Gematria

In the standard (Mispar hechrechi) version of gematria, each letter is given a numerical value between 1 and 400, as shown in the following table. In the Mispar gadol variation, the five final letters are given their own values, ranging from 500 to 900.

A mathematical formula for finding a letter's corresponding number in Mispar Gadol is: ${\displaystyle f(x)=\left(10^{\lfloor \left(x-1\right)\div 9\rfloor }\right)\times \left(\left(\left(x-1\right)\ \mathrm {mod} \ 9\right)+1\right)}$ where x is the position of the letter in the language letters index (regular order of letters), and the floor and modulo functions are used.

The value of the Hebrew vowels is not usually counted, but some lesser-known methods include the vowels as well. The most common vowel values are as follows (a less common alternative value, based on the digit sum, is given in parentheses):

Sometimes, the names of the vowels are spelled out and their gematria is calculated using standard methods.[19]

There are many different methods used to calculate the numerical value for the individual Hebrew/Aramaic words, phrases or whole sentences. More advanced methods are usually used for the most significant Biblical verses, prayers, names of God and angels, etc. These methods include:[20]

• Mispar Hechrachi (absolute value) is the standard method. It assigns the values 1–9, 10–90, 100–400 to the 22 Hebrew letters in order. Sometimes it is also called Mispar ha-Panim (face number), as opposed to the more complicated Mispar ha-Akhor (back number).
• Mispar Gadol (large value) counts the final forms (sofit) of the Hebrew letters as a continuation of the numerical sequence for the alphabet, with the final letters assigned values from 500 to 900. The name Mispar Gadol is sometimes used for a different method, Otiyot beMilui.
• The same name, Mispar Gadol, is also used for another method, which spells the name of each letter and adds the standard values of the resulting string. For example, the letter alef is spelled alef-lamed-peh, giving it a value of 1+30+80=111.
• Mispar Katan (small value) calculates the value of each letter, but truncates all of the zeros. It is also sometimes called Mispar Me'ugal.
• Mispar Siduri (ordinal value) with each of the 22 letters given a value from 1 to 22.
• Mispar Bone'eh (building value, also Revu'a, square[21]) is calculated by walking over each letter from the beginning to the end, adding the value of all previous letters and the value of the current letter to the running total. Therefore, the value of the word achad (one) is ${\displaystyle 1+(1+8)+(1+8+4)=23}$.
• Mispar Kidmi (preceding value) uses each letter as the sum of all the standard gematria letter values preceding it. Therefore, the value of Aleph is 1, the value of Bet is 1+2=3, the value of Gimmel is 1+2+3=6, etc. It's also known as Mispar Meshulash (triangular or tripled number).
• Mispar P'rati calculates the value of each letter as the square of its standard gematria value. Therefore, the value of Aleph is 1 × 1 = 1, the value of Bet is 2 × 2 = 4, the value of gimmel is 3 × 3 = 9, etc. It's also known as Mispar ha-Merubah ha-Prati.
• Mispar ha-Merubah ha-Klali is the square of the standard absolute value of each word.
• Mispar Meshulash calculates the value of each letter as the cube of their standard value. The same term is more often used for Mispar Kidmi.
• Mispar ha-Akhor – The value of each letter is its standard value multiplied by the position of the letter in a word or a phrase in either ascending or descending order. This method is particularly interesting, because the result is sensitive to the order of letters. It is also sometimes called Mispar Meshulash (triangular number).
• Mispar Mispari spells out the standard values of each letter by their Hebrew names ("Achad" (one) is ${\displaystyle 1+8+4=13}$ etc.), and then adds up the standard values of the resulting string.
• Otiyot beMilui ("filled letters", also known as Mispar gadol or Mispar Shemi), uses the value of each letter as equal to the value of its name.[22] For example, the value of the letter Aleph is ${\displaystyle (1+30+80)=111}$, Bet is ${\displaystyle (2+10+400)=412}$, etc. Sometimes the same operation is applied two or more times recursively. In a variation known as Otiyot pnimiyot (inner letters), the initial letter in the spelled-out name is omitted, thus the value of Alef becomes 30+80=110.
• Mispar Ne'elam (hidden number) spells out the name of each letter without the letter itself (e.g., "Leph" for "Aleph") and adds up the value of the resulting string.
• Mispar Katan Mispari (integral reduced value) is used where the total numerical value of a word is reduced to a single digit. If the sum of the value exceeds 9, the integer values of the total are repeatedly added to produce a single-digit number. The same value will be arrived at regardless of whether it is the absolute values, the ordinal values, or the reduced values that are being counted by methods above.
• Mispar Misafi adds the number of the letters in the word or phrase to their gematria.
• Kolel is the number of words, which is often added to the gematria. In case of one word, the standard value is incremented by one.

