THE EMPEROR'S NEW MIND
Concerning Computers, Minds, and the Laws of Physics
Roger Penrose
Oxford University Press, 1989
466 pp., $24.95
Reviews should surely be of books, not of authors; but when someone proposes radical changes to our accepted worldviews, we tend to examine his personal credentials as the first step toward establishing credibility. What then are the credentials of Roger Penrose, author of The Emperor's New Mind?
He has been a creative force in mathematics and theoretical physics for thirty-five years. While still a graduate student at Cambridge, England, in the mid-1950s, he developed Penrose's Theorem, a general theorem on plane conics with double contact, from which hundreds of other well-known results fall out as special cases. In the same period he and his father, the well-known geneticist Lionel Penrose, developed the "impossible" three-dimensional figures that form the basis of several of the artist Maurits Escher's best-known drawings.
In 1960 Penrose introduced the spinors of Elie Cartan into general relativity, where they have become a powerful and accepted analytic method; five years latter, with Ezra Newman, he found a new way to characterize space-time geometry through the Newman-Penrose constants. His best-known work in general relativity comes from the same period: the singularity theorems, which characterize the global geometry of space-time. For this work, Penrose and coworker Stephen Hawking were awarded the Wolf medal. A few years later Penrose found process by which energy can be extracted from a spinning black hole by particles that enter a certain region, dubbed the "ergosphere."
In the early 1970s Penrose made his best-known discovery, an aperiodic tiling of the plane with fivefold symmetry using just two shapes of tile. This unexpected result provide to be of practical importance with the discovery of real-world crystal structures that display similar fivefold "impossible" symmetry.
His work has been highly diverse, and all of it is characterized by ingenuity and great geometrical insight. More important, much of it is also surprising, solving problems that no one else had suspected might exist and stimulating the production of large volumes of work by later investigators.
In short, Penrose's credentials as a mathematical physicist are impeccable. Rouse-Ball Professor of Mathematics at Oxford since 1973, he is without doubt one of the world's great problem solvers. When he proposes a radically new concept, he may be right or he may be wrong, but his ideas cannot lightly be dismissed.
Mathematics and logic
The central issue of Penrose's book concerns the final limitations of computing equipment, as understood and designed according to today's theories of artificial intelligence (AI). The human brain, argues Penrose, employs procedures and involves basic physics that are quite outside the purview of AI and machine intelligence as we know it today. But although Penrose suggests this thesis in the first
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