Searching for Magic

A digital computer in the idealized world of theoretical computer science has only two resources: time and space (storage). Running out of time on large and difficult problems is usually the overriding concern. From the theoretical point of view, the simplest model of a digital computer, the Turing machine, has a single read/write head that can move only one location at a time on the storage medium (the tape), and therefore the storage used cannot exceed the time used. As far as today’s real computers are concerned, a half century of feverish hardware development has made memory dirt cheap. For