Time, TOEs, and UltraStructuralism

Mathematics, broadly speaking, is the science of patterns. Physics, broadly speaking, is the search for patterns in the natural world. Eugene Wigner’s [12] famous problem concerning the “unreasonable effectiveness of mathematics in the natural sciences” constitutes an expression of puzzlement over the empirical success of physics, based as it is on mathematics. Put this way, of course, the problem has a rather simple answer: mathematics (the science of patterns) is so effective because the natural world (the subject matter of physics) is itself patterned. The regularities of physics are instances of mathematical structures. For example, we can apply geometry to physical space because physical space has a structure that is (more or less) isomorphic to some mathematical structure. We might, in slightly different terms (and ignoring complications to do with representation), view our world as a model of the axioms of some systems of geometry (and of the axioms of quantum field theory, say—though this is debatable). However, the problem is really an old one, and there are old solutions too. Pythagoras claimed that there was no distinction between the world of physics and the world of mathematics. Plato argued there was a very great difference: it amounted to concrete versus abstract, a distinction denied by Pythagoras. For Plato the concrete world instantiated (or ‘partook of’) the abstract forms (albeit imperfectly). This Platonic account is somewhat similar to the model-based view presented above. More recently structural realists have answered the question by