By J. H. WESTCOTT
Department of Electrical Engineering, City and Guilds College, London
In this paper the only 'systems' considered will be systems of interacting quantities. A system is considered in terms of a 'model', which may be a mathematical model, e.g. a set of equations relating values of the quantities, or it may be an 'analogue', i.e. a physical system convenient for laboratory manipulation, so contrived that there is a corresponding set of quantities or variables and these are related by identical equations except possibly for 'scale factors'.
The uses of models are of two distinct kinds, belonging respectively to pure and applied science. A model may be used to express or communicate an 'understanding' of a phenomenon; e.g. that the nature of observed variations in a population is an understandable consequence of certain factors about predators, food, contagion and so on. Alternatively, it may be used as a basis for prediction and control. Something will be said later about the degree of accuracy with which the results of given situations can be predicted by means of models.
In biology such systems and models are met within the study of populations, in physiology, and in biochemistry. In economics the discussion of the behaviour of systems of such interacting quantities as incomes, savings, investment, and so on has become a central theme.
In engineering systems of interacting quantities and the use of models have been extensively discussed. The theory of control systems is essentially the theory of systems of interacting quantities. Extensive use has also been made of physical models (analogue computers). In defining an adequate model the engineer is usually much better off than the economist or the ecologist. The action of one quantity on another is often accurately known and if it is not the engineer can usually take his system apart, and measure the response of each element to suitably chosen inputs. But even in engineering this is by no means always the case. In a chemical plant or an aircraft in flight it may be technically difficult or economically impermissible to measure experimentally the separate dependencies that constitute the system. It is the purpose of this paper to describe, in the hope that they may be useful to biologists, some considerations that have arisen in the problem of model-making as it has arisen in engineering.