When Einstein Walked with Goedel: Excursions to the Edge of Thought--Jim Holt (5 stars)

[Michael]

A delightful set of 24 standard essays and 14 brief ones (a page or so) on the history of physics and math and current views on their relations. The essays highlight issues with Einstein’s theory of relativity (special and general), quantum mechanics, group theory, infinity and the infinitesimal, Turing’s theory of computability, Goedel’s incompleteness theorems, prime numbers and the Riemann zeta conjecture, category theory, topology, fractals, and the theory of truth. There are no equations, so we have to count on him to convey major discoveries and conflicting interpretations in words alone without distorting the truth. From a modest experience with the subject (a college course on quantum mechanics long ago and reads in recent years of popularizations by real physicists), I feel comfortable with Holt’s knowledge and competence as a science journalist. He achieved his goal of covering a lot of subjects on various themes:
My ideal is the cocktail-party chat: getting across a profound idea in brisk and amusing way to an interested friend by stripping it down to its essence …The goal is to enlighten the newcomer while providing a novel twist that will please the expert. And never to bore.

Successfully conveying the human aspects for all these figures is another skill that helped spur me onward. As a tiny example, the Nobel Prize winning physicist John Wheeler wondered is anyone made a theoretical connection between Heisenberg’s uncertainty principle and Goedel’s incompleteness theorem, so he knocked on Goedel’s door at Princeton’s Institute for Advanced Study. Goedel, huddled over a space heater, promptly threw him out.

Often there is a tragic element in the lives of the figures. Many of us are aware of Alan Turing’s sad state after WW2 due to the 2014 film, “The Imitation Game”, with his contributions to code-breaking kept secret, his persecution by “chemical castration” for being gay, and eventual suicide by poison apple. Holt tries to rectify the film’s inaccurate portrayal of him a “as a humorless and timorous nerd.” Here are a few more examples of nutters among the brilliant:

The creator of the theory of infinity, Georg Cantor, was a kabbalistic mystic who died in an insane asylum. Ada Lovelace, the cult goddess of cyber feminism … was plagued by nervous crises brought on by her obsession with atoning for the incestuous excesses of her father, Lord Byron. …Kurt Goedel, the greatest of all modern logicians, starved himself to death out of the paranoic belief that there was a universal conspiracy to poison him.

Holt takes a strange excursion with novelist David Foster Wallace’s 300-page exposition (“Everything and More”) on Cantor’s 19th century accomplishment in using set theory to prove some infinities and bigger than others, in effect creating a whole tower of infinities. Holt finds he succeeded in his goal of improving on “certain recent pop books that give such shallow and reductive accounts of Cantor’s proofs …the math is distorted and its beauty obscured” and “if he was sometimes in over his head, it is because he chose to wade through the deepest waters”. In contrast to Wallace’s admiration, Wittgenstein found that:

There is nothing awesome about the theory; it does not describe a world of timeless, transcendent, scarcely conceivable entities; it is really no more than a collection (finite) tricks of reasoning. One might imagine, Wittgenstein said, the theory of infinite sets was “created by a satirist as a kind of parody of mathematics”. …As a description of Cantor’s work on infinity, it is surely unjust. As a description of Wallace’s, it might be taken as a tribute.

Basically, Holt trusts the average man to appreciate major problems in physics. So many mathematicians wax poetic about the connection between beauty of their theorems and equations and truth. A new kind of Platonism is alive and well among many of the wizards, i.e. a belief that mathematicians are not inventing their formulas but are discovering timeless truths beyond space and time. However, for Holt:

The problem with this Platonist view of mathematics … is that it makes mathematical knowledge a miracle. If the objects of mathematics exist apart from us, living in a Platonic heaven that transcends the physical world of space and time, then how does the human mind “get in touch” with them and learn about their properties and relations? Do mathematicians have ESP? The trouble with Platonism, as the philosopher Hilary Putnam has observed, “is that it seems flatly incompatible with the simple fact that we think with our brains, and not with immaterial souls.”.

