“God spoke to Noach and his sons, saying: ‘ I am establishing My covenant with you and with your offspring after you.’”
The Torah relates a number of covenants made between the Almighty and human beings. The first of these covenants was made with Noach and his sons. With Abraham, God made two covenants, one regarding the Land of Israel and the second regarding circumcision. The fourth covenant was made with the Jewish people over the Torah.
Regarding the covenant of circumcision, the Mishnah states, “Great is circumcision, for 13 covenants were made on it.” The meaning of these seemingly cryptic statement is that in the Torah’s account of the covenant of circumcision, the word “covenant” (בְּ רִ ית) appears 13 times (in various forms). Regarding the covenant made with the Jewish people over the Torah, the Talmud states that, “It was made with 3 covenants, while the other [circumcision] was given with 13 covenants.”
What about the covenant made with Abraham over the Land of Israel? The verse in question is, “On that day God made a covenant with Abraham saying: ‘To your offspring I have given this Land, from the river of Egypt to the great river, the River Euphrates.’” The word “covenant” appears only 1 time.
Following the lead made by the sages, we are prompted to count the number of times the word “covenant” appears in the account of the covenant made with Noach, the Rainbow Covenant:
And God said to Noach and to his sons with him, “I now establish My covenant with you and your offspring to come, and with every living thing that is with you—birds, cattle, and every wild beast as well—all that have come out of the ark, every living thing on earth. I will maintain My covenant with you: never again shall all flesh be cut off by the waters of a flood, and never again shall there be a flood to destroy the earth.”
God further said, “This is the sign that I set for the covenant between Me and you, and every living creature with you, for all ages to come. I have set My bow in the clouds, and it shall serve as a sign of the covenant between Me and the earth. When I bring clouds over the earth, and the bow appears in the clouds, I will remember My covenant between Me and you and every living creature among all flesh, so that the waters shall never again become a flood to destroy all flesh. When the bow is in the clouds, I will see it and remember the everlasting covenant between God and all living creatures, all flesh that is on earth. That,” God said to Noach, “shall be the sign of the covenant that I have established between Me and all flesh that is on earth.”
There are 7 instances of the word “covenant” in these verses. The first thing we note is that 7 is also the number of colors associated with the rainbow; more deeply, these seven covenants correspond to the 7 Noachide laws.
To summarize our findings until now, the number of “covenants” relating to each of the covenants made between God and man are:
- Covenant of the Land of Israel: 1
- Covenant on Torah: 3
- Covenant with Noach: 7
- Covenant of Circumcision: 13
Let us call these 4 numbers “covenant numbers” and explore a bit their mathematical characteristics. Using the method known as Finite Differences, we can write:
1 3 7 13 2 4 6 2 2The base of the series made by these 4 numbers is 2, alluding to the fact that a covenant is made between 2 parties. We will see in a moment how this idea is illustrated graphically in the figurate form of the numbers in this series.
Now that we have found the base of the series, we can extend the series of covenant numbers forwards (and backwards) like so:
1 3 7 13 21 31 43 57 2 4 6 8 10 12 14 2 2 2 2 2 2If we continue to extend the series forward, we will find that the first 13 covenant numbers are: 1, 3, 7, 13, 21, 31, 43, 57, 73, 91, 111, 133, and 157
Using a method developed by Isaac Newton, we can extract the function that generates this series of numbers: f[n] = n ┴ n ┴ 1
Covenant numbers can be pictured graphically. They have the form of two triangular numbers, one over the other, with a single point (alluding to the sign of the covenant) in between. Here are the first few covenant numbers in graphic form:
Let us note that the verse describing the special relationship Noach had with God, which formed the basis for the covenant God made with him is, “And Noach found favor in God’s eyes.” The gematria of this verse is 421, which is also a covenant number, specifically, it is the covenant number of 21, or: 21 ┴ 21 ┴ 1 = 421
Now, let us look at the location of the 7 covenants in the verses quoted earlier. We find that they are the 13th, the 38th, the 57th, the 77th, the 91st, the 114th, and 133rd words in the paragraph. We might notice that every other location number is a covenants number:
- 13 is the covenant number of 3
- 57 is the covenant number of 7
- 91 is the covenant number of 9
- 133 is the covenant number of 11
It is easy to see that these are the covenant numbers of the odd numbers, with 1 and 5 missing. We might say that the covenant of 1 and of 5 need to be completed in some other way.
The covenant of 1 is 3 (note the graphic form depicted earlier). The covenant of 5 is 31. Now, if we look at the words in the 3rd and 31st locations in the paragraph, we find that they are: “to [Noach]” and “that have come out.” Amazingly the numerical values of these two words (located in covenant number locations) are themselves covenant numbers, 31 and 111.
What a beautifully complete finding! (Einayich Berechot BeCheshbon, pp. 67ff.)
