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

by Jim Holt

Inside the system, it is neither provable nor disprovable. The system, then, is incomplete, because there is at least one true proposition about numbers (the one that says “I am not provable”) that cannot be proved within it. The conclusion—that no logical system can capture all the truths of mathematics—is known as the first incompleteness theorem. Gödel also proved that no logical system for mathematics could, by its own devices, be shown to be free from inconsistency, a result known as the second incompleteness theorem.

If time travel is possible, he submitted, then time itself is impossible. A past that can be revisited has not really passed. And the fact that the actual universe is expanding, rather than rotating, is irrelevant. Time, like God, is either necessary or nothing; if it disappears in one possible universe, it is undermined in every possible universe, including our own.

A certain futility marked the last years of both Gödel and Einstein. What might have been most futile, however, was their willed belief in the unreality of time. The temptation was understandable. If time is merely in our minds, perhaps we can hope to escape it into a timeless eternity. Then we could say, like William Blake, “I see the Past, Present, and Future existing all at once / Before me.” In Gödel’s case, it might have been his childhood terror of a fatally damaged heart that attracted him to the idea of a timeless universe. Toward the end of his life, he told one confidant that he had long awaited an epiphany that would enable him to see the world in a new light but that it never came.

Our conscious now—what William James dubbed the “specious present”—is actually an interval of about three seconds. That is the span over which our brains knit up arriving sense data into a unified experience.

“Time is nature’s way to keep everything from happening all at once.”

“Time is a great teacher, but unfortunately it kills all its pupils.”

Mathematics, the aged Russell wrote, “has ceased to seem to me non-human in its subject-matter. I have come to believe, though very reluctantly, that it consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-footed animal is an animal.”

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.”

The digital universe came into existence, physically speaking, late in 1950, in Princeton, New Jersey, at the end of Olden Lane. That was when and where the first genuine computer—a high-speed, stored-program, all-purpose digital-reckoning device—stirred into action. It had been wired together, largely out of military surplus components, in a one-story cement-block building that the Institute for Advanced Study had constructed for the purpose. The new machine was dubbed MANIAC, an acronym of “Mathematical and Numerical Integrator and Computer.”

The computer, one might well conclude, was conceived in sin. Its birth helped ratchet up, by several orders of magnitude, the destructive force available to the superpowers during the cold war. And the man most responsible for the creation of that first computer, John von Neumann, was himself among the most ardent of the cold warriors, an advocate of a preemptive military attack on the Soviet Union, and one of the models for the film character Dr. Strangelove. “The digital universe and the hydrogen bomb were brought into existence at the same time,” the historian of science George Dyson has observed. Von Neumann had seemingly made a deal with the devil: “The scientists would get the computers, and the military would get the bombs.” And many scientists at the institute were by no means happy with this deal—including one who wrote STOP THE BOMB in the dust on von Neumann’s car.

We know that creativity is empirically correlated with mood-swing disorders. A couple of decades ago, Harvard researchers found that people showing “exceptional creativity”—which they put at less than 1 percent of the population—were more likely to suffer from manic depression or to be near-relatives of manic-depressives. As for the psychological mechanisms behind creative genius, those remain pretty much a mystery. 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.

The most incompetent people have the most inflated notion of their abilities. “Not only do they reach erroneous conclusions and make unfortunate choices,” the two psychologists observed, “but their incompetence robs them of the ability to realize it.”

“It is the final proof of God’s omnipotence that he need not exist in order to save us.”