e-list posting, July 2002
We are taught that there are two kinds of laws in Torah: Hoqim and Mishpatim. Mishpatim can be understood on the basis of logic, but Hoqim cannot and we are enjoined to not try.
Nevertheless, while we can never learn the “why” of Hoqim, we can identify what this word means and we can understand why we cannot learn the “why” of the Hoq-rules themselves.
The simplest place to start when attempting to understand a principle is to examine its name. We are taught that Adam assigned the names to the creatures (and in principle, to the principles) of his world according to their function. Thus a horse - SUS - is Samek/sustaining - Vov/doing - Samek/sustaining. In other words a horse is a means of carrying us and doing work for us - that’s what all the “sustaining” (the meaning of Samek) and the “doing” (or turning, i.e. “plowing”) is about. (Plowing is a means of our acquiring sustenance.)
HoQ is spelled Chet-Qof.
We know that Chet means and refers to a “fenced field,” - either its perimeter or its area. Chet refers to what physicists or mathematicians would call a boundary. (A perimeter bounds an area and an area bounds a surface, etc.)
Qof means “skull” (or monkey or copy - meaning “ape,” in English) and it refers to physical vessels or physicality in general.
So, now we know what a Hoq is. It is a physical boundary. When we are talking about the laws that Torah refers to as Hoqim we are talking about the boundaries of physicality itself.
What are the boundaries of physicality? This is simple. Before we were born we lived entirely within and confined by a three-dimensional egg-sack. Now that we are out in the world, we can move about in three dimensions. Our physical world is 3-D and we are confined to it.
Understood this way, what a Hoq is not so mysterious. Why we should find ourselves in a 3-D reality is just as mysterious as before, of course, and except for the anthropic principle which says that if it were not so we would not be here to ask these questions, there can be no explanation for this. We find ourselves in 3-D and we have to make the best of it. Even if there is an explanation of sorts, it would not explain the mystery of our being here.
The “big Hoq” is that we are here at all. We can get a sense of the power of Hoqim even if we cannot understand their mystery by examining a simple real situation.
I mentioned that before we were born we were restricted to the internal three dimensions of the egg-sack. This has enormous implications because it is this very “boundary condition” that is the guiding hand of our embryology. Here is how it works.
First we are one fertilized egg in an egg sack. No matter what the nutrients available, all that this single egg cell can do is to divide.
Each of the two identical newly-divided cells has the same environment, so they are effected the same way by the nutrients, so all they can do is to divide again.
Each of the four cells has the same environment, so they are effected the same way by the nutrients, so all they can do is to divide again.
Each of the eight cells has the same environment - all touch the same number of other cells and all are in contact with the egg-sack - so again they are effected the same way by the nutrients, so again all they can do is to divide.
But now something magical happens. Due to the fact that the egg-sack is three-dimensional, once there are sixteen cells, some of the cells must be clustered in the middle unable to be in contact with the egg-sack and some of the cells must be between the middle cluster and the egg-sack. Now there are two different environments, inside and outside, and the nutrients effect the cells inside differently than those outside and cell differentiation begins to take place. This is entirely due to the boundary conditions of the geometry of the space we live in. In 3-D no more than 12-spheres can be packed into a larger sphere where all have contact with the larger sphere. Thus some egg-cell spheres cannot be in touch with the egg-sack and must be surrounded by only other egg-cells. (In 4-D, 24 spheres could be in contact with a surrounding sphere.)
If we lived in a 4-D world and developed in a 4-D egg sack, there would be another division before cell differentiation could begin and our entire lives would be radically different if they were even possible at all.
Thus the First Hoq is 3-D (or as the kabbalists say, the “cube of space”) and even though _why_ there are three-dimensions is still a mystery, how this mystery acts in the world is not a mystery - it is a root of our being.
You might even say, “The Hoq’s on us!”
© 2002 Stan Tenen / MERU Foundation
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