Introduction To Torah Patterns

By Rabbi Boruch Horovitz

The Divine Mathematician in His Works and His Words

The Divine Designer of the pattern of Nature (that which “is”) is revealed through His works: - How great are Your works, o Lord, how deep are Your thoughts’ (Tehillim 92, 6).

Anyone contemplating the vastness, grandeur and harmony of the multiple phenomena of the cosmos, recognises the One who created and constantly sustains the Universe: ‘How great are Your works.’ The scientists who discover the deeply hidden mathematical formulae and associations in astronomy, physics, chemistry, biology and other sciences, thereby demonstrate the power of the Divine Thinker and Mathematician in the cosmos: How deep are Your thoughts and mathematical links. (‘Thought’ = ‘machshava, root chashav to reckon, to bind together.)

The Divine Designer of the pattern of Morality (that which “ought to be”) is revealed through His words:- ‘The Teaching of the Lord (the Five Books of Moshe) is perfect, it inspires the soul’ (Tehillim 19, 8).

Anyone studying its religious, philosophical, ethical, psychological, social, legal, historical and scientific aspects is inspired by its truth and harmony, and recognises its Divine Author. The scholars who have delved deeply into the text of the Torah have found hidden harmonious structures and numerical associations and patterns which demonstrate the Divine Thinker and Mathematician behind the Torah: ‘Uncover my eyes, so that I may see hidden marvels out of Your Torah’ (Tehillim 119, 18).

“The early Torah scholars were called ‘scribes’ or ‘calculators’ because they counted the letters of the Torah” (Talmud Bavli, Kidushin 30 a, based on Chronicles 1, 2, 55 and other verses). This was an aid to the preservation of an exact text for the scribes to copy, but may also indicate research into numerical patterns.

This approach to the text is included under the heading remez- ‘Hints’ in the traditional four levels of interpretation, namely: pardes=(1) Pshat = straightforward meaning; (2) Remez = Hints; (3) Drash = derived and allegorical meaning: (4) Sod = mystical meaning, described also as “the path of truth” (Ramban). “Astronomical calculations and numerical interpretations are appetisers to wisdom” (Ethics of the Fathers III, 18). Perhaps this refers to the abovementioned parallel between the mathematical investigations of the cosmos, which is most prominent in astronomy, and the numerical study of the Torah. They do not deal with the content of wisdom, but with its harmonious structure, thereby making the content of scientific and Torah wisdom pleasing and convincing to the mind.

II.The Development of Numerical Study of the Torah.

According to the straightforward meaning of the Bible — ‘Pshat’ — number and letter patterns have obvious significance.

Seven, multiples of seven, and seven squared occur: in repetition of key words and phrases; as sign of complete retribution; in connection with oaths- it has the same Hebrew root – ‘hishave’a’, in sanctified time periods: Creation, Sabbath, Festivals, Sabbatical and Jubilee Years, nuptial rejoicing, period of mourning, purification process; sacred vessels such as the Candelabrum. It appears to be the symbol of Divine harmony; the word ‘sheva’ may be connected with ‘save’a’ = satisfaction, fulfillment, completeness. It may have a parallel in Nature in the seven colors of the spectrum and the seven notes in the octave.

Ten occurs in various contexts: the number of plagues, Divine words of the Decalogue, minimum number of righteous people to save the city, number of units for measurement of Sanctuary, separation of tenth in tithing. The word ‘eser’ may be connected with ‘osher’ = wealth, abundance, unity in multiplicity. Letters have stylistic significance in the acrostics of the Aleph-Beth in some books of the Bible; in the transposition of letters - in Jeremiah 51,l; ibid 25,26.

Gematria (Gk. geometria) is mentioned amongst the 32 Hermeneutical Methods of Interpretation of the Torah, of Rabbi Eliezer son of Rabbi Yosi Hagelili, as Method No 29. (Printed at the back of Tractate Berachoth, p. 96.) This refers to numerical values of the Aleph-Beth, as well as, in a wider sense, transposition of letters, and use of initials for words, generally referred to as Notarikon (ibid No.30).

