Here we go. The articles in this promised series are going to be shorter and denser segments and come much more often. They are already written, and the time has come. There will be a separate page posted after the first segment so you will not have to refer back to each article as it is published.
Part I The Basics
In the beginning…G-d split the waters, the light, the time frame (more about that later), even Man, but before all that He needed to split the alphabet. The kabbalists tell us that the Red Sea (Endless Sea) was split from the very beginning, which they explain is the only reason why it could be physically split 2448 years later. They also tell us that on Moses’ staff were written the 72 Names and the 42-Letter Name, which were used to split the waters. But before even those essential Names existed there was the Hebrew Alef-bet, and like an egg, it needed to be cracked open.
So, what if we could show you that there is a single way to split the 22 letters of the Hebrew Alef-bet in two that would give rise to the 42-Letter Name, the 72 Names, the Torah, the concept of Israel, the primordial mathematical constant phi, the 13 attributes and much more?
This proof/study comes from a mathematical project my daughter and I have been working on together and has grown into this series of articles we prepared, the first of which is presented today. If you are mathematically oriented, please enjoy these pages to their fullest and please dig deeper and expand wherever you feel compelled. We cannot dwell on any one topic or point very long as we have a lot of territory to cover. While we hope you will see the profundity in each point we make, given the subject matter, we acknowledge that we are only scratching the surface. If you are not mathematically inclined, please do not dwell on any one equation or concept; try to take in the overall picture we are presenting, which is the real point of this paper.
First, we need to ask how many ways the 22 letters of the alef-bet can be split into 2 separate groups?
Using the formula n-subset-2, we get 2n – 1 ways, and so since in this case n = 22 letters, there are:
222 – 1 = 4,194,303 different ways.
We are going to make the leap here and assume that G-d exists and Created the alef-bet along with everything else. You do not have to. You can substitute whatever force of Creation you believe. As these articles progress, please check back in with your beliefs and assumptions as they may indeed change with what we are revealing. Nevertheless, 4194,303 different ways are a lot of options G-d was confronted with after He created the Hebrew alphabet. Abraham Avinu called them “the 22 building blocks” in his book, The Sefer Yetzirah (The Book of Formation), written 3800 years ago. We will soon understand why.
OK, so if we, or G-d, wanted to divide the 22 letters evenly into 2 equal size sets of any 11 letters each, we would use the combination formula, in which n! represents n (a number)! (factorial) meaning a multiplication series of all the integers up to that number (1 x 2 x 3 x 4…n) and thus:
705,432 is still a whole lot of choices. Yet there is only One (1) perfect one.
According to the writings of innumerable kabbalists, including R’ Shimon Bar Yochai in the Zohar, R’Isaac Luria, R’ Chaim Vital, R’Abraham Abulafia and the Baal Shem Tov, all of blessed memory, there are two matrices of Hebrew letters that were present at the beginning of the Torah and of time. Both are weaved into our daily prayers and prayer books: the 42-Letter Names (Upper and Lower) and the 72 Names (Triplets) matrix of 8 columns by 9 rows.
The Upper 42-Letter Name is comprised of 3 iterations (spelling out expansions) of the unpronounceable Tetragrammaton (יהוה).
The 3 levels contain 4, 10 and 28 letters respectively.
The Lower 42-Letter Name is comprised of the 42 initials of the Ana B’koach prayer and is arranged in a 6 x 7 matrix, which according to the Ramchal, matches the innermost gate of the Holy Temple (6 x 7 cubits) to the Holy of Holies.
The Baal Shem Tov tells us these 42 letters connect us to the 42 journeys of our soul and the 42 journeys that the Israelites made in the Exodus from Egypt to Israel, each journey delineated with the prefix mem (מ) and bet (ב), as in the Shem MemBet (מב) of gematria value 42.
It is because of these Names that the first paragraph of the 1000-letter Shema prayer, which is directly excerpted from 3 places in the Torah, has 42 words and the 2nd and 4th paragraphs have 72 words each. It is also why the first paragraph of the Amidah has 42 words, as does the last large paragraph, which in turn is flanked by two isolated verses of 42 letters each.
