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 "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. 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 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. 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 pálin (πάλιν) 'again' and drómos (δρóμος) 'way, direction'; a different word is used in Greek, karkinikós (καρκινικός) 'carcinic' (lit. 'crab-like') to refer to letter-by-letter reversible writing.

Historical development

The ancient Greek poet Sotades (3rd-century BCE) 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. 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, ΝΙΨΟΝ ΑΝΟΜΗΜΑΤΑ (or ΑΝΟΜΗΜΑ) ΜΗ ΜΟΝΑΝ ΟΨΙΝ ("Nipson anomēmata mē monan opsin") 'Wash [your] sin(s), not only [your] face', attributed to Gregory of Nazianzus; 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; though John Taylor had coined one in 1614: "Lewd did I live, & evil I did dwel" (with the ampersand being something of a "fudge"). 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. (Taylor had also composed two other, "rather indifferent", palindromic lines of poetry: "Deer Madam, Reed", "Deem if I meed".) 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). Other well-known English palindromes are: "A man, a plan, a canal – Panama" (1948), "Madam, I'm Adam" (1861), 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.

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.

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