We finished the previous article with the Taxicab Number, famous in mathematics because back in 1919 one of the brightest mathematicians, H. G. Hardy, tried to console a very sick colleague, the brightest mathematician of their day, Srinivasa Ramanujan, with a number he thought was inconsequential and that he saw on a license plate of his taxicab. Ramanujan recognized it as the sum of **2** cubes in two different ways (**1 ^{3}** +

**12**) and (

^{3}**9**plus

^{3}**10**). The Creator decided to make it the number of times that the value

^{3}**26**would be utilized in the composition of the Torah with

**26**being the value of the Name of G-d

*YHVH*(

**יהוה**).

That value **26 **is just one of the precisely **2 ^{10}** different word values in the Torah. In other words, the value

**26**occupies one vertex (point) of the

**2**vertices in a

^{10}**10**-dimensional hypercube. Is this possibly coincidental given the

**10**-dimensional space that string theory suggests we are living in? Probably not, considering that that specific amount, or sets of word values, apply to a specific number, or sets of words in the Torah. Those specific sets, when added together, give us the simple equation

**2**or

^{10}**1024**-word values plus the

**79,976**words equal exactly (

**79,976**+

**1024**) =

**81000**, which in turn equals (

**3**x

**30**),

^{3}**3**cubes of

**30**or

^{3}**27**,

**000**. It also equals (

**3**x

^{4}**10**).

^{3}The concept **26** is the value for the main Name for the Creator in the Torah, the *YHVH* (**יהוה**), utilized a total of (**1729** + **91**) = **1820** times. It is also integrally related to a cube, to the most basic cube, in that every **3**-dimensional cube has **8** vertices or corners, **6** sides or faces, and **12** edges, and (**8** + **6** + **12**) = **26**.

In the previous article, *The Path of One; The Path of the Creator*, we discussed that the Taxicab Number, **1729** was also (**1820** – **91**) and thus integrated into the Path of One that is based on **13**, the numerical value of *echad*, One. What we should now point out is that the component integers in those four cubes (**1 ^{3}** +

**12**) and (

^{3}**9**plus

^{3}**10**) or (1 + 3 + 1 + 2 + 3 + 9 + 3 + 1 + 3) equal

^{3}**26**.

Number Theory exists because numbers are concepts not fixed objects. You can temporarily assign numbers to the presence of a set of physical objects but once you remove an item in that set, the number is gone. While our universe and our entire existence is predicated on numbers, they exist only in the abstract, only in the mind of the Creator. We discussed in the previous article about Triangular Numbers that are so prevalent in the Torah how they reflect the concept that numbers never truly disappear but remain as omnipresent shadows. This is what we would call a memory, yet another concept that we cannot physically explain. These are memories in the mind of the Creator, the universal consciousness. There is nothing Man can do to change numbers or the laws of mathematics. No matter how hard we try the number 3 will always be the concept of 3, and (2 + 2) will always equal the concept of 4, no matter what symbol we use to convey that concept.

It thus behooves us to understand the best we can these abstract concepts and to accept them as gifts to help us better understand the nature of our existence. Otherwise, we are just going through life with our heads in the sand and might as well be ostriches.

That Path of One (**1** – **13** – **91** – **455** – **1820**) is based on repeatedly adding the cumulative values of repeated cycles of **13**, and as we learned it is integrated with the Names of G-d in the Torah. So, it is not surprising, even though it is not mathematically causational, that (**13 ^{2}** –

**91**) =

**78**= (

**3**x

**26**) or that (

**13**–

^{3}**1820**) =

**377**, the

**14**

^{th}Fibonacci Number, whereby the two differences (

**78**+

**377**) =

**455**in the Path of One, the value of the

**3**Aspects, or spelled-out Names of the letters, of the Name

*Ehyeh*(

**אהיה**), the highest Name of the Creator used in the Torah.

While at first the reference to the concept of the **14**^{th} Fibonacci Number and thus the field of Phi (*φ*) is momentarily out of place, nothing is out of place within the mind of the Creator. The concept or value **455** relates to the sum of the first **6** integer cubes. That sum, (**1 ^{3}** +

