Steps to an Epistemology of Simulation

Abstract

In dynamics, we use models to represent the workings of a physical system. We arrive at the model by making approximations to fundamental force laws based on assumptions about the physics. The model is expressed mathematically as either a set of differential equations, or else as a Hamiltonian function, from which we obtain differential equations using Hamilton’s formalism. Every system of well-behaved differential equations always has a definite solution. Although some scientists often call this guaranteed solution the truth, I will, for clarity, refer to it as the true solution. As we have seen, the differential equations that characterize dynamical systems theory are not usually solvable analytically, making the true solution an elusive object of desire. In the absence of direct access to the true solution, we resort to numerical methods to create approximations to the true solution.

A computer simulation for these conditions gave recurrence and we were on our way to a better analytic understanding.

Norman Zabusky (1967, p, 231)

In cybernetics, mapping appears as a technique of explanation whenever a conceptual “model” is invoked or, more concretely, when a computer is used to simulate a complex communicational process. ... Outside of cybernetics, we look for explanation, but not for anything which would simulate logical proof. This simulation of proof is something new. We can say, however, with hindsight wisdom, that explanation by simulation of logical or mathematical proof was expectable. After all, the subject matter of cybernetics is not events and objects but the information “carried” by events and objects.

Gregory Bateson (1972, p. 401)