IN THE PALACES OF MEMORY; How We Build the Worlds Inside Our Heads BY George Johnson Knopf. 255 pp. $22.95

TIME'S ARROW points only one way. Events leave traces of an unalterable past, not just in the outside world, but also stamped like moon craters on the gray terrain inside our skulls. Without memories we would be more like pebbles than potatoes. How does the brain do it? By what magic does it store memories that can be called up at will? This is the dark question that George Johnson bravely tackles in In the Palaces of Memory.

An editor of the New York Times's "Week in Review," Johnson rightly sees this as the most profound of all science questions. His previous book, Machinery of the Mind, surveyed the efforts of artificial intelligence (AI) workers to imitate thinking with digital computers. His new book cuts a wider swath. It concerns not just AI, but decades of research on actual brains.

Although many neuroscientists play colorful roles in Johnson's opening section, it centers on the controversial conjectures of Gary Lynch, now at the University of California, Irvine. There are many conflicting theories, but most of Lynch's colleagues agree with him that memory is stored by chemical changes in neurons. Neurons are the little gray cells of the brain. Billions of them, each containing thousands of different proteins and enzymes, are linked together by their nerve fibers called axons (that transmit signals) and dendrites (that receive) in an inconceivably complex network. A given neuron may be connected to a thousand others. Electrical pulses from sensory organs constantly invade this network, zipping silently through its fibers to be ferried by neuro-transmitters across tiny gaps called synapses.

Neuroscientists divide into two rival schools. The presynaptics think memories are stored mainly in those neurons that send signals across the synapses. Postsynaptics think they are stored mainly in the neurons that receive signals. We see the face of a friend. Electrical pulses from our retinas travel to the brain, where they reactivate circuits in a cluster of neurons that may spread throughout the entire brain. The cluster lights up, so to speak, and we recognize the face. Ideas are similarly stored. A universal such as cowness is simply a circuit that holds thousands of overlapping memories of cows, a kind of average picture of all the cows we have known.

About 35 years ago there was a flurry of interest in trying to simulate thinking with intricate networks of neuron-like wires and switches called neural nets. By a massive use of parallel processing, these nets could learn from experience. Marvin Minsky, MIT's famous AI pioneer, collaborated with an associate on a notorious book, Perceptrons, that almost killed neural-net research by contending it was a blind alley. Thanks to improved technology, neural nets are now the most fashionable AI field of study. This is the topic of Johnson's second section, which focuses on the work of physicist Leon Cooper, at Brown University.

Neural nets have learned how to recognize signatures and objects on assembly lines, and even how to balance a broom on its handle. Minsky now regards his attack on them as "overkill," and is pleading for a merger of neural-net theory with his own approach which relies on conventional computers that twiddle symbols. Like most other AI researchers, Minsky has as little interest in how organic brains think as airplane engineers have in how birds fly.

Johnson's third section stars the Canadian philosopher Patricia Smith Churchland, now at the University of California, La Jolla, and author of Neurophilosophy, a recent MIT textbook. For decades she has been trying to make sense of both AI and neurobiology. Essentially a pragmatist, she sees the universe as a vast mindless tinkerer which, by the bumbling process of evolution, has created brains that resemble Rube Goldberg contraptions. She has the curious notion, common to most pragmatists, that truth is less a correspondence of ideas with structures "out there," independent of minds, than the brain's efforts to order its experience in useful ways. Sentient beings on other planets, she believes, may have minds so different from ours, with such exotic physics and mathematics, that we would find their science unintelligible. If an alien in another galaxy counted stars, could it find that two stars plus two stars did not make four stars? Could an alien particle physicist conclude that a hydrogen atom has more than one electron -- maybe none at all? Are atoms really out there, or are they just figments of our minds?

Johnson's philosophical musings have little to say about any of the deepest problems. In particular he never comes to grips with self-awareness and free will, actually two names for the same mystery. Try to imagine being aware of your existence without free will, or to imagine yourself with free will but no consciousness. You'll find both impossible. How is it that an infinitesimal portion of the universe, a tiny pattern of molecules, is capable of wondering why the universe exists, amd of planning ways to alter its future? A year spent in AI research, so goes an old aphorism, is enough to make one believe in God.

John Searle, a shrewd opponent of AI metaphysics, is dismissed in two lines. Unfortunately, Johnson wrote before the appearance of Roger Penrose's explosive The Emperor's New Mind, which argues that we will never understand the brain until we know more physics, and especially know more about laws below quantum theory.

Aside from six poetic but irrelevant pages of memories about two of Johnson's trips to New Mexico, his book closes with an admission by Churchland that her subjective view of truth -- that rain in Spain falls mainly in the brain -- is one that "usually sends people absolutely crawling up the walls. But I really don't see why. If the only alternative is that there are truths in Plato's heaven, then it seems to me that the basic story has to be told in terms of the brain."

I am among those Platonists who are indeed driven up a wall by this view. Some readers will close Johnson's book by marveling at how much about the brain has been discovered in recent years. I close the book overwhelmed by how little has been learned. It will be centuries, I am persuaded, before science fully understands the mind of a mouse. Martin Gardner is the author of "The Whys of a Philosophical Scrivener" and other books about philosophy, science, mathematics and literature.