• The Cambridge Quintet
  John L. Casti
  Buy This Book.
• A Beautiful Mind
  Sylvia Nasar
  Buy This Book.

The Cambridge Quintet
John L. Casti
Perseus Books
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After nearly half a century of living with computers, quite rational people still argue about whether such machines can really think. Two people can look at the same computer and where one sees artificial intelligence, the other sees a mindless embodiment of logical rules. The same two observers, of course, might very well disagree about another human being's state of mind, one seeing a madman where the other sees a visionary or a prophet. At the heart of such differences lie our deepest beliefs, and fears, about the nature of intelligence, rationality and the human mind. Two recent books explore such issues, one as a matter of pure reason, the other as a story of genius, insanity and love. John Casti's The Cambridge Quintet is a brilliant literary invention and intellectual feast. It is the account of an imagined dinner party at Cambridge University just after World War II, hosted by the famed writer C. P. Snow to pick the brains of other great minds about the prospects of actually constructing a "thinking machine." The guests are mathematician Alan Turing, who did pioneering work on such a project, along with biologist J.B.S. Haldane, quantum physicist Erwin Schrödinger and philosopher Ludwig Wittgenstein.

The chapters of the book are divided into the various courses of the meal: the sherry, the soup, the fish and so on. And the conversation is as rich as the menu. As the guests argue for and against the possibility of a thinking machine, the eavesdropping reader gets a deliciously clear and engaging account of the problem. Turing explains lucidly how, by manipulating the symbols 0 and 1, a machine can perform logical operations; and how this is analogous to the brain, where each individual neuron is switched on or off by its stimuli. "Moreover," Schrödinger offers, "both the computer and the brain process these data into patterns. Is that the analogy you're pursuing, Turing?"

"Precisely," Turing replies. "The brain stores its data in the form of patterns created by the firing of its neurons. Each such pattern is just a listing of which neurons are on and which are off at any given moment. These patterns are then associated with what we call 'thoughts' in ways that no one yet really understands." Brushing aside his own caveat — that all this occurs in a manner that hasn't yet been elucidated &$0151; Turing holds that "intelligence is just a matter of following the right kind of rules." Several generations of scientists have followed him down this path.

At Snow's dinner, however, it is Wittgenstein, the philosopher of language, who points to the flaw in Turing's reasoning. A pattern of symbols, or language, has no meaning, he says, apart from the shared experience of people using those symbols. "To have language is to have a way of life," he insists. "Everything we say is totally bound up with what we do." Whether the essence of language is syntax (the rules) or semantics (the meaning) continues to divide linguists as well as computer scientists and philosophers, but Casti's dinner debate is as clear as it is entertaining. Because Turing and his heirs define human thinking in abstract, mechanical terms, they believe machines can think. For Wittgenstein and his heirs, thinking follows the experience of life, not just the rules of logic, and machines have it not.

Perhaps, Casti concludes, the answer will lie in a divergence we can only guess at. "This half a century of research," he observes, "has shown that these are two distinct forms of intelligence, and that for a short period they will peacefully coexist. After the current, but brief interregnum, machines and humans will go their separate ways, much as humans and dolphins parted company many millennia ago."

A Beautiful Mind
Sylvia Nasar
Simon & Schuster
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In Sylvia Nasar's A Beautiful Mind, the experience of life and the rules of logic collide head on. In this strange and deeply moving biography, the young mathematical genius John Nash, "inventor of a theory of rational behavior" and "visionary of the thinking machine," loses his mind to schizophrenia — yet decades later reawakens to win a Nobel Prize for his earlier work and take up his own mathematical investigations again.

Nasar traces Nash's youthful ascendancy as a mathematician, as he turns his attention to the geometry of imaginary spaces and the mystery of prime numbers, and the work that won a Nobel, on the theory of games. "Nash's faith in rationality and the power of pure thought was extreme," she writes. "Einstein once chided him for wishing to amend relativity theory without studying physics."

