Palindrome - AbsoluteAstronomy.com

A palindrome is a word, phrase, number

Palindromic number

A palindromic number or numeral palindrome is a 'symmetrical' number like 16461, that remains the same when its digits are reversed. The term palindromic is derived from palindrome, which refers to a word like rotor that remains unchanged under reversal of its letters...

, or other sequence of units that can be read the same way in either direction, with general allowances for adjustments to punctuation

Punctuation

Punctuation marks are symbols that indicate the structure and organization of written language, as well as intonation and pauses to be observed when reading aloud.In written English, punctuation is vital to disambiguate the meaning of sentences...

and word dividers.

Composing literature in palindromes is an example of constrained writing

Constrained writing

Constrained writing is a literary technique in which the writer is bound by some condition that forbids certain things or imposes a pattern.Constraints are very common in poetry, which often requires the writer to use a particular verse form....

. The word "palindrome" was coined from Greek roots and by English writer Ben Jonson

Ben Jonson

Benjamin Jonson was an English Renaissance dramatist, poet and actor. A contemporary of William Shakespeare, he is best known for his satirical plays, particularly Volpone, The Alchemist, and Bartholomew Fair, which are considered his best, and his lyric poems...

in the 17th century. The actual Greek phrase to describe the phenomenon is ' onMouseout='HidePop("86664")' href="/topics/Crab">crab

Crab

True crabs are decapod crustaceans of the infraorder Brachyura, which typically have a very short projecting "tail" , or where the reduced abdomen is entirely hidden under the thorax...

inscription), or simply karkinoi , alluding to the backward movement of crabs, like an inscription that can be read backwards.

History

Palindromes date back at least to 79 AD, as the palindromic Latin word square "Sator Arepo Tenet Opera Rotas" (The sower, Arepo, holds works wheels) was found as a graffito at Herculaneum

Herculaneum

Herculaneum was an ancient Roman town destroyed by volcanic pyroclastic flows in AD 79, located in the territory of the current commune of Ercolano, in the Italian region of Campania in the shadow of Mt...

, buried by ash in that year. This palindrome is remarkable for the fact that it also reproduces itself if one forms a word from the first letters, then the second letters and so forth. Hence, it can be arranged into a word square

Word square

A word square is a special type of acrostic. It consists of a set of words written out in a square grid, such that the same words can be read both horizontally and vertically. The number of words, which is equal to the number of letters in each word, is known as the "order" of the square...

that reads in four different ways: horizontally or vertically from either top left to bottom right or bottom right to top left.

A palindrome with the same property is the Hebrew

Hebrew language

Hebrew is a Semitic language of the Afroasiatic language family. Culturally, is it considered by Jews and other religious groups as the language of the Jewish people, though other Jewish languages had originated among diaspora Jews, and the Hebrew language is also used by non-Jewish groups, such...

palindrome "We explained the glutton who is in the honey was burned and incinerated" by Abraham ibn Ezra

Abraham ibn Ezra

Rabbi Abraham ben Meir Ibn Ezra was born at Tudela, Navarre in 1089, and died c. 1167, apparently in Calahorra....

, referring to the halachic question as to whether a fly landing in honey makes the honey treif
Kashrut
Kashrut is the set of Jewish dietary laws. Food in accord with halakha is termed kosher in English, from the Ashkenazi pronunciation of the Hebrew term kashér , meaning "fit" Kashrut (also kashruth or kashrus) is the set of Jewish dietary laws. Food in accord with halakha (Jewish law) is termed...

(not kosher).

פ ר ש נ ו

ר ע ב ת ן

ש ב ד ב ש

נ ת ב ע ר

ו נ ש ר ף

Another Latin palindrome, In girum imus nocte et consumimur igni ("We go wandering at night and are consumed by fire"—In girum ire is translated as "go wandering" instead of the literal "go in a circle", cf. Italian andare in giro, "go strolling or wandering around"), was said to describe the behavior of moths. It is likely from medieval rather than ancient times.

Byzantine Greeks

Byzantine Empire

The Byzantine Empire was the Eastern Roman Empire during the periods of Late Antiquity and the Middle Ages, centred on the capital of Constantinople. Known simply as the Roman Empire or Romania to its inhabitants and neighbours, the Empire was the direct continuation of the Ancient Roman State...

often inscribed the palindrome "Wash [the] sins not only [the] face" (Nīpson anomēmata mē mōnan ōpsin
Nipson anomemata me monan opsin
Nipson anomēmata mē monan opsin , meaning "Wash the sins, not only the face," or "Wash my transgressions, not only my face," is a Greek palindromic phrase which was inscribed upon a holy water font outside the church of Hagia Sophia in Constantinople...

, note ps is the single Greek letter Ψ, psi

Psi (letter)

Psi is the 23rd letter of the Greek alphabet and has a numeric value of 700. In both Classical and Modern Greek, the letter indicates the combination /ps/ . The letter was adopted into the Old Italic alphabet, and its shape is continued into the Algiz rune of the Elder Futhark...

) on baptismal font

Baptismal font

A baptismal font is an article of church furniture or a fixture used for the baptism of children and adults.-Aspersion and affusion fonts:...

s. This practice was continued in many English churches. Examples include the font at St. Mary's Church, Nottingham

St. Mary's Church, Nottingham

The Church of St Mary the Virgin is the oldest religious foundation in the City of Nottingham, England, the largest church after the Roman Catholic Cathedral and the largest mediæval building in Nottingham....

and also the font in the basilica of St. Sophia

Hagia Sophia

Hagia Sophia is a former Orthodox patriarchal basilica, later a mosque, and now a museum in Istanbul, Turkey...

, Constantinople

Constantinople

Constantinople was the capital of the Roman, Eastern Roman, Byzantine, Latin, and Ottoman Empires. Throughout most of the Middle Ages, Constantinople was Europe's largest and wealthiest city.-Names:...

, the font of St. Stephen d'Egres, Paris

Paris

Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...

; at St. Menin's Abbey, Orléans

Orléans

-Prehistory and Roman:Cenabum was a Gallic stronghold, one of the principal towns of the Carnutes tribe where the Druids held their annual assembly. It was conquered and destroyed by Julius Caesar in 52 BC, then rebuilt under the Roman Empire...

; at Dulwich College

Dulwich College

Dulwich College is an independent school for boys in Dulwich, southeast London, England. The college was founded in 1619 by Edward Alleyn, a successful Elizabethan actor, with the original purpose of educating 12 poor scholars as the foundation of "God's Gift". It currently has about 1,600 boys,...

; and at the following churches: Worlingworth

Worlingworth

Worlingworth is a village and civil parish in the Mid Suffolk district of Suffolk in eastern England. Located around ten miles south-east of Diss, in 2005 its population was 750....

(Suffolk), Harlow

Harlow

Harlow is a new town and local government district in Essex, England. It is located in the west of the county and on the border with Hertfordshire, on the Stort Valley, The town is near the M11 motorway and forms part of the London commuter belt.The district has a current population of 78,889...

(Essex), Knapton

Knapton

Knapton is a village and a civil parish in the English county of Norfolk. The village is south-east of Cromer, north-east of Norwich and north-east of London. The village lies north-east of the A149 between Kings Lynn and Great Yarmouth. The nearest railway station is at North Walsham for the...

(Norfolk), St Martin, Ludgate

St Martin, Ludgate

St Martin, Ludgate is an Anglican church on Ludgate Hill in the ward of Farringdon, in the City of London. St Martin Ludgate, also called St Martin within Ludgate, was rebuilt in 1677-84 by Sir Christopher Wren.-History:...

