Arthur I. Miller addresses the foundational problem of the fine-structure constant (the "Cosmic Number") and the historical, biographical background entailed in the search for a solution to this mostly unsolved problem. The main title is only symbolic of the goal toward which Pauli and Jung were searching: the Philosopher's Stone, or Quintessence of alchemy, the attainment of an enlightened and individuated psyche. The "Cosmic Number" is symbolic of a vital archetypal process in nature, and the physical meaning as giving the strength of the electromagnetic interaction is only part of the problem that concerned Pauli in particular. What Pauli called his "background physics" was a catalyst for linking sense perceptions with creative concepts, and 137 was the "archetypal number" for this. So not only is the fine-structure constant a dimensionless number of fundamental importance in physics, it is of key symbolic significance to Jung's depth psychology and the history of alchemy.
In his study of the archetypal ideas of Johannes Kepler and Robert Fludd from the 17th century, Pauli traced the line of their research back to Pythagoras. While Plato is only briefly mentioned in this book, significant and remarkable parallels are to be found between the geometry of Plato's ideal City of Magnesia and Wolfgang Pauli's dream, "the great vision - of the World Clock". According to John Michell the ideal City of Magnesia is a form of the Cosmological Circle from ancient geometry. "By Plato's time, the very idea of a canon of music had been forgotten everywhere except in the academies of Egypt, but he himself had evidently studied and learned it, for the number code behind it is at the root of all his mathematical allegories and provided the scientific basis of his philosophy." (Dimensions of Paradise, p.9) and "The universe, human nature, and the mind of the Creator were made commensurable by number, which Plato called the 'bond' holding all things together." (p.230).
The fine-structure constant was introduced into physics by Arnold Sommerfeld, Pauli's professor and mentor, and being captivated by the mystery of spectral lines of the atom he said, "What we are nowadays hearing of the language of the spectra is a true music of the spheres within the atom, chords of integral relationships, an order and harmony that becomes even more perfect in spite of manifold variety."(p.64). Pauli's contributions to modern physics include the Pauli exclusion principle for electrons in the atomic orbit, the theoretical prediction of the neutrino particle, the fourth quantum number related to spin, CPT symmetry related to "mirror reflections," the legendary "Pauli effect," and his exit from the world stage from room number 137. Pauli also helped Jung to develop his theory of synchronicity, or acausal connecting principle related to meaningful events. Miller quotes Max Born on p.253: "If alpha (the fine structure constant) were bigger than it really is, we should not be able to distinguish matter from ether (the vacuum, nothingness), and our task to disentangle the natural laws would be hopelessly difficult. The fact however that alpha has just its value 1/137 is certainly no chance but itself a law of nature. It is clear that the explanation of this number must be the central problem of natural philosophy." Pauli concluded that "most modern physics lends itself to the symbolic representation of psychic processes." (p.162). Readers of Carl Jung may find this book more interesting than Pauli fans, as it is more biographical and "Jungian" in content.