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Thread: Is there anything mathematics cannot fully explain?

  1. #1
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    Is there anything mathematics cannot fully explain?

    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?

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    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 )

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    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).
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    Is there anything mathematics cannot fully explain?

    Women.

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    Quote Originally Posted by HenrikOlsen View Post
    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 ...

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    Quote Originally Posted by Strange View Post
    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?

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    Quote Originally Posted by caveman1917 View Post
    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 ...

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

    Quote Originally Posted by kleindoofy View Post
    Is there anything mathematics cannot fully explain?

    Women.
    Winnar!!111
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    Quote Originally Posted by CosmicUnderstanding View Post
    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 ), 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!
    Everyone is entitled to his own opinion, but not his own facts.

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    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.

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    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.

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    Quote Originally Posted by Disinfo Agent View Post
    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?
    Conserve energy. Commute with the Hamiltonian.

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    Quote Originally Posted by kleindoofy View Post
    Is there anything mathematics cannot fully explain?

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

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    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?

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    Quote Originally Posted by Grey View Post
    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).

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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

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    ...I'm still free, you can't take the sky from me.

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    Quote Originally Posted by JohnD View Post
    ... 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.

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    Quote Originally Posted by Strange View Post
    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.
    Last edited by caveman1917; 2010-Sep-11 at 01:21 PM. Reason: italics

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    Is there anything that mathematics can fully explain?

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    Quote Originally Posted by CosmicUnderstanding View Post
    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.

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    Quote Originally Posted by Salty View Post
    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.
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    Quote Originally Posted by agingjb View Post
    Is there anything that mathematics can fully explain?
    Arithmetic.
    "Words that make questions may not be questions at all."
    - Neil deGrasse Tyson, answering loaded question in ten words or less
    at a 2010 talk MCed by Stephen Colbert.

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    Quote Originally Posted by JohnD View Post
    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.

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    Quote Originally Posted by flynjack1 View Post
    I was merely enjoying Kliendoofy's jest. ...
    Jest? What jest?

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    Quote Originally Posted by HenrikOlsen View Post
    Heh. We can't even agree on the same pentatonic scale worldwide.
    Why do that? I like variety. We can have united variety.

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