The Ultimate Reality Behind the Universe

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 2(n-1) ways, and so since in this case n = 22 letters, there are:

221 = 2,097,152 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, 2,097,152 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…

One Way

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? 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…”


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:


  1. 900
  2. 810
  3. 729
  4. 656.1
  5. 590.49
  6. 531.441
  7. 478.2969
  8. 430.46721
  9. 387.41589
  10. 348.674301
  11. 313.806871
  12. 282.426184
  13. 254.183565
  14. 228.765209
  15. 205.888688
  16. 185.299819
  17. 166.769837
  18. 150.092854
  19. 135.083568
  20. 121.575211
  21. 109.41769
  22. 98.4759212


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.   Splitting the Alef-Bet

We are assuming all 22 elements of the alef-bet existed as a single conjoined entity before they were separated, in a similar way that Light is a whole before it is broken down and separated, or filtered, into a whole spectrum of different electro-magnetic frequencies like blue, red, ultra-violet, radar, radio, e-rays, gamma rays etc.

So obviously, just as in the G-d given—unless, of course, you believe Man created light—electro-magnetic spectrum above, the order of the letters with their respective frequencies must be important on their own. It must also be important where they fall in the alphabet as well, so they can interact and blend in with their neighboring letters, just like red and yellow sharing properties and combining to form thousands of shades of orange.


This means that in order to separate every other letter from its neighbors a filter had to be applied and the bonds between the letters broken.

And once the alphabet is split apart, we can apply their corresponding numerical values in order to reveal the energy being released and what it means for us.


From א to ת and 1 to 400.


When we assign these fixed number values to the split alef-bet we get:

The two sets of 11 letters each, which form two columns, adding up to 625 and 870 respectively for Alef-Shin (א  – ש ) and for Bet – Tav ( ב  – ת ) for a total value for the alef-bet of 1495.

Once separated the letters can be taken as two separate columns or rejoined into a single line of letters.

Odds and Evens

In their natural sequencing from Alef(א) to Tav(ת) the Hebrew letters have a specific order or ordinal place in the alphabet from 1st to 22nd.

By splitting the 22 Letters down the middle, we are ostensibly splitting it into Odd and Even ordinal values.  It is a mathematical property of summing up the consecutive odd integers that they form natural squares. For example, (1 + 3) = 4 or 22, and (1 + 3 + 5) = 9 or 32 and so forth through 112.

 OK, They are Split, Now What?

The first chapter of the Torah was very much about splitting/dividing/separating things in two parts, but as with all chemistry, physics, mathematics and cooking, it is not the splitting so much as the proportions into which they are split that really matters. When we examine the natural proportions into which this simplest of splitting divided the Hebrew alphabet, we get very interesting results.  The first thing we need to do is compare the set of odd ordinal value letters to the entire alphabet.

This is the proportion, the ratio, of the smaller segment (625) in terms of its numerical value to the total value of the entire alphabet (1495), in other words, the ratio of the odd ordinal letters to the total letters.  Therefore, the Alef-Shin (א  – ש ) segment of the alphabet has a total value equal to 42% of the whole Alef – Tav(א  – ת  )

Next, we can compare the ratio of the values of the odd letter set to the even letter one, one side of the split alphabet to the other.

This is the proportion, the ratio, of the smaller segment in terms of its numerical value to the larger segment, in other words the set of odd ordinal letters compared to the even set. Therefore, the Alef-Shin (א  – ש )  side of the alphabet has a total value equal to 72% of the Bet – Tav ( ב  – ת ) side of the split.

So right off the bat, we see that this simplest of splitting of the Alef-bet into two natural proportions has yielded representations of the 42-Letter Name and the 72-Names. The same Names, which the kabbalists tell us, were used to split the Red Sea, and which were placed in the breast plate of the Cohen HaGadol in order to help guide the Israeli nation, and as we have seen, they are the same ones were used in the design of the Shema, Amidah prayers, and the Torah. Yet, this is barely the beginning.

Please note that the resultant proportion (ratio) of the larger side to the whole alphabet is necessarily:

And that the resultant proportion (ratio) of the difference of the set of even letters less the set of odd letters is necessarily, the difference between them:

Both these resultant proportions, 58% and 28% and the numbers (58 and 28) that they represent will become abundantly relevant momentarily, though we have already seen them woven into the square root sums of the 72 Names.

Rabbi Chaim Vital of blessed memory stated that all Torah light is spread by squaring and that is exemplified by the Alef-Shin(א  – ש sequence: (1 + 3 + 5 + 7 + 9) = 25


The first 5 letters of this sequence total 25, or 52, which is significant because all 11 letters sum to 625, which is 252. Now this would all be nothing more than interesting if the Torah was not called the 5 Books of Moses, and if 5 was not the square root of 25, and 25 was not the square root of 625, and 625 was not the square root of the exact number of verses, words and letters in the Torah (390,625).


Therefore, by splitting the Hebrew Alphabet in two, we have so far gotten the 42 proportion, the 72 proportion, and what could be said is the energetic source of the Torah, 625. This makes sense since the gematria of the Hebrew word for “The Crown (H’Keter),” the highest of the 10 sefirot (dimensions) is 625. Alternatively, we could say H’Keter (הכתר) was assigned to 625 accordingly. Whatever that connection really is, what there is no denying is that .625 = the exact fraction 5/8 and that 390,625 = 58 and 58% was yet another one of the specific ratios given by this simple splitting of the alef-bet.

