The Cosmic Mysticism of Sir Arthur Eddington: Exploring Mind-Stuff, E-numbers, and the Unseen World

 

Introduction: A Visionary Mathematician and His Enigmatic Quest

In my previous post, "Fine Structure Constant and Sir Michael Francis Atiyah," we explored the contributions of the great mathematician Sir Michael Atiyah and his intriguing approach to the fine structure constant, a mystery that has puzzled physicists for over a century. 

In [1] Atiyah  wrote

“There are now various ways of arriving at Eddington’s number, all by pure algebra, which appear in several different papers [5] and [9]. The simplest is

(7.2)  137 = 1 + 8 + 128 = 2⁰ + 2³ + 2⁷.

Eddington first proposed 136 = 8 + 128, based correctly on Clifford algebras as in [4], but he had difficulty justifying the additional 1 to get 137.

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Ironically, Eddington was later laughed out of court, when 137 was found to need a long string of corrections. In fact these corrections just arise from the iterative process that defines Ж , so Eddington’s two mistakes cancel each other out. Stability helps the tricky initial stage. A wobbly start acquires stability from subsequent motion in a very precise sense as on a bicycle.”

Sir A. Eddington: "A wobbly start acquires stability from subsequent motion in a very precise sense as on a bicycle."

Atiyah's work, particularly in "The Fine Structure Constant" [1], highlights the legacy of Sir Arthur Eddington, a profound figure in the realms of astronomy, physics, and mathematics. Eddington’s work delves into the mystical and mathematical fabric of the universe, revealing dimensions of thought that continue to inspire and challenge modern science.

Eddington’s Algebraic Mysticism: Unveiling the E-numbers

Sir Arthur Eddington (1882–1944), an English astronomer and physicist, was not merely a scientist; he was a visionary who sought to uncover the sacred algebraic structures governing the universe. In "The Fine Structure Constant," Atiyah praises Eddington for his exploration of these structures, notably his "E-numbers," which Eddington believed were not just mathematical curiosities but divine symbols of a higher-dimensional reality intertwined with spacetime.

Einstein and Eddington seated together at the Cambridge Observatory in 1930
(Photo: Royal Astronomical Society)

Eddington’s fascination with the number 137, the fine structure constant, is particularly noteworthy. He proposed that 137 could be derived algebraically, and while his methods were initially met with skepticism, modern physics acknowledges the importance of such dimensionless numbers in understanding the universe's fundamental laws. Eddington’s work, though often overlooked, laid the groundwork for future explorations into grand unified theories, where the echoes of his mystical insights can still be heard.

Mind-Stuff: The Foundation of Reality

Eddington's philosophical inquiries extended beyond the physical constants to the very nature of reality itself. In "The Nature of the Physical World" [2], he introduces the concept of "mind-stuff," a fundamental substance that he posits as the true basis of existence. According to Eddington, what we perceive as the physical world is a construct derived from this more basic form of reality.

This "mind-stuff" is not to be confused with our conscious minds; instead, it is a generalized substrate that underlies all reality. Eddington argues that our material world is shaped by this mental substance, much like how a college's activities are represented in bursar accounts. Consciousness, in his view, arises from this mind-stuff, challenging the traditional physicalist perspective that considers space and time as fundamental entities. Instead, Eddington suggests that they too are products of this deeper mental reality.

Science and the Unseen World: A Cosmic Perspective

In his 1929 Swarthmore lecture, "Science and the Unseen World" [3], Eddington challenges conventional notions of existence and reality. He argues that the obsession with proving the existence of entities—whether they be gods, deities, or even friends—is an intellectual trap that distracts from a more profound understanding of our relationships and the universe.

Eddington proposes that our connection with the divine, or any higher entity, transcends logical validation. He likens it to our friendships, where the need for proof is absurd. Eddington proposes that, in the highest form of spiritual experience, the soul and God share a cosmic joke, laughing together at the absurdity of trying to "prove" something so inherently beyond proof.

the soul and the divine share a cosmic joke, laughing at the futility of trying to "prove" something inherently beyond proof.

