Saturday, January 11, 2020


In Parashah Shemoth, the mathematic characteristics of the letters in the Explicit Name are concealed in the marriage, when Yitro: “...gave his daughter Tzipporah to Moshe." The circumstances surrounding this particular marriage are among the most fascinating, however the details are not found in the written Torah. We find mention of them in other sources, some of which are cited below. As you might suspect, the connection with God’s Name is in the details, so with that in mind we will reconstruct some of these details in their historical context, starting with Yitro, Moshe and Pharaoh.

Yitro and Moshe had much in common. Just as Moshe was close to Pharaoh, so too was Yitro. Yitro was one of Pharaoh’s closest advisors. Moshe was an advisor in that he was a member of the family. Just as Moshe was eventually forced to flee Pharaoh’s wrath to avoid retribution, so too was Yitro. But we’re getting ahead of the story!

Before Yitro fled from Egypt, he was actually a friend of Pharaoh (or at least as much of a friend as anyone could be, to the ruler of Egypt). Pharaoh would often walk with Yitro and they would discuss things of importance. One day they were walking through the marketplace, and Yitro saw two young girls who were for sale. The girls were twin sisters and remarkably beautiful, so beautiful in fact that Yitro suggested they purchase them. Pharaoh would take one of the girls, and Yitro the other (Midrash Talpios, Bithia / Zohar). The girls however, were not purchased as slaves. Rather, they were adopted and made daughters.

One of these girls was named Batya (Bithia) and she became the “daughter” of Pharaoh. The other girl was Tzipporah who became the "daughter” of Yitro. You may remember that it was Batya who would latter retrieve the reed boat from the river (with Moshe) after it was set adrift to save him from Pharaoh’s decree concerning the death of the first-born males. Batya would later marry Calev, and Tzipporah would later marry Moshe. Keep in mind that Moshe was with Batya in Pharaoh’s house. Since Batya and Tzipporah were twins they looked  alike. So naturally, when Moshe was forced to flee from Egypt and gets to Midian, he is surprised when he stumbles upon Yitro’s “daughter,” the young woman who is the twin sister of the “mother” who raised him. This is why the Midrash says that “Moshe married his mother.” It is not referring to Yocheved (his biological mother) or even Batya (his foster mother) but to Tzipporah who was Batya’s twin sister. But again we’re getting ahead of the story!

Since Tzipporah was not Yitro’s biological daughter, and because of her beauty, Yitro was evidently not anxious to see her given away in marriage. He therefore placed a condition upon anyone wishing to marry her. That condition is a story in-and-of itself, and it is here that we find a connection to God’s Name. You see, when Yitro fled the wrath of Pharaoh, Tzipporah was not the only thing that he took. Pharaoh had an amazing staff (sceptre) that he “inherited” after the death of Yoseph (a sceptre being one of the symbols of kingship). As the story goes, this ScePteR (of SaPhiRe) was the very same one that God had given to Adam. This scepter and a certain mantle were given to Adam in the 216th year of the first millennium as explained in the post on Bereishit and Noach, and so we see our first connection to the 216 letters of the Explicit Name. These items were the symbols of kingship (of the shepherding kind) that would be passed down to certain descendants (a facet of the birthright) until it finally reached Avraham, Yitzhak, Yaacov and eventually Yoseph.
The status of royalty (and scepter) went to Yehuda. The sceptre is mentioned in Genesis 49:10, which says that “the sceptre shall not depart from Yehuda, nor the ruler’s staff from between his legs.” The birthright however went to Yoseph (I Chronicles 5:1) and "the garments of Adam were [also] given to Yoseph" i.e. the mantle (coat) given to him by his father Yaacov (Bereishit Rabbah, Targum Yerushalami).   

As mentioned above, Adam received this mantle and scepter in the 216th year of the first millennium. He passed it to Seth (the gilgul of Hevel) after he had walked the earth as a man for 216 years, as his father before him (again see the post on Bereishit and Noach for details). Its counterpart (the royal mantle) was given to Yoseph in the 216th year of the third millennium). Each event corresponds to the number of letters of the Explicit Name, and both demonstrate the significance of its possession.