The 72 Name matrix is encoded into the 3 consecutive 72-letter verses (Exodus 14:19-21) that describe the splitting of the Red Sea,
By the way, if you sum up the square roots of the gematria values of each of these 72 triplets they total 720.0 and the sum of the square roots of the sum of each of its 9 rows is 280.0
The significance of this perfection, especially the tiny remainder .054 will be apparent and explained shortly, suffice to say this precision (1000.0) in a calculation that involves the irrational square roots of 432 different components is impressive. Moreover, the fact that both the 72 Name matrix and the 1000-letter Shema share this number 1000.0 in common is not causational, nor is it coincidental; the reason for 1000.0 will also be revealed shortly. In it lies a secret to unlocking the future and to understanding why, in a universe based on 10 sefirot (dimensions), and on base 10 mathematics to interpret it, there must be exactly 22 letters (building blocks of unique energy levels).
The square roots of the 216 number values, each ranging from 1-400, corresponding to 216 specific letters in the 72 Triplets, do not randomly line up this way, and do not form 3 lengthy very coherent Torah verses describing G-d’s actions in splitting the Red Sea unless an enormous amount of computational time and energy went into planning it. Just saying…
Since “G-d is One (Hashem Echad),” could there be One of those 705,432 different ways to split the 22 letters of the alef-bet that would reflect the numbers 42 and 72, and the numerical value for Israel, 541, and also be sequential? Also tie in that pesky remainder of .054? And maybe do even more, maybe a lot more? Indeed, there is, and it is the simplest one of all: Odds and Evens.
Using their ordinal (place count) values, we can split the 22 letters right down the middle into odds and evens, just like the Covenant of Halves, and just like the refrain in the Sefer Yetzirah, “…with a single covenant right down the middle…”
There are exactly 248 ways to split the letters into the same 42 and 72 proportions, but they are not as simple and clean and not sequential. The number 248 will be very significant to us later in the paper and we are suggesting that this is not coincidental. Neither is the fact that there are 120 of those ways that also yield the numerical value for Israel, 541, which we will explain shortly.
In order to understand the letters, we must understand the language of the universe. Just as soon as there were Hebrew letters there were specific number values assigned to them. The assigned numerical values ascend from 1 to 10, then 10 to 100 and finally from 100 to 400 according to a set exponential curve. The is the inverse of a logarithmic curve as will become important much later in this paper.
From א to ת and 1 to 400.
While we may think that assigning these values to the letters according to an exponential scale and using base 10 mathematics was very logical to the ancient Kabbalists it was a depart from the base 60 Babylonian counting system, and more significantly, it was far from random or arbitrary.
When we say the numerical values associated with each of the 22 letters are on an exponential scale, we mean they increase in value exponentially from letter to letter. In other words, they fit an exponential curve, such that y = abx where y is our letter value (for example alef = 1) and x is the ordinal value of any of the 22 letters counted from 1 -22 (for example alef(א) is 1, as the first letter), and b is the factor that guides the exponential rate of growth. This does not mean that every letter value falls directly on the curve, only that the curve (exponential model) closely fits the data (the letter values), and that the starting value (1) and ending value 400 for the letter tav (ת) are directly on the curve and in this case, the 11th letter caf (כ) of value (20) is bang on as well. It is also the square root of 400 (tav) Astonishingly, in the case of the alef-bet, that exponent is 1.313, which just so happens to match the year 1313 BCE when the Torah was received at Mt Sinai . That Mt. Sinai has a gematria value of 130, and that 13 is the gematria value of echad (One) is definitely most significant though we have a lot more to prove before we get there.
The Hebrew letters Alef, Caf and Tav anchor the curve at its ends and midpoint, while the other letters are slighting above or below the curve, This is because they are representations of energy, zones on a spectrum not fixed points, which believe it or not in mathematics is a very difficult concept. Think of the color green, there are an infinite number of wavelengths for it on the visible light spectrum, all falling within a zone of about 495 nm – 570 where the color takes over. The Hebrew letters are the same; they represent a narrow collective or bundle of similar energy frequencies, each letter at least as different from green is to yellow.
There is yet another reason we can state the values associated with the alef-bet are not arbitrary. Unlike English, these 22 Hebrew letters form the initials to their 22 names. For example, the letter alef (א) is spelled out (אלפ), whose numerical value when we sum all 3 letters is 111, in itself pretty symbolic for the 1st letter of the alef-bet.
