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Mathematical Quandaries

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Comments

  • cmk24cmk24 Member Posts: 605
    Fardragon said:

    I'm not, in any way, suggesting that string theory be dismissed, just pointing out (as most of those behind the theory would agree) it doesn't become science until it makes a testable prediction. That doesn't make it useless or wrong. It is science (and it's dependency on mathematics) that is limited. There is no reason to suppose, or any way to prove, that it is possible for science, maths, or the human brain to fully describe the universe. It's simply a process of creating and improving a model which we can understand, and use to make useful predictions.

    Actually string theory does make testable predictions, the problem is it predicts the same thing that simpler theories also predict. The unique predictions that it makes are all untestable (such as things that can't be observed by definition). So at the moment it is a more complex way to get at an answer we already knew.

  • DreadKhanDreadKhan Member Posts: 3,563
    I think he's explaining why math was used in the first place... Physics theories aren't art, they aren't something you can just pull out of your arse (no offense artists) at random and have work. Its a valid point, that math without any concrete foundation is a pipe-dream, or metaphysics.

    And I think @Musigny 's 2nd point is that QM originated before we had all the math needed to fully elaborate the theory. I don't necessarily see it as a problem inherently, but if the math isn't forthcoming eventually, the theory gets to sit on a shelf and gather dust, because it'll be metaphysics.

    If you don't find it 'fun', you don't need to discuss. The discussion will probably die down eventually.

    cmk24joluvlolien
  • cmk24cmk24 Member Posts: 605
    DreadKhan said:


    And I think @Musigny 's 2nd point is that QM originated before we had all the math needed to fully elaborate the theory. I don't necessarily see it as a problem inherently, but if the math isn't forthcoming eventually, the theory gets to sit on a shelf and gather dust, because it'll be metaphysics.

    That is not quite true, the math needed for QM (linear algebra) was developed several years before QM, but it was not known to the physicists at the time. It was not until a few years after QM was thought of that the physicists realized there was already a mathematical tool they could use to make the theory more elegant. This is not to say the physicists who first came up with QM didn't have the math to explain it, just the math they used (calculus) was not the most elegant/simplest/nicest way to go about it.

    Fun fact: the mathematician who invented linear algebra said something along the lines of "finally, a mathematical theory that has no practical application." He was not happy when physicists used it to explain QM.

    lolien
  • FardragonFardragon Member Posts: 4,374

    What's your point? Do you mean QM does break maths?

    It breaks maths until you invent new maths to fix it.

    Thus demonstrating that maths is something invented by humans to solve problems, not some universal Truth waiting to be discovered. If you can solve a problem by defining 1/0 = 42, then there is no reason not to do so.

  • joluvjoluv Member Posts: 1,944
    cmk24 said:


    That is not quite true, the math needed for QM (linear algebra) was developed several years before QM, but it was not known to the physicists at the time. It was not until a few years after QM was thought of that the physicists realized there was already a mathematical tool they could use to make the theory more elegant. This is not to say the physicists who first came up with QM didn't have the math to explain it, just the math they used (calculus) was not the most elegant/simplest/nicest way to go about it.

    Fun fact: the mathematician who invented linear algebra said something along the lines of "finally, a mathematical theory that has no practical application." He was not happy when physicists used it to explain QM.

    Linear algebra is much older than quantum mechanics. I think with that pseudo-quote, you might be referring to Hardy and his work on integer partitions. Hardy did not invent linear algebra.

  • MusignyMusigny Member Posts: 1,017
    edited April 2015
    cmk24 said:

    That is not quite true, the math needed for QM (linear algebra) was developed several years before QM

    Knowing if you can and how you can use the basic algebraic operators on both sides of the sign equal in
    ax = b
    already belongs to linear algebra.
    Not my point anyway.

  • supposedlysupposedly Member Posts: 206
    edited April 2015
    Mathematics passes no judgement about what the meaning of dividing by zero is. To math, it means as much as "Garfle the Narflak." Dividing by zero is neither possible nor impossible. It's just undefined.

    Musigny
  • joluvjoluv Member Posts: 1,944

    Mathematics passes no judgement about what the meaning of dividing by zero is. To math, it means as much as "Garfle the Narflak." Dividing by zero is neither possible nor impossible. It's just undefined.

    New question: is math sentient?

    DreadKhanlolien
  • DreadKhanDreadKhan Member Posts: 3,563
    joluv said:

    Mathematics passes no judgement about what the meaning of dividing by zero is. To math, it means as much as "Garfle the Narflak." Dividing by zero is neither possible nor impossible. It's just undefined.

