Beyond Zero and One (Andrew Smart) / quote 85 of 171
Mathematical models are not reality
Edge magazine: Many mathematicians are Platonists. They think that the Universe is made of mathematical stuff, and that the job of mathematicians is merely to discover it. I strongly deny this point of view. This does not mean, however, that I am a ‘social constructivist’ … [I believe] that mathematical constructions transcend specific human cultures. In my view, however, this is because all human cultures have the same brain architecture that ‘resonates’ to the same mathematical tunes. The value of Pi, thank God, does not change with culture! Furthermore, I am in no way denying that the external world provides a lot of structure, which gets incorporated into our mathematics. I only object to calling the structure of the Universe ‘mathematical.’ We develop mathematical models of the world, but these are only models, and they are never fully adequate. Planets do not move in ellipses—elliptic trajectories are a good, but far from perfect, approximation. Matter is not made of atoms, electrons, or quarks—all these are good models (indeed, very good ones), but ones that are bound to require revision some day. A lot of conceptual difficulties could be clarified if mathematicians and theoretical physicists paid more attention to the basic distinction between model and reality, a concept familiar to biologists.