While the example above is quite illustrative, there is a slightly different gematria cipher that extends that exponential scale 5 more places from 22 to 27 letters because 5 of the letters (ךםןףץ) take on a different shape when found at the end of a word, and thus the scale extends to 500-600-700-800-900. When we sum up the 22 irrational square roots of the spelled out 22 names of the 22 letters, we get exactly 424.242…
If you are a geek, or studied any kabbalah whatsoever, that an answer about the knowledge of the universe would tend to 42, would not surprise you. That this sum of 22 irrational numbers, which should have been quite difficult (next to impossible) to calculate thousands of years ago, sums to exactly 424.242, may raise your eyebrows a bit though. Nevertheless, if you are a geek and maybe a kabbalist too, you would know that the digit string …42424242… occurs at digit #242424 within the mathematical constant Pi (3.14….) and the symmetry with 424.242 is just a bit too contrived not to have been embedded there for some reason. It begs the question, though, how would anyone other than G-d have been able to embed that, or even have known about it 5000 years ago?
Or maybe G-d just loves algebra and knew that for X ≠ Y no other number satisfies XY = YX than 42 = 24 . For now, we will only mention the obvious connection to the #42, and that 424 is the gematria value of “Moshiach Ben David.”
We must pause and ask ourselves, before we go ahead and split the alef-bet, could these letters and counting system possibly have developed organically from pre-existing hieroglyphs as some would have you believe? With the little we have shown so far, the odds against that are astronomical. So who gave us the Hebrew letters and told us what their specific values and energy levels are?
The Hebrew letters are representations of different forms and levels of energy, according to the 10 sefirot (10-dimensional structure of the universe), and so too are the associated numbers assigned to them. This is why the relationships between them are extremely important to our understanding of the universe. This is also why they are directly related to all the core mathematical and physical elements of that universe, which we will soon prove.
The 10-dimensional structure of the universe is a modern and highly accepted concept of physics based on super string theory; it is also the basis of Kabbalistic thought, and was first described in the earliest kabbalistic writings, including Abraham’s Sefer Yetzirah 3800 years ago. In it, Abraham spends a lot of time describing “the ten Sefirot of nothingness.”
The predominant unified theory in physics for decades now has been the Super String theory, in which the smallest elements of matter are thought to be comprised of intertwining and bundled vibrating strings of energy set to 10 different levels of energy frequencies. Mathematicians have proven that this theory only works in a universe of 10 dimensions of space plus one additional one of time. There are dozens of ancient Kabbalistic texts that describe the same structure for the universe, including the addition of the 11th dimension in the tree-of-life, which they call Da’at (Knowledge). Connecting the bundled Kabbalistic dimensions are the 22 pathways of the tree of life, each connected to a specific letter of the alphabet. Moreover, and oddly symmetric, is the fact that the 3 initials of the central core of the bundled sefirot of that tree-of-life (Keter-Da’at-Tiferet) total 424. One could almost conclude that these early kabbalists had divine knowledge of the structure and workings of the universe.
Perhaps the alignment of the Hebrew alphabet with its beautiful exponential model and matching data points at the 1st, 11th and 22nd letters is a cosmic symmetry with the 11 dimensions, or with the 11-letter split we are about to show you. Or perhaps it is because of these 11 dimensions and the energies they represent that when the 22 letters are split in two, we get two juxtaposed sets of 11 letters, which when split just the right way tell a very compelling and revealing story.
That is a supposition we have yet to prove to you. What can show right away is that the 22 letters (levels) were formed in accordance with the 10-dimensional structure of space that they occupy. To keep it simple, every power of 10 represents a different dimension with 102 presenting a square and 2 dimensions and 103 representing a cube and 3-dimensional space. Every time we increase or decrease the exponential power of 10, we are either ascending or descending a level of dimensionality.
For this illustration we could start with any power of 10, but by starting with the kabbalistically complete number 1000, symbolizing 10 x 10 x 10 or 103, we are conceptually utilizing the kabbalistic concept of balance within the 3-column system. This system’s natural counterpart is the Proton-Neutron-Electron structure of the atom. It makes no difference whether we use 100 (102); 10 (101); 1 (100); or any result of raising 10n when n is an integer. Whenever we reduce any power of 10 by one order of magnitude in increments of 10% it will always take 22 iterations or 22 steps to get to the next level. To go from one dimension down to the next takes 22 steps:
It took 22 steps to get down to the 100 threshold, one order of power (103 → 102). If we were to continue another 22 steps of reduction by 10%, we would just cross the 10 threshold, and another 22 steps to get to 1, and so on and so forth. Therefore, it is obvious the numbers, or number of elements, 10 and 22, are mathematically intertwined.
Part II will follow shortly, in which we actually split the alef-bet.
Shabbat Shalom and Chodesh Tov!