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**#35 The number 137 determining the fine-structure
constant also determines the dimension 248 of E _{8}**

The number of yods in the n-tree when its triangles are tetractyses is given by

Y(n) = **50**n + 30.*

The 7-tree maps the physical plane (physical universe). It has Y(7) = 380 yods. Two yods up to the level of its apex that belong to the eighth Tree lie outside it on each side of the central Pillar of Equilibrium. There are 384 yods up to the top of the 7-tree.

The number of yods up to Chesed of the nth Tree is given by

C(n) = **50**n − 2.**

Chesed of the fifth Tree is the **31**st SL, counting from the bottom of the first
Tree. There are C(5) = **248** red yods up to this SL, which is denoted in the diagram opposite
by a circle coloured half red and half blue for a reason to be given shortly. This shows how EL ("God"), the
Godname of Chesed with number value **31**, prescribes the dimension **248** of the
rank-8 exceptional Lie group E_{8} at the heart of superstring theory. Each red yod denotes one of its
**248** roots. **248** is the number value of *Raziel*, the Archangel of
Chokmah, which is the Sephirah above Chesed on the Pillar of Mercy of the Tree of Life.

Counting from the level of the top of the 7-tree, there are (384−247=137) blue yods down to (and
including) the **31**st SL, which is coloured half red and half blue to indicate that it is a yod that
is shared by the set of 137 blue yods and by the set of **248** red yods. But this SL is the
**248**th yod, counting from the base of the 7-tree. We discover the amazing fact that the number 137
determines the very dimension **248** of E_{8}! Regarded by physicists as one of the most
mysterious numbers in physics, the number 137 determines the strength of the coupling of the electric charge of the
electron to the electromagnetic field because its reciprocal is the approximate value of the fine-structure constant: α = e^{2}/ħc
= 7.29752698(24)×10^{−3} = 1/137.0359974(44)^{†}, where e is the electrical charge of the
electron, ħ is the reduced Planck constant and c is the velocity of light *in vacuo*. The 7-tree mapping the
space-time continuum (see Article 2) has the remarkable property that the *137th
yod from its apex is the 248th yod from its lowest point, thereby relating through its geometry
two of the most important numbers in theoretical physics*. Like the number

The Pythagorean Decad relates both these numbers of deep significance to physics through the identity:

1

^{2}

2^{2}3^{2}

137 +248= 385 = 4^{2}5^{2}6^{2}

7^{2}8^{2}9^{2}10^{2}.

Notice
that the **31**st SL is the *tenth* SL from the bottom of the Pillar of Mercy.
**31** is also the *tenth* prime number after 2, the first prime number. 137 is the
33rd prime number, where 33 = 1! + 2! + 3! + 4! and 10 = 1 + 2 + 3 + 4. It demonstrates the fundamental role of
the tetractys in determining numbers central to superstring physics because the sum of the number of
permutations of 10 objects arranged in its four rows is 33, whilst Y(33) = 1680, which is the number of circular
turns that Leadbeater counted in each helical whorl of the UPA/E_{8}×E_{8} heterotic
superstring. Here is how the number 33 determines either arithmetically or geometrically the form of each
whorl of the superstring, the symmetry group E_{8} governing its forces and the fine-structure
constant. Its significance is far greater than what the religious, numerological and historical reasons for the
association of this number with Freemasonry would lead one to expect.

* Proof: The n-tree consists of (12n+7) triangles with (6n+5) corners and (16n+9) sides.
When each triangle is a tetractys, two hexagonal yods lie on each side. Number of yods in n-tree = 6n + 5 +
2×(16n+9) + 12n + 7 = **50**n + 30.

** Proof: There are 18 yods outside the (n−1)-tree up to Chesed of the nth Tree of Life. The number
of yods in the (n−1)-tree = Y(n−1) = **50**(n−1) + 30 = **50**n − 20. The number of yods
up to Chesed of the nth Tree = **50**n − 20 + 18 = **50**n −
2.

^{†} Current recommended
value.

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