Computability, Computation, and the Real World

Abstract

In 1937, Alan Turing [1] in a fundamental paper, not only set forth the foundations of what was to become theoretical computer science, but also hinted at the prospect of the "all-purpose" computers that have since become so ubiquitous [2-6]. Eduardo Caianello recognized, earlier than most, the rich interconnections between the study of theoretical models of computation and their physical implementation. In 1964 he organized a now famous conference in Ravello bringing together a number of researchers from varied disciplines to facilitate this interaction. I feel honored to have been a participant. Today more than ever, the connections between theory and practice in computer science loom large. There is the promise of models of computation based on quantum mechanics to overcome some of the difficulties associated with computational problems that seem to lead to exponential explosions. But also there are confused efforts to overcome the bounds on what is computable that Turing and other logicians established.