DOUGLAS HOFSTADTER'S new collection of essays begins with a lengthy discussion of self-reference and ends with a deeply-felt plea for nuclear sanity. An unkind reviewer might be tempted to observe that Hofstadter's concern with nuclear disarmament arises primarily from a self-referential fear that Hofstadter himself could die in WWIII; but his numerous comments on social consciousness make it clear that he really does care about his fellow Earthlings -- be they man, woman, beast or machine.

Educated as a physicist in the late 1960s, Hofstadter switched early into computer science. At the age of 34, he achieved national prominence with his first book, Godel, Escher, Bach. Well-designed and highly browsable, GEB captured the imagination of a new generation of intellectuals and won the Pulitzer Prize. When Martin Gardner stepped down as the mathematical games columnist of the Scientific American, Hofstadter was a natural choice for his successor. Most of the 33 essays in Metamagical Themas were written as Scientific American columns; "metamagical themas" being a rearrangement of the letters in "mathematical games." Since writing these essays, Hofstadter has left the Scientific American in order to concentrate on his research in AI, or artificial intelligence.

One of the main themes of Hofstadter's first book was Godel's Incompleteness Theorem. Godel's Theorem, proved by the reclusive Austrian mathematician in 1930, shows that human thought is more complex and less mechanical than anyone had ever believed. Throughout the materialistic, technology-worshipping 1940s and 1950s, the philosophical consequences of Godel's theorem were ignored. Godel's theorem was the private property of the mathematical logic establishment; and these academics were contemptuous of any suggestion that mathematics could have anything to do with something so woolly as "artificial intelligence." But, almost single- handedly, Hofstadter changed all that.

For Hofstadter, the essence of intelligence is the ability to see patterns and, having seen them, to slip them into different contexts. Metamagical Themas has not one, but two long essays that are basically meditations on what kind of a pattern can reasonably be thought of as a letter A: "The problem of intelligence, as I see it, is to understand the fluid nature of mental categories . . . To emphasize this and make the point as starkly as I can, I hereby make the following claim: The central problem of AI is the question: What is the letter 'a'?"

Historically speaking, the important part of Metamagical Themas is section V. Two new essays, "Who Shoves Whom Around Inside the Careenium?" and "Waking Up from the Boolean Dream," go into the question of how a computer program could ever learn to see and slip patterns in an intelligent way. Eloquently and convincingly, Hofstadter defends a new position that he summarizes under the rubric, "statistical emergence." His viewpoint is that a mind is something like a vat of simmering soup -- the hotter the temperature, the more disorganized the thoughts. Scraps of pattern occur at random; these pattern pieces attract each other, and sometimes they link together and freeze into large, cool thoughts. I don't think there is any doubt that Hofstadter's fellow-travelers will bring us robot consciousness by the 2050s. Apparently some of the older AI workers disapprove of Hofstadter's approach; in his own, folksy way, he is quite a revolutionary.

The pattern that recurs most often in Metamagical Themes is the notion of self-reference. We have discussions of self-mentioning sentences like: "This inert sentence is my body, but my soul is alive, dancing in the sparks of your brain." We have imaginary dialogues with robots who try to convince us they are alive; we have an introduction to the self-referential computer-language called Lisp; and we have accounts of physical and biological processes that develop in various oddly self-guiding ways.

SELF-REFERENCE is interesting but -- I've got to say this -- Themas has a lot of Douglas Hofstadter talking about Douglas Hofstadter. He tells us how fast he can solve the Rubik's Cube (remember the Cube?), how well he can play Chopin (I do wish he liked the Ramones), the funny things he says to his friends (they go to restaurants every night), how he creates (if you don't know by now, don't mess with it), how he is overcoming his sexism (get married, Doug, and then tell me about it), what various famous scientists think of his lectures (and then Feynman told me. . . .) -- on and on in a dense torrent of shameless self-regard. At the very beginning of the book, Hofstadter talks about some scribbles he keeps in his closet as being "quite possibly the most creative thing I have ever done," and observes that, as his scribbles are vaguely related to musical notation, "It is natural to wonder if I managed to jump beyond the twentieth century and make visual 21st-century music." Natural for whom, Doug?

But anyone used to reading Douglas Hofstadter will have learned to put up with this kind of thing. There's no one else like him, and he's worth it. At times his fanatic self-absorption can even be quite charming: "I myself once learned 380 digits of (the mathematical constant) pi, when I was a crazy high- school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes '999999,' so that I could recite it out loud, come to those six '9's, and then impishly say, 'and so on!'"

Curiously enough, Hofstadter's me-think translates into social consciousness. Metamagical Themas contains hard-hitting essays against sexism, racism, nuclear warfare, religious cultism, and the hoaxes of the National Enquirer. Hofstadter explains the relation between self-interest and unselfishness in a very interesting essay on the so-called "Prisoner's Dilemma." This is a kind of economic game in which two players repeatedly exchange goods, with the option of cheating (giving nothing) on any turn. The simplest strategy in this game is known as TIT FOR TAT: "Cheat if the other player cheated on the last turn; otherwise play honestly." Oddly enough, computer simulations have shown that over the course of many exchanges with many different kinds of strategies, the homespun niceness of TIT FOR TAT does much better than other, sneakier approaches.

Collections of essays do not always hang together very well. In one of this book's bibliographical notes, Hofstadter expresses a fear that Metamagical Themas is "a curious pot-pourri, bloated and muddled." He needn't worry. The essays illuminate each other wonderfully, and even the familiar essays are a pleasure to reread here with Hofstadter's candid postscripts. With Godel, Escher, Bach and Metamagical Themas, Douglas Hofstadter has ushered in a new, more personal approach to science writing. Ideas matter; and so do the people that have them.