Why is the universe describable with math?

[Cuddles]

I'm interested in why the Greeks discovered the conics and not until 2000 years later did Kepler discover their astronomical importance.

As I understand it, the Greeks only really studied pure maths and philosophy. They did almost no experiments, and the scientific method was unknown. Consider that until a few centuries ago a thrown ball was thought to fly diagonally up and then fall vertically, despite the fact that every single object ever thrown proves this wrong. Conic sections were studied as a mathematical idea, but until the idea of experimental science took off no-one even thought to apply them to the real world, especially not to abstract dots in the sky.

 

[Anacoluthon64]

If it came across that way, sorry.

OK, NP then.

What was your unstated point? I'm interested now.

The limits of computability and the choice between incompleteness and inconsistency will, if mathematics indeed provide the optimal tools for describing and modelling reality, almost certainly have a profound effect on our understanding of that reality. In many cases, certain branches and topics of mathematics exist for some time purely as interesting mathematical pursuits, and only later find a practical application. As an example, non-Euclidean geometry has found application in General Relativity - in fact, GR wouldn't exist without it. But the geometries of Riemann and Lobachevsky arose because Euclid's Parallel Postulate is an instance of an undecidable proposition in the Gödel sense.

In contrast, QM employs a technique called "renormalisation" to cancel infinities and so yield sensible and confirmable answers. Renormalisation works brilliantly, but has yet to be justified on a firm logico-mathematical basis, and it is therefore viewed with some suspicion in certain quarters. Such a justification, if it exists, will probably affect, among other things, our ideas about computability.

ETA: My point was probably too obscure, for which I apologise. Perhaps it will be a little clearer if I add that Gödel used Russell & Whitehead's work for his Incompleteness Theorem, and that Turing used some of Gödel's ideas.

'Luthon64

 

[delphi_ote]

So very glad I asked. Some interesting things to think about in all that. Thanks!

 

[skullerello]

The title kind of says it all. Why do you think the universe is describable with math?

(and please, let's not evoke fantasy multiple universes where math doesn't exist; let's talk about what there is evidence for)

The "known universe" is discribable in "math" because we developed the math that we use to describe it; when situations develope i.e. "black holes" "dark matter" our mathematics test new ways to define those anomolies within the given parameters of our understanding of our uses of "math". And, it's a fluid language. It, our math, leaves plenty of room for new discoveris; given known, observable results, we can plug in the variables. We can test to see what fits. We can, conversly, plug the known numbers (from observered situations)
Oh, crap! I'm really drunk...

 

[Blert]

Well, hmmm, actually he said that either there are statements whose truth value can't be proven either way, or there are statements that are true that cannot be derived within the system. It's a matter of choice, you see, whether you declare it inconsistent or incomplete.

Heh---serious weirdo here, but I've been toying with the notion for a little while that this is something of the difference between religion and science: one purports to explain everything, but accepts lots of little paradoxes; the other is consistent, but may not be able to prove everything that is true.

I don't really think it's a very good analogy, but it's fun to play with when I don't want to think about anything serious...

 

[Mr. Scott]

Where did all this math come from??

A very long time ago, the space between particles of matter was filled up with woo. Little by little, over time, the woo decayed and the vacuum where woo once was became filled with math. Us humans discovered that the universe was a good way to describe this math.

 

[NobbyNobbs]

Suppose it weren't describable by math, but by some other unnamed mechanism. After awhile, suppose some carbon-based life-form on an insignificant planet starts studying the universe around them. They realize there is this mechanism they need to learn to be able to describe their world. So they study this mechanism, and give it a name.

Let's suppose they call it "mathematics".

So the answer to your question is a little like saying "Hamlet was not written by Shakespeare, but by another man of the same name."