Disclaimer: I am not a physicist and I apologize for skimming over the scientific concepts presented in this post! The ideas presented here might be used to generate interesting conversations about science and philosophy but the ideas are by no means comprehensive. I don't have time to go too deep into the details!
While I concede I had a fascinating romp through the history of atomic physics and psychology, I don't recommend reading Deciphering the Cosmic Number for leisure.... It was a chore reading through the heavy physics of the book. I probably would have enjoyed it a lot more if I was concurrently studying (quantum) mechanics since it goes through Wolfgang Pauli's scientific life in depth - but for me, this book took a lot of brainpower and focus to read. The most enjoyable moments for me were when I read about the science from a historical context. We take for granted how much we know now about atomic physics and don't realize how much there is still yet to know.
Overall, this book is a synthetic piece on the lives of Wolfgang Pauli (physicist) and Carl Jung (psycho-analyst), who are in their time premiere experts of their respective fields. They come together and, essentially, muse on the mysteries of the universe. Many of these musings were represented through geometric figures, archaic symbols, and numerology. A large portion of the book focused on dream interpretation and imagery and, by extension, the mystique of consciousness and life. Interesting stuff.
You can read an excellent review about the the book and its writing style here.
What exactly is the cosmic number according to Jung and Pauli? There was a very long debate in the book between the number 3 and the number 4. Both of which represents different types of spiritual completeness.
Number 3: Represented by the Holy Trinity in Christianity and appears multiple times in biblical stories. The triangle is a representation of strength and stability and Pythagorean properties are unique in geometry. In popular culture, three is often considered an important iterative number (e.g. "third time's the charm" and the Wiccan rule of three). Our physical world is known as three dimensional.
Number 4: Pauli believed strongly that the number four was the 'next level' three. While there did exist the Holy Trinity, the addition of a fourth (probably the human spirit or some other representation) made wholeness and completion. Jung believed that there are four major archetypes within the human psyche. In Pauli's field of work, atomic physics, the fourth quantum number was necessary in understanding electrons and quantum mechanics. Originally, the theory encompassed three but was not unified before the introduction of the fourth quantum number (electron spin, ms). Our world's fourth dimension, time, is quintessential in our understanding of the perceived universe.
Reasonably, these numbers would have special meaning from a mystical perspective.
But in the end, according to Pauli, what was the real cosmic number?
The fine structure constant. Or, to remember it better, the square inverse of 137.03597.
The fine structure constant is a dimensionless quantity derived from many fundamental physical constants such as elementary charge, speed of light, and the Planck constant. It is also known as the "coupling constant" or alpha, and is used to explain the mysterious electromagnetic force that governs interaction between electrons and photons (elementary particles and light). The constant was determined while the Bohr model was the cornerstone of atomic physics in 1916. At this time, everyone knew that Bohr's model could not explain the splitting of spectral lines in H2 molecules. Thus, the introduction of this number was pivotal.
From a numerological perspective, the number is very mysterious. It finds itself related to the golden ratio and is theorized to be the value for stable matter, and thus the number that makes "life" possible.
I presume that physicists and psychologists seeking to reconcile science and consciousness would be fascinated with the idea of a constant that describes life on a fundamental level. An extension of this is the possibility of objective beauty and unity in life that springs out of the chaos and increasing entropy of the universe. (am I getting too poetic here?)
Pauli's famous quote is this: 'When I die, the first thing I shall consider asking the devil is -- What is the meaning of the fine structure constant?'
Perhaps the meaning of the fine structure constant was the answer to Asimov's The Last Question: 'Can entropy be reversed?'
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