A paper presented at the 1969 Air Force Academy Meteorological Technical Exchange Conference, on the fundamental physical limits to computer speed. Heat dissipation is the most serious apparent constraint. Switching cannot be faster than 10 (exp -11) sec because of cooling, or 10 (exp -15) sec because of indeterminancy. Present production devices switch at about 10 (exp -8) sec, so 100- to 1000-fold improvement seems to be the limit--not enough to handle complex environmental problems. Beyond that we must look to multistream (rather than serial) processing, as planned for Illiac IV. This may offer a 100-fold increase (its builders hope for many hundreds). If problems prove to be more parallel than we think, and if we push technology to its limits, the overall improvement could move toward 100,000-fold. Such a computer would require special funding, though probably less than a large particle accelerator. 8 pp.