Gematria
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Gematria

Gematria (; Hebrew: ‎ or gimatria ?, plural ? or , gimatriot)[1] is an alphanumeric code of assigning a numerical value to a name, word or phrase according to its letters. A single word can yield several values depending on the cipher used.

Gematria is a Hebrew alphanumeric code or cipher that was probably used in biblical times and was later adopted by other cultures. It is still widely used in Jewish culture. Similar systems have been used in other languages and cultures: the Greeks isopsephy, and later, derived from or inspired by Hebrew gematria, Arabic abjad numerals, and English gematria.

A type of gematria system ('Aru') was employed by the ancient Babylonian culture but, because their writing script was logographic, the numerical assignations they made were to whole words. The value of these words were assigned in an entirely arbitrary manner and correspondences were made through tables.[2] This practise was very different from the gematria systems used by Hebrew and Greek cultures, which used alphabetic writing scripts. Similar systems have been used in other languages and cultures derived from or inspired by Hebrew gematria, Arabic abjad numerals, and English gematria. There is currently no academic consensus over whether Hebrew gematria or Greek isopsephy was used first.

Gematria sums can involve single words, or a string of lengthy calculations. A well-known short example of Hebrew numerology that uses a gematria cipher is the word chai (lit. "alive"), which is composed of two letters that (using the assignments in the Mispar gadol table shown below) add up to 18. This has made 18 a "lucky number" among the Jewish people. Donations of money in multiples of 18 are very popular.[3]

Etymology

Although the term is Hebrew, it may be derived from the Greek ge?metri?, "geometry", which was used as a translation of g?ma?riy?,[4] though some scholars believe it to derive from Greek ? grammateia "knowledge of writing". It is likely that both Greek words had an influence on the formation of the Hebrew word.[5][1] Some also hold it to derive from the order of the Greek alphabet, gamma being the third letter of the Greek alphabet.[6]

The word has been extant in English since at least the 17th century from translations of works by Giovanni Pico della Mirandola. It is largely used in Jewish texts, notably in those associated with the Kabbalah. The term does not appear in the Hebrew Bible itself.[1]

History

The first documented use of gematria is from an Assyrian inscription dating to the 8th century BC, commissioned by Sargon II. In this inscription, Sargon II states: "the king built the wall of Khorsabad 16,283 cubits long to correspond with the numerical value of his name."[7]

Various scholars have raised the possibility of gematria on various occasions in the Hebrew Bible.[8][9][10][11]

As early as the 6th century BC, the first alphanumeric alphabet appears in ancient Greece in the form of the Milesian numeral system, and eventually gained usage in contexts such as divinatory Greek magic, prophecy, and so forth.[12] A sample of graffiti at Pompeii reads "I love the girl whose name is phi mu epsilon (545)".[13] According to Proclus in his commentary on the Timaeus of Plato written in the 5th century, the author Theodorus Asaeus from a century earlier interpreted the word "soul" (?) based on gematria and an inspection of the graphical aspects of the letters that make up the word. According to Proclus, Theodorus learned these methods from the writings of Numenius of Apamea and Amelius. Proclus rejects these methods by appealing to the arguments against them put forth by the Neoplatonic philosopher Iamblichus. The first argument was that some letters have the same numerical value but opposite meaning. His second argument was that the form of letters changes over the year, and so their graphical qualities cannot hold any deeper meaning. Finally, he puts forth the third argument that when you use all sorts of methods as addition, subtraction, division, multiplication, and even ratios, the sheer infinite ways to combine them will allow you to produce virtually every number for anything you're investigating.[14]

There are at least two cases of gematria appearing in the New Testament. The reference to the miraculous catch of 153 fish in John 21:11 is largely seen as an application of gematria derived from the name Eglaim in Ezekiel 47.[15][16] The appearance of this gematria in John 21:11 has been connected to one of the Dead Sea Scrolls, namely 4Q252, which also applies the same gematria of 153 derived from Ezekiel 47 to state that Noah arrived at Mount Ararat on the 153rd day after the beginning of the flood.[17] Many historians see gematria behind the reference to the number of the name of the beast in Revelation as "666", which corresponds to the numerical value of the Hebrew transliteration of the Greek name "Nero Caesar", referring to the 1st century Roman emperor who persecuted the early Christians.[18] On the other hand, another possible influence on the use of 666 in Revelation goes back to reference to Solomon's intake of 666 talents of gold in 1 Kings 10:14.[19]

