Classical physics owes much to the theory of ordinary differential equations and systems of such equations figure conspicuously in mathematical economics too. But in political science and sociology there has been resistance to a recasting of theoretical dynamical principles in differential form, no doubt because neither discipline has anything very much like a body of theoretical principles to begin with. There is Richardson's work, of course, and recently some social scientists have turned to such seductive subjects as linear control theory, optimal control theory, and the theory of differential games. 1 For the connoisseur of differential methods, however, linear control theory is disappointingly vulgar; in optimal control theory and the various theories of differential games, differential elements are subordinate since such sciences are really decision-theoretic in their overall cast. Pure differential theories have come again to prominence in ambitious works such as The Limits of Growth and World Dynamics. 2 These are volumes of studied defects, much appreciated by their critics. 3 But Forrester and Meadows do see human agents much as the physicist sees particles in a field of force -as brute and unanalysable elements. So their work is valuable as an example of the unencumbered differential method. My own concern is less with either book than with the genre: like World Dynamics, the theories that make it up are global, highly aggregated, desperately non-linear. Taken one with another, they form a collection of mathematical models of the world and it is interesting to ask for a preliminary listing of representative points in the natural critical space in which they may be evaluated.
Hadamard, in fashioning the concept of a well posed problem in analysis, had in mind a selection from among the class of possible dynamical systems of those with physical significance. Clearly, a dynamical system must admit of uniquely specified solutions if it is to be useful at all; that the solutions must vary continuously with variations in the initial conditions is a concession to the frailities of human observation and measurement: 4