The Fine-structure Number 137 in Sacred
Geometries — no more a mystery

In one of his books, the great physicist
Richard Feynman said:

"There is a most profound and beautiful question
associated with the observed coupling constant, e — the amplitude for a real electron to emit or
absorb a real photon. It is a simple number that has been experimentally determined to be close to
-0.08542455. (My physicist friends won't recognize this number, because they like to remember it as
the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal
place. It has been a mystery ever since it was discovered more than fifty years ago, and all good
theoretical physicists put this number up on their wall and worry about it.) Immediately you would
like to know where this number for a coupling comes from: is it related to pi or perhaps to the
base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a
magic number that comes to us with no understanding by man. You might say the "hand of God" wrote
that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do
experimentally to measure this number very accurately, but we don't know what kind of dance to do
on the computer to make this number come out, without putting it in
secretly! ........Richard P. Feynman (1985). QED: "The Strange Theory of Light and
Matter". Princeton University Press. p. 129.

The magnitude of the coupling constant
α =
e^{2}/ħc for the
electromagnetic field has yet to be calculated from first principles. Part of the problem is
that no one has managed to derive the magnitude of Plank's Constant h or the speed of light;
they are experimentally measured quantities whose magnitudes have no explanation as yet. The
closeness of the reciprocal of α to the number 137 has led physicists to speculate that
this number has a place in a "grand, unified theory" that truly unifies the forces of nature.
The author can now explain why it should do so. Like numbers such as
248 and 496, which are encountered in superstring
theory as the dimensions of, respectively, the rank-8 exceptional Lie group
E_{8} and E_{8}×E_{8}, the number 137 reveals itself as a
fundamental parameter that describes the mathematical properties of holistic systems. For
example, it is:

the number of
tetractyses whose yods fill up the inner form of the Tree of Life
(see #5);

the number of sides of basic triangles in the 144 Polyhedron
constructed from Type A triangles (#5);

the number of yods on average that are needed to construct
from tetractyses the faces of the Platonic solids that ancient philosophy
associated with the Elements Earth, Water, Air & Fire
(see here);

the sum of the first, second & third powers of 2, 3 & 4 on
three edges of the Tetrahedral Lambda, the tetrahedral array of 20 integers that is the
3-dimensional generalisation of Plato's "Lambda" (see here).

the number of points marking out in space the two polyhedra that
constitute the Polyhedral Tree of Life (see above);

There is, therefore, no longer a mystery about why the
"magic number" 137 appears prominently in quantum electrodynamics (QED) and why it plays such a
pivotal role in defining the physical properties of atoms through the energy levels of their
electrons. It is a
characteristic parameter of all sacred geometries (see here under the heading "137") embodying the divine blueprint, as manifested in the
physical universe of matter and its forces — in particular, the electromagnetic field described
by QED that holds atoms together. This statement is not a speculation about the metaphysical
status of the number 137 based upon religious dogma or New Age philosophy. Instead, it is a
hard, mathematical fact, as provable as any theorem of Euclid's geometry, as many
pages in this website demonstrate. Contemplate this statement, marvel at it and reflect on its profound implications. Only if
one's humanistic or materialistic philosophy has no room for the notion of the 'sacred,' as
manifested in true sacred geometries, will one continue — like Prof. Feynman and
"all good theoretical physicists" — to worry about it. There is nothing inexplicably magical or
irrational about its presence in theoretical physics. This illusion exists only for those who
cannot discern the wider, mathematical picture of the spiritual cosmos, for which the number 137
is just one of the cosmic parameters that physicists have stumbled across so far
but cannot account for, calling it "one of the mysteries of physics." Just as this number
determines the size of atoms and molecules, as well as the scale of the frequencies of the light
that they emit, so these parameters determine the isomorphic morphology of certain sacred
geometries that express the universal pattern of cosmic numbers quantifying the Divine Whole. It
is important that the reader lifts numbers like 137 out of the narrow context of physics
textbooks and research journals and recognises their wider meaning as interconnected parameters
that quantify the parts of this whole. Their archetypal status can be discerned only through
analysing these sacred geometries, understanding what their features mean by following their
correspondences and encountering these master numbers time and time again whenever they quantify
analogous properties of these geometries or other holistic systems.