Gematria makes several appearances in various Christian and Jewish texts written in the first centuries of the common era. One appearance of gematria in the early Christian period is in the Epistle of Barnabas 9:6-7, which dates to sometime between 70 and 132 AD. There, the 318 servants of Abraham in Genesis 14:14 is used to indicate that Abraham looked forwards to the coming of Jesus as the numerical value of some of the letters in the Greek name for Jesus as well as the 't' representing a symbol for the cross also equaled 318. Another example is a Christian interpolation in the Sibylline Oracles, where the symbolic significance of the value of 888 (equal to the numerical value of Iesous, the Greek version of Jesus' name) is asserted.[20] The Gnostic uses of the numerological representation of Jesus with the number 888, as the sum of the numerical values of the letters of his name, was condemned by the Church father Irenaeus as convoluted and an act which reduced "the Lord of all things" to something alphabetical.[21] Irenaeus also heavily criticized the interpretation of letters by the Gnostic Marcus. Because of their association with Gnosticism and the criticisms of Irenaeus as well as Hippolytus of Rome and Epiphanius of Salamis, this form of interpretation never became popular in Christianity[22]--though it does appear in at least some texts.[23] Another two examples can be found in 3 Baruch, a text that may have either been composed by a Jew or a Christian sometime between the 1st and 3rd centuries. In the first example, a snake is stated to consume a cubit of ocean every day, but is unable to ever finish consuming it, because the oceans are also refilled by 360 rivers. The number 360 is given because the numerical value of the Hebrew word for snake is 360. In a second example, the number of giants stated to have died during the Deluge is 409,000. The Hebrew word for 'deluge' has a numerical value of 409, thus leading the author of 3 Baruch to use it for the number of perished giants.[24]

Gematria is used several times in the rabbinic literature. One example is that the numerical value of Satan in Hebrew is 364, and so it was said that Satan had authority to prosecute Israel for 364 days before his reign ended on the Day of Atonement, an idea which appears in Yoma 20a and Peskita 7a.[20] Yoma 20a states: "Rami bar ?ama said: The numerological value of the letters that constitute the word HaSatan is three hundred and sixty four: Heh has a value of five, sin has a value of three hundred, tet has a value of nine, and nun has a value of fifty. Three hundred and sixty-four days of the solar year, which is three hundred and sixty-five days long, Satan has license to prosecute."[25] Genesis 14:14 states that Abraham took 318 of his servants to help him rescue some of his kinsmen, which was taken in Peskita 70b to be a reference to Eleazar, whose name has a numerical value of 318.

The total value of the letters of the Islamic Basmala, i.e. the phrase Bismillah al-Rahman al-Rahim ("In the name of God, the Most Gracious, the Most Merciful"), according to the standard Abjadi system of numerology, is 786.[26] This number has therefore acquired a significance in folk Islam and Near Eastern folk magic and also appears in many instances of pop-culture, such as its appearance in the 2006 song '786 All is War' by the band Fun^Da^Mental.[26] A recommendation of reciting the basmala 786 times in sequence is recorded in Al-Buni. Sündermann (2006) reports that a contemporary "spiritual healer" from Syria recommends the recitation of the basmala 786 times over a cup of water, which is then to be ingested as medicine.[27]

Still today, the use of gematria is pervasive in many parts of Asia and Africa.[28]

Methods

Standard encoding

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. It is possible that this well-known cipher was used to conceal other more hidden ciphers in Jewish texts. For instance, a scribe may discuss a sum using the 'standard gematria' cipher, but may intend the sum to be checked with a different secret cipher.