(London), and Hadleigh (Suffolk).

Simple Examples for Palindromes

1. Malayalam
2. Amma
3. Appa
4. Madam
5. Racecar
6. WOW
7. civic
8. kayak
9. level

Palindromes in ancient Sanskrit

Palindromes of considerable complexity were experimented with in Sanskrit

Sanskrit

Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...

poetry. Complex palindromes appear in the 19th canto of the 8th-century epic poem śiśupāla-vadha by Magha

Magha (poet)

Magha was a Sanskrit poet at King Varmalata's court at Srimala, the-then capital of Gujarat . Magha was son of Dattaka Sarvacharya and grandson of Suprabhadeva...

. It yields the same text if read forwards, backwards, down, up, or diagonally:

sa-
kā-	ya-	sā-	da-	da-	sā-	ya-	kā
ra-	sā-	ha-	vā	vā-	ha-	sā-	ra-
nā-	da-	vā-	da-	da-	vā-	da-	nā.
(nā	da	vā	da	da	vā	da	nā
ra	sā	ha	vā	vā	ha	sā	ra
kā	ya	sā	da	da	sā	ya	kā
sa	kā	ra	nā	nā	ra	kā	sa)

(Note: hyphen indicates continuation of same word.) The last four lines are an inversion of the first four and are not part of the verse. They are included here only so that its properties can be more easily discerned, as the up-and-down reading depends on re-reading the text back up again in each column.

The stanza translates as:

[That army], which relished battle (rasāhavā), contained allies who brought low the bodes and gaits of their various striving enemies (sakāranānārakāsakāyasādadasāyakā), and in it the cries of the best of mounts contended with musical instruments (vāhasāranādavādadavādanā).

The same work (Śiśupāla-vadha) also contains stanzas in which each line is a palindrome, and stanzas that can be read backwards to give a new stanza (semordnilaps). Such stanzas are also found in the earlier work Kirātārjunīya
Kirātārjunīya
Kirātārjunīya is a Sanskrit kavya by Bhāravi, written in the 6th century or earlier. It is an epic poem in eighteen cantos describing the combat between Arjuna and lord Shiva in the guise of a kirāta or mountain-dwelling hunter. Along with the Naiṣadhacarita and the Shishupala Vadha, it is one of...

.

This sanskrit poem was written by "nandi-ghanta kavis" in kanda style.

सारस नयना घन जघ

नारचित रतार कलिक हर सार रसा

सार रसारह कलिकर

तारत चिरनाघ जनघ नायनसरसा !
|

Palindromes in Tamil poetry

Palindromes are referred to in Tamil as Maalai Maatru (மாலை மாற்று). The earliest known palindromic verses (11 couplets) occur in the devotional poetry of Shaivism saint Sambandhar

Campantar

Tirugnana Sampantar was a young Saiva poet-saint of Tamil Nadu who lived around the 7th century CE....

who lived around the 7th Century C.E.

The first of these eleven verses runs thus -

யாமாமாநீ யாமாமா யாழீகாமா காணாகா

காணாகாமா காழீயா மாமாயாநீ மாமாயா

It refers to Shiva

Shiva

Shiva is a major Hindu deity, and is the destroyer god or transformer among the Trimurti, the Hindu Trinity of the primary aspects of the divine. God Shiva is a yogi who has notice of everything that happens in the world and is the main aspect of life. Yet one with great power lives a life of a...

as the incomparable God, the one who plays the Veena

Veena

Veena may refer to one of several Indian plucked instruments:With frets*Rudra veena, plucked string instrument used in Hindustani music*Saraswati veena, plucked string instrument used in Carnatic musicFretless...

, the beautiful one adorned with snakes, the one who destroyed Kama, whose abode is Sirkazhi

Sirkazhi

Sirkazhi , is a city and a municipality in Nagapattinam district in the Indian state of Tamil Nadu. It is located just 10 km from the Bay of Bengal; 5 km from Kollidam; 20 km from Chidambaram; 250 km from Chennai and 90 km from Pondicherry.-Geography:Sirkazhi is located at...

, who also appears as Vishnu

Vishnu

Vishnu is the Supreme god in the Vaishnavite tradition of Hinduism. Smarta followers of Adi Shankara, among others, venerate Vishnu as one of the five primary forms of God....

, and beseeches him (Shiva) to rid the devotee of impurities.

Palindromic verses are also to be found in Madhava Shivagnana Yogi's Kanchi Puranam (மாதவச்சிவஞானயோகிகள் காஞ்சிப் புராணம்) and Mahavidvaan Meenakshi Sundaram Pillai's Thirunaagaik kaaronap puranam (மகாவித்துவான் மீனாட்சிசுந்தரம் பிள்ளை திருநாகைக் காரோணப் புராணம்).

Characters

The most familiar palindromes, in English at least, are character-by-character: The written characters read the same backwards as forwards. Some examples of common palindromic words: civic, radar, level, rotor, kayak, reviver, racecar, redder, madam, toot, boob, pop and noon.

Phrases

Palindromes often consist of a phrase or sentence, e.g.: "Eva, can I stab bats in a cave?", "Mr. Owl ate my metal worm.", "Was it a rat I saw?", "A nut for a jar of tuna", "Ma is as selfless as I am", "Dammit, I'm mad!", and "A Santa lived as a devil at NASA". Punctuation, capitalization, and spacing are usually ignored, although some, such as "Rats live on no evil star" and "Step on no pets", include the spacing.

Famous English palindromes

Some well-known English palindromes are "Able was I ere I saw Elba

Elba

Elba is a Mediterranean island in Tuscany, Italy, from the coastal town of Piombino. The largest island of the Tuscan Archipelago, Elba is also part of the National Park of the Tuscan Archipelago and the third largest island in Italy after Sicily and Sardinia...

", "A man, a plan, a canal, Panama", "Madam, I'm Adam" or "Madam in Eden, I'm Adam", "Doc, note: I dissent. A fast never prevents a fatness. I diet on cod." and "Never odd or even." "Rise to vote sir" was featured in an episode of The Simpsons.

Names

Some people have names that are palindromes. A few common palindrome names are: Maham, Ada, Anna, Bob, Eve, Hannah and Otto. Lon Nol

Lon Nol

Lon Nol was a Cambodian politician and general who served as Prime Minister of Cambodia twice, as well as serving repeatedly as Defense Minister...

(1913–1985) was Prime Minister of Cambodia. Nisio Isin

Nisio Isin

, frequently written as NisiOisiN to emphasize that his pen name is a palindrome, is a Japanese novelist and manga writer. He attended and left Ritsumeikan University without graduating. In 2002, he debuted with the novel , which earned him the 23rd Mephisto Award at twenty years of age...

is a Japanese novelist and manga writer, whose real name (西尾維新, Nishio Ishin) is a palindrome in Japanese and when romanized using Kunrei-shiki

Kunrei-shiki

is a Japanese romanization system, i.e. a system for transcribing the Japanese language into the Latin alphabet. It is abbreviated as Kunrei-shiki. Its name is rendered Kunreisiki using Kunrei-shiki itself....

or Nihon-shiki

Nihon-shiki

Nihon-shiki or Nippon-shiki Rōmaji is a romanization system for transliterating the Japanese language into the Latin alphabet. In discussion about romaji, it is abbreviated as Nihon-shiki or Nippon-shiki. Among the major romanization systems for Japanese, Nippon-shiki is the most regular, and has...

