Why is the physical world described so precisely by mathematics? Every time I think about this dilemma Im stymied. At the most basic level the connection is tenuous, math deals with symbolic logic: assume certain statements, show that other statements follow, while science deals with observable phenomena: hypothesize, test, refine. Granted, the roots of math are grounded in describing the physical world, but even the most abstract mathematical ideas seem usable by science(example: group theory and quantum mechanics). Anyways, I thought this would be interesting to discuss, Ill stop now and let wiser minds continue.
A lot of abstract math is created because new science requires it. So to say how much of a coincidence it is that abstract math describes science is like saying how much of a coincidence it is that earth is so well suited for us humans.
Wow, zeta. I've thought about this question a lot, in precisely those words. It is a big mystery to me also -- especially since a lot of math ends up precisely describing some physical phenomena AFTER it is invented abstractly and uselessly. I'll say more later, but I just wanted to quickly record my amazement that someone has thought about this in such a similar way.
mathwiz, I define abstract/pure math to be mathematics which is NOT created to describe the physical world. Thus to say "A lot of abstract math is created because new science requires it" is a silly contradiction of terms.
It's a silly contradiction in terms only under your definition of abstract (not necessarily mathwiz' exact meaning) but you did not explicitly state your definition in your original post.
I feel like any abstract mathematical topic could be applied in some type of physical setting. The whole concept of "abstraction" applies to taking some sort of event or idea and simplifying it so that you can work with it in the mathematical setting.
It doesn't seem so amazing to me. You can probably 'force' any mathematical idea upon a physical setting and get results that follow suit.
frozen-tearsPosts: 1,046Registered UserSenior Member
Hm! Interesting perspective. I've also never been really amazed by math's relationship to science, because I've always believed that mathematics is a science. I suppose this takes some measure of faith, but I believe that mathematics isn't so much synthesis as it is discovery -- relationships already exist, and mathematicians find them, hypothesizing, testing, and refining just as scientists do. (What happens if the theorem is found not to work for some member of the universe? It's thrown out or modified until there is a better solution.)
So as for the relationship between math and science, do physical phenomena cause math? No -- that's absurd. Do preexisting maths cause physical phenomena? I don't know. The fact that we don't know the mechanism by which something happens does not imply that the something can't happen. Or do(es) some outside factor(s) cause both math and science? Certainly they don't simply coincide?
I think the majority of mathematicians are Platonists (correct me if I'm wrong, Ben. ) So, more to ponder -- do theorems exist that are provable, but not provable by humans? What does that imply for science?
fool, the point is that abstract mathematics, invented by humans, has been found to describe the physical world with little "forcing," like a puzzle which just fits together (without the need for reshaping the basic pieces themselves) and results in a coherent picture.
Replies to: Math And Science-How Are They Related?
It doesn't seem so amazing to me. You can probably 'force' any mathematical idea upon a physical setting and get results that follow suit.
Perhaps I don't know enough.
So as for the relationship between math and science, do physical phenomena cause math? No -- that's absurd. Do preexisting maths cause physical phenomena? I don't know. The fact that we don't know the mechanism by which something happens does not imply that the something can't happen. Or do(es) some outside factor(s) cause both math and science? Certainly they don't simply coincide?
I think the majority of mathematicians are Platonists (correct me if I'm wrong, Ben. ) So, more to ponder -- do theorems exist that are provable, but not provable by humans? What does that imply for science?