**2**+

^{3}**3**+

^{3}**4**+

^{3}**5**+

^{3}**6**) =

^{3}**441**or

**21**with

^{2}**21**being the value of the higher Name

*Ehyeh*(

**אהיה**), and

**441**being the value of

*emet*(

**אמת**), Truth. What connects this sequence, and these disparate concepts though is that (

**455**–

**441**) =

**14**or (

**1**+

^{3}**2**+

^{3}**3**+

^{3}**4**+

^{3}**5**+

^{3}**6**) +

^{3}**14**=

**455**.

And even more significantly for those who have been following this blog is that the number **14** is the central position in the *Alef-bet* and the Essential Cube of Creation, the Magic Cube of **42**, whereby all **27** horizontal and vertical values along all **3** axes and the **10** internal diagonals all equal **42**. These **27** positions coincide with the **27** ordinal values of the *Alef-bet*. We have covered this extensively and will be writing about it again in upcoming articles. Suffice to say for now that this means that every word in the Torah and in Hebrew can be derived from patterns and shapes within a **3 ^{3}** cube and that each letter in each word is bound to the concept of the Singularity of

**42**in at least

**3**different ways.

By the way, those **6 **cubes in the concept of Truth (**1 ^{3}** +

**2**+

^{3}**3**+

^{3}**4**+

^{3}**5**+

^{3}**6**) correspond to both the

^{3}**6**bundled dimensions of

*Zeir Anpin*and to the

**6**Faces of the Essential Cube of Creation, which along with the central

**14**

^{th}position equal

**378**, the numerical value of “He and His Name are One,

*Echad UShmo Echad*.” And each of those

**6**Faces has a total value of

**126**or (

**2**+

^{1}**2**+

^{2}**2**+

^{3}**2**+

^{4}**2**+

^{5}**2**), the perfect representation of

^{6}**6**-dimensional space, the

**126**cumulative vertices in all

**6**dimensions.

If we allow it, the Creator will connect all the dots for us. For example, the central **14**^{th} position and its counterpart in the *Alef-bet*, the **14**^{th} letter *Nun* (**נ**), connects to **13** different vectors of **42** Also, the total number of vectors of **42** that the **27** letters collectively always connect with regardless of how they are used in a word is **111**, as in the Name of the letter *Alef* (**אלף**), One.

Those **111** vectors total (**111** x **42**) = **4662** and when we add the collective **27** ordinal values or **378**, which is (**9** x **42**), the total works out to (**4662** + **378**) = **5040**, the exact sum of the Earth and Moon radii, **5040 **miles, which is also exactly **7** factorial or **7! **= (**7 **x **6** x** 5 **x** 4 **x** 3 **x** 2 **x** 1**) = (**120** x **42****)**.

Another example is found using a similar pattern and concept as above in that the cube of **26** less the square of **26** or (**26 ^{3}** –

**26**) =

^{2}**130**, with

^{2}**130**being the numerical value of Mt Sinai, where we received the Torah in

**1313**BCE.

It is only our own stubbornness that precludes our seeing the pictures being drawn for us.

The concept of **26** defines the basic cube and when those **26** elements of the basic cube are collapsed into a single edge of a new cube and a single square face is removed or lifted off that cube, the value of that result is **130 ^{2}**. To us, a cube is like a block that even babies can stack. To the cosmos, or the universal consciousness it is a geometric concept of a complexity beyond our comprehension.

In the previous articles we saw that the Creator besides being a Number Theorist also has a pension for all things geometrical, but we have only begun to scratch the surface. Those precisely chosen number of words are just one set of **3** quantitative elements of the Torah that equal exactly **5 ^{8}** or

**390**,

**625**, which is

**625**, and as we saw in the first article of this series

^{2}**625**is the sum of the values of the

**11**Odd interval letters of the Hebrew

*Alef-bet*.

Those **3** quantitative elements represent a hypercube of **8**-dimensions with **5** units per edge, making a **5 ^{8 }**octeract with a volume of

**390,625**.

Since the octeract has **1024** edges, it aligns precisely with the **1024** vertices of the **2 ^{10 }**Torah word value dekeract. If the simple

**3**-dimensional cubes have so much complexity and the entire Torah can be derived from a simple

**3**cube imagine what goes on with a

^{3}**10**-dimensional one.