(it is often written as NisiOisiN to emphasize this). Some changed their name in order to be a palindrome (one example is actor Robert Trebor

Robert Trebor

Robert Trebor is an American character actor, perhaps best known for his role as "Salmoneus" on the cult hits Hercules: The Legendary Journeys and Xena: Warrior Princess...

), while others were given a palindromic name at birth (such as philologist Revilo P. Oliver

Revilo P. Oliver

Revilo Pendleton Oliver was an American professor of Classical philology, Spanish, and Italian at the University of Illinois at Urbana-Champaign, who wrote and polemicized extensively for white nationalist causes....

and Korean-American Mike Kim).
Palindromic names are very common in Finland. Examples include Olavi Valo, Emma Lamme, Sanna Rannas, Anni Linna and Asko Oksa.
"Stanley Yelnats" is the name of a character in "Holes"

Holes (novel)

Holes is a Newbery Medal-winning novel by Louis Sachar. It was adapted into a screenplay for the 2003 film by Walt Disney Pictures. In 2006, Sachar published Small Steps, a companion novel featuring one of the characters from Holes.-Plot:...

, a 1998 novel and 2003 film

Holes (film)

Holes is a 2003 film based on the novel of the same name by Louis Sachar, who also wrote the screenplay, with Shia LaBeouf as the lead role of Stanley Yelnats...

Molecular biology

Restriction enzymes recognize a specific sequence of nucleotides and produce a double-stranded cut in the DNA. While recognition sequences vary widely, with lengths between 4 and 8 nucleotides, many of them are palindromic, which correspond to nitrogenous base sequences between complementary strands, which, when read from the 5' to 3' direction, are identical sequences.

Numbers

A palindromic number is a number whose digits, with decimal

Decimal

The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

representation usually assumed, are the same read backwards, for example, 5885. They are studied in recreational mathematics

Recreational mathematics

Recreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study...

where palindromic numbers with special properties are sought. A palindromic prime

Palindromic prime

A palindromic prime is a prime number that is also a palindromic number. Palindromicity depends on the base of the numbering system and its writing conventions, while primality is independent of such concerns...

is a palindromic number that is a prime number

Prime number

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

.

The continued fraction

Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on...

is a repeating palindrome when

is an integer.

Dates

Palindromic dates are of interest to recreational mathematicians and numerologists

Numerology

Numerology is any study of the purported mystical relationship between a count or measurement and life. It has many systems and traditions and beliefs...

, and sometimes generate comment in the general media. Whether or not a date is palindromic depends on the style in which it is written. The table below shows some of the most common date formats and the most recent and next palindromic dates in those styles.

Style	Most recent		Next
mm/dd/yyyy	11/02/2011	November 2, 2011	02/02/2020	February 2, 2020
dd/mm/yyyy	11/02/2011	11 February 2011	02/02/2020	2 February 2020
mm/dd/yy	11/22/11	November 22, 2011	02/11/20	February 11, 2020
dd/mm/yy	11/11/11	11 November 2011	21/11/12	21 November 2012
mm/dd/yy dd/mm/yy	11/11/11	November 11, 2011	11/11/11	November 11, 2111
m/d/yyyy	1/10/2011	January 10, 2011	2/10/2012	February 10, 2012
d/m/yyyy	1/10/2011	1 October 2011	2/10/2012	2 October 2012
m/d/yy	1/10/11	January 10, 2011	2/10/12	February 10, 2012
d/m/yy	1/10/11	1 October 2011	2/10/12	2 October 2012
yyyymmdd	20111102	2011 November 2	20200202	2020 February 2

Some dates have more than one palindromic form. For example, the date September 29, 1929, can be written as a palindrome 3 ways. Without the year, it is 9/29. With the year, it is 9/29/29 or 9/29/1929. January 10, 2011 is a four-way palindrome, as 1/10/2011, 1/10/11, I/X/MMXI, or I/X/XI. A date can be a palindrome depending on how is is said. For example, the date October 20, 2010 can be written 10/20/2010 and said as, "Ten, twenty, twenty-ten."

In Sweden the common date-style is yyyymmdd and a palindrome-date is 20111102 (the 2^nd day of November, 2011).

Acoustics

A palindrome in which a recorded phrase of speech sounds the same when it is played backwards was discovered by composer John Oswald

John Oswald (composer)

John Oswald is a Canadian composer, saxophonist, media artist and dancer. His best known project is Plunderphonics, the practice of making new music out of previously existing recordings .-Philosophy:Oswald coined the term "plunderphonics" to describe his craft in a paper called which he...

in 1974 while he was working on audio tape versions of the cut-up technique

Cut-up technique

The cut-up technique is an aleatory literary technique in which a text is cut up and rearranged to create a new text. Most commonly, cut-ups are used to offer a non-linear alternative to traditional reading and writing....

using recorded readings by William S. Burroughs

William S. Burroughs

William Seward Burroughs II was an American novelist, poet, essayist and spoken word performer. A primary figure of the Beat Generation and a major postmodernist author, he is considered to be "one of the most politically trenchant, culturally influential, and innovative artists of the 20th...

. Oswald discovered in repeated instances of Burroughs speaking the phrase "I got" that the recordings still sound like "I got" when played backwards.

In French, a more complex example has been identified with
"Une slave valse nue"
(a Slavic girl waltzes naked)

Rhythm

The Afro-Cuban rhythm "Cáscara" is a palindrome :

x0xx0x0xx0x0xx0x0xx0x (where "x" is a hit, "0" is a rest)

Classical music

Joseph Haydn

Franz Joseph Haydn , known as Joseph Haydn , was an Austrian composer, one of the most prolific and prominent composers of the Classical period. He is often called the "Father of the Symphony" and "Father of the String Quartet" because of his important contributions to these forms...

's Symphony No. 47

Symphony No. 47 (Haydn)

-Movements:Scored for 2 oboes, bassoon, 2 horns, and strings.It is in four movements:#Allegro, 4/4#Un poco adagio cantabile, 2/4#Menuetto e Trio, 3/4#Presto assai, 2/2...

in G is nicknamed "the Palindrome". The third movement, minuet

Minuet

A minuet, also spelled menuet, is a social dance of French origin for two people, usually in 3/4 time. The word was adapted from Italian minuetto and French menuet, and may have been from French menu meaning slender, small, referring to the very small steps, or from the early 17th-century popular...

and trio

Trio (music)

Trio is generally used in any of the following ways:* A group of three musicians playing the same or different musical instrument.* The performance of a piece of music by three people.* The contrasting section of a piece in ternary form...

is a musical palindrome. This clever piece goes forward twice and backwards twice and arrives back at the same place.

Wolfgang Amadeus Mozart

Wolfgang Amadeus Mozart

Wolfgang Amadeus Mozart , baptismal name Johannes Chrysostomus Wolfgangus Theophilus Mozart , was a prolific and influential composer of the Classical era. He composed over 600 works, many acknowledged as pinnacles of symphonic, concertante, chamber, piano, operatic, and choral music...

's Scherzo-Duetto di Mozart is played by one violinist as written and the second with the same music inverted.

The interlude from Alban Berg

Alban Berg

Alban Maria Johannes Berg was an Austrian composer. He was a member of the Second Viennese School with Arnold Schoenberg and Anton Webern, and produced compositions that combined Mahlerian Romanticism with a personal adaptation of Schoenberg's twelve-tone technique.-Early life:Berg was born in...

