math riddle

[UtwigMU]

Yeah definition of science:
here science (znanost) means all areas which use scientific methods, it's similar to German Wissenschaft.

In English, science also means natural science - the subject you have at school (si = naravoslovje/ de = Naturwissenschaft) where it deals with physics, biology, chemistry...

As per maths/geometry: We have defined few axioms and all things that are prooven are based uppon those. I don't know about maths but you can have noneuclidian geometry with different axioms, where things are different.

[Kurt]

We can prove things conclusively in mathematics. But that's because it isn't science. It's another division of philosophy. The entire world of mathematics is an artificial construct. It is because of that and only that that we can say things *must* be true, because that's how we have defined them.

It IS a construct. It's a careful one too. You need to prove your discoveries using other demonstratable "subsets" of mathematics (like a construction game). But since it's an invention, it is always perfected/perfectible.

Well, he's wrong. All physics is definitely not pure math.

What do you mean by that? Maths are used to construct models. Do you mean the theory behind the maths?

@Nowhere: we cannot prove everything with maths. we can only prove what is based on the theory's funding principles. see construction game: it's only a combination of existing blocks.

About Planck: maths are an integral part of physics. we couldn't construct models without them (except in cardboard I guess)

[Nowhere]

I didn't say that everything in math is proven, only (?) that in math it's possible for things to be proven beyond any doubt. (and if something can be proven math, it probably is/will).

And yes, math is integral part of physics. But physics isn't math. Even constructing models isn't. If you would use only math, you wouldn't get far (logic/methodology of science comes to mind)

[Kurt]

I didn't that everything in math was proven either. I said you can prove mathematical "things" using mathematical rules. The problem being that the set of rules is not complete yet (that's why there is still research being done in math, otherwise it'd be all written down in books and topic closed).

Things you can prove using those rules are thus intrisically proven beyond doubt _within_ that set of rules. So we're agreed on that. I add to that we don't know all the rules yet, hence we cannot prove _everything_ (extending beyond the known set).

Physics isn't math, but math is the _language_ of physics. That's why it's important to know all its words. That way you can write better theories.

When you construct models you use observations and statistics. Logic and intuition help either to setup the experiments or to find shortcuts in the maze of equations. Methodology helps you not getting lost in the process.