Glen J Culler
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, 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 gained enough recognition to develop national support and subsequently 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 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 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 one finds many systems incorporating selective aspects of the early experimental systems of both types.
In this chapter, we will bring out some of the key features of highly interactive direct control systems that have implications for continuing design effort aimed at furthering the development of experimental mathematical laboratories. We then present a brief description of the foundations of an existing facility at the University of California at Santa Barbara and illustrate its use in a typical application. Finally, we discuss some extension of the system which will provide deeper power for future experimental applications.
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Mathematical laboratories: a new power for the physical and social sciences
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