are found in most
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. In 2003, a research genome sequencing project discovered that many of the bases on the Y-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,
Computation theory
In
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
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 nk for k=1,2,... we define the density to be
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.[57]
A palstar is a concatenation of palindromic strings, excluding the trivial one-letter palindromes – otherwise all strings would be palstars.[55]
Notable palindromists
- Dmitry Avaliani (1938–2003)
- Howard W. Bergerson (1922–2011)
- Hugo Brandt Corstius (1935–2014)
- Noam Dovev (b. 1974)
- Anthony Etherin (b. 1981)
- Simo Frangén (b. 1963)
- Baby Gramps (active 1964–present)
- Pasi Heikura (b. 1963)
- Peter Hilton (1923–2010)
- Su Hui (poet) (fourth century CE)
- Velimir Khlebnikov (1885–1922)
- J. A. Lindon (c. 1914–1979)
- Demetri Martin (b. 1973)
- Leigh Mercer (1893–1977) best known for devising the palindrome "A man, a plan, a canal: Panama!"
- Georges Perec (1936–1982)
- Mark Saltveit (b. 1961)
See also
- Ambigram
- Anagram
- Ananym
- Anastrophe, different word order
- Antimetabole
- Backmasking
- "Bob" ("Weird Al" Yankovic song)
- Chiasmus
- Constrained writing
- Eodermdrome
- "I Palindrome I" by They Might Be Giants
- List of English palindromic phrases
- List of palindromic places
- Mirror writing
- Palindroma, a genus of spiders with palindromic species names
- Palindromic number
- Palindromic polynomial
- Pangram
- Tarzan yell
- Yreka, California, which has the palindromic Yreka Bakery and Yrella Gallery
References
- ^ a b Henry Peacham, The Truth of our Times Revealed out of One Mans Experience, 1638, p. 123 Archived 14 July 2020 at the Wayback Machine
- ^ a b Triantaphylides Dictionary, Portal for the Greek Language. "Combined word search for καρκινικός". www.greek-language.gr. Archived from the original on 6 May 2019. Retrieved 6 May 2019.
- ^ a b William Martin Leake, Researches in Greece, 1814, p. 85
- ^ a b H.B. Wheatley, Of Anagrams: A Monograph Treating of Their History from the Earliest Ages..., London, 1862, p. 9-11 Archived 26 March 2023 at the Wayback Machine
- ^ Jan Kwapisz, The Paradigm of Simias: Essays on Poetic Eccentricity, p. 62-68
- JSTOR j.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."
- from the original on 11 September 2022. Retrieved 10 September 2022.
- from the original on 11 September 2022. Retrieved 10 September 2022.
- ^ Fishwick, Duncan (1959). "An Early Christian Cryptogram?" (PDF). CCHA. 26. University of Manitoba: 29–41. Archived (PDF) from the original on 24 May 2022. Retrieved 13 October 2021.
- JSTOR j.ctt13x0qvn, s.v. 'palindrome', p. 596
- ^ a b "Longest palindromic word". Guinness World Records. Archived from the original on 11 December 2016. Retrieved 12 January 2017.
- ^ Soclof, Adam (28 December 2011). "Jewish Wordplay". Jewish Telegraphic Agency. Archived from the original on 21 November 2016. Retrieved 21 November 2016.
- ^ S(ilvanus) Urban, "Classical Literature: On Macaronic Poetry", The Gentleman's Magazine, or Monthly Intelligencer, London, 100:part 2:34–36 (New Series 23) Archived 26 March 2023 at the Wayback Machine (July 1830)
- ISBN 0877793549, p.54
- ^ "On Palindromes" The New Monthly Magazine 2:170–173 Archived 26 March 2023 at the Wayback Machine (July–December 1821)
- ^ a b "Ingenious Arrangement of Words", The Gazette of the Union, Golden Rule, and Odd Fellows' Family Companion 9:30 (July 8, 1848) Archived 26 March 2023 at the Wayback Machine
- ^ "Able Was I Ere I Saw Elba", Quote Investigator September 15, 2013
- ^ "Doings in Baltimore". Gazette of the Union, Golden Rule and Odd-fellows' Family Companion. 9 (2): 30. 8 July 1848.
- ISBN 0-300-10798-6).