's opera Lulu
Lulu (opera)
Lulu is an opera by the composer Alban Berg. The libretto was adapted by Berg himself from Frank Wedekind's plays Erdgeist and Die Büchse der Pandora .-Composition history:...

is a palindrome, as are sections and pieces, in arch form

Arch form

In music, arch form is a sectional structure for a piece of music based on repetition, in reverse order, of all or most musical sections such that the overall form is symmetric, most often around a central movement...

, by many other composers, including James Tenney

James Tenney

James Tenney was an American composer and influential music theorist.-Biography:Tenney was born in Silver City, New Mexico, and grew up in Arizona and Colorado. He attended the University of Denver, the Juilliard School of Music, Bennington College and the University of Illinois...

, and most famously Béla Bartók

Béla Bartók

Béla Viktor János Bartók was a Hungarian composer and pianist. He is considered one of the most important composers of the 20th century and is regarded, along with Liszt, as Hungary's greatest composer...

. George Crumb

George Crumb

George Crumb is an American composer of contemporary classical music. He is noted as an explorer of unusual timbres, alternative forms of notation, and extended instrumental and vocal techniques. Examples include seagull effect for the cello , metallic vibrato for the piano George Crumb (born...

also used musical palindrome to text paint the Federico García Lorca

Federico García Lorca

Federico del Sagrado Corazón de Jesús García Lorca was a Spanish poet, dramatist and theatre director. García Lorca achieved international recognition as an emblematic member of the Generation of '27. He is believed to be one of thousands who were summarily shot by anti-communist death squads...

poem "¿Por qué nací?", the first movement of three in his fourth book of Madrigal

Madrigal (music)

A madrigal is a secular vocal music composition, usually a partsong, of the Renaissance and early Baroque eras. Traditionally, polyphonic madrigals are unaccompanied; the number of voices varies from two to eight, and most frequently from three to six....

s. Igor Stravinsky

Igor Stravinsky

Igor Fyodorovich Stravinsky ; 6 April 1971) was a Russian, later naturalized French, and then naturalized American composer, pianist, and conductor....

's final composition, The Owl and the Pussy Cat, is a palindrome.

The first movement from Constant Lambert

Constant Lambert

Leonard Constant Lambert was a British composer and conductor.-Early life:Lambert, the son of Russian-born Australian painter George Lambert, was educated at Christ's Hospital and the Royal College of Music...

's ballet

Ballet

Ballet is a type of performance dance, that originated in the Italian Renaissance courts of the 15th century, and which was further developed in France and Russia as a concert dance form. The early portions preceded the invention of the proscenium stage and were presented in large chambers with...

Horoscope
Horoscope (ballet)
Horoscope is a ballet created in 1937 by Frederick Ashton with scenery by Sophie Fedorovich and music by Constant Lambert. It is based on astrological themes, and is reminiscent of Gustav Holst's The Planets in its musical exploration of the mystical. The story of the ballet concerns a young man...

(1938) is titled "Palindromic Prelude". Lambert claimed that the theme was dictated to him by the ghost of Bernard van Dieren

Bernard van Dieren

Bernard Hélène Joseph van Dieren was a Dutch composer, critic, author, and writer on music.Van Dieren was the last of five children of a Rotterdam wine merchant, Bernard Joseph van Dieren, and his second wife, Julie Françoise Adelle Labbé...

, who had died in 1936.

British composer Robert Simpson

Robert Simpson (composer)

Robert Simpson was an English composer and long-serving BBC producer and broadcaster.He is best known for his orchestral and chamber music , and for his writings on the music of Beethoven, Bruckner, Nielsen and Sibelius. He studied composition under Herbert Howells...

also composed music in the palindrome or based on palindromic themes; the slow movement of his Symphony No. 2

Symphony No. 2 (Simpson)

The Symphony No. 2 by Robert Simpson was completed in 1956 and dedicated to Anthony Bernard, conductor of the London Chamber Orchestra, though the first performance was in fact given by the Hallé Orchestra conducted by Sir John Barbirolli in 16 July 1957 at the Cheltenham Festival.This is one of...

is a palindrome, as is the slow movement of his String Quartet No. 1. His hour-long String Quartet No. 9

String Quartet No. 9 (Simpson)

The String Quartet No. 9 by Robert Simpson was written in response to a commission by the Delme Quartet in 1982 to mark their 20th anniversary, one which coincided with the 250th anniversary of the birth of Joseph Haydn...

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, equating to a remarkable feat in string quartet writing.

The music of Anton Webern

Anton Webern

Anton Webern was an Austrian composer and conductor. He was a member of the Second Viennese School. As a student and significant follower of Arnold Schoenberg, he became one of the best-known exponents of the twelve-tone technique; in addition, his innovations regarding schematic organization of...

is often imbued with palindromes. Webern, who had studied the music of the Renaissance composer Heinrich Isaac

Heinrich Isaac

Heinrich Isaac was a Franco-Flemish Renaissance composer of south Netherlandish origin. He wrote masses, motets, songs , and instrumental music. A significant contemporary of Josquin des Prez, Isaac influenced the development of music in Germany...

, was extremely interested in symmetries in music, be they horizontal or vertical. For one of the most famous examples of horizontal or linear symmetry in Webern's music, one should look no further than the first phrase in the second movement of the symphony

Symphony

A symphony is an extended musical composition in Western classical music, scored almost always for orchestra. A symphony usually contains at least one movement or episode composed according to the sonata principle...

, Op. 21. In one of the most striking examples of vertical symmetry, the second movement of the Piano Variations

Variations for piano (Webern)

Variations for piano, op. 27, is a twelve-tone piece for piano composed by Anton Webern in 1936. It consists of three movements:# Sehr mäßig # Sehr schnell # Ruhig fließend...

, Op. 27, Webern arranges every pitch of this dodecaphonic work around the central pitch axis of A4. From this, each downward reaching interval is replicated exactly in the opposite direction. For example, a G3—13 half-steps down from A4—is replicated as a B5—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 can be made using more complex elements. For example, Karlheinz Stockhausen

Karlheinz Stockhausen

Karlheinz Stockhausen was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th and early 21st centuries. Another critic calls him "one of the great visionaries of 20th-century music"...

's composition Mixtur
Mixtur
Mixtur, for orchestra, 4 sine-wave generators, and 4 ring modulators, is an orchestral composition by the German composer Karlheinz Stockhausen, written in 1964, and is Nr. 16 in his catalogue of works...

, originally written in 1964, consists of twenty sections, called "moments", which may be permuted

Permutation

In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...

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. By contrast, Karel Goeyvaerts

Karel Goeyvaerts

Karel Goeyvaerts was a Belgian composer.-Life:After studies at the Royal Flemish Music Conservatory in Antwerp, Goeyvaerts studied composition in Paris with Darius Milhaud and analysis with Olivier Messiaen...

's 1953 electronic composition, Nummer 5
Nummer 5
Nummer 5 met zuivere tonen is a musical work by the Belgian composer Karel Goeyvaerts, realized in 1953 and one of the earliest pieces of electronic music.-History:...

(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.

In classical music

Classical music

Classical music is the art music produced in, or rooted in, the traditions of Western liturgical and secular music, encompassing a broad period from roughly the 11th century to present times...

, a crab canon

Crab canon

A crab canon—also known by the Latin form of the name, canon cancrizans—is an arrangement of two musical lines that are complementary and backward, similar to a palindrome. Originally it is a musical term for a kind of canon in which one line is reversed in time from the other . A famous example...

is a canon

Canon (music)

In music, a canon is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration . The initial melody is called the leader , while the imitative melody, which is played in a different voice, is called the follower...

