METAMAGICAL THEMAS

More polymathic razzle-dazzle from the author of Godel, Escher, Bach (1979), the virtuoso with all the intellectual virtues except measure. Hofstadter, who nows holds the appropriately broad Walgreen Chair in Human Understanding at the U. of Michigan, Ann Arbor, has gathered here 33 wide-ranging essays, most of them published earlier as columns in Scientific American. In his crisp, lucid prose he merrily tackles such brain-teasing topics as self-referential sentences (""This statement is false"") and reflexivity in law (suppose Congress mandates that all Supreme Court decisions be made by a 6-3 majority, and the Court overrules Congress by 5-4); the mathematics of Rubik's Cube (and the related Pyraminx, Skewb, and IncrediBall); the analogies between cubology and particle physics; the structure of Lisp (a computer language used in AI); the Prisoner's Dilemma (roughly the problem of whether it is logical to trust anyone, and how far); the Turing Test (determining whether a machine answering my questions has a human agent ""behind"" it); and so on, and so on, and so on. But Hofstadter doesn't limit himself to puzzles. He crusades against sexism in language (and gives the participants in a dialogue on thinking machines the neuter names of Pat, Sandy, and Chris); he offers a lesson in the probabilities of a nuclear doomsday, discusses Chopin scores as complex visual patterns, and puts down some of the loonier champions of parapsychological phenomena. Hofstadter badly needs to cut down: the book is immense (over 850 pages), highly uneven (some parts readily accessible, others quite specialized), over-ambitious (encompassing amateurish ventures into fiction). In any case, readers are free to browse through this astonishingly varied collection until exhaustion, however much tinged with admiration, sets in.