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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 = e2/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 E8 and E8×E8, 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.

List of topics

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The 7-tree mapping space-time embodies the number 137 in the fine-structure constant and the superstring structural parameter 168.


The inner form of the Tree of Life embodies the number 137.


The Type C pentagon embodies the number 137.


The Tetrahedral Lambda embodies the number 137.


The five (and the first four) Platonic solids embody the number 137.


The Polyhedral Tree of Life.


The 144 Polyhedron.


 The disdyakis triacontahedron embodies the number 137 and the superstring structural parameters 840 & 1680.

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