ABSTRACT
Computers are now fast enough for the simulations to be carried out quickly, and so it is practical to explore a large number of cases. Computation is emerging as a major new approach to science, supplementing the long-standing methodologies of theory and experiment. A simple computer such as an adding machine can solve only a small subset of these problems. There exist universal, or general-purpose, computers, however, that can solve any computable problem. The mathematical processes that can be described by a computer program are not limited to the operations and functions of conventional mathematics. There is one major difference between most existing computers and physical systems or models of them: computers process information serially, whereas physical systems process information in parallel. The possibility of undecidable questions in mathematical models for physical systems can be viewed as a manifestation of Godel's theorem on undecidability in mathematics, which was proved by Kurt Godel in 1931.
