Screenshot of Gemaṭriel.

Gemaṭriel is a gemaṭria calculator, which performs multiplex number processing and provides indispensable tools for studying the Jewish heritage, religion, and numerology. (Program features are discussed infra.)

Gemaṭria ( [or in the modern Hebrew spelling]) is a Jewish form of numerology (at times the word gemaṭria can simply mean geometry or rather calculus). Although its name is of Greek origin, gemaṭria came to be recognized as a distinctly Jewish term  perhaps due to the influence of Pythagorean number symbolism in the works of Philo Judæus of Alexandria, a noted Jewish philosopher of the first century C.E. who wrote in Greek, and because the similar method used in the Greek language by the Gnostics and countless ancient thaumaturges is usually referred to as isopsephy (ἰσοψηφία or, more commonly, ἰσόψηφος).

It is not unreasonable to note here that Philo extolled Essenes, the Jewish sectarians of the late Second Jerusalem Temple and early Talmudic era (Every Good Man is Free 12), whom Flavius Josephus, a contemporary of Philo, equated with Pythagoreans (Antiquities of the Jews 15:10[4]; cf. Philo, ibid. 1), and Rabbi Menashe ben-Israel, one of the most outstanding Jewish literati of the 17th century, asserted in his remarkable work Nishmath Ḥayyim (The Living Soul 4:21; this entire book is available here) that Pythagoras derived his wisdom from traditional Jewish teachings, the view also affirmed by Josephus (Against Apion 1:22).

It has been suggested that gemaṭria is a corrupted form of either (1) γεωμετρία (geometry in the sense of reckoning as in γεωμετρέω) or (2) γραμματεία (normally understood as scribes position; here, considering that the word γράμμα in Greek can denote not only a letter but a number, the term may mean post of mathematician), or it may even be (3) a compound of γάμμα (gamma, the third letter of the Greek alphabet) and τρία (three).

The underlying principle of gemaṭria as it is used in the Jewish theology and exegesis  being one of the thirty-two traditional hermeneutic rules of Bible interpretation attributed to Rabbi Eliezer, the son of Jose the Galilean  is a mystical correlation between entities with identical numerical values. The latter are obtained through reckoning of the names of these entities in Hebrew letters substituted for particular numbers. Gemaṭria has been already mentioned in the beginning of the opening treatise Berakhoth (8a) of the Babylonian Talmud where 903 types of death are derived from the numerical value of the word (issues) in Psalm 68. Hebrew letters, moreover, play a vital role in theurgy as attested in the same treatise (Berakhoth 55a): Bezaleel knew how to permute the letters by which the heaven and the earth were created (cf. Philo, On the Change of Names 9). This idea has been further developed in the ancient Book of Creation (Sefer Yetzirah [ ])  particularly in its second chapter where it is stated that the Demiurge formed every present and future creature by means of Hebrew letters.

In the classical or normative gemaṭria (often referred to as [mispar hekhreḥi  essential number]), the first ten letters of the Hebrew alphabet are assigned the integer values from 1 to 10, the next nine letters represent the denary values from 20 to 100, and the final three letters correspond to the higher hundreds 200, 300, and 400 accordingly. (Some less used techniques consider five final Hebrew letter forms [] as the hundreds that follow 400, thus extending the numerical scope of the alphabet to 900.) To produce figures that are bigger than or different from these numbers, greater letter values are normally grouped with (and added to) smaller ones in declining order, i.e., 500=400+100 (), 600=400+200 (), 666=400+200+60+6 (), etc. Letters are usually rearranged if their combination spells a word that may have ominous significance. The same guideline holds true for mnemonic and auspicious patterns. For instance, the letters in (344=300+40+4 [annihilation]) often undergo permutations to produce the same number without this words original sinister meaning; on the contrary, the number 18 may be represented as (8+10 [life]) instead of proper but meaningless (10+8). This principle has also been habitually used in my writings (visit my site for examples). The symbol is routinely placed before the last letter (as in Hebrew abbreviations) to indicate that one is dealing with a number. In older texts, this symbol was often placed in the middle of a word, substituted with dots or dashes over letters, or omitted altogether. Similarly, when a number is represented by only one letter, it is usually followed by the symbol.

Besides the classical method of calculating gemaṭria described above, other techniques  at times extremely complex  may also be employed. Of particular interest are the methods called Atbash () and Albam (), which are fully utilized in this Windows program. The former folds the alphabet (i.e., its twenty-two letters) in half and interchanges converging letter values, while the latter additionally twists the other part of the alphabet prior to that operation. Both of these techniques are succinctly mentioned in the Midrash Rabbah (Numbers 18:21) where (Sheshach/Babylon) in Jeremiah 25:26 and (Tabeal/Remaliah) in Isaiah 7:6 are given as respective examples of gemaṭria mentioned in the Bible.

Contrary to popular belief, gemaṭria has never been restricted to mystical arts. Inasmuch as in classical Hebrew, akin to the Roman numbering system familiar to Western civilization, numbers are represented by letters (with zero and negative integers likewise being nonexistent), gemaṭria has been widely used for calendar notations (such as the New Year of Trees holiday called   The Fifteenth [9+6=15] of Shevaṭ) or for bibliographical citations (for instance,   chapter seven). Moreover, it is virtually impossible to study copious Hebrew religious responsa, unless one knows how to reckon numerical values of countless references found therein.