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 "chiasic" referring to the cross shaped Greek letter "χ

Chi (letter)

Chi is the 22nd letter of the Greek alphabet, pronounced as in English.-Greek:-Ancient Greek:Its value in Ancient Greek was an aspirated velar stop .-Koine Greek:...

" This is usually a form of reference to the crucifixion for example, the crucifixus section of the Bach B-minor Mass. The purpose of such palindromic balancing is to focus the listener on the central movement much like one would focus on the center of the cross in the crucifixion. Other examples are found in Bach's Cantata BWV 4, "Christ lag in Todesbanden", Handel's Messiah and the Fauré Requiem.

Musical content

Hüsker Dü

Hüsker Dü was an American rock band formed in Saint Paul, Minnesota in 1979. The band's continual members were guitarist Bob Mould, bassist Greg Norton, and drummer Grant Hart....

's concept album Zen Arcade
Zen Arcade
Upon its release Zen Arcade received positive reviews in many mainstream publications, including NME, The New York Times and Rolling Stone. In his review for Rolling Stone, David Fricke described Zen Arcade as "the closest hardcore will ever get to an opera .....

contains the songs "Reoccurring Dreams" and "Dreams Reoccurring", the latter of which appears earlier on the album but is actually the intro

Introduction (music)

In music, the introduction is a passage or section which opens a movement or a separate piece. In popular music this is often abbreviated as intro...

of the former song played in reverse. In similar manner, The Stone Roses

The Stone Roses

The Stone Roses are an English alternative rock band formed in Manchester in 1983. They were one of the pioneering groups of the Madchester movement that was active during the late 1980s and early 1990s...

' first album

The Stone Roses (album)

The Stone Roses is the debut album by English rock band The Stone Roses, released on Silvertone Records in 1989. It cemented the band's reputation among critics, and is still rated by some as one of the most important albums ever...

contains the songs "Waterfall

Waterfall (The Stone Roses song)

"Waterfall" is the 9th single from The Stone Roses. It was the fourth single taken from their debut album The Stone Roses. It was released on 30 December 1991 and reached #27 in the UK.-Track listing:7": [Silvertone ORE 35]...

" and "Don't Stop", the latter of which is, in essence, the former performed backwards. The 12" and CD formats of their single Elephant Stone

Elephant Stone

"Elephant Stone" is the third single by The Stone Roses and their first release on Silvertone Records. Originally released in October 1988, it showcased the group's growing confidence and incorporation of dance rhythms...

feature the B-side "Full Fathom Five", which is an alternate mix of the title track played in reverse.

The title track of the 1992 album entitled UFO Tofu
UFO Tofu
UFO Tofu is the third album released by Béla Fleck and the Flecktones, released in 1992. The title is a palindrome, which is also a musical theme in the title track, according to the album's liner notes.- Reception :...

by Béla Fleck and the Flecktones

Béla Fleck and the Flecktones

Béla Fleck and the Flecktones is a primarily instrumental group from the United States, that draws equally on bluegrass, fusion and jazz, sometimes dubbed "blu-bop". The band formed in 1988, initially to perform once on the PBS series Lonesome Pine Specials. The Flecktones have toured extensively...

is said by its composer to be a musical palindrome.

In 2003, the city of San Diego, California

San Diego, California

San Diego is the eighth-largest city in the United States and second-largest city in California. The city is located on the coast of the Pacific Ocean in Southern California, immediately adjacent to the Mexican border. The birthplace of California, San Diego is known for its mild year-round...

commissioned sculptor Roman DeSalvo and composer Joseph Waters

Joseph Waters

Joseph Waters is an American classical composer. He also mounts experimental electronic music festivals attempting to bridge the gap between contemporary popular genres and the avant-garde Western classical tradition.-Creative Projects:...

to create a public artwork in the form of a safety railing on the 25th Street overpass at F and 25th Streets. The result, Crab Carillon, is a set of 488 tuned chimes that can be played by pedestrians as they cross the overpass. Each chime is tuned to the note of a melody, composed by Waters. The melody is in the form of a palindrome, to accommodate walking in either direction.

"Starálfur", from Sigur Rós

Sigur Rós

Sigur Rós is an Icelandic post-rock band with classicaland minimalist elements. The band is known for its ethereal sound, and frontman Jónsi Birgisson's falsetto vocals and use of bowed guitar. In January 2010, the band announced that they will be on hiatus. Since then, it has since been announced...

's Ágætis byrjun
Ágætis byrjun
Ágætis byrjun is the second album by the Icelandic post-rock band Sigur Rós, which was released in 1999. Ágætis byrjun was recorded between the summer of 1998 to the spring of 1999 with producer Ken Thomas, and became Sigur Rós's breakthrough album, both critically and commercially...

has the strings part palindrome.

The song "You Can Call Me Al

You Can Call Me Al

"You Can Call Me Al" is a song by Paul Simon, the first single released from his album Graceland. The song originally charted in the U.S. at No. 44 in October 1986 but it was reissued with greater promotion in March 1987 and hit No. 23. In the UK it peaked at No. 4, while in Sweden and the...

" by Paul Simon

Paul Simon

Paul Frederic Simon is an American singer-songwriter and guitarist.Simon is best known for his success, beginning in 1965, as part of the duo Simon & Garfunkel, with musical partner Art Garfunkel. Simon wrote most of the pair's songs, including three that reached number one on the US singles...

features a palindromic bass run performed by Bakithi Kumalo.

Lyrics

The song "I Palindrome I

I Palindrome I

I Palindrome I is an EP from They Might Be Giants. The title song also appears on Apollo 18 , released in 1992 by Elektra Records.The "I Palindrome I" track itself contains numerous visual, musical, word, letter and conceptual palindromes....

", by They Might Be Giants

They Might Be Giants

They Might Be Giants is an American alternative rock band formed in 1982 by John Flansburgh and John Linnell. During TMBG's early years Flansburgh and Linnell were frequently accompanied by a drum machine. In the early 1990s, TMBG became a full band. Currently, the members of TMBG are...

, features palindromic lyrics and imagery. The 27-word bridge is word-symmetrical.

"Weird Al" Yankovic

"Weird Al" Yankovic

Alfred Matthew "Weird Al" Yankovic is an American singer-songwriter, music producer, accordionist, actor, comedian, writer, satirist, and parodist. Yankovic is known for his humorous songs that make light of popular culture and that often parody specific songs by contemporary musical acts...

's song "Bob", from his 2003 album Poodle Hat
Poodle Hat
Poodle Hat is the Grammy Award-winning 11th studio album by "Weird Al" Yankovic. It was released on May 20, 2003 on Volcano Records. The album debuted at number 17 on the Billboard 200. The album was released on an Enhanced CD...

, consists of rhyming palindromes and parodies the Bob Dylan

Bob Dylan

Bob Dylan is an American singer-songwriter, musician, poet, film director and painter. He has been a major and profoundly influential figure in popular music and culture for five decades. Much of his most celebrated work dates from the 1960s when he was an informal chronicler and a seemingly...

song "Subterranean Homesick Blues

Subterranean Homesick Blues

"Subterranean Homesick Blues" is a song by Bob Dylan, originally released in 1965 as a single on Columbia Records, catalogue 43242. It appeared 19 days later as the lead track to the album Bringing It All Back Home. It was Dylan's first Top 40 hit, peaking at #39 on the Billboard Hot 100. It also...

".

