Mind Games

By Stephen Hawking and Roger Penrose
Princeton University Press, 141 pp.

If there were such a thing as the World Professional Heavyweight-Theory Debating Society, this would be the title bout. It would be held at Caesar’s Palace. It would be available on pay-per-view.

Up for grabs? Bragging rights to the biggest theoretical explanation of them all, the explanation of absolutely everything — The Nature of Space and Time.

In this corner, his accomplishments all the more astonishing because of the severity of his infirmity . . . well known to the media and fans of quantum physics as the Isaac Newton of his day . . . Lucasian Professor of Mathematics at the University of Cambridge . . . Stephen Hawking.

And in this corner, a dangerous opponent . . . the author of The Emperor’s New Mind . . . a man whose ideas are subtly, subversively opposed to Hawking’s . . . Rouse Ball Professor of Mathematics at the University of Oxford . . . Roger Penrose.

There’s the bell, and the two contenders come out thinking.

General relativity, you folks at home will recall, describes the architecture of the universe on the grandest, cosmological scale. Quantum physics, meanwhile, explains things at the smallest, subatomic dimensions. But at the point of creation (the Big Bang) or at sidereal singularities (black holes), the impossibly big becomes the impossibly small, and one or other set of equations breaks down into gibberish. They can’t both be right.

At issue here is whether and in what regard quantum physics and general relativity can be reconciled in a grand unified theory. In alternating chapters, this slim volume reproduces a series of lectures sponsored by the Isaac Newton Institute – three by Hawking, three by Penrose – culminating in a final Q&A. Dust off your calculus. You’re going to need it.

Round One: Hawking sets the pace with his account of “Classical Theory.”

“Define I+(p) to be the set of all points of the spacetime M that can be reached from p by future-directed timelike curves . . . There are similar definitions in which plus is replaced by minus and future by past. I shall regard such definitions as self-evident.” Me too.

Round Two: Penrose responds with the concept of cosmic censorship, which seems to imply that what one cannot observe cannot happen, although he takes pains to insist that his inability to prove this principle is not – as Hawking perversely suggests – evidence of its veracity. So there.

Round Three: Hawking speculates that if there can be macroscopic black holes – points in space with the gravitational pull of collapsed stars – there might be microscopic black holes, sucking in matter then disappearing. “Maybe,” he ponders, “that is where all those odd socks went.”

Round Four: In a reworking of Schrödinger’s famous thought experiment, Penrose spends an entire chapter metaphorically killing and unkilling a cat.

Round Five: Hawking’s handling of the equations shows that we live in “an isotropic and homogenous expanding universe with small perturbations.” At this point, I felt a splitting headache coming on and had to lie down for a nap.

I didn’t wake up until well into Chapter Six, only to learn that “projective twistor space can be co-ordinatized by the ratios of four complex numbers.” “This,” Penrose concedes, “is usually where people start to get confused.”

Officially confused, I went out into the back yard and looked up at the night sky. It really is beautiful. And which of them is right, Hawking or Penrose? Beats me. That’s a secret known only to the inner circle of the mathematical cognoscenti, and even they are divided. What good is an explanation almost no one can understand?eg

  • Globe and Mail March 21, 1996