Is mathematics real or not?
|August 6, 2013||Posted by News under Mathematics, News|
Four scientists weigh in, on behalf of the Japanese Kavli Foundation:
Max Tegmark (pro real): It’s actually an old idea. Even Galileo exclaimed that the universe is a grand book written in the language of mathematics because he was wowed by all the astronomic regularities discovered in his time, for instance the precise circular or elliptical orbits of planets. Long afterwards, a whole set of subatomic particles were predicted by mathematical principles and then discovered, the Higgs boson being the most recent example. Even the possibility of curved shape of outer space was predicted centuries earlier by non-Euclidian geometry. So nature is clearly giving us hints that the universe is mathematical. I’ve taken it to the extreme by proposing that our entire physical reality isn’t just described by math, but that it is a mathematical structure, having no properties besides mathematical properties.
Brian Butterworth (anti-real): We’ve pinpointed an area of the human brain where there’s a specialist neural network that responds to counting the number of objects in a set. This area of the brain can recognize numbers across modalities. In other words, it can recognize three cats, three tones or three wishes. A similar area in the brain of the monkey does the same job. We even discovered the guppy — a small fish with a tiny brain — has one system for detecting small sets of up to four objects and one for larger sets. My argument is that we evolved a brain-based system for detecting and comparing the number of items in groups. Humans have developed symbolism for these numbers and elaborated on them to create the kinds of mathematics that Max and Simeon need to describe the universe. Numbers are not necessarily a property of the universe, but rather a very powerful way of describing some aspects of the universe.
TKF: (moderator)So you disagree with Dr. Tegmark’s notion that electrons are merely numbers?
Brian Butterworth (anti-real):Yes, because in order to have a physical explanation for phenomena, you have to have a cause for it. But how can a number be a cause? It’s true that you can use numbers to describe electron properties, but that doesn’t mean those numbers are actually a property of that physical object. Twoness is a property of a set of objects, such as two cups, or two electrons. But it is independent of the kinds of objects that are in the set for which it is a property. A set of two cups is different from a set of two electrons so twoness can’t have the same causal property for cups and electrons.
Why not? Thoughts? More.