palindrome

This article covers the word or phrase type. For the film see Palindromes .

As a palindrome ( ancient Greek παλίνδρομος palíndromos "running backwards") are words , word series or sentences that, when read backwards, make exactly the same text or at least make sense. Upper / lower case, word boundaries and punctuation marks may need to be changed when reading backwards.

The sator square is based on a sentence palindrome

A word palindrome is a word that reads backwards to produce the same word (e.g. mount ). The palindromes also include words that, when read backwards, result in another meaningful word (e.g. shelf - warehouse ); in this case the palindrome is a special form of the anagram . In the case of a sentence palindrome , the sentence read forwards and backwards is the same. A palindrome can also consist of several sentences. There are even poems in palindromic form.

The linguistic concept of the palindrome was adopted in other areas, that is, palindromes do not necessarily have to consist of letters. There are number palindromes (about 2442). In computer science , a palindrome is a string of characters that is read both forward and backward. The genetics knows palindromic sequences in DNA - or RNA chains. There are palindromes in music too.

Palindromes in Linguistics

Word palindromes

Examples

• Hannah
• Next
• Otto
• Shelf storage
• Mount
• Relief pillars
• pensioner

See also : German word palindromes

Otto , Reittier and Rotor are also Morse code palindromes, as they consist exclusively of symmetrical Morse code. Examples of Morse code palindromes that no longer result in palindromes in Latin letters are du ( — · ·, · · —) or an ( · —, — ·).

The German lyric poet and children's book author Josef Guggenmos wrote a nursery rhyme about a giant whose name is also a palindrome: the giant "Mutakirorikatum".

According to the 1997 Guinness Book of Records , the longest German single-word palindrome is a 13-letter relief pillar . The compound is already mentioned as an example for palindromes in Meyer's Large Konversations-Lexikon of 1905. His "discovery" is often attributed to the philosopher Arthur Schopenhauer - an assertion that does not stand up to scrutiny. The word relief pillar is almost only known as an example for palindromes, otherwise the technical term pilaster is preferred. By the way, the word Retsina canister with 15 letters is longer than the relief pillars . According to the Guinness Book of Records, the longest word palindrome of all languages ​​is the Finnish word saippuakivikauppias (" soap stone seller") with 19 letters.

With some palindromes of the shelf storage type (composition with a word joint in the middle), an even more complex palindrome can be formed by inserting a suitable additional palindrome in the middle, such as next to it : shelf storage . However, the meaningfulness of the result required in the definition is doubtful in such cases, since words such as sub-rack storage are not used in real language.

Sentence palindromes

Examples of German sentence palindromes

• Love is victor; she is always active when she is suffering.
• A golden, good virtue: never lie!
• Never threaten a horde!
• A negro with a gazelle never hesitates in the rain.
• Erika only fires unfaithful fakirs.
• O genius, the Lord honor your ego!
• Did Tim never wear such light-colored trousers with a belt?

See also : German sentence palindromes

Examples of English sentence palindromes

• A man, a plan, a canal - Panama. - German: "One man, one plan, one canal - Panama." (With reference to the Panama Canal .)
• Madam, I'm Adam. - German: "Madam, I am Adam." (With reference to Adam and Eve .)
• Never odd or even. - German: "Never odd or even." (Even and odd numbers are meant .)
• Was it a car or a cat I saw? - German: "Was that a car or a cat that I saw?"

Japanese set palindromes

→ Main article : Kaibun

Artistic use

The classical philologist Friedrich August Wolf lost his professorship in 1806 with the dissolution of the University of Halle by Napoleon . He is believed to be the author of an elaborate Latin palindrome, which, even if read backwards, remains a poem made up of correct distiches . Reading forward, the text addressed to Napoleon is a prophecy of victory in the Battle of Trafalgar . In retrospect, the opposite results: Napoleon's defeat in this battle is prophesied, and his name is no longer Bonaparte , but Malaparte . However, it is only in the broader sense a palindrome, since the Latin poem is not to be read letter by letter, but word by word backwards.