But Nash rarely "studied" the problems he worked on, preferring to prove everything from scratch rather than read what others had already done. And it was this originality that led him to his greatest insights.

Nash's work on game theory, for a doctoral thesis at Princeton, provided a new basis for modern mathematical economics. Princeton's John von Neumann, who invented game theory, had searched in vain for ways to make it apply to the real world of economic competition. When young Nash brashly proposed a solution to the problem, von Neumann rejected it. But Nash demonstrated that decentralized decision-making could be analyzed rationally, and revolutionized economics.

At the age of 30, a year after marrying an adoring physics student, and as he was about to be made a full professor at MIT, Nash began acting irrationally, threatening his wife for hiding secrets from him, complaining that aliens from outer space were ruining his career, declining an academic offer from another university because, he said, he was soon to become the emperor of Antarctica.

Nash had always been odd, described by others as aloof, spooky, enigmatic. So for several months his pregnant wife, Alicia, was torn by fears for his sanity and doubts about the consequences of seeking psychiatric help. When she had him committed to a mental hospital, some of Nash's colleagues and friends attacked her and insisted he was sane. Nash, in fact, got a lawyer and a psychiatrist to convince a judge that he was sane; he was soon released.

The years that followed were a nightmare of erratic wanderings, delusions, intermittent jobs secured by academic friends, incarcerations and therapies, and eventually a kind of implosion into a strange solitude. For almost two decades, while his fame spread among economists, Nash wandered the Princeton campus as a wraith, a gaunt figure known as The Phantom who scribbled bizarre notations on blackboards, haunted the library and sometimes turned up at academic teas.

Throughout all these terrible years, Alicia followed him, protected him as best she could, raised their son and gave Nash a home. The strain on her was enormous. Several times she had him committed to asylums, but refused to authorize shock therapy, which Nash feared would impair his memory. At one point she divorced him but continued to shelter him as a "boarder." Her pain was doubled when their teenage son, Johnny, a promising young mathematician, was struck by schizophrenia.

As Alicia did, the Princeton community sheltered Nash with compassion. When he wandered into the computer center, students taught him some basics and left him alone. And then, miraculously, in the late 1980s Nash began to recover his sanity. A student at the computer center recalled: "In the early stages he was making up numbers out of names and being worried by what he found. Gradually, that went away. Then it was more mathematical numerology. Playing with formulas and factoring. It wasn't coherent math research, but it had lost its bizarre quality. Later it was real research."

Then, in October 1994, Harold Kuhn, a mathematics professor at Princeton and Nash's closest friend, conveyed some incredible news. "I have something to tell you, John," he began. An important telephone call, Kuhn informed Nash, would be coming from Stockholm, from the Executive Secretary of the Swedish Academy of Sciences: "He's going to tell you, John, that you have won a Nobel Prize."

Nash later described his own recovery as requiring the same kind of willpower as dieting: "If one makes an effort to rationalize one's thinking, then one can simply recognize and reject the irrational hypotheses of delusional thinking." And in this same vein, while he now spends much of his life devotedly caring for and nurturing his 38-year-old schizophrenic son, Nash says, "I don't think of my son...as entirely a sufferer. In part, he is simply choosing to escape from the world."

Considering the life of John Nash makes any academic debate about pure logic and intelligence seem dry indeed. For all his faith in rational behavior, Nash's mind would not have survived were it not for Alicia's great love, and he seems to have learned this lesson. Now in his 70s, with an office at Princeton to pursue mathematics, he finds his real place at home. He sets his clock by Alicia, Nasar writes: "Stubborn, reserved, self-centered, and jealous of his time (and money) as he is, Nash does nothing without consulting Alicia first, defers to her wishes, and tries to help her, whether it is by washing the dishes, straightening out a problem at the bank, or going with her to family therapy every Monday night. She is the one to whom he faithfully reports the day's events, whom he ran into, what the lecture was about, what he ate for lunch. They argue about money, the housework, Johnny, social engagements, but he has committed himself to making her life easier and more joyful."

Reviewer Paul Trachtman is based in New Mexico.

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