If we did not have so much more material to cover, we might linger on the fact that the total and exact number of verses, words and letters in the 5 Books of Moses (390,625) is precisely 58, which is 5 raised to the 8th power. You can find much more on that in The Genesis Prayer and in numerous articles at It could also be said that the Torah being designed around 58 is thus possibly analogous to the 8-dimensional root projection of the super symmetric 248 dimensional E 8 Lattice tied to string theory and other quantum models of the greater universe, especially with the the Phi proportions designed into it, but all that will be more apparent as we go on.

Just in case we thought for even a second that this was coincidence, the Creator designed the 304805 letters of the Torah in just such a way so that their total gematria sofit—using those 5 final letters we spoke of earlier—worked out to (5800.54)2 or (5800.02 + 625).  Here again we find that pesky .54 remainder yet again, the one we saw with the sum of the 144 square roots of the 72 Names, 1000.054. Hmm!

Imagine the enormity of the task of making sure there was just the right number of letters and words assigned to just the right amount of verses covering all 5 Books, divided into 54 portions.  That is nearly 400,000 separate and overlapping elements to juggle. If we consider all the underlying mathematical encoding, which utilizes a multitude of different gematria ciphers and quantitative instruments there are millions of elements.

When we listen to the Torah, we need to pay attention to every letter, knowing that there is a unique spectrum of energy in each one, and that each one was placed exactly where it is for specific reasons. Like with the electromagnetic spectrum, if we tune into the right frequencies, the light we can receive from the Torah is varied, powerful, and endless. The Kabbalists explain in the Zohar and elsewhere that the Hebrew vowels–a series of dots and dashes–help fine tune and decide which frequency within their specific ranges the individual letters will connect with. The cantillation marks with their resultant changes in how the letters/words are sung help string together various frequencies within those ranges.  For those unfamiliar with the Torah, it is hand-scribed as it has been for 3330 years without modification and without the vowels and cantillation marks that the reader must memorize and superimpose in his mind.

Is it possible that really smart men 3330 years wrote all 80,000 words by trial and error on cured animal skins and ink made from crushed insects, and that they also made all those calculations to 6 or more decimal places without even the most rudimentary counting devices? If you think there is even the remotest possibility of that, you then have to ask yourself to what end would they have done that monumental task? Seems like a whole lot of work to put into something that you have no idea if it would survive intact into the near future, let alone thousands of years far enough into the future when the technology would finally be invented to decipher all those encoded equations and algorithms.

It is a moot point because the task would have been impossible; nevertheless, we have digressed. It is said that G-d is on the details, so returning to the simple splitting of the 22 letters of the Hebrew alphabet into the same 11/11 odd – even proportion, we can put it under the microscope of small gematria, whereby each value assigned to a letter is reduced to a single digit by dropping the zeros (i.e. 1 is 1; 10 is 1 and so 100 is 1). Rather than add up the digits, which we could do as well, we are going to use the more graphic aspect of this cipher and take alef-bet-gimmel as 123 and not 1+2+3.

Taking one from column A and one from column B gives us (12+34+56+78+91+23+45+67+89+12+34) = 541, the gematria of “Israel.” And if we did add up that small gematria (1 +2 + 3 + 4…3 + 4) of the 22 individual letters it would total exactly 100, which is nice as a natural square (102), though much more astounding is that 541 is the 100th Prime number. As astonishing as that is, how much more so is it that the numerical value 541 is found exactly 625 times in the Torah.

It is beginning to feel as if G-d put a whole lot of thought and purpose in Creating the alef-bet, and in designing it so that it would split in just the right way to give birth to the Torah.  Then like fractals, when we zoom into a detailed aspect of the Torah we see a repetitive pattern in which the sum of the 11 initials (דצכעדשבאחמב) of the 10 plagues also sum to 541, Israel, with their ordinal value also totaling 100. Then peering a deeper we see that the last 2 initials (מב) of the final plague equal 42.

To wrap up this section, we recall that 625, both the core of the Torah and the sum of the set of 11 odd ordinal value letters, is also 25 squared, which itself is the sum of the first five of those letters. This makes the number 25 the 4th root of the Torah’s total number of words, letters and verses. The reason this is significant is that the average of the first 25 prime numbers is exactly 42.4, yet again the numerical value of Moshiach Ben David and also the sum of all 22 Hebrew letters (424.242).  Moreover,  25 x 4 = 100, which is the sum of the small gematria of those same 22 letters, while the 100th Prime number is the number 541 (Israel) and the numerical value 541 is found 625 times in the Torah.  This ties together very nicely, but only if it were designed that way.

Of course, this would have had to have happened several thousand years before the Israelites supposedly started using the decimal system, except that much of what we discussed above does not work unless the decimal system is used.

So yes, it could only have been designed this way, and it had to have been designed this way from the actual Creation of the Hebrew Letters and from the assigning of their numerical values.  This was designed even before the Torah was designed to integrally incorporate them in every way imaginable. The question that remains is why?

In Part III we will begin to incorporate Phi.

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