An Exercise in Infinity: Reviewing Jim Holt’s When Einstein Walked With Gödel

Gödel and Einstein were friends

In When Einstein Walked With Gödel, Jim Holt takes us into a series of scientific and philosophical problems, achieving the effect of a guided tour through some of the most important problems in mathematics, philosophy, and yes, even physics. Holt has an easy way with a hard problem, and as someone who has studied a variety of these problems for many years, I still found real value in Holt’s work even after the third or fourth listen via Audible.

My experience with this book began about half a decade ago, when I read it as part of the research endeavor that would ultimately germinate into the Worldview Ethics project of 2023 and beyond. The review you’re reading now is part of a ten-book review series, put together in order to provide a written train of thought that a curious reader will be able to follow for more information in the vein of Worldview Ethics. Like Worldview Ethics, When Einstein Walked With Gödel manages to survey a vast territory. Essays discuss everything from Sir Francis Galton, the father of both statistics and eugenics, to the career of Saul Kripke and the course of the second half of the twentieth century in analytical philosophy.

Each chapter in WEWWG manages to stand effectively alone as well as with the others to tell a sweeping narrative. Though Holt does not seem inclined to put all of this together for the reader, the book is a veritable fountain of inspiring stories, each grounded in the history of science and philosophy. From the portrait of Gödel (which is not entirely flattering) to an account of the nature of a debate that captivated the American Philosophical Association, the reader is repeatedly provided with both quality information and masterful storytelling.

Worldview Ethics readers will find a wealth of perspective in this work, providing what is perhaps the most concise account of its manifold subjects possible while still satisfying the curious reader’s appetite for details. There is no book that can provide the reader with a better understanding of the immediately preceding period in philosophy and science upon which to build something new.

Let’s take a quick look at a few of my favorite essays to understand the concepts a reader can find in When Einstein Walked With Gödel.

Sir Francis Galton

The essay about Francis Galton is a complex piece that is ambiguous about the man’s character. On the one hand, Galton was a decorated scholar, the father of modern statistics among other towering achievements. Yet on the other hand, Galton also must be remembered as the father of eugenics, a troubled pseudoscience to say the least. Holt writes this essay with his reader in mind, coming right out in the introduction and argues that it’s worth understanding how Galton went wrong with eugenics even though it an “evil concept” that was “misbegotten from the start,” (Holt, 52). Holt’s wit in the tale empowers a quick, yet thorough, account of the life and science of Galton.

In this essay, the reader will find a fascinating history of ideas ranging from the bell curve to genetics, statistics, and of course, eugenics. In my view, of course, the most interesting thing of all is the brief discussion of the future of eugenics: parents gaining increasing levels of control over the sort of traits their offspring may possess.

In my view, ethics is the study of what human beings do and why. Things that are wrong are said to be wrong because they self-contradict and fail to reach their goals due to this fault in the reasoning behind them. Eugenics, as detailed by Holt in his essay, is hence problematic not because it is utterly wrong to tamper with one’s genome - after all, anyone who selects a mate and has a child with that person has, in the process of the selection of a partner, made a choice that will forever impact the genetic makeup of said child. So we know that we do this on an individual level, and that the horrific eugenics experiments of the twentieth century were misguided because they involved attempting to scale this personal choice to the societal level.

Nonetheless, Holt leaves us with a question worthy of some rumination: where are the limits going to be, tomorrow? What about the next day, or ten years or more from now? Scientists are interested in treating disease, but at some point in the near future they will turn their attention to creating healthier, more fit human beings. The problems that are likely to occur when this transition takes place will require a great deal of anticipation and planning if they are to be addressed.

Turing & Computation

Alan Turing was not well-portrayed by Benedict Cumberbatch, and the account in “The Imitation Game” was not particularly accurate, Holt argues. Wittgenstein and Turing measured wits and worked together, with Turing’s familiar intellectual acuity serving him well. Ada Lovelace was intellectually un-gifted (at least toward mathematics!), Holt informs us. And beauty is revealed to be deeply related to mathematics, for mathematicians at least. Section 2 is of great interest, introducing a reader to the mathematics of chaos theory and to the theory of computation after explaining why mathematical concepts are considered to be beautiful.