Decimal Hebrew Glyph
1 Aleph ?
2 Bet ?
3 Gimel ?
4 Dalet ?
5 He ?
6 Vav ?
7 Zayin ?
8 Het ?
9 Tet ?
Decimal Hebrew Glyph
10 Yod ?
20 Kaf ?
30 Lamed ?
40 Mem ?
50 Nun ?
60 Samekh ?
70 Ayin ?
80 Pe ?
90 Tsadi ?
Decimal Hebrew Glyph
100 Kof ?
200 Resh ?
300 Shin ?
400 Tav ?
500 Kaf (final) ?
600 Mem (final) ?
700 Nun (final) ?
800 Pe (final) ?
900 Tsadi (final) ?

A mathematical formula for finding a letter's corresponding number in Mispar Gadol is: 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.

Vowels

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):

Decimal Vowel Glyph
6
Patach

?
10 (1)
Hiriq

 ?

Holam

 ?

Shuruk

 
Decimal Vowel Glyph
16 (7)
Kamatz

?
20 (2)
Zeire

?

Sh'va

?
26 (8)
Reduced patach

?
Decimal Vowel Glyph
30 (3)
Segol

?

Kubutz

?
36 (9)
Reduced kamatz

?
50 (5)
Reduced segol

?

Sometimes, the names of the vowels are spelled out and their gematria is calculated using standard methods.[29]

Other methods in Hebrew

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, etc. These methods include:[30]

  • 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 Aleph is spelled Aleph-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[31]) 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 .
  • 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 Gimel 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 Gimel 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 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.[32] For example, the value of the letter Aleph is , Bet is , 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 Aleph 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.

Related alphabet 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 and Rashi, in which the name ("Sheshek") is thought to represent (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.[33]

Some authors provide lists of as many as 231 various replacement ciphers, related to the 231 mystical Gates of the Sefer Yetzirah.[34]

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.[35] Some known methods are recursive in nature and are reminiscent of graph theory or make a lot of use of 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 the 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 , , , , , or , which adds up to . Sometimes combinations of repeating letters are not allowed (e.g., is valid, but is not). The original letter itself can also be viewed as a valid combination.[34]

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.[29] 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.[36]

Absolute value

The most common form of Hebrew gematria is used in the Talmud and Midrash, and elaborately by many post-Talmudic commentators. It involves reading words and sentences as numbers, assigning numerical instead of phonetic value to each letter of the Hebrew alphabet. When read as numbers, they can be compared and contrasted with other words or phrases - cf. the Hebrew proverb ?    (nichnas yayin yatza sod, lit. "wine entered, secret went out", i.e. "in vino veritas"). The gematric value of ("wine") is 70 (?=10; ?=10; ?=50) and this is also the gematric value of ("secret", ?=60; ?=6; ?=4)‎.[37]

Use in other languages

Greek philosophy

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.[38]

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.[39][40]

English Gematria

The first numerical cipher that is known to be assigned to the English Alphabet was by Cornelius Agrippa in 1533, in his work De Occulta Philosopha. There is no evidence that this cipher was actually used for the purposes of gematria or numerology, however, since 2018 a modern version of his cipher has been popularly employed by many numerologists and conspiracy theorists who use the Gematrix Gematria Calculator or the Gematrinator Calculator.

The Hermetic Order of the Golden Dawn employed a transliterated version of the Standard Hebrew Cipher, using digraphs to represent letters such as shin ? (Sh), tav ? (Th), and tsade ? (Ts or Tz). Aleister Crowley learned the transliterated English cipher from the Golden Dawn, but he also claimed to be in possession of the "true numerical keys" to the Bible and the Book of the Law which he called "The Key of it All". He never published these keys during his lifetime, but left a numerical riddle (AL II:76) in the Book of the Law and said that his successor would reveal it.

Since the death of Aleister Crowley (1875-1947) a number of people have proposed numerical ciphers for the purposes of numerology with the Book of the Law. The ALW cipher (also known as the New Aeon English Qabalah) was proposed by James Lees in 1976. In 2015, cryptographer Bethsheba Ashe discovered a gematria cipher that worked with both the Bible and the Book of the Law, and encoded the Shematria Gematria Calculator with its values. This cipher is not used for numerology, but for a formal rhetorical system of early mathematics that was used by biblical authors and Aleister Crowley.