Baby Gramps

Baby Gramps

Baby Gramps is a guitar performer, who, though born in Miami, Florida, has been based in the Northwest USA for at least the last 40 years. He is famous for his palindromes...

is known for songs where the lyrics are made up of palindromes.

Names and titles

In 1975, the Swedish pop group ABBA

ABBA

ABBA was a Swedish pop group formed in Stockholm in 1970 which consisted of Anni-Frid Lyngstad, Björn Ulvaeus, Benny Andersson and Agnetha Fältskog...

had a hit single titled "SOS

SOS (ABBA song)

Agnetha Fältskog's version was the second single from her fifth Swedish solo-album Elva kvinnor i ett hus . It was the only song from this album not to have been composed by Fältskog herself....

", a unique occasion in which a song's title and the name of its recording artist are both palindromes.

The Grateful Dead

Grateful Dead

The Grateful Dead was an American rock band formed in 1965 in the San Francisco Bay Area. The band was known for its unique and eclectic style, which fused elements of rock, folk, bluegrass, blues, reggae, country, improvisational jazz, psychedelia, and space rock, and for live performances of long...

's 1969 album Aoxomoxoa

Aoxomoxoa

Aoxomoxoa is the third studio album by the Grateful Dead. It was originally titled Earthquake Country. Many Deadheads consider this era of the Dead to be the experimental apex of the band's history. It is also the first album with Tom Constanten as an official member of the band...

is a notable early use of palindrome in the title of a popular music album.

In 1992, the grunge

Grunge

Grunge is a subgenre of alternative rock that emerged during the mid-1980s in the American state of Washington, particularly in the Seattle area. Inspired by hardcore punk, heavy metal, and indie rock, grunge is generally characterized by heavily distorted electric guitars, contrasting song...

band Soundgarden

Soundgarden

Soundgarden is an American rock band formed in Seattle, Washington in 1984 by singer Chris Cornell, lead guitarist Kim Thayil, and bassist Hiro Yamamoto...

released an EP

Extended play

An EP is a musical recording which contains more music than a single, but is too short to qualify as a full album or LP. The term EP originally referred only to specific types of vinyl records other than 78 rpm standard play records and LP records, but it is now applied to mid-length Compact...

called Satanoscillatemymetallicsonatas or SOMMS; the title is a palindrome and puns on the supposed connection between the Devil and heavy metal

Heavy metal music

Heavy metal is a genre of rock music that developed in the late 1960s and early 1970s, largely in the Midlands of the United Kingdom and the United States...

music.

On Boris

Boris (band)

is a Japanese experimental rock band, known for often combining and switching between different music genres including drone metal, sludge metal, noise rock, psychedelic rock, ambient and pop...

and Sunn O)))

Sunn O)))

Sunn O))) is an American doom metal band known for its synthesis of diverse genres including drone, ambient, noise, and black metal. Supported by a varying cast of collaborators, the band has two core members: Stephen O'Malley and Greg Anderson .-History:Sunn O))) is named after the Sunn...

's collaborative album "Altar

Altar (album)

Altar is a collaboration album between Japanese doom band Boris and American drone doom duo Sunn O))), released on October 31, 2006 through Southern Lord Records. A limited two-CD edition was released on October 23 via Southern Lord with a 28 minute bonus track with Sunn O))), Boris, and Dylan...

", the vinyl version included a full disc, double-sided bonus track entitled "Satan Oscillate My Metallic Sonatas" (in reference to the Soundgarden EP of the same name), in which the various instruments (mainly guitars) are introduced one at a time on side one, and then fade out in reverse order on side two. Kim Thayil of Soundgarden appears on this track.

The Fall of Troy

The Fall of Troy

The Fall of Troy was an American progressive math rock trio from Mukilteo, Washington. The trio consisted of Thomas Erak , Andrew Forsman and Frank Ene...

made a song with the famous palindrome "A Man, A Plan, A Canal, Panama" as the title.

The first and last tracks on Andrew Bird

Andrew Bird

Andrew Bird is an American musician, songwriter, and multi-instrumentalist.- Early life and the Bowl of Fire :...

's album Noble Beast
Noble Beast
Noble Beast is American singer-songwriter Andrew Bird's fifth solo studio album released on January 20, 2009. Two songs from this album were previewed on his webpage, "Oh No" and "Carrion Suite", while the entire album was made available by NPR as a streaming feed...

form a palindrome ("Oh No" and "On Ho!") and the seventh track is a palindrome in itself: "Ouo". He has also mentioned palindromes in earlier music, giving his songs names like "11:11" "T'N'T" and "Fake Palindromes" (although the last title is not a palindrome itself). He also mentions palindromes in the lyrics of the song "I" and the "I" redux "Imitosis".

"racEcar" by Vitamin Party

Vitamin Party

Vitamin Party is a San Francisco/Bay Area "DIY" rock-punk band which formed in 2004. Their style shows influences of lo-fi, indie, post-modern punk with straight forward rock and roll...

features a repeating chorus of "A Man, A Plan, A Canal, Panama" (the title itself is palindromic).

"Never Odd or Even", which was to be the title of the first album by Aleka's Attic

Aleka's Attic

Aleka's Attic were an alternative folk/rock band from Gainesville, Florida formed by River Phoenix and his sister Rain.-History:The original line up of Aleka's Attic included River as lead singer and played guitar; his younger sister Rain sang, but, contrary to many incorrect reports, did not play...

, the band formed by the late River Phoenix

River Phoenix

River Jude Phoenix was an American film actor, musician, and teen icon. He was the oldest brother of fellow actors Rain, Joaquin, Liberty, and Summer Phoenix.Phoenix began acting at age 10 in television commercials...

, is a palindrome.

"If I Had a Hi-Fi

If I Had A Hi-Fi

If I Had a Hi-Fi is the sixth studio album by American alternative rock band Nada Surf. It was released on June 8, 2010 and consists only of covers.The album title is a palindrome.-Track listing:Original artists in brackets#"Electrocution"...

", a 2010 cover album by American alternative rock band Nada Surf

Nada Surf

Nada Surf is an American alternative rock band. Formed in 1992, the New York band consists of Matthew Caws , Ira Elliot and Daniel Lorca .-Early years:...

, is a palindrome.

Miles Davis

Miles Davis

Miles Dewey Davis III was an American jazz musician, trumpeter, bandleader, and composer. Widely considered one of the most influential musicians of the 20th century, Miles Davis was, with his musical groups, at the forefront of several major developments in jazz music, including bebop, cool jazz,...

and Black Sabbath

Black Sabbath

Black Sabbath are an English heavy metal band, formed in Aston, Birmingham in 1969 by Ozzy Osbourne , Tony Iommi , Geezer Butler , and Bill Ward . The band has since experienced multiple line-up changes, with Tony Iommi the only constant presence in the band through the years. A total of 22...

both had albums called "Live Evil". Inversely, Lynch Mob and Diamond Head

Diamond Head (band)

Diamond Head are an English heavy metal band formed in 1976 in Stourbridge, England. The band is recognised as one of the leading members of the New Wave of British Heavy Metal and is acknowledged by later bands like Metallica and Megadeth as an important early influence.-Early history:Formed by...

had albums called "Evil Live".

D.R.U.G.S. has two songs that are palindromes on the self-titled debut album, "Mr. Owl Ate My Metal Worm" and "Laminated E.T. Animal".

The Asian-American teenage Riot Grrrl band Emily's Sassy Lime

Emily's Sassy Lime

Emilys Sassy Lime was an all-Asian American teenage riot grrrl trio from SoCal, formed in 1993 by Wendy and Amy Yao, and Emily Ryan. According to Experience Music Project, they formed after sneaking out of their homes one night to see a Bikini Kill and Bratmobile show, striking up a...