The extent to which the essays work together to prove their point, to which they speak to one another, is a major strength of Holt’s work here. The groupings are intelligent and the logic is revelatory even as we learn about advanced mathematics and engage directly with some of the most difficult rational discourse of the previous few generations.

The star of the show in section 2 is the way in which abstractions can be compared to one another, even though it is never mentioned directly. Read these three essays to get a sense for where the limits are in advanced mathematics and the rational systems this edifice is built from.

Kurt Gödel: An Eccentric Genius

The book opens with a lovely description of Kurt Gödel as a “strange and ultimately tragic man,” (Holt, 4). From his valitudinarian’s diet to the company he kept and his tendency to paranoia. The dialogues between Einstein and Gödel must have been fascinating, as these were two of the preeminent minds in physics and logic at the time. From our vantage point almost a hundred years later, it is still possible to empathize with certain of the questions Einstein had about quantum mechanics and that Gödel wrestled with about time.

Einstein’s critique of quantum mechanics may have misled him, but there is a definite strangeness to the idea that the world we perceive is ultimately, if one looks closely enough, just energy. The substance that matter seems to have at the human scale dissipates as we break things apart and everything ends up being made out of energy fields. The mystery is real: traveling fast enough seems to reduce the distance between points even in relativistic physics, but Democritus being wrong in the supposition that, at the smallest level, the world would turn out to be composed of indivisible atoms, simply seems like an utterly reasonable foundational idea about how the world is.

Likewise, Kurt Gödel had a bone to pick with time in light of both relativity and quantum mechanics. There is still essentially no arrow of time at the quantum level, and even renowned physicists of later generations such as Richard Feynman have never discovered a definitive physical basis for what we perceive as the one-way motion of the present moment. Einstein solved Poincarè’s unresolved physics problems; Gödel cast down the notion that mathematics was a complete science people were uncovering bit by bit, like archaeologists digging up ancient fossils. Instead, mathematical intuition aside, the door was opened for thinkers including both myself and Roger Penrose to make arguments about the minds of living things to transcend logical systems.

In a way, it is reassuring to see the great frustrations of the elite thinkers of the previous century: we all find our limits one way or another! In another sense, we find a reminder that science is a process and not a treasure hunt with a definitive conclusion for us to look forward to.

The People vs. Saul Kripke

Saul Kripke is a name I heard a lot back in grad school. A distinguished philosopher and professor emeritus at CUNY in New York City, I once applied to his department for the opportunity to earn a Ph.D in philosophy. This was in 2015-2016, so most of the drama we are about to discuss was already in the rear-view mirror and Kripke’s fame was winding down. However, the philosophy of language and logic is entwined deeply with Kripke’s thought after the events discussed in this essay. Interestingly, the discussion of whether these ideas were originally Kripke’s or not mirrors the issue of naming by resolving into the question of whether or not Kripke was a genius alongside Wittgenstein.

As I argued in Formal Dialectics, the linguistic part of reality is separate from the real world. We could think of what can and can’t be said as a virtual layer on top of reality that we interface with by activities like naming. Is it a sunny day if we don’t call it one? The concepts Kripke deals with are significant because they help us understand what we’re doing as we navigate the conceptual webs of meaning we spend so much time interacting with.

Which is it, then? Is Kripke the progenitor of the new theory of reference or not?

