The 360 Degrees of a Sphere

This post has been re-written to correct the wording of the previous version and to include specific information related to the gematria for expansions of the Name known as the Tetragrammaton. 

In a previous construct we examined the circle/circumference defined by the 36 handbreadths on the face of the luchot. We then showed how the hemisphere associated with that circumference in turn defined the fine-structure constant to the 4th decimal place. In this construct we will examine those handbreadths and the 360 divisions of that circle/circumference more closely.

Have you ever wondered why there are 360 degrees in a circle or sphere? Unlike other systems of measurement, a degree is not a measure of length or breadth. Rather it is a portion of something that may vary in size. Why 360 portions? Why not divide a circle into 10 parts, or 100 parts? Why not increase the resolution to 1,000 parts, e.g. 1,000 degrees in a circle? What person or group of people decided that a circle should be measured in terms of 360 parts, and why?

The answer may surprise you. It is actually self-embedded in the geometry of the luchot. In other words, the geometry itself creates the divisions. You will see exactly how it does this in a moment, but before doing so, we should first lay some ground work in order for you to understand the significance of this measurement.

At one point in the distant past, the mind of man (more specifically Adam) was able to perceive certain things without having to measure them. You can demonstrate this concept for yourself by testing the limits of your own consciousness.

Have a friend throw two or threes coins onto a tabletop. There is no need for you to count them because you can immediately “see” how many coins were thrown. However, have them throw down a higher number of coins, ten or more, and you can no longer see or perceive the number without taking the time to count the coins.

At one time human consciousness was far superior to what it is today. Language was hard-wired into the consciousness of mankind. How do we know? God tested man by bringing the animals before Adam to see if he could “see” (perceive) their names (their inherent energetic properties as expressed in certain letters).
 
Human consciousness suffered a serious setback when Adam “fell” into what we perceive as a physical universe. Having lost this exalted level of consciousness, he could no longer see “from one end of the universe to the other.” Things that had been obvious before, like his understanding of mathematic relationships or the energetic properties that allowed Adam to “see” without “the need to count,” were no longer obvious. Now it would be necessary for him to carefully examine “the measure” of any given thing, before he could see the intrinsic link between God and His creation.

Still, Adam had an advantage, because even after the fall, man still had that one comprehensive language consisting of 70 times the vocabulary we have today, words that when taken together, more clearly reveal the underlying connections between God and creation. However, things went from bad to worse after the incident at Bavel (the tower of Babel) when that one all-encompassing language became fragmented. It wasn’t that everyone was speaking seventy different languages. It was that the one original language was fragmented into seventy different parts and the obvious connections were all but gone. Knowledge of God was obscured and the mind of man occluded to the point that he could no longer see God in the nature of the world around him.

Remember this as we examine in the paragraphs ahead, why a circle must be divided into 360 parts, and how these 360 divisions correlate with the original language and the letters of God’s Name.

If you’ve read the previous constructs provided throughout this blog, then you’ve already been exposed to anthropomorphic terms related to measurement, terms such as faces and hands, cubes, cubits (the measure of a specific cube) feet, yards, fathoms etc. However we’ve not yet examined the fingers of the hand(breadth) or what part they play in the measurement of things, or how they might factor into the original more comprehensive language.
 
The hand consists of four fingers and a thumb. If we say that someone has five fingers, it is understood that one is different from the others. However, there is a more obscure word that can be used for both fingers and thumbs. It is the word “digit,” and it has a double meaning. It not only refers to fingers and thumbs, but also to numbers. That’s logical! We sometimes use our fingers (digits) to count. Look into any dictionary and you’ll find the following: Digit = Noun: 1) any of the numerals from 0 to 9, especially when forming part of a number; and 2) a finger (including the thumb) or toe.

From previous posts it is easy to see that the imperial (sacred) handbreadth (in the measure of the shnei luchot) is more than just a measurement by which to perceive aspects of the physical universe. It also alludes to how the “Hand” of God created, or more specifically how God measures or otherwise rules the physical world. In the process, it also reveals the connection between these units of measure and God’s Name. 

Hands and faces? What about the finger (of God) i.e. the five digits of the hand? What role do they play in the measure of things? In the preceding paragraphs we asked the question: “What person, or group of people decided that we should measure a circle in terms of 360 parts (degrees).” The answer is: no one.  Nor did any group decide that it should be divided into 360 parts. The divisions were self-embedded in the nature of geometry as revealed by the shnei luchot. It was one of those things that was obvious to primordial man who possessed an elevated state of consciousness. Can this be proven? 