's name is palindromic.

Long palindromes

The longest palindromic word in the Oxford English Dictionary is the onomatopoeic tattarrattat, coined by James Joyce

James Joyce

James Augustine Aloysius Joyce was an Irish novelist and poet, considered to be one of the most influential writers in the modernist avant-garde of the early 20th century...

in Ulysses
Ulysses (novel)
Ulysses is a novel by the Irish author James Joyce. It was first serialised in parts in the American journal The Little Review from March 1918 to December 1920, and then published in its entirety by Sylvia Beach on 2 February 1922, in Paris. One of the most important works of Modernist literature,...

(1922) for a knock on the door. The Guinness Book of Records gives the title to detartrated, the preterit and past participle of detartrate, a chemical term meaning to remove tartrate

Tartrate

A tartrate is a salt or ester of the organic compound tartaric acid, a dicarboxylic acid. Its formula is O−OC-CH-CH-COO− or C4H4O62−.As food additives, tartrates are used as antioxidants, acidity regulators, and emulsifiers...

s. Rotavator, a trademarked name for an agricultural machine, is often listed in dictionaries. The term redivider is used by some writers but appears to be an invented or derived term—only redivide and redivision appear in the Shorter Oxford Dictionary. Malayalam, an Indian language, is of equal length.

According to Guiness World Records, the Finnish

Finnish language

Finnish is the language spoken by the majority of the population in Finland Primarily for use by restaurant menus and by ethnic Finns outside Finland. It is one of the two official languages of Finland and an official minority language in Sweden. In Sweden, both standard Finnish and Meänkieli, a...

word saippuakivikauppias (soapstone

Soapstone

Soapstone is a metamorphic rock, a talc-schist. It is largely composed of the mineral talc and is thus rich in magnesium. It is produced by dynamothermal metamorphism and metasomatism, which occurs in the areas where tectonic plates are subducted, changing rocks by heat and pressure, with influx...

vendor), a 19 letter word, is claimed to be the world's longest palindromic word in everyday use. A meaningful derivative from it is saippuakalasalakauppias (soapfish bootlegger). An even longer effort is saippuakuppinippukauppias (soap dish

Soap dish

A soap dish holds a bar of soap when not in use for hand washing or other cleaning, near a washing area such as a bathtub or washbasin. Soap dishes are made from waterproof materials such as plastic, ceramic and metal. Soap dishes may be mounted on the wall. For liquid soap or foam soap a soap...

wholesale vendor). Almost equally long is the Estonian

Estonian language

Estonian is the official language of Estonia, spoken by about 1.1 million people in Estonia and tens of thousands in various émigré communities...

word kuulilennuteetunneliluuk (the hatch a bullet flies out of when exiting a tunnel).

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). In French, Oulipo writer George Perec's "Grand Palindrome" (1969) is 5,556 letters in length. In Hebrew, Noam Dovev wrote a 303-word, 1111-letter palindromic story called "Do god".

Biological structures

In most genome

Genome

In modern molecular biology and genetics, the genome is the entirety of an organism's hereditary information. It is encoded either in DNA or, for many types of virus, in RNA. The genome includes both the genes and the non-coding sequences of the DNA/RNA....

s or sets of gene

Gene

A gene is a molecular unit of heredity of a living organism. It is a name given to some stretches of DNA and RNA that code for a type of protein or for an RNA chain that has a function in the organism. Living beings depend on genes, as they specify all proteins and functional RNA chains...

tic instructions, palindromic motifs are found. However, the meaning of palindrome in the context of genetics is slightly different from the definition used for words and sentences. Since the DNA

DNA

Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms . The DNA segments that carry this genetic information are called genes, but other DNA sequences have structural purposes, or are involved in...

is formed by two paired strands of nucleotides, and the nucleotides always pair in the same way (Adenine

Adenine

Adenine is a nucleobase with a variety of roles in biochemistry including cellular respiration, in the form of both the energy-rich adenosine triphosphate and the cofactors nicotinamide adenine dinucleotide and flavin adenine dinucleotide , and protein synthesis, as a chemical component of DNA...

(A) with Thymine

Thymine

Thymine is one of the four nucleobases in the nucleic acid of DNA that are represented by the letters G–C–A–T. The others are adenine, guanine, and cytosine. Thymine is also known as 5-methyluracil, a pyrimidine nucleobase. As the name suggests, thymine may be derived by methylation of uracil at...

(T), Cytosine

Cytosine

Cytosine is one of the four main bases found in DNA and RNA, along with adenine, guanine, and thymine . It is a pyrimidine derivative, with a heterocyclic aromatic ring and two substituents attached . The nucleoside of cytosine is cytidine...

Guanine

Guanine is one of the four main nucleobases found in the nucleic acids DNA and RNA, the others being adenine, cytosine, and thymine . In DNA, guanine is paired with cytosine. With the formula C5H5N5O, guanine is a derivative of purine, consisting of a fused pyrimidine-imidazole ring system with...

(G)), a (single-stranded) sequence of DNA is said to be a palindrome if it is equal to its complementary sequence read backwards. For example, the sequence ACCTAGGT is palindromic because its complement is TGGATCCA, which is equal to the original sequence in reverse complement.

A palindromic DNA

DNA

sequence can form a hairpin

Stem-loop

Stem-loop intramolecular base pairing is a pattern that can occur in single-stranded DNA or, more commonly, in RNA. The structure is also known as a hairpin or hairpin loop. It occurs when two regions of the same strand, usually complementary in nucleotide sequence when read in opposite directions,...

. Palindromic motifs are made by the order of the nucleotide

Nucleotide

Nucleotides are molecules that, when joined together, make up the structural units of RNA and DNA. In addition, nucleotides participate in cellular signaling , and are incorporated into important cofactors of enzymatic reactions...

s that specify the complex chemicals (protein

Protein

Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

s) that, as a result of those genetic

Genetics

Genetics , a discipline of biology, is the science of genes, heredity, and variation in living organisms....

instructions, the cell

Cell (biology)

The cell is the basic structural and functional unit of all known living organisms. It is the smallest unit of life that is classified as a living thing, and is often called the building block of life. The Alberts text discusses how the "cellular building blocks" move to shape developing embryos....

is to produce. They have been specially researched in bacteria

Bacteria

Bacteria are a large domain of prokaryotic microorganisms. Typically a few micrometres in length, bacteria have a wide range of shapes, ranging from spheres to rods and spirals...

l chromosomes and in the so-called Bacterial Interspersed Mosaic Elements (BIMEs) scattered over them. Recently a research genome sequencing project discovered that many of the bases on the Y-chromosome

Y chromosome

The Y chromosome is one of the two sex-determining chromosomes in most mammals, including humans. In mammals, it contains the gene SRY, which triggers testis development if present. The human Y chromosome is composed of about 60 million base pairs...

are arranged as palindromes. 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 frequently in proteins, but their role in the protein function is not clearly known. It has recently been suggested that the prevalence existence of palindromes in peptides might be related to the prevalence of low-complexity regions in proteins, as palindromes are frequently associated with low-complexity sequences. Their prevalence might be also related to an alpha helical formation propensity of these sequences, or in formation of proteins/protein complexes.

Computation theory

In the automata theory

Automata theory

In theoretical computer science, automata theory is the study of abstract machines and the computational problems that can be solved using these machines. These abstract machines are called automata...