This perspective invites us to move beyond sterile metaphysical arguments and embrace the realization that some aspects of reality are beyond the dichotomy of existence and non-existence—they simply are. Eddington’s insights offer a potential reconciliation between science and spirituality, suggesting that both domains might find common ground in the shared joy of a deeper understanding of the cosmos.

Egregors and Mind-Stuff: Beyond the Reach of Science

In [3] Eddington addresses the “unseen world” hiding behind the symbols of science as follows:

“Natural  law  is  not  applicable  to  the  unseen world behind the symbols, because it is unadapted to  anything  except  symbols,  and  its  perfection is  a  perfection of symbolic linkage.  You cannot apply such a scheme to the parts of our personality which  are  not measurable  by symbols  any more than you can extract the square root of  a sonnet." 

Here I do not fully agree with Eddington. While it is true that attempting to take square root of a sonnet is not very productive, it is also not productive to take a square root of of the equality sign “=”. But sonnets can be analyzed in other, more productive and scientific ways. We can analyze the information contained in a sonnet, its complexity, its impact on the consciousness level. We can analyze its “egregor” character, even if egregors are still beyond the reach of science. 

While Eddington’s notion of the "unseen world" behind the symbols of science might seem esoteric, it opens the door to exploring concepts that are currently beyond the reach of modern science. One such concept is the "egregor," a collective consciousness or psychic entity that emerges from the shared beliefs and intentions of a group.

An egregor is more than just the sum of individual thoughts; it is a dynamic, influential presence shaped by collective human activity. This idea brings us back to Eddington’s mind-stuff—an enigmatic substance that, while not fully understood, might one day be accessible through new scientific methodologies. Just as quantum theory is used in daily life without being fully comprehended, the mind-stuff could become a tool for future scientific exploration and control.

Mind-Stuff - an enigmatic substance that, while not fully understood, might one day be accessible through new scientific methodologies.

Conclusion: Eddington’s Legacy and the Future of Science

Sir Arthur Eddington’s work, spanning the mystical and mathematical realms, continues to challenge and inspire. His exploration of the fine structure constant, mind-stuff, and the unseen world invites us to reconsider the foundations of reality and the limits of scientific inquiry. Eddington’s insights suggest that the universe is not merely a physical construct but a profound interplay of mind and matter, hinting at dimensions of existence that remain largely unexplored.

As we advance in our scientific endeavors, it is crucial to remember Eddington’s legacy. His work reminds us that the pursuit of knowledge is not just about understanding the material world but also about embracing the mysteries that lie beyond. In doing so, we might one day bridge the gap between science and spirituality, uncovering deeper truths about the nature of reality and our place within it.

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References

1. M. Atiyah, “The Fine Structure Constant” (2018).
2. A.S. Eddington, “The Nature Of The Physical World”, Cambridge University Press 1929. Link.
3. A.S. Eddington, Swarthmore lecture, “Science and the Unseen World”, George Allen & Unwin Ltd 1929. Link.

Fine Structure Constant and Sir Michael Francis Atiyah

 Sir Michael Francis Atiyah (22 April 1929 – 11 January 2019) wasn't just a mathematician; he was a magician of numbers, a wizard whose work could turn the most abstract mathematical ideas into something akin to pure magic. His groundbreaking contributions linked geometry and topology in ways that fundamentally transformed modern mathematics. Atiyah was not just any mathematician; he co-developed the Atiyah-Singer Index Theorem - a concept so profound that it's like discovering a hidden treasure map using nothing but a mathematical compass. This theorem creates a bridge between differential equations and the topological properties of shapes, making it one of the most intriguing ideas in the mathematical universe. Along the way, Atiyah collected nearly every top prize in mathematics, from the prestigious Fields Medal to the Abel Prize, firmly establishing himself as one of the grand wizards of the mathematical world.

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The Enchanted Forest of Mathematics: Atiyah's 2018 Abel Prize Talk

In his 2018 Abel Prize talk at the International Congress of Mathematicians (ICM), Michael Atiyah did more than just give a lecture; he took his audience on a mesmerizing journey through the enchanted forest of mathematics. With the skill of a master storyteller, he wove together tales of numbers, geometry, and physics, revisiting some of his greatest mathematical adventures, including the renowned Atiyah-Singer Index Theorem. All that he did with humor.

