Noach: Mathematics

Daily Insight #2

In yesterday’s article we saw how parshat Noach reaffirms the creation described inparshat Bereisheet. Mathematically, there are two beautiful numerical relationships that connect the two words: Bereisheet (בראשית ) and Noach (נח ). To understand them both we will have to learn some new concepts in arithmetic. Have no fear though. A child in grade school should have no problems with these ideas. In fact, if you have children that age (or older), this is a great opportunity to introduce them (and yourself) to Torah arithmetic, which is how Hashem meant us to study mathematics all along (no trig or calculus in the Torah curriculum).

The midpoint series

Every odd integer has a middle point. If you are not particularly mathematically inclined, you can see the midpoint by imagining the number represented by coins placed on a table to form a line. The midpoint is simply the middle coin. So, for example if you have 13 coins lined up, the middle coin, which is equidistant from both ends of the line, is 7.1

In mathematical notation we can write that:

n ┴ 1 (2n ┴ 1), where the new symbol denotes the midpoint of an integer number.

The next step is to note that as long as the midpoint of an odd number is itself odd, it too has a midpoint. Going back to our previous example. 7 13, but since 7 is odd it too has a midpoint: 4 7. But, 4 is even and does not have a midpoint. Thus, we can write a midpoint series beginning with 4 like this:

4 7 13

It is easy to see (hopefully) that every integer used as a starting point will create a midpoint series. Of course, not all integers create unique midpoint series; only even integers create unique midpoint series. You should be able to convince yourself (and your children) that any odd number belongs to one and only one unique midpoint series. Moreover, we can say that there exists a special relationship between every odd number and exactly one even number that is the even number that begins the midpoint series to which that odd number belongs.

Let us look at the first few numbers in the midpoint series starting with the first few even numbers 2, 4, and 6:

2 3 5 9 17 33 65 …
4 7 13 25 49 97 …
6 11 21 41 81 161 …

Looking at the last midpoint series that starts with 6, using our previous insights we can say that any odd number appearing in this series has a special relationship with the even number 6. That relationship is defined in Kabbalah as a relationship of male (the odd number) to female (the even number). In other words, the final even number is the kingdom (the feminine point) of all the other odd numbers, which are an infinite series of males surrounding it.

The relationship between the final even number and all the odd numbers in its midpoint series can be likened to an onion with a singular core [the kingdom] surrounded by layers upon layers of peels [the male odd numbers]. This is not an image of many different males connecting with one female, but rather there is only one male whose many layers represent increasing proximity to his predestined soul-mate.2

Noah, the first kingdom of creation

Now, you may have already guessed that בראשית (913) and נח (58) share exactly this type of relationship. Since נח is an even number let us write out the midpoint series it creates:

58 115 229 457 913 …

Thus we may write that נח is the feminine aspect of בראשית . In other words, Noah, as an individual was the first kingdom, the first embodiment of the truly feminine sefirah of kingdom that God had been searching for from the moment of creation. That is why “Noah found favor in the eyes of the Almighty.”3

Letter filling

The second mathematical relationship is far simpler. Every letter in Hebrew can be “filled,” as it is called by the Arizal, by writing the letter out as it would be pronounced. Thus, the filling of the letter א is אלף , of ב is בית , etc. Using letter filling, let us write out בראשית :

בית ריש אלף שין יוד תו

This is the first filling of the word בראשית . Let us now fill the first filling to arrive at the second filling of בראשית :

בית יוד תו ריש יוד שין אלף למד פא שין יוד נון יוד וו דלת תו וו

The value of the second filling is 3364. But, amazingly 3364 = 582, or נח · נח ! The square of a number, as discussed in earlier articles, represents the consummate state of that number.

As we will now see, these two beautiful mathematical connections between Noach and Bereisheet correspond to a run and return, the dynamic involved in every lasting relationship.

Creation searching for Noach

In Hebrew, the name “Noah” means “repose” or “rest.” On the repetition of the name “Noah” in the first verse of parshat Noach (“These are the chronicles of Noah, Noah was a righteous person…”), the Zohar writes that each mention of the name refers to a different type of “repose” that Noah represents: repose for the spiritual world and repose for the physical world.4 Noah, as an individual with a life story, offered repose to both the spiritual and physical realms. Repose for the spiritual requires the individual to yearn to ascend to spiritual heights. Repose for the physical requires that the individual yearn to connect with the mundane in order to bring out its Godliness. Thus, repose for the spiritual involves an upward motion in the soul and in the psyche, while repose for the physical stems from a downward motion in the soul. An upward motion together with a downward motion is described in Kabbalah and Chassidut as a “run and return,” perhaps the most important dynamic involved in leading a truly full life that connects the spiritual with the physical. The source of the run and return dynamic is found in Ezekiel’s prophecy of the Divine chariot.5 Ezekiel saw that the living beings would run to and return from their source in the Divine. The run therefore corresponds to an upward motion, the return to a downward motion.