It was therefore perfectly natural for Pharaoh to covet this sceptre and the title that it implied (assuming he understood its significance). So too did Yitro, but apparently for different reasons (since it was made of sapphire) which is why he stole it from Pharaoh before fleeing Egypt. 

When Yitro arrives in Midian and settles there, he uses his powers of occult to plunge the staff into the bedrock behind his house. There it would remain until one was found worthy to pull it from the stone, someone who would unite his people and lead them to freedom; and someone worthy of marrying his daughter Tzipporah. If that sounds familiar, it should. It is the premise of the Arthurian legend (King Arthur of mythic renown). Indeed the story of Moshe was taken into the diaspora by Jews who were fleeing roman persecution. Many of these people ended up in the British Isles (the origin of the term brit-ish, is itself found in the Hebrew words for covenant (brit) and man (ish). The story of how Moshe came to remove the real “sword in the stone” is rather interesting. There were many men who desired Tzipporah, but none were able to pull the staff from the ground. One day after Moshe arrived, he was walking through the garden and saw this unusual staff. There were strange marks on it which tradition says were the letters of a mystical Name of God. The Maharal says that it consisted of 10 letters corresponding to the 10 sayings of creation and that the [polar] opposite of each letter was a letter pertaining to one of the 10 plagues that Moshe would see when he returned to Egypt to free the people from bondage. But once again we’re getting ahead of the story!

When Moshe grasped the scepter, the power preventing it from being removed from the ground by anyone but God’s intended, immediately yielded to the one who was destined to possess it. Tzipporah married Moshe and the rest is history (except of course the real identity of the mythical King Arthur in British mythology). The above stories are loaded with allusions that one could contemplate without end. If you remember anything from this post, remember that the scepter—which was the symbol of kingship not only for Israel, but of all mankind—the scepter, with it's inherent connection to the 216 letters (as detailed in the post on Bereishit and Noach) —the scepter, that was passed from king to king before and after the flood—was miraculously pulled from the stone only by Moshe, who was the intended leader of Israel. Also remember that the star tetrahedron is a mathematic or geometric representation of the merging of male and female, which is a form of marriage like the marriage of Tzipporah and Moshe.

Now, about that sceptre....

 It is said that the sceptre (or ruler’s staff) was created on Friday evening (the 6th day) on the twilight of creation, like the measure for any given dimension of the combined cubic form of the luchot (6 handbreadths). Adam received the sceptre while he was in a garden (the Garden of Eden) just as Moshe retrieved it from a garden (at Yitro’s). When Adam died it was given to Enoch and after Enoch, it was given to Noah’s son Shem (who brought it aboard the ark). Shem gave it to Avraham and Avraham to Yitzhak. It was eventually given to Yaacov who brought it to Egypt during the famine (in the Hebrew year 2238). Yaacov bequeathed it to Yoseph but when Yoseph died it became the property of Pharaoh, who acquired all of Yoseph’s belongings (Shemoth 3, 2:21 Me’Am Lo’Ez pg. 67).


It is said the Yitro desired it because it was made of sapphire. Sapphire? In Hebrew, the word is “sanphirinon” (Shemoth Rabbah 8:3) spelled סנפירינון (samech-nun-peh-yud-resh-yud-nun-vav-nun sophit) which comes from the greek word σαπφειρινον meaning “sapphire-like.” 

Sound familiar? It should. The substance is the same as that of the block that Moshe saw under the throne of God (in Mishpatim) which was later divided and brought down as the luchot (6 handbreadths x 6 handbreadths x 3 handbreadths times 2 tablets = 216 or the same number of elements in the matrix as there are letters in the Triad Name). It is the substance with a clarity of “72” having a trigonal (three-sided) crystalline structure that alludes to the Signature of the Architect (see the post on the nature of sapphire).

There are people who would like to know where this scepter is today. However, I very much suspect that it will not be found at all. Rather, it will seek out the individual to whom it belongs at the proper time, much like the anointing oil that fled from Ishai’s sons, but flowed toward David HaMelech.