Michael Atiyah at ICM 2018 Rio de Janeiro (in my personal vision)

Atiyah reflected on how these seemingly abstract concepts have surprising and deep connections to the real world, musings that felt like whispers of the universe's deepest secrets. With the charisma and flair of a seasoned wizard, he suggested that the most profound truths in mathematics are like hidden spells, waiting to be discovered by those brave and curious enough to explore them. It was a fitting farewell from one of the most brilliant minds to ever grace the field of mathematics.

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The Fine Structure Constant: A Bold and Controversial Proposal

Atiyah's talk was not just a stroll down memory lane. He also presented a bold and speculative idea about one of the most mysterious constants in physics: the fine structure constant. This constant is crucial because it governs the strength of electromagnetic interactions, yet its precise value has long puzzled physicists.

Atiyah proposed an innovative approach to deriving the value of this constant, one that intertwined deep mathematical concepts with the mysteries of the physical universe. He traced his ideas back to the work of Euler, von Neumann's theory of factors, and Clifford algebras, seamlessly blending his lifelong passion for mathematics with his curiosity about the physical world. His discussion was both intriguing and controversial, sparking debate and reflecting his enduring spirit of exploration, even in his later years.

Abel Lecture — The future of mathematical physics: new ideas in old bottles — M. Atiyah — ICM2018 

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The Calculations: No Cigar, But Still a Magical Journey

Atiyah's proposal stirred quite a bit of discussion, particularly on forums like the Physics Forum, where physicists debated whether he had uncovered new links between arithmetic and physics. Viktor T. Toth, a notable contributor to the discussion, analyzed Atiyah's 2018 preprint using Maxima software, ultimately concluding that Atiyah's proposal did not match the expected value of the fine structure constant. Undeterred, I decided to dive into the calculations myself using Mathematica.

Using Atiyah's formula, the value of the inverse of the fine structure constant, 1/α (which he denoted by the Cyrillic letter Ж), came out as 0.160262—significantly different from the expected 137.0359992, making it about 854 times smaller than the expected value. In short, no cigar here. In fact, it was a true disaster.

But Atiyah's story doesn't end with a simple miscalculation. His paper delves into much more advanced mathematics, suggesting that Ж might be similar in nature to π. Atiyah speculated that just as Euler’s formula

links π with complex numbers, there might be a similar elegant formula for Ж involving noncommutative quaternions. From there, he ventured into von Neumann factors, traces, and infinite products, sketching ideas that are as challenging to comprehend as they are fascinating. While he didn’t provide all the answers, Atiyah’s speculations open up tantalizing possibilities that invite further exploration.

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Conclusion: The Legacy of a Mathematical Wizard

Michael Atiyah's work remains a testament to the power of curiosity, creativity, and courage in the world of mathematics. While his attempt to link the fine structure constant to deep mathematical ideas may not have yielded the expected results, it exemplifies the adventurous spirit that drove him throughout his life. Atiyah's legacy is not just in the theorems he proved or the prizes he won, but in the magical way he connected different realms of mathematics and physics, inspiring future generations of mathematicians to explore the unknown. Whether or not his ideas about the fine structure constant will stand the test of time, they will undoubtedly continue to provoke thought and inspire wonder.

In the end, Sir Michael Atiyah leaves behind a legacy that, like all great magic, will continue to captivate and challenge those who dare to dream big in the world of mathematics.

Related links

• M. Atiyah , “The Fine Structure Constant” (2018)
• M. Atiyah, “Arithmetic Physics – Abel Lecture” (2018)
•  “Atiyah and the Fine-Structure Constant“ on Sean Carroll's blog
• “Riemann hypothesis, the fine structure constant, and the Todd function” post on John D. Cook blog
• "A fantastic journey through Atiyah's mathematical mind", IMPA blog

P.S. 18-08-24 I thank to Viktor T. Toth for pointing it to me that Atiyah's  Ж was supposed to denote 1/α, and not α, as I had it in the original version of this post.