See also

Notes

  1. ^ a b c d  This article incorporates text from a publication now in the public domainSolomon Schechter and Caspar Levias (1901-1906). "GEMA?RIA". In Singer, Isidore; et al. (eds.). The Jewish Encyclopedia. New York: Funk & Wagnalls.CS1 maint: uses authors parameter (link)
  2. ^ LIEBERMAN, Stephen (1987). "A Mesopotamian Background for the So-Called Aggadic 'Measures' of Biblical Hermeneutics?". Hebrew Union College Annual. 58: 157-225. JSTOR 23508256.
  3. ^ "Chabad.org Chani Benjaminson".
  4. ^ "Gematria" at Dictionary.com
  5. ^ "gematria". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.) Oxford English Dictionary
  6. ^ Benjamin Blech, The Complete Idiot's Guide to Jewish Culture, p. 395 (2004)
  7. ^ Daniel Luckenbill, Ancient Records of Assyria and Babylonia, vol. 2, University of Chicago Press, 1927, pp. 43, 65.
  8. ^ Knohl, Israel. "The Original Version of the Priestly Creation Account and the Religious Significance of the Number Eight in the Bible". Retrieved 2019.
  9. ^ Knohl, Israel (2012). "Sacred Architecture: The Numerical Dimensions of Biblical Poems". Vetus Testamentum. 62 (#2): 189-197. doi:10.1163/156853312x629199. ISSN 0042-4935.
  10. ^ Hurowitz, Victor (2012). "Proverbs: Introduction and Commentary". Miqra LeYisrael. 1-2.
  11. ^ Stephen Lieberman, "A Mesopotamian Background for the So-Called Aggadic 'Measures' of Biblical Hermeneutics?", Hebrew Union College Annual (1987), pp. 157-225
  12. ^ Juan Acevedo, Alphanumeric Cosmology form Greek into Arabic, Mohr Siebeck 2020 pp 40-41
  13. ^ Adela Yarbro Collins, Cosmology and Eschatology in Jewish and Christian Apocalypticism, Brill 2000, p116.
  14. ^ Tzahi Weiss, Sefer Ye?irah and its Contexts, Pennsylvania 2018, 26-28.
  15. ^ Richard Bauckham, "The 153 Fish and the Unity of the Fourth Gospel", Neotestamentica 2002.
  16. ^ Mark Kiley, "Three More Fish Stories (John 21:11)", Journal of Biblical Literature 2008
  17. ^ George Brooke. The Dead Sea Scrolls and the New Testament. Fortress Press 2005, pp286-97
  18. ^ Craig Koester, Revelation: A New Translation with Introduction and Commentary, Yale University Press, 2014, pg. 598
  19. ^ Bodner & Strawn, "Solomon and 666 (Revelation 13.18)", New Testament Studies (2020), pp. 299-312.
  20. ^ a b This and several other examples of the appearance of gematria are given in D.S. Russell. "Countdown: Arithmetic and Anagram in Early Biblical Interpretation". Expository Times 1993.
  21. ^ Juan Acevedo, Alphanumeric Cosmology from Greek to Arabic, Mohr Siebeck 2020 p. 159
  22. ^ Tzahi Weiss, Sefer Ye?irah and its Contexts, Pennsylvania 2018, 21-26, 28.
  23. ^ Ibid., 28-29.
  24. ^ Gideon Bohak. Greek-Hebrew Gematria in 3 Baruch and in Revelation. Journal for the Study of the Pseudepigrapha 1990.
  25. ^ The given text of Yoma 20a is from the William Davidson translation.
  26. ^ a b Shah & Haleem (eds.), The Oxford Handbook of Qur'anic Studies, Oxford University Press, 2020, pp581, 587-88
  27. ^ Katja Sündermann, Spirituelle Heiler im modernen Syrien: Berufsbild und Selbstverständnis - Wissen und Praxis, Hans Schiler, 2006, p. 371.
  28. ^ Kravel-Tovi & D. Moore, Taking Stock: Cultures of Enumeration in Contemporary Jewish Life, The Modern Jewish Experience (Indiana University Press, 2016), 32, 71; Holt, Culture and Politics in Indonesia (Equinox Publishing, 2007), 81; Leslie & Young, Paths to Asian Medical Knowledge, Comparative Studies of Health Systems and Medical Care (Berkeley: University of California Press, 1992), 261.
  29. ^ a b Sefer ha-Malchut, "Sifrei Chaim", Jerusalem, 2008
  30. ^ Moshe Cordovero, Pardes Rimmonim
  31. ^ Toras Menachem - Tiferes Levi Yitzchok Vol. I - Bereshis, p. 2, fn. 7
  32. ^ the spelling of the name of the number comes from the Talmud
  33. ^ Moshe Cordevero, Sefer Pardes ha-Rimonim, ?
  34. ^ a b Elazar Rokeach, Sefer ha-Shem
  35. ^ Encyclopedia Judaica Vol. 7, 2007, p. 426
  36. ^ Commentary to Sefer Yetzirah, attributed to Saadia Gaon, 6:4; Rabbi Aryeh Kaplan, Sefer Yetzirah, "WeiserBooks", Boston, 1997, pp. 220-221
  37. ^ Babylonian Talmud, tractate Sanhedrin 38a, see of Zuckermann, Ghil'ad (2006), "'Etymythological Othering' and the Power of 'Lexical Engineering' in Judaism, Islam and Christianity. A Socio-Philo(sopho)logical Perspective", Explorations in the Sociology of Language and Religion, edited by Tope Omoniyi and Joshua A. Fishman, Amsterdam: John Benjamins, pp. 237-258.
  38. ^ Davies & Allison, William & David (2004). A Critical and Exegetical Commentary on the Gospel According to Saint Matthew. Continuum International Publishing Group. p. 164.
  39. ^ Marc Hirshman, Theology and exegesis in midrashic literature, in Jon Whitman, Interpretation and allegory: antiquity to the modern period. Brill, 2003. pp. 113-114.
  40. ^ John Michell, The Dimensions of Paradise: Sacred Geometry, Ancient Science, and the Heavenly Order on Earth, 2008. pp.59-65 ff.