In 1968 the artist André Thomkins created , with others, palindromes, which were installed in the execution of street signs on the outside wall of the restaurant of the artist Daniel Spoerri . They mainly dealt, sometimes in an absurd way, with the topic of “eating and cooking” in the broadest sense, for example: “pure is syrup”, “often turn trout plates in the stove”, “bürle knurre grub milk - limburger runkelrüb” (ch = 1 letter). Further palindromes were found inside the old town restaurant. The bar on Düsseldorf's Burgplatz no longer exists. 21 of these palindrome signs can be seen today in the Giardino di Daniel Spoerri , an art and sculpture park in southern Tuscany.

In contemporary poetry, the palindrome is used by individual authors as a stylistic device, e.g. B. in the texts of Titus Meyer .

Further examples:

• The French writer Georges Perec wrote palindromes with well over 1000 words in the form of letters or poems that can be read completely backwards.
• The musician Weird Al Yankovic recorded the song Bob in 2003 , in which every single line of text forms a sentence palindrome. The song was a parody of Bob Dylan's "Subterranean Homesick Blues".
• In 2003, the poet Anton Bruhin created the "mirror poems". In 2005 his work 500 typograms and 10,000 palindromes was published . All 10,000 palindromes begin with “row” and end with “here”.

Oddities

• Among the scientific names for genera and species in biology are some palindromes, see list of bizarre scientific names from biology .
• There are also internet http://www.addresses in palindromic form if you ignore parts like , for example ed.xozzox.de.
• With the song SOS by the pop group ABBA , the song title and at the same time the name of the band is a palindrome.
• The puzzle author CUS traced the origin of the word palindrome back to Sarah Palin in his book The strange lexicon of the German language . In the same book he explained the nonsense of this claim under the heading of phantom words .

Phonetic palindromes

A phonetic palindrome is a piece of spoken language that sounds almost the same when spoken backwards. Backward pronunciation is usually implemented technically (backward playback function of an audio program), since people cannot speak exactly backward. Usually it is a question of short speech sequences and constructed sentences. In order to achieve harmony as possible, the speaker can use a slightly different pronunciation at the critical points.

Number palindromes

Palindromes of numbers give the same value when viewed from the front as from the back (e.g. 151). This also includes prime numbers (see prime number palindrome ). Prime numbers that, when read backwards, do not result in the same value but a different prime number, are called mirp numbers .

Date palindrome

Date palindromes are very similar to number palindromes, e.g. E.g. 02/20/2002 or 02/02/2020, and time palindromes, e.g. B. 13:31.

February 2, 2020 was a global palindromic day. The calendar date 02/02/2020 can be read from both sides using both European and US notation . This was the last time on 11.11.1111. The next two global palindromic days are 12.12.2121 and 03.03.3030.

Palindromes in Computer Science

In theoretical computer science , more precisely the theory of formal languages , a mathematical formalism was developed for dealing with strings of characters , which are also called words in the theoretical context .

definition

The definition that a palindrome is a word which, when written backwards, results in the same word, is formally written as follows:

A palindrome is a word above the alphabet with the property ${\displaystyle u}$ ${\displaystyle \Sigma }$

${\displaystyle u=u^{R}}$,

where means that the operator of mirroring (or reversing the order of the characters) is applied to the word . ${\displaystyle u^{R}}$ ${\displaystyle ^{R}}$ ${\displaystyle u}$

Note that a palindrome doesn't necessarily have to make sense here; the corresponding word only needs to be built symmetrically around its center.

Symmetrical decomposition

The following applies

${\displaystyle u=v\,v^{R}=w^{R}\,w}$,

if (word length) is even, or ${\displaystyle |u|}$

${\displaystyle u=v\,c\,v^{R}=w^{R}\,c\,w}$,

if is odd, where (finite words) and (is a character of the alphabet). ${\displaystyle |u|}$ ${\displaystyle v,w\in \Sigma ^{*}}$ ${\displaystyle c\in \Sigma }$

You can see this by inserting, e.g. B .:

${\displaystyle u^{R}=(v\,c\,v^{R})^{R}=(v^{R})^{R}\,c^{R}\,v^{R}=v\,c\,v^{R}=u}$

For example, you can

${\displaystyle u={\mbox{GNUDUNG}}}$

disassemble with

${\displaystyle v={\mbox{GNU}}}$and , ${\displaystyle c={\mbox{D}}}$

so that

${\displaystyle u=v\,c\,v^{R}={\mbox{GNU}}\,{\mbox{D}}\left({\mbox{GNU}}\right)^{R}={\mbox{GNUDUNG}}}$.

