Tocher's Principle of Modelling: Practical Significance and Mathematical Implications

Abstract

This paper describes an important principle of modelling put forward by the late K. D. Tocher, namely that a clear distinction should be made between a system modelled and problems about the system. An example illustrates the many different practical problems one may be led to solve about a given economic system, e.g. an industrial firm. The example also shows that problems often result from the solutions to other problems, and thus cannot all be simultaneously anticipated. This suggests the need for a modelling system which, given a model of a system, may be used to solve any problem about the system.

The overall problem can be described as that of solving an underdetermined system of equations. The precise meaning of the problem is defined for the case of sparse systems. Finally, the main features of a computer program based on Tocher's philosopy are outlined.

Keywords:

• system of equations
• sparse system
• underdetermined system
• structural analysis
• interactive modelling
• modelling system