References

  • Acres, Kevin, Data integrity patterns of the Torah: A tale of prime, perfect and transcendental numbers, Research Systems, Melbourne, 2004 [1]
  • Clawson, Calvin C., Mathematical Mysteries: The Beauty and Magic of Numbers, Perseus Books, 1999
  • Davies, William David and Allison, Dale C., A Critical and Exegetical Commentary on the Gospel According to Saint Matthew, Continuum International Publishing Group, 2004
  • Davis, John J. Biblical Numerology. Grand Rapids, MI: Baker Books, 1968.
  • Hughes, J. P., Suggestive Gematria, Holmes, 2008
  • Genesis Rabbah 95:3. Land of Israel, 5th Century. Reprinted in, e.g., Midrash Rabbah: Genesis. Translated by H. Freedman and Maurice Simon. Volume II, London: The Soncino Press, 1983. ISBN 0-900689-38-2.
  • Deuteronomy Rabbah 1:25. Land of Israel, 5th Century. Reprinted in, e.g., Midrash Rabbah: Leviticus. Translated by H. Freedman and Maurice Simon. Volume VII, London: The Soncino Press, 1983. ISBN 0-900689-38-2.
  • Klein, Ernest, Dr., A comprehensive etymological dictionary of the English language: Dealing with the origin of words and their sense development thus illustrating the history and civilization of culture, Elsevier, Oxford, 7th ed., 2000
  • Lawrence, Shirley Blackwell, The Secret Science of Numerology - The Hidden Meaning of Numbers and Letters, New Page Books, 2001
  • Menninger, Karl. Number Words and Number Symbols: A Cultural History of Numbers. Cambridge: MIT Press, 1969.
  • Ratzan, Lee, Understanding Information Systems: What They Do and Why We Need Them, ALA Editions, 2004
  • Rawn, Jonathan D. Discovering Gematria: Foundational Exegesis and Primary Dictionary. 1,968 pp. Gematria Publishing, 2008.
  • Sefer hamilim. Qonqordantzia hakhadash (lekol haTanakh). Lebovits-Kest Memorial, B'nei-Torah Compact Library, Printed in Israel
  • Zeitler, William. Musical Gematria. Musica Arcana, 2013, ISBN 978-1-940630-02-1

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