Gödel, Escher, Bach provokes thought about thought. In this sense, as in its very structure, the book is recursive. When Hofstadter makes the following comment about Bach’s Musical Offering, he is speaking about his own work as well:One cannot look deeply enough into the Musical Offering. There is always more after one thinks one knows everything. . . . Things are going on on many levels. . . . There are tricks with notes and letters. . . . There is beauty and extreme depth of emotion; even an exultation in the many-leveledness of the work comes through.

Clearly, the Pulitzer Prize committee and hundreds of thousands of readers who bought Gödel, Escher, Bach exulted in its many-leveledness, too, but the book has provoked controversy as well as admiration. Some reviewers complained about its length, its quirky style, and its scope. Other popularizers of scientific ideas— Stephen Jay Gould, Loren Eiseley, Lewis Thomas, Carl Sagan—may reveal less literary inventiveness but do not provoke a paraphrase of Gertrude’s plea to Polonius: “Less matter, with less art.” Hofstadter, certain critics claim, may bemuse rather than amuse his audience.

Some musical theorists have objected that Bach seems dragged into the book because Hofstadter wanted to discuss the composer, not because his music is truly recursive. The “Canon per Tonos” is clever, but it does not rely on paradox in the way that Gödel’s theorem or Escher’s prints do. Researchers in artificial intelligence are also divided on the merits of Hofstadter’s theories; some experts in this field refute his definition of machine intelligence as well as his proposed method of achieving that goal. Whereas Hofstadter would build his programs from the bottom up and let the computer combine elements freely, others believe that a program must contain all instructions, including the information about when to make a particular choice.

Underlying Hofstadter’s view of intelligence, both human and artificial, is the assumption that the brain is hardware, the mind software. Neurophysiology, biology in general, and past experiences of the individual and humankind are irrelevant to an understanding of creativity. This same philosophy informs The Mind’s I: Fantasies and Reflections of Self and Soul (1981), which Hofstadter edited with the philosopher Daniel C. Dennett.

The Mind’s I includes an article by John Searle, professor of philosophy at the University of California, Berkeley. Searle argues that even if one could program a computer to say, “I’m thirsty,” no one would think that the machine wants a drink. Similarly, when a computer solves a mathematical problem, it has no understanding of the numbers. Mathematician and computer pioneer Alan Turing established a test for intelligence: If a machine can convince a person that another human is responding to questions, then that machine is intelligent. Searle rejects that measure, arguing that sophisticated circuitry can now fool many people even though its creators would not claim intelligence for it. Searle concludes that Hofstadter and his followers mistake simulation for duplication, the ability to produce an answer with the capacity for understanding it.

In 1981, Hofstadter succeeded Martin Gardner as the mathematics columnist for Scientific American. In 1985, he collected the essays which had appeared in his column, together with seven new ones, in Metamagical Themas. The same wit, range of interest (from linguistic paradoxes to nuclear war), and concern about the mind apparent in Hofstadter’s earlier writings are evident here, but his optimism about reproducing human intelligence is tempered. Indeed, he seems to lean toward J. R. Lucas’ view that Gödel’s theorem limits the capacity of any program to reproduce human thought—though Hofstadter suggests that the theorem may also imply restrictions on the extent of human creativity. Hofstadter’s reservations about machine intelligence may derive in part from his own unsuccessful efforts to create programs that solve problems intuitively rather than mechanically. His writings show how much researchers have learned about the intricacies of the brain and mind, about Strange Loops and Tangled Hierarchies, but they also reveal that no one has yet unraveled what John Donne called “the subtle knot that makes us man.”