As you know, the Russian language is quite voluminous in terms of variety of turns and expressions. One of the varieties of lexical elements are palindromes. Examples for children that best illustrate this concept can be found among the classics. For example, in Fet: "And the rose fell on Azora's paw." If you carefully look at the words, you will notice that the sentence can be read in both directions: from the beginning (from left to right) and from the end (from right to left). And in each case, the expression will sound the same. These are sentences, but there are also palindrome words. Examples that most clearly illustrate the concept will be given below.
Definition
What is a palindrome? This concept has Greek roots and literally translates as “running back” or “running again”. In some cases, palindromes, examples of which will be given below, take any set of characters symmetrical with respect to their middle. The longest combination of this type is considered to be saippuakauppias (from Finnish - a soap seller). There are quite interesting English palindromes:
“Madam, I'm Adam” is a representation of a man to a lady (Madam, I am Adam).
To this the lady can modestly respond with a “flip-flop”: “Eve” (Eve).
Not only sentences or letter sets are symmetrical. Palindromes verses are quite common:
I rarely hold a cigarette with my hand ...
I'm sitting here sincerely
Fiercely creating in silence,
Once again
Good luck to the child,
I’ll load it once
Yes, glad!
It can be read both from the beginning and from the end.
Brief historical background
Speaking of what a palindrome is, it should be said that “shifters” are known from the most ancient times. Often they were given a magical sacred meaning. Palindromes have appeared, examples of which can be found in a variety of languages, presumably in the Middle Ages. In classical Russian literature there is reliable information about the author’s “changeling” written by Derzhavin: “I’m going to eat the sword of the judge.” The first attempt to compose a long, multi-line rhymed palindromic work was made by Velimir Khlebnikov (the poem “Razin”). But the flowering of this artistic direction reached only the 1970-1990th years. Palindromes, examples of which can be found in the works of Vladimir Gershuni, Nikolai Ladygin, Dmitry Avalini and Elena Katsyuba, began to be studied in more detail in the literary and literary direction in the 1990s. The studies were actively carried out mainly by German Lukomnikov and Alexander Bubnov.
Theorists and practitioners have identified various borderline forms. For example, a werewolf. This text is read from left to right differently than back: “The world is comfortable” (auth. Sergey Fedin). Speaking of what a palindrome is, one should also mention rare forms of this artistic direction: these are syllabic, bilingual “shifters”. The latter are text that can be read in one direction in one language and vice versa in another. What other rare palindromes are there? Various examples can be given. There is a form of “symmetric” combination, in which reading is not carried out in the opposite, but as if in a propagated form: socolzokol, boar caban and others.
Interest in direction
It should be said that palindromes, examples of which will be given further in the article for clarity, were of interest to scholars of vocabulary, writers, poets, writers at different times to different degrees. It is noteworthy that in the seventies of the last century it was impossible to publish such works. This was mainly due to the fact that the desire for "formalism" at that time was not welcomed in the literature. At the very beginning of the development of this artistic direction, all the writers of the “shifters” were well acquainted with each other, they knew, one might say, in the face of each other. To date, many works have seen the light in anthologies. But most of them remained unpublished.
Genres
Palindrome phrases, or “aphorisms,” were very popular. Some of them could even cause a smile (due to their artistic characteristics). In many cases, the combination inside the shifter attracted attention not only with its non-standard form, but also with a certain humorous content. Separate lines can even be collected in a poetic work. However, if the combinations pretend to poetry after all, then they should not be allowed any discounts on the unusual forms. In other words, everything must be preserved - rhythm, rhyme, size - as in standard, ordinary poetic works. "Symmetry" in such cases added only a rhythmic and sound game. Many poets managed to find "almost palindromic" forms. Different authors such revolutions created the beauty of sound. Speaking about what a palindrome is, one cannot but consider lyrical poetic works created using these art forms. Many of them contain a share of humor, but, despite this, they can be taken quite seriously. Some symmetrical expressions fit well into the music. In some cases, a poetic work can consist of one “shifter” divided into lines. In this case, they talk about monopalindrome.
Poetry
Of particular interest against the background of the study of palindromes is the creativity of the Block. Being a symbolist poet, he paid quite a lot of attention to the rhythmic and sound organization of works. In his poem The Twelve, Alexander Blok’s achievements in sound and rhythmic directions are clearly traced. Goldstein translated all this work of Blok into the language of palindromes. Moreover, the author notes that in the process it was possible to preserve the rhyme, rhythm, composition of the entire poem almost everywhere. Having remade The Twelve, Goldstein notes that, in his opinion, some shifted accents even increase intonation to a certain extent.
Symmetry in numbers
In addition to letter combinations, expressions and whole works, there are palindrome numbers. This definition is used for apparent symmetry in the record. Natural numbers in this case will be read from left to right and vice versa in the same way. An odd or even number of characters can be arranged symmetrically. Numerical palindromes are found in different systems with their own names. So, there is a category of “curly” signs: 1001, 676 and others. Such "palindromic" forms are found among Fibonacci numbers, Smith numbers .
Math actions
Numeric palindromes may result from operations on other characters. Martin Gardner, the author of the book “Have an Idea!”, Being a well-known popularizer of science, puts forward a certain hypothesis. If you take a positive integer (any) and add the inverse to it (consisting of the same numbers, but in reverse order), then repeat the action, but with the amount received, then at one of the steps you get a palindrome. In some cases, it is enough to perform addition once: 213 + 312 = 525. But usually at least two operations are necessary. So, for example, if you take the number 96, then, having made sequential addition, a palindrome can be obtained only at the fourth level:
96 + 69 = 165
165 + 651 = 726
726 + 627 = 1353
1353 + 3531 = 4884
The essence of the hypothesis is that if you take any number, after a certain number of actions a palindrome will be received. Examples can be found not only in addition, but also in exponentiation, root extraction and other operations.
Interesting couples
In groups of primes, very interesting patterns can be seen if specific numbers are present, for example, primes are 1 and 3. So, simple two-digit numbers will be ordered pairs: 31-13 and 13-31, five out of six three-digit primes, including 2 “Werewolf”: 313 and 131, pairs of shifters: 113-311 and 311-113. The resulting pairs in all the cases presented are clearly expressed in the form of numerical squares. In general, in mathematics you can find quite a lot of digital patterns.
Palindromes in other areas of human activity. Biology
The structure of nucleic acids provides for the presence of relatively short, mutually complementary regions. They have the so-called "mirror sequences" of nucleotides capable of forming duplexes. In the human genome, the total number of such “shifters” is estimated to range from one hundred thousand to a million. Moreover, according to observations, their distribution over the DNA structure is uneven. Palindromes in the biological sense have the ability to provide an increase in the amount of information without increasing the number of nucleotides. Of particular importance "symmetrical forms" are in the formation of certain types of nucleic acids - transport RNA, for example.
Music
Palindromic pieces of music are played “as usual” in accordance with the rules. After the play is completed, the notes are turned over. Then the piece is played again, but the melody will not change. Iterations can be present as many as you like, while it is not known what is the bottom and what is the top. These pieces of music can be played together, while reading music from both sides at the same time. Examples of such palindromic works are The Way of the World, written by Mosheles, and The Table Melody for Two, composed by Mozart.