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Mathematics in Yitro: Connecting Creation with Torah



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Math in Parashat Yitro: Connecting creation with Torah

Multiples of Havayah and Elokim

The first of the Ten Commandments reads,[1] “I am Havayah your God who has taken you out of the land of Egypt, from a house of bondage” and in the original Hebrew, אָנֹכִי י־הוה אֱ־לֹהֶיךָ אֲשֶׁר הוֹצֵאתִיךָ מֵאֶרֶץ מִצְרַיִם מִבֵּית עֲבָדִים.

The value of this verse is 2495, or 5 times 499, which is the value of God’s Name, Tzevakot (צְבָאוֹת), and since this Name consists of 5 letters, 499 is also the value of Tzevakot’s “run and return”: צ צב צבא צבאו צבאות באות אות ות ת must also equal 2495.[2] We saw the special significane of the Name Tzevakot in our article on parashat Bo (5780). Here too the Torah is alluding to the Name Tzevakot as revealed by Channah, Samuel’s mother.

To appreciate another special property of 2495, we need to recall the unique mathematical property possessed by 1118, which is the gematria of our most essential decleration of Jewish faith in one God, “Hear O’ Israel, Havayah is our God, Havayah is one” (שְׁמַע יִשְׂרָאֵל הוי' אֱ־לֹהֵינוּ הוי' אֶחָד). This essential decleration of our faith in God being one draws an identification between the Name Elokim (אֱ־לֹהִים),[3] alluding to God’s imminent aspect[4] and God’s essential Name, Havayah (י-הוה), referring to God’s transcendental aspect, thereby stating that Elokim is Havayah and both are one. The value of Elokim (אֱ־לֹהִים) is 86, the value of Havayah (י-הוה) is 26 and 1118 (the gematria of the entire verse) is the smallest number that is a multiple of both 26 and 86 (their least common denominator), illustrating mathematically the unification of Havayah and Elokim!

Now, the two numbers before and after 2495 are a multiple of 86 (Elokim) and a multiple of 26 (Havayah), respectively. 2494 is 29 times Elokim (86) and 2496 is 96 times Havayah (26)!

The Shema series of numbers

This already presents a meaningful connection between the Ten Commandments and the unification of Havayah and Elokim that is the basis of the Shema, the essential statement of faith, as above. But, let us continue our analysis of this number 2495 by asking: What other integers possess the same property: that the integer before them is a multiple of Elokim (86) and the integer following them is a multiple of Havayah (26)?

The number before 2495 that possesses this property is 1377. The integer before, 1376 is the product of Elokim and 16 and the integer following it, 1378 is the product of Havayah and 53. 1377 itself is related to parashat Yitro, our parashah since it is the product of “I am” (אָנֹכִי), the first word of the first commandment, whose value is 81 and 17, where Yitro is the 17th Torah portion from Genesis!

The number before 1377 that possesses this property is 259. The integer before, 259 is the product of Elokim and 3 and the integer following it, 260 is the product of Havayah and 10. 259 itself is the value of “Reuben” (רְאוּבֵן).

Now, let us look at the rule generating this number by looking at the differences between them:

259      (┴ 1118)            1377                (┴ 1118)            2459

Amazingly, the differences between the numbers is 1118, the value of the Shema, the smallest common denominator of Elokim and Havayah, prompting us to name this linear series, the Shema series of numbers, formally generated by the function:

f[n] = 1118n ┴ 259.

It follows then that the next number with this property after 2459 can be found by adding another 1118, giving us 3613, which is the interface number of 43 (or 432 plus 422). The sum of the first 4 numbers in the Shema series is 7744, the square of 88.

Connecting creation with the Torah

The qualitative significance of the numbers in the Shema series is that they serve as a medium between the Name Elokim representing creation, or more formally “the workings of creation” (מַעֲשֵׂה בְּרֵאשִׁית) and the Name Havayah, representing the Giving of the Torah at Mt. Sinai. The Giving of the Torah at Mt. Sinai is considered the implicit illustration, “the workings of the chariot” (מַעֲשֵׂה מֶרְכָּבָה). The workings of the chariot were revealed more explicitly by the later prophets, with the most detailed description appearing in the first chapter of Ezekiel.

Where the world was created with the Ten Utterances of creation, the Torah was given through the Ten Commandments, and while God is concealed behind the veil of creation, He is revealed through the letters of the Torah. These numbers thus serve as a conduit representing the link between the two—creation and Torah—a link that is alluded to in the verse, “Ten [and] ten per ladle”[5] (עֲשָׂרָה עֲשָׂרָה הַכַּף). In effect, these numbers elevate the Name Elokim found in the Ten Utterances of creation to the Elokim found in relation to the Workings of the Chariot and described in the phrase, “Elokim’s chariot is twice ten-thousand [and] two thousand”[6] (רֶכֶב אֱ־לֹהִים רִבֹּתַיִם אַלְפֵי שִׁנְאָן), to the state in which Elokim is included in the chariot of God’s Name, Havayah, the secret of the Ten Commandments first three words, “I am Havayah, your Elokim” (אָנֹכִי י־הוה אֱ־לֹהֶיךָ). Furthermore, the value of the Name Tzevakot, 499, is 5 times “Havayah your Elokim” (י־הוה אֱ־לֹהֶיךָ) from the first commandment together with “Havayah is one” (הוי' אֶחָד), from the Shema.

Extending the series

We might continue to ask whether there are other integers with a similar property, except that the multiple of 86 will follow said integers and the multiple Havayah will precede them. To find them we can simply extend the Shema series into the negative numbers and then take the absolute value of the numbers we generate.

The number before 259 is obtained by subtracting 1118, arriving at -859. The absolute value of |-859| is 859 and 858 is Havayah (26) times 33 and 860 is Elokim (86) times 10. Continuing we will obtain 1977 and then 3095. We can interlace the two parts of the series, the positive branch and the absolute value of the negative branch together obtaining the following integers:

259      859      1377    1977    2495    3095    3613 ..

Notice that now the differences between the numbers are 600 and 518, repeatedly. Of course the sum of 600 and 518 is 1118. This new division of 1118, the Shema, into 600 and 518 is a truly new result, and in the Shema itself is reflected by a division of the verse into the two letters shin (ש), totaling 600 and the rest of the letters:

שְׁמַע יִשְׂרָאֵל הוי' אֱ־לֹהֵינוּ הוי' אֶחָד = 600

שְׁמַע יִשְׂרָאֵל הוי' אֱ־לֹהֵינוּ הוי' אֶחָד = 518

This newly discovered division based on the Shema series can motivate further insight into the Shema.



[1]. Exodus 20:2.

[2]. The easiest way to see this is by pairing the parts of the run with the parts of the return. צ is completed by באות, צב is completed by אות, צבא by ות, and צבאו by ת, which together make up 4 times צבאות, plus an additional complete צבאות make up 5 times צבאות, or 2495.

[3]. In the Hebrew, Elokim appears in the possessive  form, “our Elokim” (אֱ־לֹהֵינוּ).

[4]. I.e., how God is present throughout mundane reality, throughout nature. Indeed, Elokim (אֱ־לֹהִים) equals the value of “nature” (הַטֶּבַע).

[5]. Numbers 7:86.

[6]. Psalms 68:18.

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