Talmudic literature contains many examples of Gematria: - E.g. Yihyeh, gematria 30, indicating that Nazarite vow normally lasts 30 days. — (Nazir 5a, Bamidbar 6,5).

39 categories of forbidden work on Sabbath: eleh hadevarim = 36+3 (Shabbath 70 a, Shemoth 35,1).

The minimum amount of dough from which challah must be separated is the volume of 43-1/5 eggs. The gematria of challah is 43. (Bamidbar Rabba, 18.)

The number of retainers mustered by Abraham is given as 318 (Bereshith 14, 14). This is the gematria of Eliezer. (Nedarim 32a.).

Most authorities regard these derashot as asmachta, as a peg, a mnemonic, and not as an original Halachic source (see commentary of Rambam on Nazir, 1,1, and Rosh in Shita Mekubezeth, Nazir 5a); however cf. Midrash Tanaim, Introduction, and midda 29, for a divergent opinion.

Nachmanides in his Sefer Hage’ula writes:- “In my reliance upon Gematria, a person might claim that it is nonsense, because it is possible to interpret verses in an evil and strange manner by these calculations. We declare that a person may not use Gematria in any manner that comes to his mind, but we have a tradition from our Talmudic Sages that certain Gematrioth were handed down to Moshe at Sinai as a mnemonic for that which was transmitted verbally, in Aggada and in Halacha. It is like the Gezera Shava - analogy based on same key-word - upon which many basic Torah laws depend, which can also be misused to deduce matters that are evil and contradict the Torah, but the Sages declared: ‘A person may not compose a Gezera Shava himself’.”

Early Kabbalistic literature contains mystical and symbolic numerical structures connected with the letters of the Aleph Beth and with the 3 plus 7 = 10 Sephiroth. In Sefer Yetzira, Sefer Habahir, and the Zohar many aspects of the structure of Torah, the structure of Nature, the structure of man, are described according to these concepts.

The extent to which some of the great scholars “counted” the letters of the Torah is illustrated by Saadya Gaon’s Piyyut on the Aleph Beth, wherein each stanza of the acrostic has words the numerical value of which is equivalent to the number of times that letter appears in the Bible.

The following Medieval works contain many “letter” interpretations and Gematrioth:

Midrash Haserot Vi-yeterot.

Midrash Aggada of R. Moshe Ha-darshan.

The works of R. Eliezer of Worms, (the “Rokeach”).

R. Yaakov and Abraham Abulafia.

R. Yaakov ben Asher, (the “Baal Haturim”).

R. Nathan Nota Shapira, (the “Megale Amukoth”).

R. Eliyahu, the Gaon of Vilna.

Maharal of Prague, in his kabbalistic-philosophic exposition of Torah concepts, has a wide range of symbolic numerical explanations, e.g.:-

6 = the 3 dimensional concrete world of Nature

= 6 directions of the phenomena.

7 = the centre point, which is abstract, but co-ordinates the 6.

= the mind, the noumenon, the image of all the six directions as one unit.

= the mind which conceives and coordinates the Time-Space of the Cosmos and brings    harmony to the variety of phenomena.

8 = The Supernatural dimension, the Sechel ha-niv’dal represented by miracles, and the miraculous Revelation of Torah.

III. The Modern Period

It is in more recent times, however, that the “numerical” interpretation of the Torah text has gathered a new momentum, from a variety of angles:-

1) With the development of the scientific discovery of mathematical formulae in the structure of energy and matter in all spheres, there has emerged an upsurge in the study of ‘Harmonics’. Common mathematical structures have been uncovered in astronomy, physics, chemistry, biology, music and other areas. cf. Haase, R. Grundlagen der Harmonikalen Symbolik; Kayser, H. Lehrhuch der Harmonik; Borchard R. Our harmonious Cosmos.

