Zoom Talk (Work in Progress): Erik Curiel (MCMP)
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What to Do When You Can't Solve Equations
In essentially every physical theory in real use today, we know vanishingly few exact solutions to the theory's equations of motion or field equations, and even then almost always only under the condition of exact symmetries or other such unrealistic idealizations. Much philosophical work has been done on analyzing the nature of various strategies used to produce "approximate" solutions and models, such as perturbative expansions and numerical simulations, as used in much if not most real scientific practice. I will examine another kind of strategy physicists use when the equations cannot be exactly solved for situations of interest, viz., the production of general theorems about generic properties of such solutions and the formulation of plausible general principles capturing generic aspects of the behavior one expects such solutions to manifest. Such general results are often used to construct a peculiar kind of model of physical systems, what I call a "principle model", which seems not to have been studied before in the literature. I illustrate the idea with a few examples, and conclude with a few general lessons that the character of these models suggests for our understanding of the structure of knowledge in physics.