Not all mathematical proofs are elegant. In the case of the “Four Color Problem”, the proof that any map of geometrical elements can be colored with four colors without any adjacent regions getting a common color took over 700 pages of arguments and a zillion computer calculations of all the permutations. Conversely, beautiful elegant equations can lead one astray. In the case of string theory, we have a brilliant mathematical system based on vibrating membranes in nine dimensions which aims to unify the major laws of physics. It has captured the imagination and life efforts of many theoretical physicists for three decades. Because of the inaccessible six extra dimensions, experimental tests of the theory have not been possible. Moreover:
In a space of more than three dimensions, there would be no stable planetary orbits. (This was proved over a century ago by Paul Ehrenfest). Nor would there be stable orbits for electrons within atoms. Therefore, there could be no chemistry, and hence no chemically-based life forms, in a world of more than three spatial dimensions. …
So it should not come as a surprise that we find ourselves living in a three-dimensional world. (Physicists call this “anthropic” reasoning). …And we can surely sympathize with the aspiration of Mr. Square [a 2-D character in “Flatland”]—not to mention assorted Theosophists, Platonists, and cubists—to rise up into the splendor of the fourth dimension and beyond. But we need not follow them. For intellectual richness and aesthetic variety, a world of three dimensions is world enough.

I also learned some more about Einstein’s long struggle to pin down what was wrong with the standard model of quantum mechanics. Instead, of simply objecting to it on the basis of core uncertainties in reality (“God does not play dice with the universe”), he made a significant contribution in revealing it to violate the fundamental principle of locality, which posits “that the world consists of separately existing physical objects and that these objects can directly affect one another only if they come into contact” or “through causal intermediaries that bridge the distance between them.” His collaborative thought experiment known as EPR in 1927 proposed an electron in a box which then gets partitioned and the two halves moved far apart; according to the standard theory, opening one box to detect the electron, collapsing the probability wave, is predicted to instantaneously to cause the other box to be empty, a “spooky action at a distance” he took as evidence of the theory’s insufficiency. Unfortunately for Einstein’s stubborn resistence, John Stewart Bell much later designed a variant of EPR involving paired photons which allowed experimental testing. So called quantum entanglement between particles was indeed proven to involve “spooky action at a distance” according to at least three replication Thus, we must accommodate a new conception of space and the possibilities of some kind of “holistic” principle.

One chapter that was especially entertaining has Holt running around and asking notable physicists how the universe and humanity will end. Recent changes in cosmology have shaken people up. For a long time the Big Bang and movement of galaxies away from each other was predicted to be slowed by gravitational attraction, perhaps leading to a Big Crunch and another cycle. I empathize with little Alvy in Woodie Allen’s “Annie Hall”, who was much distressed with an expanding universe, despite reassurances of his psychiatrist and mother that things are safe for zillions of years and Brooklyn shows no signs of expanding. Now with unknown “dark energy” causing everything to accelerate away from each other, we are back to the idea of a “heat death”, where all matter is scattered and degraded to a virtual nothing (unless dark energy runs out of steam). Most physicists don’t really worry how all will end, while others project we will overcome the problems such as adapting ourselves to energy forms in a dust cloud or by building quantum tunneling devices to move us to another universe. In my case, I appreciate Holt’s use of the anthropic principle and a Copernician assumption of humans as not so special and likely in the Bell curve of the normal distribution to predict a duration of humankind as at most a few millions of years, in line with other mammalian species.

All in all a fun read and I think accessible to most general readers.

[KateNZ]

Amazing review, Michael.

I am sorely tempted to give this a go, though a lot of it might end up being lost on me - the history of science and the personalities involved are so interesting though

[Nikki]

Thanks for the thorough review! I'm intrigued, I think I'll add this one to my list (which seems to be growing a lot faster since I joined this group...)

[Michael]

Nikki wrote: "Thanks for the thorough review! I'm intrigued, ..."

KateNZ wrote: "Amazing review, Michael.
I am sorely tempted to give this a go, ..."

Thanks for responding. Once you try one essay, and you are amazed to understand him on a challenging topic, its like a bowl of popcorn.