Something fun to consider: your opinion is welcome.?

Question

Does mathematics obey nature, or does nature obey mathematics?

This is like the chicken or the egg. I believe in God, so my opinion will be based on that. If you do not, that's ok and feel free to give your opinion, but please don't bash anyone for their belief.

It's like the question Einstein asked: Did God have a choice when he created the Universe?

I think the Universe started with blueprints. Those blueprints dictate how matter and energy would interact. Those blueprints are based on mathematics. So, it is my opinion that the math came first.

Thus, I believe nature obeys mathematics. For example, in Newton's Apparatus, there's only one way those balls will bounce given the initial position. If two balls are pulled back, two balls will fly up on the other side. They have no choice but to do that in order to conserve both energy and momentum.

Therefore, I believe God didn't have a choice. If He wanted a Universe like this, all of the laws had to be the way they are.

Mathematics is not an approximation of nature. It is only an approximation because we do not have 100% of the information needed for an exact answer/outcome.

I don't believe that mathematics is solely a human construct. The math concept is there regardless if we call it one thing or another. This is where I beleive math is not invented, only discovered. The planets were moving around the sun in accordance with the invere square law long before Newton discovered calculus in order to describe that motion.

I believe math is more than a model. It outlines rules for nature.

For example: consider Newton's Apparatus. You ask: why can't two balls fly off after only one ball struck initially? Answer: energy wouldn't be conserved: meaning the left side and right side of the conservation equation would not be equal. So, the balls are confined to an outcome where symbols on the left equal the symbols on the right in an equation on a piece of paper.

Its something to think about.

Answer 1

Neither. Mathematics is simply a formal tool of logic that is sometimes useful in describing Nature. Nature is not bound by mathematics and exists independently of it.

There is no “right” mathematics formalism. Each math form, if it is self-consistent, is a tautology proving nothing. Which is not to say that math isn’t useful; clearly it is. But it is useful in the sense that a socket wrench is useful for tightening or loosening nuts and bolts. A socket wrench isn’t essential for the existence of either nuts or bolts and an open-end wrench, or a pair of pliers, may sometimes be used in its place. Or consider a nut or a bolt that cannot be gripped by a wrench, but you nevertheless find them together holding something fast. One may wonder how that could be, or who made it that way, and for what purpose, but having been observed it simply is.

God’s Universe is pretty much like that inscrutable nut and bolt: we observe with whatever senses and intellect are provided each of us, and may or may not come to a personally satisfactory understanding of what we observe, but as long as our conclusions are not contradictory we are free to believe what we want and no one should say our beliefs are irrational or wrong. My personal belief is God made everything. Maybe He did it for a final exam in God school, or maybe it was just homework, or maybe He just wanted to be Creative. Whatever. We probably can not, of our own will, know the full extent of His Creation. He (probably) set up the rules to work that way.

Oh, and on un-wrenchable nut and bolt: the nut was heated until it expanded enough to clear the threads on the bolt and then it was slipped over the threads and allowed to cool.

Did God have any choice on the “rules” of this Universe? I’m sure He did, but the particular rules He chose must have been in accordance with His desire for how things would behave. Who knows? Maybe the rules are changing as we consider all of this. After all, we are pretty much isolated from what is REALLY happening in the Universe by the speed of light. The rules could have changed a few billion years ago and we just don’t know about it yet.

Answer 2

Each science e.g. "Mathematics" "Physics" "Chemistry" represents our attempt to understand what's going on in nature. e.g. the laws for addition were discovered by placing 3 pebbles next to 5 pebbles and then counting. The laws for multiplication were discovered by making a rectangle of 3x5 pebbles and then seeing how many pebbles are needed to fill out the rectangle. And so forth.

It can actually be proved that there is no way of knowing whether mathematics is an exact model of the way numbers work in the world. In fact there are some areas of advanced mathematics where you have to decide how you want to do things. If you allow the axiom you can prove some things; if you refute the axiom you can prove other things; but in the real world there is no way to find out if the axiom is true. So in a sense mathematics is "broader" than the real world.

Answer 3

I too believe in God. But I figure that he didn't need "blueprints". If He had a plan for the universe, it would transcend any mathematical models.

But I agree math came first since math is entirely a theoretical concept with no need for a universe to make it consistent.

But I don't think it necessarily follows that nature "obeys" mathematics...simply that mathematics came first. Keep in mind that our mathematical models we use in physics are only models...they don't necessarily represent any "reality". Electrons don't really bounce on little springs

Answer 4

I never thought of it like that before (which doesn't happen very often).
I guess I have a lot to think about before I go to bed tonight!
I don't want to agree just yet, but you're probably correct.

Still, the mathematic is created by humans for human use. Humans can know only that which is given by nature. So nature influences our conception of what mathematics is. This is like that there is no such thing as a perfect circle.

Answer 5

Mathematics is a human invention that helps us order and understand the world. In my opinion it is the best and most fundamental invention for that understanding. Nothing in nature is mathematically exact except counting things. All measurements are approximations and therefore math is a method for understanding and ordering those approximations. We got most of our mathematics from observations of nature.
Nature -----> math

Answer 6

I think mathematics and nature simply are. Neither one obeys the other. They just simply exist.