An understanding of the “foundation stone” (the primordial luchot) was one of those things originally hardwired into human conscious, one of those things that allowed him to “see” (perceive) God on a level that we can now only imagine. The correlation between the geometry of the stone and God's Name or Names is discussed earlier in the post/meditation on the "42 Letters in Sapphire" and it provides a glimpse into the validity of this assertion.

The three-dimensional geometric models of the luchot below are provided to show beyond a reasonable doubt that certain things were in fact hardwired into human consciousness. Through these models the student has the means to reconstruct the knowledge lost to man in ages past. Both are geometric representations of the luchot in their divided side-by-side form, as opposed to their combined cubic state (the divided form is that which parallels the Triad Havayah of 72, or 216 letter Name of 72 triplets). 

The model below shows the 6 “hands” of the “stone’s” first dimension (with 30 “digits”) that trace back to a point at infinity forming the opposing angle. Think of the point as the ultimate quantum singularity from which the universe emerged.

Click to Enlarge

Contemplate the above geometry carefully and understand that the 216 cubic handbreadths (correlating with the 216 letters of the Explicit Name) are the basis for the 360 digits/degrees in a sphere. It is very easy to see once its been pointed out to you!

A right triangle such as that pictured above, has corner of 90 degrees. The sum of its two remaining angles is also 90 degrees (basic geometry). In the case of the luchot, when the 12 handbreadths of any given side are rotated back to intersect with the opposing side of 12 handbreadths (shown in blue above) it creates a triangle where the two remaining angles are 30 and 60 degrees respectively (again basic geometry). The three angles of any triangle will always add up to 180 degrees (half of a circle) and the four angles of a square or rectangle will always add to 360 degrees. Study the geometry displayed above and below carefully.

The measure for each of the angles in "digits" defined by the handbreadths happens to be the same as the measure of each angle in degrees. This measure defines the number of divisions/portions (degrees) in both the four corners of a square and the four quadrants that we find in a circle or sphere.

This is true either for the hemispheres in the two halves of the cube, or as a sphere within their combined cubic form. They are in fact, quite literally, “the digits” of the hand(breadths) by which the stone is measured. That is why we measure a circle in terms of 360 degrees. This knowledge was originally inherent in man’s understanding of reality. Today it must be contemplated before it can be understood within the context of God's Explicit Name.

The measure of the mishkan should also come to mind where the two opposing north and south walls are each 180 handbreadths. The two together are 360 handbreadths, like the number of degrees in the four angles of each face and the 360 divisions of the sphere within the stone.

Before Bavel (the Tower of Bavel) there was a single language. It was a more comprehensive language and it revealed aspects of reality that have since been lost to man. In Hebrew, the word for "degree" is maala. It is spelled the same as the word maale, which means "ascent." What does this have to do with geometry of the stone(s) or consciousness?  It is through gematria (geometry) that one begins the ascent required for man to return to the edenic level of awareness (wisdom) once possessed by Adam. This is just one example of how words in several languages, now fragmented, were originally combined to reveal a much larger reality.

This more comprehensive language can be demonstrated by looking at words like DiGit and  DeGree. The first thing to point out is that, in English, two of the root letters are the same. Why? The words “digit” and “degree” are actually measuring the same thing, albeit in a slightly different way. The "D" in Hebrew is a Dalet which means "door" and the G in Hebrew is a gimmel that is something that is "given" (which is in proportion to what is received). The written "D" in English is a semi-circle with its ends connected by a straight line, like the track of a door that swings open to 180 degrees. The connection that it has to a door or a half circle is obvious. In Hebrew, not only does the letter mean "door," but it takes the form of a door that is open to 90 degrees (ד).

When the diagonal or hypotenuse extends between the corners of the luchot (grey in the photo) rather than the 30, 60, 90 degree triangle mentioned previously (shown in blue in the photo) then the remaining angles measure 26.565, and 63.43 degrees respectively. The “h,” measurement (which is shortest distance between the corner of the 90 degree angle and the hypotenuse) is 51.96 cm (52). In addition to these numbers, the hypotenuse of the angle between the corners of either tablet creates a right triangle with two 45 degree angles. Keep in mind that the above measurements are all created within an area of 72 square handbreadths.