Detection of palindromes

The language

${\displaystyle L=\{vv^{R}|v\in \Sigma ^{*}\}}$

(the set of finite even-length words that are a palindrome) is not regular ; H. you cannot specify a regular expression that specifies or a finite automaton ( i.e. a machine with finite memory) that manages to recognize (i.e. to decide whether a word belongs to the language or not). ${\displaystyle L}$ ${\displaystyle L}$ ${\displaystyle L}$

Since arbitrarily long, even if finite, words have to be examined, an infinite amount of memory is potentially required in order to memorize and then to compare with. One can show that a nondeterministic push-down automaton is sufficient for recognition, e.g. B. by specifying a context-free grammar . However, there is no deterministic push-down automaton that recognizes this language. ${\displaystyle v}$ ${\displaystyle v^{R}}$

Recursive definition

The inductive or recursive definition for palindromes is as follows:

1. The empty word (the word of length 0, the “empty string”) is a palindrome. ${\displaystyle \epsilon }$
2. Every word of length 1 is a palindrome. ${\displaystyle x}$
3. If there is a symbol and a palindrome, then it is a palindrome. ${\displaystyle a}$ ${\displaystyle x}$ ${\displaystyle {\mathit {axa}}}$
4. No other word is a palindrome.

Context-free grammar for palindromes

The inductive definition above is the starting point for constructing a context-free grammar for palindromes.

To simplify matters, the alphabet is limited to two symbols, i.e. a binary alphabet . Then one can derive all binary word palindromes with the following productions : ${\displaystyle \Sigma =\{0,1\}}$

${\displaystyle S\to 0\,|\,1\,|\,\epsilon }$

${\displaystyle S\to 0S0\,|\,1S1}$

The palindromes (empty word), and can be generated immediately from the start symbol . The remaining palindromes are obtained by first generating a symmetrical word in both directions and then replacing the non-terminal symbol in the middle with one of the terminal symbols . ${\displaystyle S}$ ${\displaystyle \epsilon }$ ${\displaystyle 0}$ ${\displaystyle 1}$

Examples

• ${\displaystyle S\Rightarrow 0S0\Rightarrow 01S10\Rightarrow 011S110\Rightarrow 011\epsilon 110=011110}$
• ${\displaystyle S\Rightarrow 0S0\Rightarrow 010}$

Palindromes in Molecular Genetics

Palindromic sequences (A) in the double strand can base-pairing with similar ones in the single strand to form the stem (C) of a loop (B) of hairpin structures (here DNA)

In molecular genetics , short DNA strands in a double strand are called palindromes if the two strands have the same sequence in opposite directions. Such sections of DNA often serve as a recognition sequence for restriction enzymes . The enzymes attach to the corresponding section and cut through the DNA double strand in a characteristic way.

Example: The recognition sequence of the EcoRI enzyme

Recognition sequence	Restriction cut
5'-GAATTC-3' 3'-CTTAAG-5'	5'-G AATTC-3' 3'-CTTAA G-5'

Restriction enzymes are an extremely important tool in molecular genetics. Because the recognition sequence is characteristic of every enzyme, it allows DNA molecules to be cut up in a targeted manner. Since a piece of a few bases long protrudes from one of the two strands at the interface (see sticky ends ), DNA fragments can also be reassembled in an equally targeted manner.

Sequences in the nucleotide sequence in the single strand of a DNA or RNA are also referred to as palindromic sequences if two regions of the same molecule correspond in such a way that one sequence read in the opposite direction resembles the other sequence. Intramolecular base pairings between these regions lead to double-strand-like attachments, which together with the resulting strand loop are also called hairpin structures .

Functionally, these formations occur in various contexts, for example in the regulation of gene expression through attenuation in bacteria.

Palindromes in Music

Music palindromes are pieces of music or music sequences that sound the same forwards and backwards played or, because of the fading of tones, sound almost the same. The cancer canon is the prime example. The minuet in Joseph Haydn's Symphony No. 47 in G major is composed as a palindrome, as is the transformation music in Act 2 of the opera Lulu by Alban Berg (→ excerpt from the score ).

