Pauli became one of Jung's regular clients.
The two shared similar obsessions. Both were scientists, but each feared that physics would always be missing something if it neglected the inner workings of the mind.
Jung obsessed over mental archetypes - primitive, subconscious symbols hard-wired into our perception of the world - and was fascinated by c a fiendishly complex branch of Jewish mysticism.
Pauli, for his part, was enamoured by Johannes Kepler, who tried (unsuccessfully) to explain the structure of the solar system in terms of geometry alone. He was also intrigued by a lesser known contemporary of Kepler - Robert Fludd, a member of the Rosicrucian secret society, who believed that simple geometrical forms held the key to unlocking the cosmos. As Pauli struggled with problems in quantum physics, Miller explains, he felt "the need for a fusion of physics with Jung's analytical psychology in order to understand first the unconscious and then the conscious".
Pauli began experiencing bizarre dreams and turned to Jung for help in making sense of them. The dreams featured a startling mix of geometrical figures, motifs from physics (clocks and pendulums) and mysterious figures reminiscent of Jung's archetypes (the serpent eating its tail, a veiled woman and an ape-man, to name a few). Although Pauli described 400 dreams to Jung, these visits were kept a secret; when Jung wrote about them, he referred to his famous patient only as a "great scientist cats should start adding stupid captions to pictures of humans.".
Numerology is never far beneath the surface of Miller's story. Whether you can observe a thing or not depends on the theory which you use. It is the theory which decides what can be observed. Pauli was troubled by the number 137. As physicists pored over the equations that determine the spectra of the chemical elements, a particular combination of physical constants kept cropping up. Referred to as the "fine structure constant", it combined the speed of light (crucial in Einstein's relativity) and Planck's constant (the heart of quantum theory), along with the magnitude of the charge of an electron. By themselves, each of these has to be expressed in some particular units (say, metres per second for the speed of light), but combined, the result is a unitless "pure number". Arnold Somerfeld first worked out its value as 0.00729, equivalent to (roughly) 1/137.
Why 137? Pauli obsessed over it, and he wasn't the only great physicist to do so: Arthur Eddington, Enrico Fermi and Richard Feynman all took stabs at it over the years. Meanwhile Jung, with his knowledge of Kabbalah, also found enormous significance in 137. Every letter in the Hebrew alphabet has a number associated with it, and - lo and behold - the letters in the word "Kabbalah" add up to 137. Remarkable - or a meaningless coincidence.
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The history is fascinating, as are the insights into the personalities of these great thinkers. Miller, however, seems oddly accepting of Pauli and Jung's musings, which these days we would label pseudoscience. And Miller's thesis that their ideas are bearing fruit today, with the study of consciousness "a burgeoning field of research using concepts from quantum mechanics", is somewhat exaggerated.
