There are actually five "dual" mathematic constructs in a cube. We will focus here on just one, which is essentially the mathematic (geometric) "source" of the magen david. This construct defines the points, lines and faces of a certain regular convex polyhedron known as a tetrahedron. When the underlying mathematic construct that defines the elements of a tetrahedron is "married" to its polar opposite (another tetrahedron facing the opposite direction) the combination defines the properties of what is called a star tetrahedron (or stella octangula). This three-dimensionally complex geometry casts a two-dimensional shadow known as a magen david.
We actually have an obscure tradition that the shnei luchot were tetrahedrons, however this should be understood within the context of the above geometry (shown in the model below) rather than being taken literally.
When you do the math, you will note that the marriage between two tetrahedrons (pictured below as a reflection within a cube) results in a sub-division within the original tetrahedrons. where the "star" has 24 small faces with 3 triangular corners. The 24 faces with 3 corners hides the number of triplets in the Name (24 x 3 = 72) and the triangular nature of each corner hides the total number of elements (216) reflected in this aspect of its geometry. The Triad Havaya of 72, is thus mathematically hidden in the geometry of the "magen" in three-dimensional form. The magen david is a relatively new symbol in Judaism. However the sages of Israel understood the significance of the geometry as it pertains to the luchot and the letters of God's Name.
If you've read the essential constructs in order, then you know the volumetric measure for each of the luchot was 108 cubic handbreadths (each 'half being 108). The geometry of each tetrahedral construct within the combined cubic form of the luchot (tablets) consists of 36 triangular corners: 3 x 36 = 108 such corners (108 on one tetrahedron and 108 on the other). The primary characteristics of the cube and its measurement, as it relates to the Name, are dependent on the measure of the cube (its specific size) but the geometric characteristics of the elements in a star tetrahedron are not. They are completely static and built into the nature of its geometry regardless of size, yet they are identical. These combined characteristics constitute a "point of convergence" between its "measure" and its "geometry, and are together a primary example of the signature geometry (the mathematic characteristics of God's Name) in the blueprint for creation (the evan shetiyah or "foundation stone").
For the purpose of this page it is sufficient to recognize that the magen david is a two-dimensional shadow of a three-dimensional construct within a cube, and that its geometry corresponds to the mathematic characteristics of God's One Explicit Name with 3 x 72 or 216 letters. A representation of the star within a cube and its resulting shadow is pictured below. The next construct is about: The Nature of Sapphire
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Could you please provide a source for the tradition you mention that the Luchot were tetrahedral in shape.
ReplyDeleteNote to all: I was asked for a source on "the luchot [being] tetrahedral in shape."
ReplyDeleteThe assertion was made by the author of one of the books in my library. However, the author did not say that the luchot were tetrahedral "in shape," but rather, merely that they were tetrahedrons, and even that should not be taken literally, since tetrahedral geometry is an intrinsic function of cubic geometry. I'm in the process of writing Part III of "The Eight Dimensions," which goes into great detail on this subject. At the time I read the commentary in question, I was not intending on creating this blog, so I did not make note of specific details. I would however like to include his name, the book and specific page number when I complete the pending post, and will look for it in the coming weeks.
I discussed the issue of the Tablet's shape in my essay Squared vs. Rounded Tablets, published not long ago.
ReplyDeleteThe question has been asked if this is a merkava. Strictly speaking, no it is not. The path of ma’aseh merkava (a chariot) is a meditative device (essentially a specific technique) used by kabbalists (to travel) that involves the permutation of letters. It also entails a great deal more, and thus it is impossible to do the question justice in a brief response like this. If you would like more information on the subject, I recommend that you start with R. Aryeh Kaplan’s book entitled “Meditation and Kabbalah” published by Aaronson. Insofar as the question regarding the magen david as a merkava is concerned, the geometry of a three-dimensional magen david does correlate with the letters of the Name, as well as numbers. The “thirty-two paths of wisdom” for example, are the 22 letters and the 10 (base) numbers (corresponding to the sephirot) derived from aspects of geometry in the combined cubic form of the luchot, and as such, can be used in meditation. However, it would not be appropriate to reveal specific details in this forum.
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