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I am grateful for suggestions and assistance from J. Ambjorn, N. Margolus, O. Martin, A. Odlyzko, and T. Shaw, and for discussions with J. Avron, C. Bennett, G. Chaitin, J. D. Farmer, R. Feynman, E. Fredkin, M. Gell-Mann, R. W. Gosper, A. Hoogland, T. Toffoli, and W. Zurek. I thank S. Kauffman, R. Landauer, P. Leyland, B. Mandelbrot, and A. Norman for suggesting references. The symbolic manipulation computer language SMP (Wolfram et al., 1981) was used in some of the calculations. Some of this work was done before I resigned from Caltech; computer calculations performed at Caltech were supported in part by the U.S. Department of Energy under Contract Number DE-AC-03-81-ER40050.