View Full Version : Is there anything mathematics cannot fully explain?

CosmicUnderstanding

2010-Sep-09, 03:56 PM

I've always heard mathematics is the language of nature, and that makes sense to me.

So, is it possible to have an event occur in nature that cannot be fully explained by math? Have we come across anything that just defies any possible formula we could assign to it?

Strange

2010-Sep-09, 04:22 PM

I assume you don't mean the "why are we here" type questions. There are many things for which we have no practical way of finding solutions (N-body problem and others that can only be solved by simulation). There are a large number of open or unproved questions (http://en.wikipedia.org/wiki/Millennium_Prize_Problems or http://en.wikipedia.org/wiki/Hilbert%27s_problems, for example). And then there is Godel's incompleteness theorem which showed that any formal system must always be incomplete.

(I'm sure a mathematician or philosopher will be along shortly to say more :))

HenrikOlsen

2010-Sep-09, 04:55 PM

Mathematics can't explain anything, at all.

What it can do is show that something is consistent with a set of assumptions, it can't tell you anything about the assumptions themselves (except if you pick a set that includes a contradiction it will tell you).

kleindoofy

2010-Sep-09, 10:01 PM

Is there anything mathematics cannot fully explain?

Women. ;)

Strange

2010-Sep-09, 10:59 PM

Mathematics can't explain anything, at all.

True. If slightly pedantic :)

I think "explain" could be taken to mean describe / predict / formalize in this context ...

caveman1917

2010-Sep-09, 11:47 PM

I think "explain" could be taken to mean describe / predict / formalize in this context ...

Wouldn't the answer then be no?

Godel's theorem is descibed mathematically, as is the reason why we can't find analytical solutions for the N-body, etc.

How would one even communicate an event if one couldn't describe it mathematically?

Strange

2010-Sep-10, 12:01 AM

Godel's theorem is descibed mathematically, as is the reason why we can't find analytical solutions for the N-body, etc.

Very true.

I guess there is also a difference between things we can't currently do versus things that can't be done even in principle. And the latter break down into those we have have proved can't be done and those which are yet to be decided one way or the other. And the latter break down into those where it can, in principle, be proven (we just don't know how yet) and those where no such proof is possible ...

slang

2010-Sep-10, 12:08 AM

Some love this type of question. Others hate it. I'm not sure math can explain it fully.

Is there anything mathematics cannot fully explain?

Women. ;)

Winnar!!111

Cougar

2010-Sep-10, 01:44 AM

I've always heard mathematics is the language of nature... So, is it possible to have an event occur in nature that cannot be fully explained by math? Have we come across anything that just defies any possible formula we could assign to it?

Nothing in science is "fully explained" by anything. The scientific method accepts each understanding as conditional - upon future observations that may enhance or modify the understanding.

Then again, Differential equations can describe quantitatively many physical processes that occur "in nature." Tensor calculus/modern geometry is used in General Relativity (I am told :whistle: ), and abstract algebra/group theory is apparently instrumental in describing features of particle physics...

But, as mentioned, humans are part of nature. There are certainly lots about humans where "formulas" could not be assigned!

Ivan Viehoff

2010-Sep-10, 08:39 AM

Mathematics doesn't explain anything in the same sense that the English language doesn't explain anything, each is merely the language by which explanations are communicated.

Disinfo Agent

2010-Sep-10, 12:06 PM

There are many disciplines where knowledge cannot be expressed in terms of mathematical equations: psychology, sociology, history, much of biology, an important part of economics... But if by 'mathematics' we also mean statistics, then I have a hard time thinking of an area of inquiry where collecting data and at least looking at frequencies doesn't help.

Grey

2010-Sep-10, 01:44 PM

But if by 'mathematics' we also mean statistics, then I have a hard time thinking of an area of inquiry where collecting data and at least looking at frequencies doesn't help.And so then we need to know what we mean by "explain". Do we mean "provide a complete predictive description of", or do we mean "provide some insight into the workings of"? Or somewhere in between?

flynjack1

2010-Sep-10, 02:42 PM

Is there anything mathematics cannot fully explain?

Women. ;)

Took the word(s) right out of my mouth.