    New question: is math sentient?
    One wonders....

    lolien
  • skinnydragonskinnydragon Member Posts: 110
  • FardragonFardragon Member Posts: 4,374
    edited April 2015

    Mathematics passes no judgement about what the meaning of dividing by zero is. To math, it means as much as "Garfle the Narflak." Dividing by zero is neither possible nor impossible. It's just undefined.

    Garfle (verb): to clean with a small wire brush.

    Narflak (noun): a sort of combined window and perch, used in bird feeders.

    Also see: Borogove.

    joluv
  • BelgarathMTHBelgarathMTH Member Posts: 4,753
    Re the discussion about string theory vis a vis philosophy of science: Isn't that issue why we have the academic field of physics divided into "theoretical physics" and "experimental physics"?

    In the television program "The Big Bang Theory", the division of the field is a running thematic source of comedy between Sheldon, who is a theoretical physicist who believes that his is the more glamorous sub-field requiring superior intellect, and Leonard, an experimental physicist who sometimes resents Sheldon's superiority complex and lack of respect for experimental physics (not to mention Howard's "lowly" engineering).

    Here is an interesting site where an undergraduate asks for, and receives, advice about which sub-discipline of physics to choose:
    http://www.quora.com/Theory-or-Experiment-how-does-one-choose

    My point is that theory and experiment need each other to become good science. While experiment can stand on its own as science, and in fact is part of the definition of science, it needs a constant source of new ideas to fuel its progress and growth. Theoretical physics and mathematics provide that fuel.

    Without experiment, though, they become philosophy rather than science. For example, Ptolemy's model of the solar system was backed up by perfectly good mathematics and theory, and was (mostly) backed up by observation and good prediction. It was also absolutely *wrong*. It took the invention of newer, better tools of observation to figure out just how wrong it was.

    So, I see theoretical physics and mathematics as giving us a steady stream of new ideas to test. Very often, those abstract ideas are decades or even centuries ahead of our having advanced enough tools of observation to start the experimental phase of scientifically testing those ideas.

    That's where engineers and inventors come in. Better supercolliders and space-based telescopes, anyone? Wormholes, warp engines and transporters? You never know where advanced theories and mathematics can lead us, as long as there is freedom to question, to be skeptical and doubtful, and have cooperation between the fields that come up with the theories and the fields that build and invent observational devices and do the testing. It's a symbiosis and synergy of all academic disciplines that progresses knowledge and humanity.

  • joluvjoluv Member Posts: 1,944

    Re the discussion about string theory vis a vis philosophy of science: Isn't that issue why we have the academic field of physics divided into "theoretical physics" and "experimental physics"?

    I was so with you...

    In the television program "The Big Bang Theory"

    ...and then you lost me.

    supposedly
  • supposedlysupposedly Member Posts: 206

    Re the discussion about string theory vis a vis philosophy of science: Isn't that issue why we have the academic field of physics divided into "theoretical physics" and "experimental physics"?

    There's also Mathematical Physics

  • cmk24cmk24 Member Posts: 605

    Re the discussion about string theory vis a vis philosophy of science: Isn't that issue why we have the academic field of physics divided into "theoretical physics" and "experimental physics"?

    There's also Mathematical Physics

    And in the field of astrophysics there is also "observational physics." It is difficult to do "experiments" on things that happened many 100s to millions of years ago.

  • supposedlysupposedly Member Posts: 206
    cmk24 said:

    Re the discussion about string theory vis a vis philosophy of science: Isn't that issue why we have the academic field of physics divided into "theoretical physics" and "experimental physics"?

    There's also Mathematical Physics

    And in the field of astrophysics there is also "observational physics." It is difficult to do "experiments" on things that happened many 100s to millions of years ago.
    It is time for more... experiments

    joluvGod
  • GodGod Member Posts: 1,115
    DreadKhan said:

    Knowability of the universe is a pain in the butt for science, because the 'Theory of Everything' is the goal, but it's also a mirage; the closer you get, the further away it seems to get (the more answers we find, ever more questions are created).

    It doesn't just seem to get further away. It does get further away. Ever further, infinitely.
    The universe, while constrained, is boundless in a sense. It is a system of perpetual divisions that conscientiously strives to remain a mystery. Quite a well-designed one, if I do say so myself.

  • Fiendish_WarriorFiendish_Warrior Member Posts: 309
    edited April 2015
    Been ridiculously busy lately but still read. Anyway, watched this oldie but goodie today. Feynman on mathematics and physics:

    JuliusBorisov
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