In Search of Mathematical Simplicity
After HaRav Ginsburgh first taught about these three all-inclusive sins in the Od Yosef Chai Yeshivah in Shechem, he contemplated the Torah portions in which they appear from a quantitative perspective. The sin of eating from the Tree of Knowledge is in parashat Bereishit, the 1st parashah in the Torah. The sin of the Golden Calf is described in parashat Ki Tissa, the Torah’s 21st parashah. The sin of the Spies appears in parashat Shelach, the 37th parashah. These three numbers—1, 21, and 37—can be seen as a series.
A basic technique used to analyze series is the “finite differences” method. It is the discrete equivalent of finding the derivative of a function and was originally developed by Isaac Newton. If numbers in a series have a constant second “finite difference” they form a quadratic series. For example, the number 1 3 6 form a quadratic series since we can write:
1 3 6
2 3
1
The difference between 1 and 3 is 2, the difference between 3 and 6 is 3, and the difference between the differences (2 and 3) is 1, also known as the base of the series. We can use the base to find the next number in this series:
1 3 6 10
2 3 4
1 1
The next number is 10. We can use the base to continue generating the rest of the numbers in the series.
Now, let us return to the three numbers 1, 21, and 37. Arranging them in the finite differences form we get:
1 21 37
20 16
-4
But we can do better by assuming that there is a missing number in this sequence, between 1 and 21. If we add the number 9, we get the following:
1 9 21 37
8 12 16
4 4
By adding the 9, we have speculated that there is another all-inclusive sin in the Torah’s 9th parashah, which happens to be parashat Vayeishev. Another thing that has changed is that the base of the series is now 4, which itself alludes to there being 4 all-inclusive sins. One more important change is the average value of the four numbers: 1, 9, 21, and 37. Their sum is 68, which means their average is 17, the value of the word for sin (חֵטְא). One should immediately question this gematria, since the value of “sin” (אֵטֵח) is 18. However, there is one exceptional instance of the word in the Torah where it is written without the alef, regarding a situation in which the congregation inadvertently worshipped in a forbidden way. They then bring “a he-goat as a sin offering” (עִזִּים אֶחָד לְחַטָּת ְ עִירׂוּש). Since the average value is 17, we are pointed in the direction of the Torah’s 17th parashah, which is Yitro, suggesting that the remedy to all the all-inclusive sins is found in the Giving of the Torah described in that parashah. Because the Torah is what designates what is a sin and what is not, it follows that only the Torah can also annul a sin through the path of teshuvah.
Before identifying the all-inclusive sin in parashat Vayeishev, the 9th parashah, let us see what the number preceding 1 is. We can find it by extrapolating backwards:
-3 1 9 21 37
4 8 12 16
4 4 4
It may sound a little strange, but if we follow the numbers logically, we can say that the negative 3rd parashah is the third parashah backwards from Bereishit, which is Nitzaveem. Parashat Nitzaveem contains what is known as the parashah of teshuvah, a beautiful allusion to the sages’ statement that “teshuvah preceded the Creation of the world.”
One more point that will be important for our construction of the partzuf of the all-inclusive sins in a moment is to look at the number of verses in these parashot. In the 1st and 9th—Bereishit and Vayeishev—there are 146 and 112 verses, respectively. Their sum is 258. In the 21st and 37th parashot—Ki Tissa and Shelach—there are 139 and 119 verses, respectively. Again, their sum is 258. This both provides additional mathematical support for adding the 9th parashah as well as setting the stage to dividing the 4 all-inclusive sins into 2 pairs, just as the first two letters of God’s essential Name, Havayah are known as “the concealed” (תֹהַנִּסְתָּר) and the final two letters are known as “and the revealed” (תֹוְהַנִּגְל).
But what is even more interesting is that the number of verses in parashat Yitro—the Torah’s 17th parashah, which we said is the remedy to the all-inclusive sins—is 72, which is 4 times 18, or 4 times the value of “sin” (אֵטֵח), alluding to its being the remedy for these 4 sins.
