I’ve recently seen a couple of interesting posts pondering to what degree mathematics models actual real world objects.
For an upcoming episode of the Rationally Speaking podcast, Massimo Pigliucci and Julia Galef interviewed Max Tegmark, who seems to believe that all of reality is ultimately mathematical. Note that Tegmark doesn’t mean that it is precisely described by mathematics, but that it is mathematics. Massimo is skeptical, while noting that mathematics is so useful it’s hard to imagine it doesn’t in some way relate to real world objects.
Jason Rosenhouse, who I’m very happy to see blogging again after a break, highlights an interview with Edward Frenkel, who seems to believe that while mathematical objects exist, they are outside of the physical world and consciousness. While noting that this belief is common among mathematicians, Jason expresses skepticism, but like Massimo, he also seems to believe that mathematics relates to something in the world.
This seems to be a timeless question. Personally, I think mathematical concepts do model real world patterns, at least to some degree of approximation. A mathematical model is either right or wrong. That rightness or wrongness ultimately resolves to how well it relates to real world problems.
Of course, you could say that since mathematics doesn’t exactly match real world patterns, that it’s just a useful tool invented by humans. But you could say that about anything. A tree exists, except that our conception of a tree is just a mental model we use to describe a complex evolving pattern of elementary particles. Our model of a tree never matches the reality exactly. Therefore, we could say that the tree concept is just a tool for humans.
From a certain point of view, that view is true. But I’m not sure how useful that truth is, except perhaps to caution us about the limitations of our understanding of reality.
- When your tutor is one of your best friends (questadmissions.com)
- Theoretical portraits of mathematical understanding (3) (joannalake.wordpress.com)
- Would Math Exist Without Us? (dish.andrewsullivan.com)
- On the Objective Existence of Mathematics (cmcraes.wordpress.com)
- Mathematics = root of Science (uninnumerate.wordpress.com)
- We are connected to this Earth (joannalake.wordpress.com)
- Is Mathematics Unnatural? (MrHonner.com)