bjshnog said:
I was considering making a thread for this, but I couldn't work out if I would receive a lock/ban for it, but it might fit in this thread. :D
Over the last few weeks, I've kind of fallen into an obsession with the apparent symmetry between mathematics and physics, which threatens to drive me completely insane. I'll try to keep my question short and concise.
Is it possible for anything to exist or logically interact with other systems, which does not follow mathematical patterns entirely? If so, is there really any difference between "reality" and pure mathematics?
Also, how can I stop myself from going insane?
The relationship between the philosophy of science and science itself is very closely tied to the relationship between crackpot science and real science. Crackpots often claim to have some fundamental philosophical difference from the mainstream that makes their theory correct.
The relationship between mathematics and science is usually to say that mathematics is the language of science, and scientists cannot really say anything more about mathematics beyond that. Mathematicians may feel more compelled to "Platonize" mathematical objects and see the language analogy as lacking, since they often study mathematical objects that have no physical counterpart.
As for staying sane, one thing that helped me was Tim Gowers advice about mathematics, which was basically not to ask what mathematical objects are, but to study how they behave. You will go insane if you try to figure out the meaning of ##\sqrt{-1}## , but if you instead, study what properties it has, you'll fare much better.
Physicists can then use this behavior to model the behaviors of physical phenomena which seem to match. There are lots of applications of imaginary/complex numbers in physics, for example.
Of course a crackpot would possibly read all sorts of philosophical meaning into mathematical objects, hence claiming either that the entire world is imaginary, thus a product of the mind, or alternatively lambasting the physical sciences which use imaginary numbers as made up nonsense. I think both extremes come from a lack of understanding of how to think about mathematics.
And this is why we don't have a philosophy forum anymore... I feel the hammer coming!
-Dave K