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
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
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
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,
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.