In my reading of the situation, scientific revolutions often involve contributions by a public of people interested in a problem; Poincaré thereby gets just a little credit for Einstein’s theory of Relativity because he listed the problems to be solved which inspired the patent office employee, perhaps. It seems that there is here, again, a compression happening that isn’t getting talked about. The issue is this: a discussion between a lot of people contains a web of information each has contributed to. These discussions are dialectical in nature, and the more diverse the ideas they contain are, the more far-reaching their conclusions can be. In classes and studies generally, Kripke became an expert on the philosophy of reference discussions of his day. In his books, he formulated the understanding of this subject matter that he had been able to cultivate. However, he may have omitted references he needed to include to provide all of the information about where he got his ideas from, so perhaps a certain amount of backlash from the other discussion participants is merited.

Nonetheless, one comes away from this essay with a sense that Holt is deliberately sculpting something quite remarkable in “Truth and Reference: A Philosophical Feud,” and it does an excellent job of characterizing the sorts of things analytical philosophers have been up to for the past 50 years or thereabouts.

Questions in Physics

The Copenhagen Interpretation is a question from the field of physics that has been solved, resulting in Bell’s Theorem. Still, the question of whether the subject of quantum mechanics is in focus or not bears some consideration. In Holt’s essay, Bell’s Theorem is concisely enumerated along with the other nuts and bolts of an open conceptual question in physics: why don’t relativity and quantum mechanics match up? From the point of view of relativity theory, a way of understanding the physical world, which works very well on large objects, quantum mechanics is nonsense. And yet, the predictions made by quantum mechanics have enabled endless advancements in communication and information technologies. If the theory didn’t resemble the world, why would it be so effective for designing working machinery?

As Jim Holt puts it, the Copenhagen interpretation of quantum mechanics was, according to Albert Einstein, a blurry picture of a sharp reality. Einstein’s criticism of the Copenhagen interpretation, namely that the particle/wave duality is ridiculous, involves calling into question the measurement which collapses the quantum state of superposition of the particles in question. For Einstein, entanglement is also sketchy - “spooky action at a distance.” One interesting idea that comes to mind here is that there is an assumption that a mind’s being conscious of something in the world does not have any direct impact upon the thing - that is, the observer is unobserved by the object. As Bell proved, observation has a real and measurable impact in quantum mechanics.

In the Worldview Ethics conception of an individual person, minds are taken to be enactive - that is, they do not operate upon the world from a unique, isolated situation in which they remain unaffected by the computations they perform. Instead, minds are continuously changing in every way that matters - neurons translocate, metabolic resources are continuously rerouted according to metabolic needs as well as metacognitive ones. The discussions of quantum fields by Roger Penrose still seem a bit beyond the boundary of physics to prove, but the specific character of relationships between entangled particles and a way of understanding the electromagnetic field component of consciousness are both at least potentially interesting theoretical destinations.

Wrapping up

When Einstein Walked With Gödel is a fascinating read that provides us with a strong grasp of some of the most interesting problems in science & philosophy. Holt’s painstaking mathematical characterizations are easy to follow as well as revealing, and his capable mind tackles even the most abstruse philosophical problems with the same rigorous ease. I recommend for any enthusiast in the vein of work I am building for Worldview Ethics to have a read of Jim Holt’s collection of essays to get a deep feel for the less explored terrain near the forefront of rational thinking today.

This review will constitute the fourth in the series, and the final introductory section review. Together with Outlive, The Runaway Species, and The Patterning Instinct, our high-level overview of the mind is now concluded! We will dive deeper into the language problems we find in advanced mathematics in the next series of reviews, which will include Complexity: A Guided Tour, Deep Thinking, and The Strange Order of Things. Melanie Mitchell does an excellent job with an introduction to complexity theory, updating us on the status of mathematics. Garry Kasparov tells us the story of the supercomputer that became world chess champion in 1997 to reveal a stunningly clear picture of artificial intelligence that is essential in the age of ChatGPT. And finally, Antonio Damasio bridges us from individual brains to cultures of human beings, building what may be the first neuroscientific model of distributed cognition in the process.

*Thanks for reading this piece! It is part of a broader investigation into the literature around consciousness and artificial intelligence. Find the index of these works at https://worldviewethics.cent.co/ .*