Kabbalists immediately recognize those integer values. All of them correspond to the gematria of the Tetragrammaton and its 4 expansions (the Name has a gematria of 26 and the gematria of its expansions are 72, 63, 45 and 52 respectively). The number of elements in a cube is also 26 (6 faces, 8 points or corners and 12 vertices or edges = 26) alluding to the secrets of the Name contained within its geometry and  its measurements. 

If this were the only instance of these numbers in the geometry of this cube, it might be considered a coincidence, but these specific integers can be found in many places throughout the measurements of the luchot. Since its volume (after being divided) mirrors the Triad Name of 72 and since it’s linear measurements (before division) consist of 42 sets of 42 linear handbreadths (mirroring the number of letters in the Name used by the Sages to go before the throne of God) it would be more appropriate to say that what we are seeing is a mathematic example of how God’s Name rules the universe.

There is an additional aspect to these numbers that have further implications. The measurements are of course all expressed in the form of Base-10 numbers. The 26 of the Tetragrammaton is Base-10 and the first letter of God's Name is a yud (י) which has a gematria of 10. Its remaining letters are hey-vav-hey (הוה) which have a gematria of 5-6-5, and so the angle with 26.565 degrees would seem to have additional implications. Moreover, these measurements arise from the geometry of a cube with a volume of 216 Cubic Handbreadths which is specifically 6 handbreadths to the 3rd power. There just happens to be 343 points of intersection between the linear handbreadths of such a cube, both within and without. So these numbers would seem to reflect the geometry of this cube (6 to the power of 3 with 343 points of intersection). Again, one might consider this to be a coincidence but there are just too many coincidences of this type within the measure of this one cube.

Its measure appears to be based on a divine system of measurement that has a direct connection to the letters of God’s Name or Names. The cube that is guarding these secrets contains many instances of Pi in both the imperial system of measurement and the metric system of measurement. One such instance is the ratio of the sphere within the cube, to the volume of the cube that surrounds it (which is well known). This volumetric measure is Pi divided by six regardless of the unit of measurement you use, but another example is the circumference of the circle that is defined by each of its six sides. The circumference of these six circles is Pi cubits (on the outside surfaces) just as the circumference of the sphere is Pi cubits (on the inside) all being imperial. However, the linear measure of the outside is also Pi, but it is Pi divided by 6 meters (metric). Since there are six sides, the total measure of all six sides is 6 x Pi:6 or simply Pi meters. So we have Pi Cubits and Pi Meters within the same cube. This is true only in this one specific cube (the combined form of the shnei luchot). Pi is an irrational number. Its decimal fractions go on forever without repeating, so it is truly Ein Sof (עין סוף). The six measures of the angel’s rod in the book of Ezekiel (40:5) are a one-dimensional representation of the six, two-dimensional faces of this cube (Pi Meters). 

It is alluded to in many of our sources like Bava Basra 14a which gives the dimensions of the luchot in handbreadths, but it is sometimes referred to in its cubic form as “the Cube of Metatron,” where the root letters of the name (MTR / mem-tet-resh) refer to measurement. We see this in words like MeTRic and MeTeR, as well as words like MeTRonome (an instrument that measures) and Meterology (the measure of weather). The full title of the angel Metatron is "Metatron Sar HaPanim” which is usually translated as "the minister of the interior,” but its literal meaning is "the [measuring] of the (six) faces.” Contemplate that for even a moment and you will see the significance of both the cube and the angel’s rod mentioned in Ezekiel. The angel was MeTatRon. 

All of this considered, the cube that bears the signature of God’s Name within its geometry, becomes the common denominator between both systems of measurement. The only thing that I would add is that considering everything said above, it is inappropriate to translate the Hebrew word A-M-A-H (which means forearm) as “Cubit” for reasons that should be obvious. The amah/forearm is not a cubit. It is at best an approximation. There were maybe 4 or 5 different lengths for the forearm used in Israel during biblical times, indicating that the forearm was not an exact system of measurement. It was clearly an estimate for the measure of a specific cube, and it was that cube that gave mankind the cubit. The Sages never referred to the length of their forearm as a cubit. Instead they called it what it was... a forearm. They did so because it was the forearm that was used to estimate this measuement. Depending on the size of the man, it varied in length. Hence so many versions of the measure. It is the average length of this estimate that is debated to this day.

The next construct elaborates on the Name in the geometry of the stone(s): Fixed in Stone