- ^ Do you give it up?: A collection of the most amusing conundrums, riddles, etc. of the day, London, 1861, p. 4 Archived 7 April 2023 at the Wayback Machine
- ^ Pryor, G.H. (September 1930). "In the Realm of the Riddle". Baltimore and Ohio Employes Magazine. Baltimore and Ohio Railroad. p. 60.
- ^ "Google nGrams frequencies". Archived from the original on 29 December 2022. Retrieved 29 December 2022.
- ^ Mark J. Nelson (7 February 2012). "Word-unit palindromes". Archived from the original on 12 February 2013. Retrieved 18 November 2012.
- ^ "Never Odd Or Even, and Other Tricks Words Can Do" by O.V. Michaelsen (Sterling Publishing Company: New York), 2005 p124-7
- arXiv:1602.06208 [math.NT].
- ^ "Universal Palindrome Day". 2 February 2020. Archived from the original on 6 August 2020. Retrieved 3 February 2020.
- ^ "#PalindromeDay: Geeks around the world celebrate 02/02/2020". BBC. 2 February 2020. Archived from the original on 2 February 2020. Retrieved 2 February 2020.
- ^ Held, Amy (2 February 2020). "Why A Day Like Sunday Hasn't Been Seen In 900 Years". NPR. Archived from the original on 3 February 2020. Retrieved 3 February 2020.
- S2CID 161346520.
- ISBN 978-2846220361.
- ^ "Section titled "On Burroughs and Burrows ..."". Pfony.com. Archived from the original on 5 February 2012. Retrieved 23 April 2012.
- ^ Reversible audio cut-ups of William S. Burroughs' voice Archived 13 March 2008 at the Wayback Machine, including an acoustic palindrome in example 5 (requires Flash)
- ^ Michaelsen, O.V. (1998). Words at play: quips, quirks and oddities. Sterling.
- ^ @OED (17 September 2015). "The longest palindrome defined in the OED is 'tattarrattat', meaning 'a knock at the door'. It was used by James Joyce in 'Ulysses'. (2/2)" (Tweet) – via Twitter.
- ISBN 978-1-936694-38-9.
...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 ...
- ISBN 978-81-223-0799-3.
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 ...
- Daily Telegraph. London. 10 November 2010. Archivedfrom the original on 10 March 2011. Retrieved 30 April 2011.
- ISBN 0-306-80810-2).
- ISBN 978-0-333-90334-6.
- ^ "Demetri Martin's Palindrome". Yale University. Mathematics Department. Archived from the original on 29 June 2010. Retrieved 17 February 2014.
- ^ Twardzik, Tom (25 October 2016). "Celebrate Bob Dylan's Nobel with Weird Al". Popdust. Archived from the original on 13 August 2022. Retrieved 15 June 2021.
- ^ "Lulu". British Library. Archived from the original on 25 September 2021. Retrieved 7 August 2021.
- ^ A helpful list is at http://deconstructing-jim.blogspot.com/2010/03/musical-palindromes.html Archived 6 August 2020 at the Wayback Machine
- ^ Lloyd, Stephen. Constant Lambert: Beyond the Rio Grande (2014), p. 258
- ISBN 978-3-7957-0249-6.
- ^ 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.
- ISBN 0-415-94391-4. Retrieved 14 April 2011.
- ^ "2003 Release: Mechanism Preserves Y Chromosome Gene". National Human Genome Research Institute (NHGRI). Archived from the original on 1 December 2017. Retrieved 21 November 2017.
- PMID 2128128.
- S2CID 28294669. Archived from the original(PDF) on 14 December 2019. Retrieved 17 February 2011.
- ^ PMID 18547401.
- S2CID 29569626.
- ^ ISBN 978-981-02-4897-0
- S2CID 61800864
- Zbl 1271.11073
Further reading
- ISSN 0043-7980.
- The Palindromist. Palindromist Press, 1996–.
- ISBN 978-0486206646.
- ISBN 978-0006523086
- Stephen J. Chism. From A to Zotamorf: The Dictionary of Palindromes. Word Ways Press, 1992. ISBN 978-0963515209.
- Michael Donner. I Love Me, Vol. I: S. Wordrow's Palindrome Encyclopedia. Algonquin Books, 1996. ISBN 978-1565121096.
External links
- Chisholm, Hugh, ed. (1911). . Encyclopædia Britannica. Vol. 20 (11th ed.). Cambridge University Press. p. 633.
- "Palindromes". Several languages. European Day of Languages (EDL).
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