Why Does the World Exist: An Existentia - By Jim Holt Page 0,80

up—or down?—a staircase that goes nowhere, and Waterfall, which shows a perpetually descending circuit of water. (I once heard the philosopher Arthur Danto say that every philosophy department should keep an impossible object around the office, to instill a sense of metaphysical humility.)

Penrose, I knew, is an unabashed Platonist. Over the years, in his writings and public lectures, he has made it clear that he takes mathematical entities to be as real and mind-independent as Mount Everest. Nor has he been shy about invoking the name of Plato himself. “I imagine that whenever the mind perceives a mathematical idea it makes contact with Plato’s world of mathematical concepts,” he wrote in his 1989 book, The Emperor’s New Mind. “The mental images that each [mathematician] has, when making this Platonic contact, might be rather different in each case, but communication is possible because each is directly in contact with the same eternally existing Platonic world!”

What really piqued my interest, though, was Penrose’s occasional hint that our own world was an outcropping of this Platonic world. I first noticed such hints in his second book for a popular audience, Shadows of the Mind, which came out in 1994 and, like its intellectually daunting predecessor, was an improbable bestseller. Penrose began by arguing, based on an appeal to Gödel’s incompleteness theorem, that the human mind had powers of mathematical discovery that exceeded those of any possible computer. Such powers, Penrose contended, must be essentially quantum in nature. And they would be understood only when physicists had discovered a theory of quantum gravity—the holy grail of contemporary physics. Such a theory would finally make sense of the bizarre interface between the quantum world and classical reality—and, in the bargain, it would reveal how the human brain leapfrogs the bounds of mechanical computation into full Technicolor consciousness.

Penrose’s ideas on consciousness did not impress many brain scientists. As the late Francis Crick irritably jibed, “His argument is that quantum gravity is mysterious and consciousness is mysterious and wouldn’t it be wonderful if one explained the other.” Yet there was more to Penrose’s agenda than that. The very title of his book, Shadows of the Mind, was a double entendre. On the one hand, it was meant to suggest that the electrical activities of our brain cells, usually thought to be the cause of our mental life, are mere “shadows” cast by deeper quantum processes going on in the brain, which are the true springs of consciousness.

On the other hand, “shadows” harkened back to Plato—specifically, to Plato’s Allegory of the Cave, from Book VII of the Republic. In this allegory, Plato likens us to prisoners chained in a cave and condemned to look only at the rock wall in front of them. On that wall they see a play of shadows, which they take for reality. Little do they realize that there is a world of real things behind them which is the source of these shadowy images. If one of the prisoners were to be liberated from the cave, he would initially be blinded by the sunlight outside. But as his eyes adjusted, he would come to understand his new surroundings. And what would happen if he returned to the cave to tell his fellow prisoners about the real world? Unused to the darkness after his time in the sunlight, he would be unable to make out the shadows they took for reality. His tale of a real world outside the cave would “provoke laughter.” The other prisoners would say that “he had returned from his journey aloft with his eyes ruined,” and that “it was not worthwhile even to attempt the ascent.”

This outside world in the Allegory of the Cave stands for the timeless realm of Forms, wherein genuine reality resides. For Plato, the inhabitants of this realm included abstractions like Goodness and Beauty, as well as the perfect objects of mathematics. Was Penrose, in suggesting that what we took to be reality consisted of “shadows” of such a realm, merely trafficking in neo-Platonist mysticism? Or did his almost unrivalled grasp of quantum theory and relativity, of singularities and black holes, of higher mathematics and the nature of consciousness, afford him genuine insight into the mystery of existence?

I did not have to journey far to obtain enlightenment on this matter. Waiting for the elevator one day in the lobby of the mathematics building at New York University, I saw an announcement that Penrose would soon be coming to Manhattan. He had been invited to deliver