Here I would like to revert to the number 666, which was brought up earlier in the text. In the Christian Bible (Revelation 13:18), it has been mentioned as the number of the beast who is believed to appear at the end of time (some manuscripts, such as the Codex Ephræmi Syri Rescriptus, have the number 616 instead). Numerous individuals mathematically tried to connect 666 with popes and kings, tyrants and presidents, etc. Calculations of that kind make little sense and only add to unintelligent conspiracy theories in view of the fact that the words []  Cæsar Nero[n]; a Roman emperor who lived at the time of New Testament compilation and was also thought to return as apocalyptic incarnation of evil (cf. the antique allegorical description of this ruler in the beginning of the fifth book of Sibylline oracles where his name [signified by the Hebrew letter ] is additionally associated with the number 50)  in gemaṭria equal 666 or 616 (if the final letter that stands for 50 is omitted). Moreover, the verse in I Kings 10:14 (repeated in II Chronicles 9:13) clearly indicates that the number 666 has little association with anything nefarious. Indeed, the words (the holy ark) found in II Chronicles 35:3 have the numerical value of 666. Besides, it is very easy to produce a legitimate Hebrew phrase, which, through the same gemaṭria, endorses this number (cf. Ibn Ezra on Genesis 14:14), for instance: . ([He is a] servant of the Lord, and [he is a] great righteous one, and [he is] pleasant in the sight of the Lord.) Thus, without much difficulty, the beast becomes the beauty.

The above paragraph is an important example of how careful one must be with such calculations and, additionally, is a solemn warning not to toy with numbers for religious goals. An individual requires expertise in the entire Judaic tradition prior to employing methods of gemaṭria, since it has been shown that they can be applied to both reasonable and irrational calculations. There is an old Jewish joke that (cholent [stew]; 9+300+1+30+70+50+9=469) or (kugel [casserole]; 100+6+3+70+30=209)  the traditional Saturday victuals of Ashkenazic Jews  have the same numerical value as (Sabbath; 300+2+400=702). When someone objects that the numerical values of these viands are less than the value of (variant spellings, which omit the letter , have even smaller values than that of ), that person is facetiously advised to take another portion of food to make up the deficiency.

It has been pointed out, especially by those exploiting the anti-Semitic stereotype of the Jewish financier, that Jews are good at making  presumably evil  calculations. The art of gemaṭria proves them wrong. Instead of a covetous capitalist, gemaṭria techniques portray a noble sagacious mathematician pondering over pure knowledge. This authentic Jewish mind occupied with ingenious calculations equally manifests itself in an Orthodox cabalist  such as the 17th century Rabbi Nathan N. Shapiro (the author of the book Megalleh Amuḳoth [   He Discovers Deep Things] that largely deals with gemaṭria) whose only goal was glorifying God while expecting nothing in return (he likewise took no money for serving as a rabbi in Kraków)  or in a secular scientist  such as a modern mathematician Grigori Y. Perelman (Григорий Яковлевич Перельман) who recently rejected the Fields Medal and million-dollar prize for proving the Poincaré conjecture that had puzzled humankind during the past hundred years.

The interface of this program is fairly intuitive, nevertheless, certain features are described below in greater detail. The application provides two ways for entering Hebrew texts: through the on-screen keyboard or via the Windows clipboard. To use the latter, copy any text typed in Hebrew in any Windows application and click the Clipboard Gemaṭria button. Hebrew characters will be correctly processed even if given texts contain multiple languages. Bear in mind, though, that many computer fonts produced by typographers (including a number of fonts made by me at the turn of the century) before the Unicode standard became widespread have Hebrew glyphs in the place of Latin characters. All texts for Gemaṭriel must be in the Windows Hebrew / Unicode encoding or at least copied that way to the clipboard. Texts typed with aforementioned pseudo-Hebrew fonts must be converted into the Windows Hebrew / Unicode encoding first.

Sometimes an amount of entered words and a quantity of their letters may be added to the generated value of gemaṭria. My program also calculates these numbers (they appear in square brackets). The following abbreviations are utilized: +W = gemaṭria + words, +L = gemaṭria + letters, +WL = gemaṭria + words + letters. Words are disregarded in the Clipboard Gemaṭria mode, inasmuch as the clipboard algorithm analyzes texts, which may contain non-Hebrew characters, and, therefore, the results for words can be unpredictable. The generated value of gemaṭria is occasionally reduced to a single-digit integral. Such computations the program makes only for initial values of gemaṭria and not for bracketed ones.

The Leningrad Codex (Codex Leningradensis)  one of the most ancient, accurate, and complete Masoretic Hebrew texts of the Bible  served as the basis for Pentateuch words, which were meticulously entered into this application the way they occurred in the Bible with both Ḳeri and Khethiv (   [what is] read and [what is] written) variants preserved, thus providing a user with a comprehensive Torah exploration tool. As an auxiliary addition, the Pentateuch Words apparatus also shows a photograph of the initial verses of Genesis (15) as they appear in the Leningrad Codex.

Windows ExecutableDownload Gematriel (1.21 MB [requires Microsoft Windows 95 or later]).