In the meantime, since this blog is about the mathematic and geometric Signature of God’s Name, it is at this point worth mentioning something that is referred to as “the emblem of fractal geometry,” which some mathematician’s have referred to as “the Thumbprint of God.” It is the "end result" (assuming it actually ends, which it does not) of an applied formula pertaining to a form of geometry that seems to exist somewhere between dimensions. What is unique about this form of geometry is that its most basic component is a "triplet," best represented by a broken line and fixed by two identical additional lines. However, it is also represented in triangular form, for example, in the Sierpinski fractal mentioned in last week’s post. All of this might sound cryptic, but what it means is that no matter how infinitely large or small (the number of iterations) may be, they can be represented by the same two-dimensional elements. Those elements are the components of a magen david, which is a shadow of the star tetrahedron (the three-dimensional construct to which we’ve referred so many times, because of its connection to the letters of the Triad Name.) One of the best examples of fractal geometry in action is shown below. This one is referred to as the Koch Snowflake and the example is animated to the 7th iteration.

What this amounts to is the fact that mathematicians all over the world have been staring at this concept for many years without ever realizing its underlying significance, or that the geometry has a connection to the letters of God’s Name. Certain curves in fractal geometry are a prime example. The 20 segment curve where DS = 2.160 (to the 2nd decimal place) and the step in the generator is minimal (k = 2) is shown below. This equates to a 2-dimensional orthographic projection of 1 side (of 8 sides) on the star tetrahedron, that subdivides into 72 triangular corners. No one seems to have noticed the connection to the royal seal (magen david) or the 216 letters of God's Explicit Name.

The large upside-down triangle in the middle
is the two-dimensional shadow of
the stellation of the opposing tetrahedron

A mathematician by the name of Benoit Mandelbrot (Yale University) (who revealed the M-set) is really the father of fractal geometry. It was he who coined the term fractal. Mandelbrot was a Jew who grew up in Nazi occupied France. He spent 4 years eluding capture and deportation to the camps. When he was young he was fascinated by visual geometry. It was from this fascination that fractal geometry emerged.

Fractal geometry is actually a whole new kind of mathematics and it makes some traditional mathematicians a bit nervous. Unlike traditional math that defines smooth curves and comfortable shapes, fractal geometry can define everything in the universe from the craggy projections of mountains below to the movement of the clouds above, in fact literally everything. If you think the mathematic or scientific community is unaware of this, think again. It has created a firestorm of controversy! For more information on fractal geometry and its significance, watch Nova Season 36, Episode 4, entitled "Hunting the Hidden Dimension."

Meanwhile, in consideration of all the above (and in the interest of curiosity) let’s advance a hypothetical description of the sapphire sceptre. It is for the most part a story or fable; a parable of sorts (for purpose of instruction) the kind of tale that one might tell to children (and mathematicians) about what the sceptre might look like, and those who were destined to inherit it. 

Like all stories, this one starts at the beginning and so we’ll start with the usual: “Once upon a time,” and add that there was a king who wished to give his son the keys to the kingdom. Along with that birthright, he would provide his son (and his son’s descendants) with the symbols of kingship which included a sceptre and a royal mantle. The king wished to hide his signature within these things so that if the identity of the rightful heir was ever challenged, the signature could be revealed and remove all doubt. And so he created a scepter, a staff by which his descendants would be known, a staff that a shepherd might use to protect his flock. 

The king in this fairytale was much more than just a king. He was also the mathematician of mathematicians, and so he decided to place his signature upon the staff in these terms, so they would match the numbers that not only reflect  the letters of his name, but the geometry of the royal seal and the official documents and records of the kingdom.

To that end, he made a staff with 3 sides, like a triangle (a 2-dimensional shadow of a tetrahedron) where the length of each side was 3 “fingers” (3/5th’s of a hand of 5, and fractionally the same as 6/10ths, or ‘.6’ of one hand, which happens to also be a static measurement of 5.236 centimeters, if one bothers to put his fingers to a calculator).