There is a special property of **390**,**625** or **5 ^{8 }**and it has exactly

**8**factors, each a multiple of

**5**(5, 25, 125, 625, 3125, 15625, and 78125) and the sum of their

**8**inverses (1/5, 1/25…) equals

**1024**x 10

^{–5}. While the

**5**elements and the

^{8}**2**– or

^{10}**1024**-word values can take on specific geometric shapes in

**8**and

**10**dimensions, they also form networks of symmetric matrices.

That value **1024** that keeps coming is the also the square of **32** or **32 ^{2}**, which has been known since antiquity to be aligned with the

**32**Names

*Elohim*(

**אלהים**) in the Torah’s first chapter, the

**32**Names

*Elohim*(

**אלהים**) of Creation, which form the

**32**vertices of the

**2**or

^{5}**5**-dimensional Hypercube, and which the ancient Kabbalists called the

**32**Paths to Wisdom.

Now, it would be amazing if those **5 ^{8}** or

**390,625**quantitative elements also would have worked out to the sum of

**2**cubes, but they do not. They are off by

**30**from the sum of (

**52**+

^{3}**63**), as in the ordinal value (

^{3}**30**) of the Name of One,

*Alef*(

**אלף**) and the square root of (

**10**–

^{3}**10**), but we can assume the Creator had other intentions when He designed the Torah other than matching license plates. Nonetheless, the sum of (

^{2}**11**+

^{3}**73**) is off from precisely

^{3}**390**,

**625**by the square root of

**3**. To be clear, the equation is (

**11**+ (

^{3}**73**+

**√**

**3**/

**10**)

^{2}**) =**

^{3}**390,625**. What makes this seem purposeful is that the square root of

**3**, while always significant in mathematics, is also the diagonal of a Cube, specifically the Cube of

**1**whose volume is One, and moreover, the gematria value of the Torah’s first verse (Genesis

^{3}**1**:

**1**) that relates simply and accurately to both Pi (π) and Phi (

*φ*) is the

**73**

^{rd}Triangular Number, the sum of the integers from

**1**to

**73**.

The second of those **5 ^{8}** quantitative elements are the

**5845**verses. When we separate out the

**13**verses of the

**10**Commandments, about which we will soon explain in another upcoming article why they are a special separate entity, we are left with

**5832**or

**18**verses, a cube of

^{3}**18**per edge, which may be related to the

**1800**

*YHVH*(

**יהוה**) in the

**3**

^{rd}phase of the Torah, and given what we have seen about open cubes, to the result of (

**3**–

^{3}**3**) =

^{2}**18**.

Moreover, it is not a coincidence that there are **5** Books of Moses, or that those **5 ^{8}** quantitative elements also relate to the

**2**hypercube in that 1/

^{8}**2**= .00

^{8}**390625**, a fact the Creator wanted us to be well aware since the gematria of the Ark of the Covenant (

**הארן**) is

**256**or

**2**, and this is where Moses was told to store the Torah. The Ark (

^{8}**הארן**) is the inverse of the Torah in that

**5**=

^{8}**390**,

**625**and

**1**/

**2**=

^{8}**.00390625**, thus

**10**/The Ark = The Torah.

^{8}We may not be meant to ever understand these concepts fully, but we are meant to grasp that the Torah is our entrance to the universal consciousness and that every aspect of our existence is accessible through it.

These are not the only quantitative elements in the Torah and in addition to the **5 ^{8}** words, verses, and letters, we have the matrix of

**248**columns by

**42**rows that each Torah is scaffolded on. Taking out the

**16**blank rows between the Books, there are exactly

**22**rows and columns, a cube of

^{3}**22**, as in the

**22**Names of the Hebrew Letters.

The **27** Hebrew letters wrap up into a **3 ^{3}** cube. The

**5832**verses fold up into a

**18**cube, which is

^{3}**216**or

**6**cubes of

^{3}**3**. The rows and columns form a matrix that folds into a

^{3}**22**cube. The letters, words and verses in the Torah form a

^{3}**5**hypercube that fits in the

^{8}**2**hypercube Ark. The word values in the Torah form a

^{8}**2**hypercube while the word values and number of words form

^{10}**3**cubes of

**30**. Like triangles and Triangular Numbers, to the Creator cubes are a concept that unfolds from multiple dimensions at once. What we see is a projected snapshot of a process. Indeed the

^{3}**401273**words, verses, letters, rows, and columns in the Torah reflects the symmetry of the

**248**dimensions of the E

**8**Lattice.

Altogether the **5 ^{8}** words, verses, and letters plus the

**22**rows and columns =

^{3}**401,273**words, verses, letters, rows, and columns for the

**5**quantitative Elements. We keep emphasizing quantitative because they can be physically counted and thus cannot be open to interpretation, not even after thousands of years. Also, because their solid structure stands as proof that the Torah was given to Man as a whole complete entity, as was the

*Alef-bet*, the key to deciphering it. The alternative is that ancient Man not only had a profound understanding of the mathematics of the Cosmos and extraordinary computational skills, but was also capable of keeping track and organizing hundreds of thousands of letters, words, verses, word values, Names, paragraphs, chapters, and Books to form specific overlapping layers and networks of Cubes, Triangles, and hypercubes, and that is without even considering the gematria ciphers that give the Torah infinite complexity. According to archeologists they would have done this with sheafs of reeds and mounds of stones while trying to fend for themselves in the desert.

