Theo Todman's Book Collection (Book-Paper Abstracts)

Foreword by Martin Gardner (Full Text)

1. Many great mathematicians and physicists find it difficult, if not impossible, to write a book that non-professionals can understand. Until this year one might have supposed that Roger Penrose, one of the world's most knowledgeable and creative mathematical physicists, belonged to such a class. Those of us who had read his non-technical articles and lectures knew better. Even so, it came as a delightful surprise to find that Penrose had taken time off from his labours to produce a marvellous book for informed laymen. It is a book that I believe will become a classic.
2. Although Penrose's chapters range widely over relativity theory, quantum mechanics¹, and cosmology, their central concern is what philosophers call the ‘mind—body problem'. For decades now the proponents of ‘strong Al' (Artificial Intelligence)² have tried to persuade us that it is only a matter of a century or two (some have lowered the time to fifty years!) until electronic computers will be doing everything a human mind can do. Stimulated by science fiction read in their youth, and convinced that our minds are simply ‘computers made of meat' (as Marvin Minsky once put it), they take for granted that pleasure and pain, the appreciation of beauty and humour, consciousness, and free will are capacities that will emerge naturally when electronic robots become sufficiently complex in their algorithmic behaviour.
3. Some philosophers of science (notably John Searle, whose notorious Chinese room thought experiment³ is discussed in depth by Penrose), strongly disagree. To them a computer is not essentially different from mechanical calculators that operate with wheels, levers, or anything that transmits signals. (One can base a computer on rolling marbles or water moving through pipes.) Because electricity travels through wires faster than other forms of energy (except light) it can twiddle symbols more rapidly than mechanical calculators, and therefore handle tasks of enormous complexity. But does an electrical computer ‘understand' what it is doing in a way that is superior to the ‘understanding' of an abacus? Computers now play grandmaster chess. Do they 'understand' the game any better than a tick-tack-toe machine that a group of computer hackers once constructed with tinker toys?
4. Penrose's book is the most powerful attack yet written on strong Al. Objections have been raised in past centuries to the reductionist claim that a mind is a machine operated by known laws of physics, but Penrose's offensive is more persuasive because it draws on information not available to earlier writers. The book reveals Penrose to be more than a mathematical physicist. He is also a philosopher of first rank, unafraid to grapple with problems that contemporary philosophers tend to dismiss as meaningless.
5. Penrose also has the courage to affirm, contrary to a growing denial by a small group of physicists, a robust realism. Not only is the universe ‘out there', but mathematical truth also has its own mysterious independence and timelessness. Like Newton and Einstein, Penrose has a profound sense of humility and awe toward both the physical world and the Platonic realm of pure mathematics. The distinguished number theorist Paul Erdos likes to speak of ‘God's book' in which all the best proofs are recorded. Mathematicians are occasionally allowed to glimpse part of a page. When a physicist or a mathematician experiences a sudden ‘aha' insight, Penrose believes, it is more than just something 'conjured up by complicated calculation'. It is mind making contact for a moment with objective truth. Could it be, he wonders, that Plato's world and the physical world (which physicists have now dissolved into mathematics) are really one and the same?
6. Many pages in Penrose's book are devoted to a famous fractal-like structure called the Mandelbrot set after Benoit Mandelbrot who discovered it. Although self-similar in a statistical sense as portions of it are enlarged, its infinitely convoluted pattern keeps changing in unpredictable ways. Penrose finds it incomprehensible (as do I) that anyone could suppose that this exotic structure is not as much ‘out there' as Mount Everest is, subject to exploration in the way a jungle is explored.
7. Penrose is one of an increasingly large band of physicists who think Einstein was not being stubborn or muddle-headed when he said his ‘little finger' told him that quantum mechanics⁴ is incomplete. To support this contention, Penrose takes you on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, the bewildering paradoxes of quantum mechanics⁵, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, the structure of the brain, and scores of other topics at the heart of current speculations. Are dogs and cats ‘conscious' of themselves? Is it possible in theory for a matter-transmission machine to translocate a person from here to there the way astronauts are beamed up and down in television's Star Trek series? What is the survival value that evolution found in producing consciousness? Is there a level beyond quantum mechanics⁶ in which the direction of time and the distinction between right and left are firmly embedded? Are the laws of quantum mechanics⁷, perhaps even deeper laws, essential for the operation of a mind?
8. To the last two questions Penrose answers yes. His famous theory of ‘twistors' — abstract geometrical objects which operate in a higher-dimensional complex space that underlies space-time — is too technical for inclusion in this book. They are Penrose's efforts over two decades to probe a region deeper than the fields and particles of quantum mechanics⁸. In his fourfold classification of theories as superb, useful, tentative, and misguided, Penrose modestly puts twistor theory in the tentative class, along with superstrings and other grand unification schemes now hotly debated.
9. Since 1973 Penrose has been the Rouse Ball Professor of Mathematics at Oxford University. The title is appropriate because W. W. Rouse Ball not only was a noted mathematician, he was also an amateur magician with such an ardent interest in recreational mathematics that he wrote the classic English work on this field, Mathematical Recreations and Essays. Penrose shares Ball's enthusiasm for play. In his youth he discovered an ‘impossible object' called a ‘tribar'. (An impossible object is a drawing of a solid figure that cannot exist because it embodies self-contradictory elements.) He and his father Lionel, a geneticist, turned the tribar into the Penrose Staircase, a structure that Maurits Escher used in two well-known lithographs: Ascending and Descending, and Waterfall. One day when Penrose was lying in bed, in what he called a ‘fit of madness', he visualized an impossible object in four-dimensional space. It is something, he said, that a four-space creature, if it came upon it, would exclaim ‘My God, what's that?'
10. During the 1960s, when Penrose worked on cosmology with his friend Stephen Hawking, he made what is perhaps his best known discovery. If relativity theory holds ‘all the way down', there must be a singularity in every black hole where the laws of physics no longer apply. Even this achievement has been eclipsed in recent years by Penrose's construction of two shapes that tile the plane, in the manner of an Escher tessellation, but which can tile it only in a non-periodic way. (You can read about these amazing shapes in my book Penrose Tiles to Trapdoor Ciphers.) Penrose invented them, or rather discovered them, without any expectation they would be useful. To everybody's astonishment it turned out that three-dimensional forms of his tiles may underlie a strange new kind of matter. Studying these 'quasicrystals' is now one of the most active research areas in crystallography. It is also the most dramatic instance in modern times of how playful mathematics can have unanticipated applications.
11. Penrose's achievements in mathematics and physics — and I have touched on only a small fraction — spring from a lifelong sense of wonder toward the mystery and beauty of being. His little finger tells him that the human mind is more than just a collection of tiny wires and switches. The Adam of his prologue and epilogue is partly a symbol of the dawn of consciousness in the slow evolution of sentient life. To me he is also Penrose — the child sitting in the third row, a distance back from the leaders of Al - who dares to suggest that the emperors of strong AI have no clothes. Many of Penrose's opinions are infused with humour, but this one is no laughing matter.