Hierarchical approaches to mathematics of technological change

Abstract

Technological change is an enormously complex and diverse phenomenon. To deal with it quantitatively, a classification scheme is needed that reflects this complexity and yet permits separate aspects of technological change to be described. In this paper, a hierarchical approach is presented that is suitable for describing many kinds of technological change. The hierarchy is three dimensional and connects technologies in time, in function and to each other. The virtues of this classification are that it clearly defines the objects of study, it can limit the scale of the analysis by treating particular members of the hierarchies and it can progressively extend the analysis by including more members of the hierarchies. The study of technological change should then start with a systems analysis to determine the structure of the hierarchies of interest for a particular technology or set of technologies. Once this is done, a member or members of the hierarchy are selected for analysis and the time evolution can be described in terms of systems of equations for the parameters defining the members of the hierarchy. The structure of the hierarchy determines the relation of the equations among various technological systems. For technologies considered as sets of devices, this procedure leads to nested sets of coupled equations. The evolution of performance parameters and the capture of market share by a new product are known to follow logistic type equations. Thus, while the overall complexity of the mathematics reflects the complexity of technological change, the individual parts of the mathematical structure are straightforward.