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 and Rashi, in which the name ששך ("Sheshek") is thought to represent בבל (Babylon).[1]
• 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. "Fe" 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 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 Moshe Cordevero.[23]

Some authors provide lists of as many as 231 various replacement ciphers, related to the 231 mystical Gates of the Sefer Yetzirah.[24]

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.[25] Some known methods are recursive in nature and are reminiscent of the graph theory or use heavily combinatorics. Rabbi Elazar Rokeach 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 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 sums of all possible unique letter combinations, which add up to the value of a given letter. For example, the letter Hei, which has the standard value of 5, can be produced by combining ${\displaystyle 1+1+1+1+1}$, ${\displaystyle 2+1+1+1}$, ${\displaystyle 3+1+1}$, ${\displaystyle 4+2}$, ${\displaystyle 2+2+1}$, or ${\displaystyle 2+3}$, which adds up to ${\displaystyle 30}$. Sometimes combinations of repeating letters are not allowed (e.g., ${\displaystyle 2+3}$ is valid, but ${\displaystyle 3+1+1}$ is not). The original letter itself can also be viewed as a valid combination.[24]

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 systems 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 Valley, a Spanish-Moroccan Kabbalist of the 15th–16th century.[19] Rabbi David ha-Levi's methods take into consideration the numerical values and other properties of the vowels as well.

Kabbalistic 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.[26]

The first attested use of gematria occurs in an inscription of the Assyrian ruler Sargon II (727–705 BCE) stating that the king built the wall of Khorsabad 16,283 cubits long to correspond with the numerical value of his name.[28]

The extant examples of use in Greek come primarily from the Christian literature. Davies and Allison state that, unlike rabbinic sources, isopsephy is always explicitly stated as being used; however, this is a dubious conclusion to make because it relies solely on the pure assumption that there is no hidden isopsephy in Christian literature.[29]

Plato (c. 427–347 BC) offers a discussion in the Cratylus, involving a view of words and names as referring (more or less accurately) to the "essential nature" of a person or object and that this view may have influenced – and is central to – Greek gematria.[30][31]

The Latin-script languages exhibit borrowing of gematria methods dating from the early Middle Ages after the use lapsed following the collapse of the Roman Empire in the 5th century AD.

Many researchers connect the "Number of the Beast", referred to in the Book of Revelation of the New Testament, with Hebrew gematria as used by the early Jewish Christians. According to such interpretations, the number in question, six hundred sixty-six (666; see Revelation 13:18) originally referred to the Roman emperor at the time, Nero Caesar. The Greek version of Nero's name (Neron Kaisar) transliterates into Hebrew as נרון קסר‎ (NRON QSR), and yields a numerical value of 666 (${\displaystyle 50+200+6+50+100+60+200=666}$).[32] Likewise, the early textual variant of six hundred sixteen (616) can be calculated by using the Latin version of Nero's name (Nero Cæsar) which transliterates into Hebrew as נרו קסר‎ (NRO QSR) — (${\displaystyle 50+200+6+100+60+200=616}$).[33]