Why Does the World Exist: An Existentia - By Jim Holt Page 0,79

concluded that the objects contemplated by mathematicians must exist in another world, one that is eternal and transcendent. And today’s mathematical Platonists agree. Among the most distinguished of them is Alain Connes, holder of the Chair of Analysis and Geometry at the Collège de France, who has averred that “there exists, independently of the human mind, a raw and immutable mathematical reality.” Another contemporary Platonist is René Thom, who became famous in the 1970s as the father of catastrophe theory. “Mathematicians should have the courage of their most profound convictions,” Thom has declared, “and thus affirm that mathematical forms indeed have an existence that is independent of the mind considering them.”

Platonism is understandably seductive to mathematicians. It means that the entities they study are no mere artifacts of the human mind: these entities are discovered, not invented. Mathematicians are like seers, peering out at a Platonic cosmos of abstract forms that is invisible to lesser mortals. As the great logician Kurt Gödel, among the staunchest of Platonists, put it, “We do have something like a perception” of mathematical objects, “despite their remoteness from sense experience.” And Gödel was quite sure that the Platonic realm which mathematicians imagined themselves to be perceiving was no collective hallucination. “I don’t see any reason why we should have less confidence in this kind of perception, i.e., in mathematical intuition, than in sense perception,” he declared. (Gödel also believed in the existence of ghosts, but that is another matter.)

Many physicists also feel the allure of Plato’s vision. Not only do mathematical entities seem to be “out there”—eternal, objective, immutable—they also appear to be sovereign over the physical universe. How else can we account for what the physicist Eugene Wigner famously called the “unreasonable effectiveness of mathematics in the natural sciences”? Mathematical beauty has time and again proved to be a reliable guide to physical truth, even in the absence of empirical evidence. “You can recognize truth by its beauty and simplicity,” said Richard Feynman. “When you get it right, it is obvious that it’s right.” If, in Galileo’s phrase, the “book of nature is written in the language of mathematics,” this could only be because the natural world itself is inherently mathematical. As the astronomer James Jeans picturesquely put it, “God is a mathematician.”

To a devout Platonist, though, this invocation of God is merely a bit of superfluous poetry. Who needs a creator when mathematics by itself might be capable of engendering and sustaining a universe? Mathematics feels real, and the world feels mathematical. Could it be that mathematics furnishes the key to the mystery of being? If mathematical entities do exist, as the Platonists believe, they must exist necessarily, from all eternity. Perhaps this eternal mathematical richness somehow spilled over into a physical cosmos—a cosmos of such complexity that it gave rise to conscious beings who are able to make contact with the Platonic world whence they ultimately sprang.

This is a pretty picture. But could anyone who is not in the habit of eating lotus leaves take it seriously?

I had the impression that at least one quite rigorous thinker did: Sir Roger Penrose, the emeritus Rouse Ball Professor of Mathematics at Oxford. Penrose is among the most formidable mathematical physicists alive. He has been hailed by fellow physicists, notably Kip Thorne, for bringing higher mathematics back into theoretical physics after a long period in which the two fields had ceased to communicate. In the 1960s, working with Stephen Hawking, Penrose used sophisticated mathematical techniques to prove that the expansion of the universe out of the Big Bang must have been a precise reversal of the collapse of a star into a black hole. In other words, the universe must have begun as a singularity. In the 1970s, Penrose developed the “cosmic censorship hypothesis,” which says that every singularity is cloaked by an “event horizon” that protects the rest of the universe from the breakdown of physical laws. Penrose has also been a pioneer of “twistor theory,” a beautiful new approach to reconciling general relativity with quantum mechanics. In 1994, Queen Elizabeth bestowed a knighthood on Penrose for such achievements.

Penrose also has a penchant for oddities. As a graduate student, he became obsessed with “impossible objects”—that is, physical objects that seem to defy the logic of three-dimensional space. His success in “constructing” one such impossible object, now known as the “Penrose tribar,” inspired M. C. Escher to create two of his most famous prints: Ascending and Descending, which depicts a gaggle of monks endlessly tromping