2) Number Symbolism as a key to understanding the repetition of words, phrases and passages in the text of the Bible has been recognized even by Biblical scholars far removed from the traditional approach, such as M. Buber and U. Cassutto. B. Jacob went much further in discovering a common, symbolic number-structure also in the measurements of the Sanctuary, Temple, holy vessels, numbers of offerings, geneologies, chronology, the festivals. See his works “Der Pentateuch”, 1905, 1908. “Die Abzaehlungen,” 1909.

3) It was O. Goldberg who uncovered a more comprehensive number symbolism of 7 and 26.

4) The discovery of the key 7 x 10 x 26 = 1820 (70 x 26), as a hidden formula, was described by Rav P.Z. Hurvitz. It illustrates the principle “The Torah consists of the Divine Names”.

5) Rabbi M.B. Weissmandel in ‘Torat Hemed’ developed the application of “spacing” which is already used in the works of R. Bachya and the Gaon of Vilna.

For example: Look at the first passage of the Torah. Starting with the first word, בראשית (“in the beginning”), we mark the letter ת, which is at the end of the word. After the ת  we count forty-nine letters to the left and mark the fiftieth letter. That will be the letter ו of the word תהום . After this ו, we count another forty-nine letters and mark the fiftieth letter which is the letter ו of the word וירא. After the ו we omit another forty-nine letters and mark the fiftieth letter, which is ה of the word אלקים. All together we have marked every fiftieth letter from the letter ת of בראשית. These letters, in the order in which they appear, make up the word ת-ו-ר-ה (Torah.)

6) T. Weksler in his “Hidden Traditions” and other articles, demonstrates the use of 613 as a hidden symbol (already mentioned extensively by the Gaon of Vilna) as well as squared numbers.

The Gematria of the Patriarchs, Matriarchs and the 12 tribes = 70 x 70 = 4900.

7) Rabbi S.D. Sassoon found that in the separate paragraphs of the Torah, the number of words in the passage was often reflected in the numerical value of the key word in the passage, or a multiple thereof. E.g. Exodus 13, 1-16 which deals with the sanctification of the firstborn (bechor) and has, (apart from the introductory sentence) 228 words, the Gematria of bechor.

8) The method of “spacing” has been developed recently by Dr. E. Ripps, Dr. M. Katz and Rav Yaniv and others. These results are now being subjected to rigorous mathematical testing to evaluate their true significance.

IV. Qualifications of Numerical Interpretation

The remez (allusive) approach to the Sacred Text has to be understood as an aid to pshat, but should not be the major approach to the understanding of the Torah. It deals with form rather than content. It can nevertheless have educational value in appreciation of the Divine Harmony inherent in the Torah. It has proven itself as a potent factor in transforming sceptics into believers in the Divinity of Torah.

It is important to differentiate between numerical interpretations which are mere mnemonics applied arbitrarily to associated ideas in Torah, and on the other hand, systematic number-symbolism demonstrating definite patterns and ideas, which demonstrate a Divine Harmony. It is the latter which calls for strong development in the Computer Age.

The question has been raised:- If this mode of research were to produce conclusive proof of the supernatural origin of the Torah, would it not remove free-choice from man, and would he not be forced to accept Torah as Absolute Truth?

But I do not think this is something we need worry about. Even when the Children of Israel had witnessed G-d speaking and had experienced many miracles, they still retained an evil inclination, they rebelled and sinned with the Golden Calf. There is other conclusive evidence for the Divinity of the Torah, but this does not remove the inclination to sin amongst those who perceive this evidence.

Perhaps since we are removed so far in time from the experience of Revelation and prophecy, God has counter-balanced the weakening of the impact of Revelation by granting us the evidence of fulfilled predictions, confirmations by archeology, scientific truths and mathematical patterns to enable us to discover the truth of Torah in our time.