See also

• Ambigram (a point-symmetrical lettering)
• Ananym (a name written backwards)

literature

• John E. Hopcroft , Jeffrey Ullman : Introduction to Automata Theory, Languages ​​and Computation. Addison-Wesley, Reading MA et al. 1979, ISBN 0-201-02988-X ( Addison-Wesley Series in Computer Science ; the old version, more demanding).
• Karl Günter Kröber: A donkey never reads - mathematics of palindromes. Rowohlt-Taschenbuch Verlag, Reinbek bei Hamburg 2003, ISBN 3-499-61576-2 .
• Hansgeorg Stengel : AnnasusannA. A pendulum book for right and left readers. Eulenspiegel-Verlag, Berlin 2004, ISBN 3-359-01484-7 .
• Gerhard Rexin: Palindrome. In: Real Lexicon for Antiquity and Christianity . Volume 26, Hiersemann, Stuttgart 2015, ISBN 978-3-7772-1509-9 , Sp. 785-803.
• Gerhard Rexin: On the history of some Latin palindromes. In: Mittellateinisches Jahrbuch 50, 2015, pp. 39–58.

Web links

Wiktionary: Palindrome  - explanations of meanings, word origins, synonyms, translations

• Palindrome blog trauerfreuart.de
• List of German palindromes
• List with English palindromes (English)
• World's Longest Palindrome Sentence? (English)
• Latin palindromes in the Latin Wiktionary

Individual evidence

1. ^ The Brockhaus in One Volume, 2008.
2. ↑ ^{a b} Duden online: Keyword palindrome and explanation of the term . Duden speaks of a "stricter requirement for a palindrome" in the case that reading backwards gives exactly the same result as reading forward.
3. ↑ Palindrome at Wissen.de , with links to various dictionaries
4. ↑ palindrome in Meyers Great Conversational Lexicon. 1905.
5. ↑ See Schopenhauer and the palindromes in the palindrome blog "Trauerfreuart", May 9, 2008.
6. ↑ Retsina canister is mentioned online in Duden as an example of palindromes .
7. ↑ Longest palindromic word guinnessworldrecords.com
8. ↑ Latin:

   Vaticinor tibi quod navalis laurea cinget

   Tempora nec magnas spes mare destituet;

   Deiciet tua gens cunctas nec Gallia victrix

   Denique frangetur litus ad Albionum;

   Sors bona non mala sors concludet proelia, qua re

   Saecula te dicent PARS BONA non MALA PARS.

   Translation:

   I prophesy to you that the victory laurel will crown the sea battle

   The sea will not disappoint your temples and your great hopes;

   Your nation will overthrow all others, and victorious France will not

   Finally crashed on the coast of England;

   good fate, not bad fate will end the war, that's why

   Will the age call you BONAPARTE, not MALAPARTE.

   Translation for declining reading:

   MALAPARTE, not BONAPARTE, the age will call you, why

   The war will end bad destiny, not good destiny;

   On the coast of England the victorious will finally be shattered

   France and all others will not bring down your nation;

   The sea will disappoint the great hopes, and your temples

   Will not crown the victory laurel of the sea battle. I prophesy this to you.

9. ^ André Thomkins: Palindromes on street signs in the palindrome blog "Trauerfreuart", December 16, 2007.
10. ^ Armin Steigenberger : News from Wolkenkuckucksheim. Signatures Magazin, May 6, 2015, accessed May 8, 2015 . 
11. ↑ Le Grand Palindrome de Georges perec. Retrieved October 3, 2018 . 
12. ↑ The song Bob
13. ^ Anton Bruhin: Row here - 500 typograms and 10,000 palindromes . Urs Engeler, Vienna / Basel 2005, ISBN 978-3-905591-91-0 .
14. ↑ ed.xozzox.de , with reference to a few other URL palindromes.
15. ^ CUS : The strange lexicon of the German language . Eichborn-Verlag, Frankfurt 2009, ISBN 978-3-8218-6061-9 .
16. ↑ Examples of phonetic palindromes (German)
17. ↑ For the first time in over 900 years - Today is a very special day. In: Blick online from February 2, 2020.
18. ↑ Palindrome Day: 02/02/2020 - a historical date. In: Frankfurter Allgemeine Zeitung of February 2, 2020.