The reason this number for the **5** elements is so astonishing is that **401**,**273** is precisely **248**,**000**(*φ*) or **248**,**000** times Phi (*φ*) packets of information for the **5** Books of Moses, whose **5** Names equal **2480,** and whose **2 ^{10}** value positions total

**524800**.

Since all Torah knowledge tends toward and points to *Alef* (One) and since the square root of **5** is at the core of Phi (*φ*) and of the Torah, it is not surprising that **248**/√**5 **=** 111 **(*Alef*), which aligns with the **111** vectors of **42** that integrate the **27** Letters of the *Alef-bet* folded up in a **3 ^{3}** cube.

We have explained in depth in our more challenging on-line Books, *The Ultimate Reality Beyond the Universe* and *The Journey* how the Torah is connected to the **248** dimensions of the E** _{8}** Lattice hyper structure and symmetry, and we will do so again in more accessible upcoming articles. Nonetheless, those

**5**elements are equal to (√

^{8 }**5**)

**, which is significant because Phi(**

^{16}*φ*) = (

**1**+ √

**5**)/

**2**. A little basic algebra and we get √

**5**= (

**2**

*φ*–

**1**). This in turn means that the sum of the

**11**Odd Letters,

**625**= (

**2**

*φ*–

**1**)

**and that (**

^{8}**2**

*φ*–

**1**)

**=**

^{16 }**390**,

**625**, the sum of the

**3**main quantitative elements of the Torah. Therefore, both the

**3**main elements of the Torah and the

**5**main ones are directly related to Phi(

*φ*).

As it happens **31** is the **11**^{th} Prime Number. We also saw **11 ^{3}** in the equation (

**11**+ (

^{3}**73**+

**√**

**3**/

**10**)

^{2}**) =**

^{3}**390,625**. The ancient Kabbalists who knew how to interpret the Torah and language using the various ciphers of gematria had realized early on that there was a system of

**11**

*sefirot*or spheres, which can be translated as dimensions, and they are organized geometrically as the Tree-of-Life, specifically into

**2**stacked cubes with the lower cube conforming to the

**6**bundled dimensions of

*Zeir Anpin*. The highest of those

*sefira*/dimensions is named

*H’Keter*, the Crown, and its gematria value is

**625**. The next highest is

*Chochma*, Wisdom, and its gematria value is

**73**. The value

**248**is not a

*sefira*/dimension, but is the gematria value of Abraham, an energetic archetype or field and it represents

**248**dimensions.

This leads us to the equation that the square root of the **3** main Torah Elements divided by the **6** bundled dimension of *Zeir Anpin* (**625**/**6**) is equivalent to the matrix of the **42** Rows times the **248** Columns: (**625** x **10 ^{2}**)/

**6**= (

**42**x

**248**). We will get more into this as we get more comfortable with the basic designs, concepts, and technology built into the Torah.

We can translate the Torah into any language we want, but only one retains the Divine and impossibly complex properties it was originally imbibed with. Nonetheless, every number and figure in the Torah is designed to convey information to us in multiple ways. That figure of **401273** elements is just another way of expressing Pi (π) in that **40**/**12.73** = π. And this is only the edge of the surface; every physical attribute, concept, hyper-dimensional geometry and symmetry, and mathematical constant we have and many we have yet to conceive are clearly embedded in the Torah. And they are readily available to us.

Using an ancient gematria cipher that was rediscovered as a modern Number Theory concept, we can multiple the digits in a number and divide it by the sum of the digits in that number. When we apply it to the Torah’s first verse of **28** letters and **7** words and multiple it by **28**/**7** we get **3.141545** or Pi (π).

When we apply to the **5** main and **3** main quantitative elements of the Torah together, we get **1000**√**42** or **6480** while the **10648** rows and columns plus the **5832** verses, in other words the cubes of **22 ^{3}** and

**18**together equal

^{3}**16480**.

Beyond and behind all the other concepts there is always the concept of **42**.