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Is math real? Is physics math describable?

  1. May 28, 2008 #1


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    This question arised somewhere else (https://www.physicsforums.com/showthread.php?t=236919). It started with

    This made me wonder - is math real? I don't mean real like a hammer - math is competely abstract, there is no doubt about it. However, is math really a game? Once we have made some basic assumptions and added some definitions, world that emerges is not random. We can discover its properties but statements that are true are already true and statements that are false are already false - even if we don't know them yet. So when we work on some branch of math we are not creating it - we are in fact uncovering construction that was there from the very beginning. It was there even before we have selected axioms and definitions.

    Now, why is math so efficient tool in describing physics phenomena? Could be the reason is similarity - there is a set of axioms (rules, definitions) underlying all physics, and these axioms define all physics - just like some simple sets of axioms and definitions create huge branches of math. I am not aiming at Equation Of All Equations here, One To Rule Them All, One That Will Answer All Questions, 42. I just wonder if the fact, that now and then we hear that someone have realized that some esoteric math theory perfectly describes fine details of observable physiscs is not some sort a sign that these worlds (math & physics) are in a way parallel? Just like in math some statements are false, in physics some things can't happen - for the same reason. They are prohibited by logic. And just like in math starting point (set of axioms and definitions) generates whole world even before we start to think about possible outcome, whole world of physics is generated by some starting point. (Don't ask me what this starting point is - I have no idea).

    If the math analogy is OK, looks like our physics has a good starting point, that leads to many emergent properties.

    Disclaimer: English is my second langugae - and I am not sure if I wrote exactly what I mean. Hopefully I did.
  2. jcsd
  3. May 28, 2008 #2
    English is my third language. No wait, fourth ! Whatever :smile:

    Is this a poll ?

    Some think we discover math (platonists). Other prefer to think we construct them. This discussion can be very interesting.
    That's a very good question indeed !

    Did you check Wigner ?
    The Unreasonable Effectiveness of Mathematics in the Natural Sciences
  4. May 29, 2008 #3
    Road to Reality

    The Road to Reality Penrose R. is a mathematical one.
    Last edited: May 29, 2008
  5. May 29, 2008 #4
    "Don't confuse the map with the territory."
  6. May 30, 2008 #5
    Try this interesting essay, called Mathematics and the language of nature by David Peat.
  7. May 30, 2008 #6
    I hold mathematics to be an unambiguous and precise language for describing relations, quantities and so on. Therefore, there is no surprise in mathematics being effective in the natural sciences. Saying that it is a surprise that mathematics is effective in the natural sciences is like claiming that the fact that English is effective in the natural sciences is surprising. The fact that clear descriptions of relations and quantities and so on are useful in the natural sciences is hardly surprising.

    I guess this rules out platonism and intuitionism for me. I think I subscribe to some combination of formalism, mathematical realism, and mathematics as a language.
  8. May 30, 2008 #7


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  9. May 30, 2008 #8


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    Wigner link was already posted here by humanino - and it is relevant.

    The most important point - for me - being, I am not the only one to think about these things :wink:
  10. May 30, 2008 #9


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    Oy.. I should have read the thread more carefully.

  11. May 30, 2008 #10
    Not that it particularly matters for the discussion at hand, but it appear that Wigner is a creationist. Well, at least some character assassinations are valid. In any case, both Howell and Steiner has made a similar argument before. Richard Carrier discussed the argument in detail here.
  12. May 30, 2008 #11
    Not that I think about it, there is a good deal of chance that I first read this with your initial link "in an earlier thread" So, I should thank you :smile:
  13. May 30, 2008 #12
    I strongly oppose to that statement. Most important of all, by the time Wigner was alive, the mere word "creationism" did not carry the heavy controversial weight it does today. So using this word, purposedly or not, is an anachronism.

    A few friends of mine sharing more or less the same point of view as experssed by Wigner would be pretty upset to be called creationists :frown:

    Honestly I did not read the entire link. Can you however show me where Wigner is mentionned ?
    Last edited: May 30, 2008
  14. May 30, 2008 #13

    Eugene Wigner appears to be the author of that article. Creationist was probably a too strong word, and the remark he made was just brief.
  15. May 30, 2008 #14
    I'm sure religion is not the most popular thing to discuss here (or any other diverse community), but I do have to point out that you can't use science to back up your disbelief of a creator; if anything, science proves there is a creator. I'm not religious but I'm just saying that science can only explain what the big bang was, not what lit the fuse. :)

    edit: btw, my statement about science proving there is a creator is referring to the understanding that things don't spontaneously begin to exist out of nowhere.
    Last edited: May 30, 2008
  16. May 30, 2008 #15
    If math is not real like a hammer, it's real like a ____?

    I don't know what 'real' is other than what is physical. I think math is real like a hammer.

    So these aliens show up one day from Andromeda. And they've got the same hammer! It's the quadradic equation. Well, it's kind of the same hammer, after applying some symbolic conversion and other mathematical gyrations, it's the same hammer, sorta'.
    Last edited: May 30, 2008
  17. May 31, 2008 #16
    Like Moridin said, math is a language. It's a purely syntatic language used for describing and manipulating raw data. It may seem like math is intrinsic to the universe but that's only because it's based (originally) on observations of the relationships and constants seen in reality so that it can be used to model it, and with physics and quantum physics it's often only through these models that we can "see" what is going on. It's taken thousands of years to develope the language and it's models to accomidate the ways that it's used to model reality today. No one simply looked at the world and "uncovered" it's hidden math.

    Zero: The Biography of a Dangerous Idea is a very good book that can give you an idea of the history behind the development of math.
  18. May 31, 2008 #17


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    In addition, I'd like to note that math doesn't perfectly describe reality, but it's very easy to manipulate and "fit" to reality, as it was designed.
  19. May 31, 2008 #18
    If anything, math (as a concept) tells us more about consciousness and intelligence than it does about reality.
    The brain is made in such a way that it quantifies and abstracts things from each other, and then in some mysterious way processes the information.
    This is the foundation for 'everything' about the mind.
    When a human applies morality, it's a way of processing data in a meaningful way with something that symbolizes the essence of something.
    In the same manner 1 + 1 = 2, the 1 is a symbol of a quantity, and the 2 is the processing of these two 1's.

    But the most important thing to note, is that like someone else said, the map is not the territory itself.
    The map can be used to describe a lot of things to great detail, but they are two separate things, and in the end, the map has no connection or link to the territory itself.
    The connection is imo once again made in the brain of a conscious being like a human.
    We cannot say "this math perfectly describes the form, motion and weight of this hammer, therefore the form, motion and weight exists in the real world."
    We can't in any way describe something objectively, there will always be from a viewpoint of sorts, and math is also a viewpoint, it is a way of perception.

    In my opinion of course.
  20. May 31, 2008 #19
    From another point of view, you can consider that Nature does not perfectly fits in the mathematical model :smile:
    So Nature seems always more complex than a simple finite number of axioms.

    Most importantly, this is the only unambiguous language.

    But you do not address the universal aspect of mathematics. Let me recap the procedure
    • (1) Choose a set of axioms
    • (2) Derive logically all provable theorems
    • (3) Conjecture new axioms, independent from the previous ones, to enrich your formal system and go back to (1) (possibly getting a Field medal in between)
    From Godel and Turing's works we know that this cannot be performed by an automatic machine. Mathematicians need creativity to guess new axioms.

    Once the axioms are chosen, there is no freedom to departe from the rigourous rules of logical derivations. But new axioms already wait for you to discover them, in the form of true but unprovable statements. Just another point of view :smile:
  21. May 31, 2008 #20
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