Editing Gematria (section)

===Related transformations===
Within the wider topic of gematria are included the various alphabet transformations, where one letter is substituted by another based on a logical scheme:
* ''[[Atbash]]'' exchanges each letter in a word or a phrase by ''opposite'' letters. Opposite letters are determined by substituting the first letter of the Hebrew alphabet (''aleph'') with the last letter (''tav''), the second letter (''bet'') with the next to last (''shin''), etc. The result can be interpreted as a secret message or calculated by the standard gematria methods. A few instances of ''atbash'' are found already in the Hebrew [[Bible]]. For example, see [[Jeremiah]] 25:26, and 51:41, with [[Targum Jonathan|Targum]] and [[Rashi]], in which the name ששך ("Sheshek") is thought to represent בבל ([[Babylon]]).<ref name=JE>{{JewishEncyclopedia|url=http://www.jewishencyclopedia.com/articles/6571-gematria|title=GEMAṬRIA |author=[[Solomon Schechter]] |author2=Caspar Levias}}</ref>
* ''Albam'' – the alphabet is divided in half, eleven letters in each section. The first letter of the first series is exchanged for the first letter of the second series, the second letter of the first series for the second letter of the second series, and so forth.
* ''Achbi'' divides the alphabet into two equal groups of 11 letters. Within each group, the first letter is replaced by the last, the second by the 10th, etc.
* ''Ayak bakar'' replaces each letter by another one that has a 10-times-greater value. The final letters usually signify the numbers from 500 to 900. Thousands is reduced to ones (1,000 becomes 1, 2,000 becomes 2, etc.)
* ''Ofanim'' replaces each letter by the last letter of its name (e.g. ''peh'' for ''aleph'').
* ''Akhas beta'' divides the alphabet into three groups of 7, 7 and 8 letters. Each letter is replaced cyclically by the corresponding letter of the next group. The letter [[Tav (letter)|Tav]] remains the same.
* ''Avgad'' replaces each letter by the next one. ''Tav'' becomes ''aleph''. The opposite operation is also used.
Most of the above-mentioned methods and ciphers are listed by Rabbi [[Moses ben Jacob Cordovero|Moshe Cordevero]].<ref>Moshe Cordevero, ''Sefer Pardes ha-Rimonim'', ''שער האותיות''</ref>

Some authors provide lists of as many as 231 various replacement ciphers, related to the 231 mystical Gates of the ''[[Sefer Yetzirah]]''.<ref name="Sefer ha-Shem">Elazar Rokeach, ''Sefer ha-Shem''</ref>

Dozens of other far more advanced methods are used in Kabbalistic literature, without any particular names. In Ms. Oxford 1,822, one article lists 75 different forms of gematria.<ref>''Encyclopedia Judaica Vol. 7'', 2007, p. 426</ref> Some known methods are [[Recursion|recursive]] in nature and are reminiscent of [[graph theory]] or make a lot of use of [[combinatorics]]. Rabbi [[Eleazar of Worms|Elazar Rokeach]] (born c. 1176 – died 1238) often used multiplication, instead of addition, for the above-mentioned methods. For example, spelling out the letters of a word and then multiplying the squares of each letter value in the resulting string produces very large numbers, in orders of [[10^12|trillions]]. The spelling process can be applied recursively, until a certain pattern (e.g., all the letters of the word "[[Talmud]]") is found; the gematria of the resulting string is then calculated. The same author also used the sums of all possible unique letter combinations, which add up to the value of a given letter. For example, the letter [[He (letter)|Hei]], which has the standard value of 5, can be produced by combining <math>1 + 1 + 1 + 1 + 1</math>, <math>2 + 1 + 1 + 1</math>, <math>3 + 1 + 1</math>, <math>4+1</math>, <math>2 + 2 + 1</math>, or <math>2+3</math>, which adds up to <math>30</math>. Sometimes combinations of repeating letters are not allowed (e.g., <math>2+3</math> is valid, but <math>3 + 1 + 1</math> is not). The original letter itself can also be viewed as a valid combination.<ref name="Sefer ha-Shem" />

Variant spellings of some letters can be used to produce sets of different numbers, which can be added up or analyzed separately. Many various complex [[formal system]]s and recursive algorithms, based on graph-like structural analysis of the letter names and their relations to each other, [[modular arithmetic]], pattern search and other highly advanced techniques, are found in the "Sefer ha-Malchut" by Rabbi David ha-Levi of the [[Draa|Draa Valley]], a Spanish-Moroccan Kabbalist of the 15th–16th century.<ref name="Sefer ha-Malchut">Sefer ha-Malchut, "Sifrei Chaim", Jerusalem, 2008</ref> Rabbi David ha-Levi's methods also consider the numerical values and other properties of [[Niqqud|the vowels]].

Kabbalistic [[Jewish views of astrology|astrology]] uses some specific methods to determine the astrological influences on a particular person. According to one method, the gematria of the person's name is added to the gematria of his or her mother's name; the result is then divided by 7 and 12. The remainders signify a particular planet and Zodiac sign.<ref>Commentary to [[Sefer Yetzirah]], attributed to [[Saadia Gaon]], 6:4; Rabbi Aryeh Kaplan, Sefer Yetzirah, "WeiserBooks", Boston, 1997, pp. 220–221</ref>