CosmicUnderstanding

2010-Sep-10, 04:57 PM

Those are all some amazing and insightful answers! I apologize for not clarifying, but yes I did in fact mean 'explain' in the context of being capable of calculating or predicting certain natural events. I hadn't even considered topics such as biology, psychology, etc etc. Perhaps there is a way to assign numbers and formulas to those areas of our reality also, but we haven't put them in the correct "format" yet?

Disinfo Agent

2010-Sep-10, 07:59 PM

And so then we need to know what we mean by "explain". Do we mean "provide a complete predictive description of", or do we mean "provide some insight into the workings of"? Or somewhere in between?I would delete the word 'complete' from your definition. Otherwise, I agree with it. As for the contrast between describing and explaining, it seems to me that the two usually go hand in hand. It's true that sometimes researchers come up with models that 'describe' adequately while giving little insight. But in the long run such descriptions tend to lead to incorrect predictions, too (a recent old example (http://www.bautforum.com/showthread.php/107589-Can-we-finally-test-Bode-s-Law)).

JohnD

2010-Sep-10, 08:23 PM

flynjack1

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Originally Posted by kleindoofy

Is there anything mathematics cannot fully explain?

Women.

Took the word(s) right out of my mouth.

_____________________________________

Wheras you, presumed males, are logical, sequential and entirely explicable.

Well, excuse me if I leave to your testosterone and move on to another, less boring group in this cocktail party.

I hope it will comprise a roughly equal number of the sexes, and so be a lot more original and amusing.

John

The Backroad Astronomer

2010-Sep-10, 08:38 PM

Yes.

http://www.bautforum.com/showthread.php/107604-Are-all-teenage-girls-the-same

kleindoofy

2010-Sep-10, 09:27 PM

... Wheras you, presumed males, are logical, sequential and entirely explicable. ...

How on Earth did you ever reach that conclusion?

Put in a syllogism, you just said:

All cats are blue.

It's not a cat.

Therefore it is not blue.

Sorry, that's illogical.

But perhaps female and indescribable by math. :lol::lol:

caveman1917

2010-Sep-11, 01:19 PM

I guess there is also a difference between things we can't currently do versus things that can't be done even in principle. And the latter break down into those we have have proved can't be done and those which are yet to be decided one way or the other. And the latter break down into those where it can, in principle, be proven (we just don't know how yet) and those where no such proof is possible ...

That gets it all ;)

The real question here seems to be what is meant by "explain".

An experiment giving a set of parameters considering them all free, doesn't explain a thing about what has been measured, but even a set of free parameters is a mathematically described system.

agingjb

2010-Sep-11, 05:49 PM

Is there anything that mathematics can fully explain?

Salty

2010-Sep-11, 09:50 PM

I've always heard mathematics is the language of nature, and that makes sense to me.

So, is it possible to have an event occur in nature that cannot be fully explained by math? Have we come across anything that just defies any possible formula we could assign to it?

Well, that claim for mathematics doesn't displace the claim that music is the international language.

I seriously doubt that mathematics can explain romance between a man and woman. Heh heh heh. Maybe some one can write a mathematical formula that describes romance between a man and woman; but that's still a far cry from explaining it.

HenrikOlsen

2010-Sep-11, 10:22 PM

Well, that claim for mathematics doesn't displace the claim that music is the international language.

Heh. We can't even agree on the same pentatonic scale worldwide.:D

Moose

2010-Sep-11, 11:56 PM

Is there anything that mathematics can fully explain?

Arithmetic.

flynjack1

2010-Sep-12, 02:57 PM

flynjack1

Originally Posted by kleindoofy

Is there anything mathematics cannot fully explain?

Women.

Took the word(s) right out of my mouth.

_____________________________________

Wheras you, presumed males, are logical, sequential and entirely explicable.

Well, excuse me if I leave to your testosterone and move on to another, less boring group in this cocktail party.

I hope it will comprise a roughly equal number of the sexes, and so be a lot more original and amusing.

John

I was merely enjoying Kliendoofy's jest. Fact: best mathematician I personally know is a female. Fact: worst mathematician I know is also female. Conclusion obvious. But I don't see any reason to believe that human psyche is reducible to mathematic terms. Including that of humor apparently.

kleindoofy

2010-Sep-12, 08:11 PM

I was merely enjoying Kliendoofy's jest. ...

Jest? What jest? ;)

Salty

2010-Sep-12, 10:00 PM

Heh. We can't even agree on the same pentatonic scale worldwide.:D

Why do that? I like variety. We can have united variety.

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