/sci/ - Science & Math

>maths is anything more than a good approximation of the way the world works.

This is true. We can keep adding things to math to make it more and more accurate... but we live in a universe of limits so we can get infinitely close but not actually solve it.

Its not that the Universe is 'written' in the language of maths, rather just maths gives us a medium to explain how some of it works.

It's already accepted that it is just an approximated means to describe the universe.

Platonic worlds or the "Platonic third world" is the maths based version of the universe - where perfect geometry and laws exist.
When we apply mathematics to the real world it's obvious that it is only going to be an approximation.

>>1077734

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"It is only proper to realize that our mathematics is largely a historical accident."
-John von Neumann

>completely knowable
Kurt Gödel would like to have a word with you.

>>1077741
>>1077743

Looks like most people so far have agreed that maths can't perfectly explain the universe. In that case, I perhaps should have opened by asking "How do you know that maths CAN'T perfectly explain the universe?"

I don't see how you can assert that either side is true at this stage, and I'd invite you to try and justify your assertion.

>>1077748
I looked up the "Platonic third world" and nothing much came up. Why is it obvious? My physics professors sure seem to think we'll eventually have a perfect theory.

Let me just check that we're not talking across purposes. I am not talking about things like the fact that we might model a CD as being a circle when in fact it is not a true, perfect circle. Modelling things as simpler versions is obviously only an approximation and is not what I am talking about.

>>1077785
I don't know enough about the Incompleteness Theorem to weigh in on that. Does it have implications that affect theoretical physics? I was unaware that it had a lot of significance outside of maths, and I am not a mathematician.

>Physicists often assume that the universe is written in the language of maths.
Stopped reading right there.

>>1077928
Ok then byebye maybe I'll catch you later in a magnets thread.

I like to think of philosophy as a bunch of people saying, "But what if we looked at it like this..." So, I would ask you to consider the possibility that math is not some Platonic knowledge, that it inhabits no realm higher or lower than any other kind of knowledge. Instead, I ask you to look at math as "the language of certainty." What implications would this have for your thesis? What problems arise from this perspective?

>>1077736

>lrn2PhilosophyOfScience
>lrn2OrigingOfMathmatics

>>1077805
Just because entire mathematical theories may be incomplete, this doesn't imply that the subset which describes interactions in a physical theory must be part of that incompleteness. So, yeah, you can basically ignore Godel for your purposes.

Turing completness indicates that all systems of sufficient complexity can be used to describe and compute eachother, therefore math wins.

>>1078004
>>1077928
Pfft. Your arrogance people is pointless and annoying. The nature of mathematics isn't obvious. I'm >>1077759 and von Neumann's stance is far from widespread, most mathematicians are actually platonists.
Besides philosophy of science is full of shit, bad advice.

>>1078017
>Just because entire mathematical theories may be incomplete, this doesn't imply that the subset which describes interactions in a physical theory must be part of that incompleteness.
No, but Gödel's theorems do (assuming the logical theory of physics is sufficiently powerful, which according to my rather limited knowledge of physics is the case). This means (again, with the assumptions stated above) that even with a perfect theory of physics, there are still questions about physics (albeit pathological) that we cannot answer.

>Physicists often assume that the universe is written in the language of maths.
No, they don't. They just notice that the language of maths is a convenient language to describe the universe in, which is something completely different.

>>1078104
This simply does not follow. The mathematical formalism required to derive a sufficiently powerful model of physical interactions may be incomplete, I don't disagree. But the model of interactions may be completely covered by proofs. Just because Peano arithmetic is incomplete doesn't mean we cannot decide the multiplication of two numbers, for example.

>>1078137
>The mathematical formalism required to derive a sufficiently powerful model of physical interactions may be incomplete, I don't disagree.
My point is about the reverse case - if we can derive (the axioms of) a sufficiently powerful mathematical formalism from the laws of physics, then the physics must be just as incomplete as the mathematical formalism.

>>1078174
That is a very big 'if'. If the universe is finite, you are SOL.

Mathematics is...counting. Are we destined to count...forever?

>>1078179
Really? Why? (Note my rather limited knowledge of physics I described earlier.) Aren't (say) Newton's laws of motion (yes, I know they're inaccurate thanks to relativity and all that stuff, but the same argument probably applies to more modern physics as well) or Maxwell's equations sufficient to prove Peano arithmetic?

ITT: Bitches don´t know bout my Gödel´s theorem

>>1078210
No - Peano arithmetic is fully complete for an infinite number of strange definitions of 'number', 'sucessor' and 'zero'. For example, Peano arithmetic is fully complete if you define 'zero' as 'one' and 'sucessor' as 'the previous number divided by two' (so the fifth number in this sequence is 1/32)

Physics only fits one possible set of axioms in Peano arithmetic

>>1077736
>What do you guys think?

OP IS A FAGGOT

OP's faggotry is too faggy

i think OP doesnt know much about science

>>1078210
>>1078235

Thanks for the interesting discussion, it took a while for me to understand it.

If the mathematics of the universe were found to be inherently incomplete, this wouldn't necessarily justify the "maths can only approximate reality" position. I'll compare it to something on more familiar territory; the Heisenberg Uncertainty Principle. The HUP states that there is a maximum accuracy with which we can know the product of the momentum and position of a particle - it's pretty common in pop physics, so I'll assume you've heard of it.

Since the HUP does not come down to the accuracy of our measuring tools and is a fundamental property of the system, one could argue either that "our theory isn't good enough to know everything" or equally "this is the way the universe itself ACTUALLY is - it has uncertainties. The universe IS an uncertain system."

The same second argument, it seems to me, can be made about a universe that is not completely knowable mathematically - either that's a limit of maths, or else that's the way the universe really is.

Final analogy because I feel I've explained poorly: If you look through a telescope and see a blurry planet and nothing else is in the sky, how can you tell if you're seeing a blurry planet or if your lens is dirty?

>>1078215
This. I don't know why this thread even exits.