Draw from the Model and Imitate the Antique (1979)

Abstract

Boundary conditions, like field equations, are proposed by theorists who dare represent nature by mathematical hypotheses. “Draw from the model and imitate the antique,” said Rubens. The tradition shows us that only after a theory has been formulated can existence theorems be proved. In framing boundary conditions, just as in framing field equations, the theorist outlines Nature as best he can from what little of herself she lets him see through the fogs with which she modestly covers her sincerity. To do so, he follows the forms and practices that his masters, the great theorists of old, have taught him by example. He demonstrates the properties that solutions must have in order to satisfy his conditions. Like his great forebe-ers he runs the risk that solutions of the kind he analyses may not exist: that all his labor may be spent on describing a few of the countless attributes of the null set. The tradition gives him hope as well as example.