Deciphering the Cosmic Number by Arthur I. Miller from University College London is an intriguing, yet occasionally frustrating, book that tackles a fascinating and complex subject. The book explores the personal and professional relationship between physicist Wolfgang Pauli and psychologist Carl Jung during the first half of the 20th century. In doing so, it examines the origins of scientific discovery and the nature of reality.

In the early twentieth century physics had become increasingly detached from what most of us think of as the “real world.” The subatomic particles described by quantum physics exist beyond our direct perception — their nature can only be inferred as a side effect of their behavior. And their observed behavior was increasingly bewildering, even contradictory.

With his famous “uncertainty principle” Werner Heisenberg demonstrated that we can never know both the position and the momentum of a subatomic particle beyond a certain degree of accuracy. An elementary particle such as a photon or an electron behaves both as a discrete particle and as a wave of energy. It was difficult to imagine. As Heisenberg wrote to Pauli in 1926, “What the words ‘wave’ or ‘particle’ mean we know not any more; [we are in a] state of almost complete despair.” Scientists debated whether a mental model of the world of quantum events was even possible.

Pauli found in Jung’s theories of the psyche a way to reconcile the worlds of science and intuition, of mathematical rationality and intuitive understanding.

Pauli originally sought out Jung as a therapist to address his personal problems — his self despair, his drinking and carousing, and the tragedy of his mother’s suicide following his father’s abandonment of the family for another woman.

But long after the psychological counseling concluded, Pauli stayed in contact with Jung. He saw in Jung’s theories — such as “synchronicity,” the connectedness of random and yet meaningful events — a way to comprehend the increasingly bizarre world of quantum physics.

Although well-researched and copiously annotated, Deciphering the Cosmic Number is, at times, desultory and confusing. The chronology of the narrative is occasionally jumbled. Although some of this is to be expected from a dual biography, the book jumps around more than is necessary, even within the narrative of one of its subjects.

The text occasionally struggles to explain its difficult scientific theories clearly (admittedly a challenging task given the complexity of these ideas). You may find yourself turning to Wikipedia or elsewhere for more lucid explanations of some of the concepts described in the book.

In other instances, details are glossed over. After explaining Jung’s concepts of introversion and extroversion, Miller correctly observes that “Jung was the first to coin these two terms, which have since become common currency.” True enough, but it is worth noting that the way these terms are commonly used differs from Jung’s definition. Jung’s personality traits focused on whether the individual gives primary value to external sensations or internal experience — which is different from common parlance which uses these terms as synonyms for being outgoing or shy. There exist, for example, shy extroverts.

Miller explores at some length the contrasting world views of the late Renaissance thinkers Johannes Kepler and Robert Fludd. Kepler’s work, although rife with astrological, alchemical, and mystical allusions, relied on mathematics as its foundation. Fludd’s views were based largely on his mystical and spiritual insights. Fludd preferred to demonstrate his ideas using pictures rather than mathematics, and condemned Kepler as a “vulgar mathematician” who relied on “quantitative shadows.”

In Jung’s categorization of personality types, Pauli found a model for the differing views of Kepler and Fludd. Miller writes:

Pauli recognized Kepler and Fludd as opposing psychological types — Kepler the thinking type and Fludd the feeling type. Thus his knowledge of Jungian psychology had revealed to him the limitations of modern science.

Elsewhere, however, opportunities to explain the often divergent views of modern science in Jungian terms are left unexplored.

For example, at an early age, Pauli is intrigued by the ideas of his godfather, positivist Ernst Mach. As Miller explains:

As a boy [Pauli] was spellbound by the scientific equipment in Mach’s apartment. Its ultimate purpose, said Mach, was to eliminate unreliable thinking — to demonstrate that the only thing that was really out there was what you can experience with your senses. The rest was all metaphysics — quite literally beyond physics and not worth considering, mere illusion.

With the unfolding of relativity theory and quantum physics in the twentieth century, science was increasingly concerned with events beyond direct perception. Miller describes Pauli’s puzzlement over this as follows:

Atoms could not be experienced with the senses. Did that mean they were merely “metaphysical” in Mach’s pejorative sense? Were they not part of the elaborate scientific theories which made predictions that could be proved in the laboratory? … The message of relativity theory seemed to be that scientists should look beyond what was immediately perceptible by the senses.

This divergence of viewpoints can also be viewed in terms of Jungian personality types, with Mach the “sensation” type Pauli the “intuition” type. Yet this point is never raised (perhaps because Pauli himself never reached this conclusion).

The “mystical” or “cosmic” number 137 that forms the book’s title and is the focus of its final chapter refers to the fine structure constant of atomic spectra. This discussion, however, comes across as more of a diversion than a unifying theme of the book. The lists of coincidences of Kabbalistic words and torturous interpretations of equations that can produce 137 are particularly vexing. It’s hard to fathom the relevance of the fact that 8π(8π⁵/15)^1/3 happens to be 137.348. Or why it matters that 10^{82943.99629/(32×666)}/666 = √137.

Furthermore, it turns out that the pattern of spectral lines that gave rise to interest in the number 137 isn’t actually 1/137 as originally believed. This fraction is only an approximation of the actual sequence of lines (which, we learn, is closer to 1/137.035999084). As Miller himself states, after many more examples of calculations that yield results containing the number 137, “Sadly, all these are pure coincidence with no scientific basis.”

Miller may have been drawn to using this device to frame his tale because Pauli died in room 137 of the Red Cross Hospital in Zurich. This coincidence (or would Jung and Pauli have seen it as synchronicity?) may have been too tantalizing to resist using as a literary device to shape the book’s narrative. However, Pauli’s puzzlement over the appearance of this ratio in nature seems like a tangential detour from the book’s main theme of the blending of science and psychology in the first half of the twentieth century.

Despite these shortcomings, the book addresses an important topic in the history of scientific discovery — the conflict between rationality and intuition, scientific reason and mystical insight.

We naturally look at history through the filter of the present . We study scientific advancement by looking back at the trail that led to our current beliefs. In doing so, we tend to emphasize the “scientifically correct” and ignore all else.

Yet the path to modern science travels through religion and mysticism. School children learn of Pythagoras because of his geometric theorems. His mystical ideas about numbers, the music of the spheres, and the reincarnation of the soul after death are not as emphasized. We often see Copernicus as an early rationalist because his views of a sun-centered universe were considered heresy by the Church. But for Copernicus, placing the sun at the center of the world mirrored his view of an all-seeing God at the center of creation.

Even though based on scientific analysis and quantitative data, the insights of scientists and philosophers nonetheless spring from their psyches. Pauli found in Jung’s psychology a way to unite the disparate worlds of rationality and intuition, of science and mysticism, of Kepler and Fludd. As Miller states, “Pauli’s focus was the process of scientific theory and particularly its irrational side. Though scientific theories are expressed in mathematical terms, the initial discovery of the theory is essentially an irrational — not a rational — process.”

The book is a valuable addition to the history of science and psychology for those fascinated by these topics, but its occasionally opaque explanations and disjointed chronologies may be of little interest to the casual reader.

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