Computation and State Machines

Preface For quite a while, I've been disturbed by the emphasis on language in computer science. One result of that emphasis is programmers who are C++ experts but can't write programs that do what they're supposed to. The typical computer science response is that programmers need to use the right programming/specification/development language instead of/in addition to C++. The typical industrial response is to provide the programmer with better debugging tools, on the theory that we can obtain good programs by putting a monkey at a keyboard and automatically finding the errors in its code. I believe that the best way to get better programs is to teach programmers how to think better. Thinking is not the ability to manipulate language ; it's the ability to manipulate concepts. Computer science should be about concepts, not languages. But how does one teach concepts without getting distracted by the language in which those concepts are expressed? My answer is to use the same language as every other branch of science and engineering—namely, mathematics. But how should that be done in practice? This note represents a small step towards an answer. It doesn't discuss how to teach computer science; it simply addresses the preliminary question of what is computation.