The first relationship, that נח is the feminine even number that begins the midpoint series ofבראשית , illustrates the spiritual movement of an upward run. From the moment of creation, reality is seeking to find its source. This is the driving force behind all questions of identity: “Know where you come from, and [then you will] know where you are going.” The original even number in every midpoint series represents the point of origin. Surprisingly, this point is feminine in its nature, and is alluded to in the verse: “The woman of valor is the crown [the source] of her husband.” And this search is continual: “Tzadikim have no rest, neither in this world nor the next.” They are forever searching for an earlier point of origin.6 What is this point of origin? Rebbe Hillel of Paritsch explains that as far back (or high up) as we look, we will find that the very first aspect of God that He revealed is His sefirah of kingdom. In other words, that the point of origin of all the myriad phenomena that make up the universe is that God is King. And, as we explained, kingdom is feminine.

But, what does it mean that the feminine origin of “In the beginning” is “Noach”? It means that no matter how long a person has been searching for his or her origin, for the feminine source, he or she still feels at the beginning of the search. There is no room here for despair and no room for fatigue. This search is always rejuvenating and must always be conducted with an air of freshness.

When focused on the feminine source and conducted with quick and light movements of the soul, this search is sure to be met with success. And the success will come in the form of “A day that is all Shabbat and repose forever and ever.”

Filling the World with Offspring

The second mathematical relationship (the second filling of בראשית equals נח squared) reveals a returning movement, where returning in this context means experiencing the goodness and satisfaction of the physical realm by receiving nachas from one’s offspring.

After the deluge, Noah himself was the progenitor of the entire human race. How does this relate to letter-filling? The Ba’al Shem Tov taught that every word in the Torah can be understood as both masculine and feminine. The filling of a word in Kabbalah represents the offspring that every word can create. The first filling represents the children; the second filling represents the grandchildren. The Arizal limited the filling to two generations, following the Talmudic adage that the compassion of fathers for their offspring extends only two generations including only children and grandchildren.
Every child (and therefore grandchild) is considered a filling, or fulfillment of the parents. In other words, to completely realize one’s potential requires procreation. Without this, something of a person remains forever concealed (even from him or her self) and sterile. Thus, the two stage filling of a word represents its total fulfillment; its complete realization and extension into reality. The two stage filling of בראשית , the word that represents creation more than any other, represents the total fulfillment of creation itself in both the figure of Noah and in the theme of reaffirmation of creation found in parshat Noach. Noah represents the fulfillment of all the potential inherent within the heavens and the earth, just as the children and grandchildren embody all the potential inherent within their parents.

Fulfillment through the filling, of both a word and the earth with offspring employs the returning vector of the run and return dynamic. This is the vector that gives repose to the mundane, to the physical realm, which seeks to realize its full potential. In essence this repose is the complete revelation of all that is hidden in potential in the parents. In Hebrew, the word “square” (as in 582) is a synonym for procreation.7

1. In an earlier insight we saw that 7 and 13 are one of the most important pairs of numbers in the Torah. If you recall, we also mentioned that, relative to one another, 7 is feminine and 13 masculine. Today we will get a Kabbalistic explanation for identifying them as such.

2. This is a powerful metaphor for understanding the nature of relationships between men and women. Talk of men becoming connected to their so-called feminine side is common today. Using this metaphor we can understand that at the heart of every male there is indeed feminine energy surrounded by increasing layers of masculinity, which can be defined as feelings of self and ego. At the very core of every male is his soul-mate. This also teaches us that in relationships, it is up to the man to peel away layers of self until he can truly connect and find his feminine soul-mate. We shall later see that this process of peeling away layers is actually a spiritual process, which requires a man to search for his true ego-less self.

3. In The Art of Education, we explain that in Hebrew there are 8 different synonyms for beauty. חן , “grace,” which is the reverse of נח , corresponds to the sefirah of kingdom.

4Zohar 58b.

5. Ezekiel 1.

6. When a new student would come to the Ba’al Shem Tov, the first thing he would ask him was: “How far back do you remember.” There is a section of Rebbe Nachman’s story the Seven Beggars that deals with this concept. Just as much as one seeks to recall the past, Rebbe Nachman speaks of recalling the future, for as we said, a tzadik, and all Jews aretzadikim, has no rest, neither in this world [which stems from the past] nor the next [which lies in the future]; the origin of both is one and the same.

7. See Numbers 23:10.

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