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Has any equation ever been proved

  1. Sep 19, 2012 #1
    I'm re-examining. My mathematics is merely college major level. I am not involved with it in the direct or academic sense anymore, but I still think about it a lot.

    My certainty is that there can not be "one" of anything in an actual sense - in terms of quantum position and time. I am unique, but to say there is one of me is an approximation, correct? The particles I am constructed of are in motion, adding to me, subtracting from me every moment.

    Thus, to say there is one of me is a construct of our mind. "One" being the imaginary number we learned in Kindergarten. It's use is as a generalization to permit discussion, description, equation. Yet I'll put that aside - for the sake of argument, let's say there is one of everything that is in the physical world.

    It follows though that there can not be "two" of anything. Again, "two," another imaginary concept in number. One fork plus one fork = one fork plus one fork. Both forks are in a physical sense very different, at the lower level - albeit it not to our eye per se. So again, the fork is being generalized by anyone who would say "there are two forks." Generalizing them as "two" could actually be an insult. (How would you feel if standing next to Hitler, someone described the setting as having "two people"). So such a statement would be false, unless one were to call a "fork," the word, the concept, an actual individual entity of the world. Though we all know it is not - we know that it only holds together as a fork due to a multitude of forces acting on it, which are ever modifying, and that no two forks are alike.

    If it is impossible to have "two," then how can any equation be proved? Is it only an approximation of the world? Is it only a description we make to the best of our ability? The fork is a construct of the mind, so proving there are two forks is merely proving the imaginary construct that will only exist as long as humans or other intelligent beings exist. But it does not prove anything in terms of the physical world.

    So has any equation really ever been proved?
    Am I in the correct forum? :)
  2. jcsd
  3. Sep 19, 2012 #2

    It sounds like more of a philosophy question. But even then, it's more about the real world than about mathematics.

    Mathematically, 1 + 1 = 2 is a theorem. It can be proved starting from the basic rules of logic.

    In the real world, you do have a point that one apple plus one apple is really ... this apple plus that apple. Since the apples are not identical to each other (and as you point out, are not even identical to themselves over time) it could be argued that it makes no sense at all to call them two apples. Before you can call them two apples, you have to apply some kind of abstraction transform that ignores the tiny molecular variations in the apples, so that you can regard each of them as a representative of some abstract Platonic realm of appleness.

    This is a sensible discussion; but it's a matter of philosophy, not math or physics.
  4. Sep 19, 2012 #3
    Now I hate this kind of discussion, so I won't really get involved, but mathematics does not attempt to prove anything "in terms of the physical world", it has no concern for silly things like atoms and quantum systems.
  5. Sep 19, 2012 #4
    I do apologize for getting into a discussion that is of the "hated" variety. But if you could indulge me for a bit further? That brings me back to the equations aspect of my question - so then anything proved with numbers is imaginary, or another words proof of an imaginary concept. Would that be a correct statement?
  6. Sep 19, 2012 #5
    And thanks Steve for taking my question head on. Your response was very helpful to me.
  7. Sep 19, 2012 #6
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