Physics of Continua
THE TWO ALTERNATIVES with respect to the structure of matter, continuity and discreteness, have been recognized in the earliest stages of science and have at all times inspired controversies. They raise a tantalizing problem, for though matter appears to be continuous, it does show atomic structure on more careful examination; and though its structure be atomic as it is now conceived to be, who can say whether the stuff composing the elementary particles that make up an atom is not ultimately continuous? It is not likely that the age-old problem will ever receive an empirical solution. The "true" answer, if there be one, may hide itself forever in the uncertainties of immediate experience (Chaps. 4, 6). The question, then, is not whether matter is continuous but how theories succeed when they regard as a continuum the construct which they take to be their system.
Modern physics has largely lost interest in, and sensitivity to, the conceptual delicacies of the continuum problem, while mathematics, perpetuating the curiosity of ancient Greece, is appropriately aware of them and is finding ways for dealing with old paradoxes. It is perhaps even more important that the mathematician is seeking to make the discrete compatible with the continuum by studying and learning to handle continuous functions with discontinuities or singularities. Measure theory of point sets has already achieved a great deal in this direction. But on the whole the physicist, as we have said, shows at present little interest in these developments. It seems likely that set theory will be applied to the structure of matter in the near future, but the convenience and the success of traditional methods for describing