, a set of all palindromes in a given alphabet

Alphabet

An alphabet is a standard set of letters—basic written symbols or graphemes—each of which represents a phoneme in a spoken language, either as it exists now or as it was in the past. There are other systems, such as logographies, in which each character represents a word, morpheme, or semantic...

is a typical example of a language

Formal language

A formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...

that is context-free

Context-free language

In formal language theory, a context-free language is a language generated by some context-free grammar. The set of all context-free languages is identical to the set of languages accepted by pushdown automata.-Examples:...

, but not regular

Regular language

In theoretical computer science and formal language theory, a regular language is a formal language that can be expressed using regular expression....

. This means that it is, in theory, impossible for a computer with a finite amount of memory to reliably test for palindromes. (For practical purposes with modern computers, this limitation would apply only to incredibly long letter-sequences.)

In addition, the set of palindromes cannot be reliably tested by a deterministic pushdown automaton

Deterministic pushdown automaton

In automata theory, a pushdown automaton is a finite automaton with an additional stack of symbols; its transitions can take the top symbol on the stack and depend on its value, and they can add new top symbols to the stack....

and is not LR(k)-parseable

LR parser

In computer science, an LR parser is a parser that reads input from Left to right and produces a Rightmost derivation. The term LR parser is also used; where the k refers to the number of unconsumed "look ahead" input symbols that are used in making parsing decisions...

. 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 longest palindromic substring

Longest palindromic substring

In computer science, the longest palindromic substring or longest symmetric factor problem is the problem of finding a maximum-length contiguous substring of a given string that is also a palindrome. For example, the longest palindromic substring of "bananas" is "anana"...

of a given input string in linear time.

Semordnilap

Semordnilap is a name coined for a word or phrase that spells a different word or phrase backwards. "semordnilap" is itself "palindromes" spelled backwards. According to author O.V. Michaelsen, it was probably coined by logologist Dmitri A. Borgmann and appeared in Oddities and Curiosities, annotated by Martin Gardner, 1961. Semordnilaps are also known as volvograms, heteropalindromes, semi-palindromes, half-palindromes, reversgrams, mynoretehs, reversible anagrams, word reversals, or anadromes. They have also sometimes been called antigrams, though this term now usually refers to anagrams with opposing meanings.

These words are very useful in constructing palindromic texts; together, each pair forms a palindrome, and they can be added on either side of a shorter palindrome in order to extend it.

The longest single-word English examples contain eight letters:

stressed / desserts
samaroid (resembling a samara
Samara (fruit)
A samara is a type of fruit in which a flattened wing of fibrous, papery tissue develops from the ovary wall. A samara is a simple dry fruit and indehiscent . It is a winged achene...

) / dioramas
rewarder / redrawer
departer / retraped (construction based on the fact that verb trape is recorded as an alternative spelling of traipse)
reporter / retroper (construction based on the fact that trope is recorded as a verb, meaning "to furnish with trope
Trope (literature)
A literary trope is the usage of figurative language in literature, or a figure of speech in which words are used in a sense different from their literal meaning...

s")

Other examples include:

was / saw
god / dog
gateman / nametag
enoteca
Enoteca
Enoteca is an Italian word, derived from the Greek word Οινοθήκη, which literally means ”wine repository” , but is used to describe a special type of local or regional wine shop that originated in Italy. The concept of an enoteca has also spread to some other countries...

/ acetone
deliver / reviled
straw / warts
star / rats
lived / devil
live / evil
diaper / repaid
smart / trams
spit / tips
stop / pots
bats / stab

The poem Lost Generation is a line-by-line semordnilap. When the lines are read in reverse order, it becomes new poem.

Non-English palindromes

Palindromes in languages that use an alphabet

Alphabet

ic writing system

Writing system

A writing system is a symbolic system used to represent elements or statements expressible in language.-General properties:Writing systems are distinguished from other possible symbolic communication systems in that the reader must usually understand something of the associated spoken language to...

work in essentially the same way as English palindromes. In languages that use a writing system other than an alphabet (such as Chinese), a palindrome is still a sequence of characters from that writing system that remains the same when reversed, though the characters now represent words rather than letters.

The treatment of diacritic

Diacritic

A diacritic is a glyph added to a letter, or basic glyph. The term derives from the Greek διακριτικός . Diacritic is both an adjective and a noun, whereas diacritical is only an adjective. Some diacritical marks, such as the acute and grave are often called accents...

s varies. In languages such as Czech and Spanish, letters with diacritics or accents (except tilde

Tilde

The tilde is a grapheme with several uses. The name of the character comes from Portuguese and Spanish, from the Latin titulus meaning "title" or "superscription", though the term "tilde" has evolved and now has a different meaning in linguistics....

s) are not given a separate place in the alphabet, and thus preserve the palindrome whether or not the repeated letter has an ornamentation. However, in the Nordic languages

North Germanic languages

The North Germanic languages or Scandinavian languages, the languages of Scandinavians, make up one of the three branches of the Germanic languages, a sub-family of the Indo-European languages, along with the West Germanic languages and the extinct East Germanic languages...

, A

A is the first letter and a vowel in the basic modern Latin alphabet. It is similar to the Ancient Greek letter Alpha, from which it derives.- Origins :...

, Å

Å represents various sounds in several languages. Å is part of the alphabets used for the Alemannic and the Bavarian-Austrian dialects of German...

and Ä

"Ä" and "ä" are both characters that represent either a letter from several extended Latin alphabets, or the letter A with an umlaut mark or diaeresis.- Independent letter :...

/Æ

Æ is a grapheme formed from the letters a and e. Originally a ligature representing a Latin diphthong, it has been promoted to the full status of a letter in the alphabets of some languages, including Danish, Faroese, Norwegian and Icelandic...

, as well as O

O is the fifteenth letter and a vowel in the basic modern Latin alphabet.The letter was derived from the Semitic `Ayin , which represented a consonant, probably , the sound represented by the Arabic letter ع called `Ayn. This Semitic letter in its original form seems to have been inspired by a...

and Ö

"Ö", or "ö", is a character used in several extended Latin alphabets, or the letter O with umlaut to denote the front vowels or . In languages without umlaut, the character is also used as a "O with diaeresis" to denote a syllable break, wherein its pronunciation remains an unmodified .- O-Umlaut...

/Ø

Ø — minuscule: "ø", is a vowel and a letter used in the Danish, Faroese, Norwegian and Southern Sami languages.It's mostly used as a representation of mid front rounded vowels, such as ø œ, except for Southern Sami where it's used as an [oe] diphtong.The name of this letter is the same as the sound...

, are all distinct letters and must be mirrored exactly to be considered a palindrome.

The longest palindrome in the Dutch language, according to the Dutch Guinness Book of World Records, is koortsmeetsysteemstrook, which translates into English as thermometer. The Dutch Wikipedia states, however, that Hugo Brandt Corstius, in his book, Opperlandse taal- en letterkunde, came up with the longest existing Dutch palindrome—potstalmelkkoortspilstaalplaatslipstrookklemlatstop—which has no definitive meaning, although it consists of legitimate Dutch words.

External links

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

History

Simple Examples for Palindromes

Palindromes in ancient Sanskrit

Palindromes in Tamil poetry

Characters

Phrases

Famous English palindromes

Names

Molecular biology

Numbers

Dates

Acoustics

Rhythm

Classical music

Musical content

Lyrics

Names and titles

Long palindromes

Biological structures

Computation theory

Semordnilap

Non-English palindromes

See also

External links