Mathematical laboratories: a new power for the physical sciences

Abstract

The concept of a mathematical laboratory has been developing throughout the lifetime of computers. The capabilities made available in systems supporting these laboratories range from symbolic integration, differentiation, and polynomial and power series manipulation, through mathematical simulation, to direct control experimental systems. About 1961 two trends, one toward what has become known as "on-line" computation, the other toward "time-sharing" had gained enough recognition to develop national support, and subsequently they have come to represent what is now known as modern computation. An on-line system provides interactive facilities by which a user can exert deterministic influence over the computation sequence; a time-sharing system provides a means by which partial computations on several different problems may be interleaved in time and may share facilities according to predetermined sharing algorithms. For reasons of economy it is hard to put a single user in direct personal control (on-line, that is) of a large-scale computer. It is equally (or even more) difficult to get adequate computation power for significant scientific applications out of any small-scale economical computer. Consequently, on-line computing has come to depend upon time-sharing as its justifiable mode of implementation. On the other hand, valuable on-line applications have formed one of the major reasons for pushing forward the development of time-sharing systems. At present, both efforts have reached such a stage of fruition that we find many systems incorporating selective aspects of the early experimental systems of both types.