When Einstein Walked with Gödel: Excursions to the Edge of Thought

by Jim Holt

Physicists talk about finding the “theory of everything”; well, set theory is so sweeping in its generality that it might appear to be “the theory of theories of everything.”

The Fractalist is not a flowing memoir; indeed, it has a fractal roughness of its own.

Occasionally, there are jarring notes of hauteur (“I reach beyond arrogance when I proclaim…”) and injured merit (“I don’t seek power or run around asking for favors … Academia found me unsuitable”).

Training ourselves to conceive of “a more spacious Space” than that of our three-dimensional world may enlarge our imagination and contribute to the progress of science. And we can surely sympathize with the aspiration of Mr. Square—not to mention assorted Theosophists, Platonists, and cubists—to rise up into the splendor of the fourth dimension and beyond.

But mathematicians, like the rest of us, think with their brains. And it is hard to see how a physical system like the brain could interact with a nonphysical reality. As the philosopher Hilary Putnam observed, “We cannot envisage any kind of neural process that could even correspond to the ‘perception of a mathematical object.’”

As Cantor himself once declared, “The essence of mathematics is freedom.”

Two years later, the fifty-two-year-old von Neumann lay dying of bone cancer in Walter Reed Army Hospital, disconcerting his family by converting to Catholicism near the end. (His daughter believed that von Neumann, an inventor of game theory, must have had Pascal’s wager in mind.) “When von Neumann tragically died, the snobs took their revenge and got rid of the computing project root and branch,” the physicist Freeman Dyson later commented, adding that “the demise of our computer group was a disaster not only for Princeton but for science as a whole.”

A book provides a “steady drip” of information that through sustained concentration we can transfer by means of this thimble with little spillage. But on the web, Carr writes, “we face many information faucets, all going full blast.

No study has shown that Internet use degrades the ability to learn from a book, though that doesn’t stop people from feeling that this is so; one medical blogger quoted by Carr laments, “I can’t read War and Peace anymore.”

This sort of “outré posturing” by intellectuals rankles with Carr because, he thinks, it enables ordinary people “to convince themselves that surfing the Web is a suitable, even superior, substitute for deep reading and other forms of calm and attentive thought.”

“The Net’s interactivity gives us powerful new tools for finding information, expressing ourselves, and conversing with others,” but it “also turns us into lab rats constantly pressing levers to get tiny pellets of social or intellectual nourishment.”

So which fits better with your ideal of eudaemonia, deep reading or power browsing? Should you set up housekeeping in Sleepy Hollow or next to the information superhighway? The solution, one might decide, is to opt for a bit of both.

That’s understandable: it’s the product of blind evolution, not of rational engineering. Unlike a computer, which assigns each bit of information a precise address in its data banks, human memory is organized contextually.

Unrehearsed memories soon sink into oblivion.

About the only point generally agreed on is that, as Pinker put it, “geniuses are wonks.” They work hard; they immerse themselves in their genre.

To understand the birth of the universe, we need a theory that “unifies” general relativity and quantum mechanics. That is the theoretical physicist’s dream.

Its proponents now inveigh against what they call “the myth of uniqueness and elegance.”

“A good, honest look at the real world does not suggest a pattern of mathematical minimality,” says the Stanford physicist Leonard Susskind, who seems to have no regrets about string theory’s having “gone from being Beauty to the Beast.”

The current problem with physics, according to Smolin, is basically a problem of style. The initiators of the dual revolution a century ago—Einstein, Bohr, Schrödinger, Heisenberg—were deep thinkers, or “seers.” They confronted questions about space, time, and matter in a philosophical way. The new theories they created were essentially correct. But “the development of these theories required a lot of hard technical work, and so for several generations physics was ‘normal science’ and was dominated by master craftspeople,” Smolin observes. “The paradoxical situation of string theory—so much promise, so little fulfillment—is exactly what you get when a lot of highly trained master craftspeople try to do the work of seers.” Today, the challenge of unifying physics will require another revolution, one that mere virtuoso calculators are ill-equipped to carry out. And the solution, presumably, is to cultivate a new generation of seers.

“God does not play dice,” he famously said. But it was not randomness per se that bothered Einstein. Rather, it was his suspicion that the appearance of randomness in quantum mechanics was a sign that the new theory didn’t tell the whole story of what was going on in the physical world.

Yet a deeper understanding of entanglement and nonlocality is also crucial to resolving the perennial argument over how to “interpret” quantum mechanics—how to give a realistic account of what happens when a measurement is made and the wave function mysteriously and randomly “collapses.” This is the very problem that vexed Einstein, and it is one that still vexes a small and contentious community of physicists (like Sir Roger Penrose, Sheldon Goldstein, and Sean Carroll) and philosophers of physics (like David Z. Albert, Tim Maudlin, and David Wallace) who continue to demand from physics the same thing that Einstein did: a unified and intelligible account of how the world really is.

Spinoza went to the contrary extreme, declaring, “A free man thinks least of all of death.”