He would make the length of each side equal to 24 handbreadths. That way, the combined length of the 3 sides would be 72 handbreadths (alluding to his name). However, 72 handbreadths also just happens to be 2 x π (Pi) in meters which is one of the fundamental aspects of mathematics.

The 24 handbreadths of each side (that are each 3 fingers in length) therefore end up being .666 x π (Pi) in meters (a little more than the height of a man). The 3 fingers and the .666, together would also bring to mind the 3sixes” describing the measure and the ratio of the king's blueprint (6 x 6 x 6) that would be used to define the kingdom.

6 x 6 x 6 Handbreadths

A handbreadth is 1/6 of a royal or sacred cubit. It is 1/6th of 1/6th of π (Pi) meters. That's 8.72666 centimeters (there are 6 of these handbreadths in a cubit). Please note the sequence of integers in the fractional portion: 8.72666. Thus, the length of 3 “fingers,” would be 5.236 centimeters which coincidentally happens to be 10 times the ratio of a cubit to a meter (which is .5236) as defined within the primordial torah (luchot) as the ratio between the volume of the sphere within, and the cube without (that ratio being well known in mathematics). Seriously? Must be a coincidence!

You may already understand the meaning of this fairytale. The king is God and the kingdom is the physical universe (creation). The blueprint for the kingdom is the combined cubic form of the luchot (the principle having been adequately demonstrated in the post on the primordial torah).
The combined cubic form of the luchot was coincidentally .5236 meters per side (6 handbreadths = .5326 meters). When it was divided and given to Israel it would have 10 commandments (just as the measurement of any given side of the sceptre would be a factor of 10 in relation to the aforementioned ratio). All of the numbers for our hypothetical sceptre allude to the King’s system of measurement, by which all things are calculated and compared, both physical and non-physical.

The 3 original or primary sides that are each 3 fingers in length (and 24 handbreadths in length) further allude to the King’s Signature (in the geometry of the star tetrahedron) since it has 24 small triangular faces that ultimately define (3 x 24 or) 72 triangular corners (72 x 3 = 216) as depicted in one of the figures above dealing with fractal geometry. The Signature would thus be hidden from the casual observer.

Click to Enlarge

You may  remember that in the narrative of our story above, we said that when “the king” designed the scepter, he started with a triangle of 3 sides. In the picture above, you can see what happens when the fractal set previously mentioned is applied to just the third iteration. There are many possibilities. I like this one because it so eloquently reveals the mathematic and geometric connection between the Name, the royal seal (magen david) and the luchot.

Needless to say, the above story is just a story, except for the mathematic and geometric correlations that do in fact connect to God’s Name; and the substance of the sceptre actually being like-sapphire, which it is; and the fact that the length of 3 “fingers” is exactly 10 x .5236 centimeters; or that the ratio of those 3 fingers to a hand (with its 10 fingers) is 6/10ths (.6) and also 1/6th of the ratio of a cubit to a meter (.5236); and that the sapphire cube that is 6 x 6 x 6 handbreadths really is a cube of 1 cubit, or .5236 meters; or that the 10 commandments that were part of the divided cube (luchot) were “a measure” by which man is judged; all of which is factual. 

Nevertheless, the description in our story is just hypothetical. It is full of coincidences pertaining to actual facts and thus hypothetical. Whether it is in anyway true, is anyone’s guess. It is posited here, because it is perfectly acceptable to draw logical inferences from known facts. And besides, it made for a good story and served as the vehicle for revealing how certain fundamental numbers and ratios really do correspond to God’s Name and the many things mentioned in the Torah!


Author's Note: The scepter that is modeled above (shown without the head so that the facets of the staff can be examined) is 6 handbreadths in length (like each dimension of the evan shetiyah). It has 48 external facets with a total length to the 288 handbreadths, like the "288 sparks" (explained by the ARI) that equate to the shattering of the vessels. The total length of these facets is equal to the number of square handbreadths on the surface of the luchot (288 square handbreadths). The number 288 is the sum of 216 (the number of letters in God's Name) and 72 (which is the number of triplets pertaining to this Triad Name). The head of the scepter (not shown) is a sapphire star tetrahedron.

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