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 "22/02/2022", or 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 Henry Peacham in 1638.Henry Peacham, The Truth of our Times Revealed out of One Mans Experience, 1638, p. 123 The concept of a palindrome can be dated to the 3rd-century BC, although no examples survive. The earliest known examples are the 1st-century AD Latin acrostic word square, the Sator Square (which contains both word and sentence palindromes), and the 4th-century Greek Byzantine sentence palindrome nipson anomēmata mē monan opsin.William Martin Leake, Researches in Greece, 1814, p. 85
Palindromes are also found in music (the table canon and crab canon) and biological structures (most genomes include palindromic gene sequences). In automata theory, the set of all palindromes over an alphabet is a context-free language, but it is not regular.
Etymology The word palindrome was introduced by English poet and writer Henry Peacham in 1638. It is derived from the Greek roots () and () ; a different word is used in Greek, () () to refer to letter-by-letter reversible writing.
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, since it is sometimes possible to make a sotadean line by reversing a dactylic hexameter.Jan Kwapisz, The Paradigm of Simias: Essays on Poetic Eccentricity, p. 62-68Alex Preminger, ed., Princeton Encyclopedia of Poetry and Poetics, 1965, , s.v. 'Sotadean', p. 784The 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."
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-Olim-Milo-Amor", which is also written as an acrostic square. Indeed, composing palindromes was "a pastime of Roman landed gentry".
Byzantine baptismal fonts were often inscribed with the 4th-century Greek palindrome, (or ) ("Nipson anomēmata mē monan opsin") 'Wash [your] sin(s), not only [your] face', attributed to Gregory of Nazianzus;Alex Preminger, ed., Princeton Encyclopedia of Poetry and Poetics, 1965, , s.v. 'palindrome', p. 596 most notably in the basilica of Hagia Sophia in Constantinople. The inscription is found on fonts in many churches in Western Europe: Orléans (St. Menin's Abbey); Dulwich College; Nottingham (St. Mary's); Worlingworth; Harlow; Knapton; London (St Martin, Ludgate); and Hadleigh (Suffolk).
A 12th-century palindrome with the same square property is the Hebrew palindrome, פרשנו רעבתן שבדבש נתבער ונשרף perashnu: 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 philosopher Abraham ibn Ezra, and referring to the halachic question as to whether a fly landing in honey makes the honey treif (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 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;S(ilvanus) Urban, "Classical Literature: On Macaronic Poetry", The Gentleman's Magazine, or Monthly Intelligencer, London, 100:part 2:34–36 (New Series 23) (July 1830) though John Taylor had coined one in 1614: "Lewd did I live, & evil I did dwel" (with the ampersand being something of a "fudge"Richard Lederer, The Word Circus: A Letter-perfect Book, 1998, , p.54). 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."On Palindromes" The New Monthly Magazine 2:170–173 (July–December 1821)"Ingenious Arrangement of Words", The Gazette of the Union, Golden Rule, and Odd Fellows' Family Companion 9:30 (July 8, 1848) (Taylor had also composed two other, "rather indifferent", palindromic lines of poetry: "Deer Madam, Reed", "Deem if I meed".H.B. Wheatley, Of Anagrams: A Monograph Treating of Their History from the Earliest Ages..., London, 1862, p. 9-11 ) 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)."Able Was I Ere I Saw Elba", Quote Investigator September 15, 2013 Other well-known English palindromes are: "A man, a plan, a canal – Panama" (1948),By Leigh Mercer, published in Notes and Queries, 13 November 1948, according to The Yale Book of Quotations, F. R. Shapiro, ed. (2006, ). "Madam, I'm Adam" (1861),Do you give it up?: A collection of the most amusing conundrums, riddles, etc. of the day, London, 1861, p. 4 and "Never odd or even" (1930).
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.
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.
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."Never Odd Or Even, and Other Tricks Words Can Do" by O.V. Michaelsen (Sterling Publishing Company: New York), 2005 p124-7
+ ExampleInitial orderReversed orderI cannot believe thatI cannot believe that
Sentences and phrases
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.
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. Lon Nol (1913–1985) was Prime Minister of Cambodia. Nisio Isin is a Japanese novelist and manga writer, whose pseudonym (西尾 維新, Nishio Ishin) is a palindrome when romanized using the Kunrei-shiki or the Nihon-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 actor Robert Trebor and rock-vocalist Ola Salo), while others were given a palindromic name at birth (such as the philologist Revilo P. Oliver, the flamenco dancer Sara Baras, the runner Anuța Cătună, the creator of the Eden Project Tim Smit, and the Mexican racing driver Noel León).
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 exists is an unsolved problem in mathematics about whether there is a number that won't become a palindrome when it is 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.
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 11/11/11 11:11 or long digits as in 2 February 2020.
A notable palindrome day is this century's 2 February 2020 because this date is a palindrome regardless of the date 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". Other universal palindrome days include, almost a millennium previously, 11/11/1111, the future 12/12/2121, and in a millennium 03/03/3030.
In speech
A phonetic palindrome is a portion of speech that is identical or roughly identical when reversed. It can arise in context where language is played with, for example in slang dialects like verlan. In the French language, there is the phrase (), phonetically . John Oswald discussed his experience of phonetic palindromes while working on audio tape versions of the cut-up technique using recorded readings by William S. Burroughs.Reversible audio cut-ups of William S. Burroughs' voice , including an acoustic palindrome in example 5 (requires Flash) A list of phonetic palindromes discussed by word 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".
Longest palindromes