A note on a variational problem in biology and sociology

The author's suggestion that the behavior of an individual or of a society may be described not by maximizing the satisfaction function but by maximizing the integral of it over a period of time (Rashevsky,Mathematical Biology of Social Behavior, rev. ed., p. 233, Chicago: The University of Chicago Press) has been considered applicable to other biological functions in a recent paper by R. Rosen (Bull. Math. Biophysics,24, 279–290, 1962). It is pointed out that the possibility of introducing such variational principles into biology or sociology requires that the corresponding functions depend explicitly and in a nonlinear manner on the rate of change of some of the variables. An example of a satisfaction function is given that describes the behavior of an individual who derives more satisfaction from the process of approaching a goal than from the actual goal itself.