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Geometry Reality debate

  1. Who cares ?

    1 vote(s)
  2. Merely a tool

    3 vote(s)
  3. The language we use to describe reality

    10 vote(s)
  4. A universal construction, independent of experience

    9 vote(s)
  5. A very beautiful art

    6 vote(s)
  1. Mar 16, 2007 #1
    I was just having this very old, neverending debate. I would like to have your opinion about this. It all started with geometry, but I think the argument extends to mathematics altogether.

    According to my friend, mathematics first come from experiment and thus belong to the category of physical models of the world. In my opinion, mathematics belongs to the ideal platonic world.

    I will first re-phrase my opinion since it is eaiser for me :smile:
    Considering that
    • one can study mathematics without knowing anything about the outside world : I know of a blind geometry professor
    • the physical world we use as a source of inspiration to choose the geometry we want to study, but we can invent (but see later) as many as we want, as wild as we can think of :smile:
    I think mathematics exist independent of the physical world. At the very least, mathematics are universal, a circle is a circle no matter if I am a french man, or an alien in another galaxy...

    He, on the contrary, argues that everything comes from experiment, and that just like other physical models of reality, geometry somehow belongs to physics. The mathematics we choose to study come from experiment, and are thus a reflection of the physical world

    The all debate actually seems to stem from the The Unreasonable Effectiveness of Mathematics in the Natural Sciences.

    I also want to push the two previous opinions to their extreme :

    One could consider that mathematics are just a toolbox. If a piece of mathematics serves no practical purpose it is useless, should be disregarded and not taught.

    I am even among those who think that mathematics is just like art, because I often experience deep esthetics feelings while reading a mathematical proof, intense as one can feel while contemplating a painting of listening to a beautiful musical composition. I do not want to develop to much at this stage and/or go into philosophical consideration, but earlier I would rather have said discover instead of invent since I think mathematics exist per se, before we know them, in the platonic world.
    Last edited: Mar 16, 2007
  2. jcsd
  3. Mar 16, 2007 #2

    George Jones

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    As I said in post #16 of this thread, I'm with Godel, Hardy, and Penrose, i.e. I am a Platonist.

    "... and there is no sort of agreement about the nature of mathematical reality among either mathematicians or philosophers. Some hold that it is 'mental' and that in some sense we construct it, others that it is outside and independent of us ... I believe that mathematical reality lies outside of us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our 'creations', are simply our notes of our observations."

    G. H. Hardy

    From this other post, it appears that Hurkyl disagrees.
    Last edited: Mar 16, 2007
  4. Mar 16, 2007 #3


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    A nice book on this subject is The Philosophy of Space and Time by Hans Reichenbach.
  5. Mar 16, 2007 #4
    See signature :smile:
  6. Mar 16, 2007 #5
    "It is the merest truism, evident at once to unsophisticated observation, that mathematics is a human invention."

    -Bridgman, P. W.
  7. Mar 16, 2007 #6

    Chi Meson

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    You left out the option of:

    "merely one of the parts of the whole."
  8. Mar 16, 2007 #7
    It remains the most singularly beautiful and powerful invention of mankind. Now the beauty is not always accessibility to the common man, but the utility is without debate. Even our best "art", fails this test.
  9. Mar 16, 2007 #8


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    "Disagrees" is too strong a word -- I simply think the answer to this question is entirely irrelevant to actually doing mathematics.
  10. Mar 16, 2007 #9
    Im an engineer, they are a tool for me. I care about the physics, not the math. All that matters is that I get the right answer. I dont care about things like the limit of 0.9999 =1, it wont explain why an airplane flies, or what the stresses are in a beam.
    Last edited: Mar 16, 2007
  11. Mar 16, 2007 #10
    Perhaps, you're being a little narrow minded re this. Engineering w/o math is like your best prayer and a rain dance. You may have no use for exactitude. But the principles upon which you design anything should hopefully come from the heart of mathematic principle. Try it w/o and wait to be sued. Won't be long.
  12. Mar 16, 2007 #11
    I think you misread what I wrote. I said I use math as a tool, I dont care about the formalisms behind it. The formalisms have trivial importance to me.
  13. Mar 16, 2007 #12
    Most of us do, but I also believe that math sometimes get short shrift when it comes to theoretical mathematics. Often in the history of science and engr, the math has been sitting around for some time waiting for an application. Its any engineer's mother, and not to me dismissed casually as in I have only use for the teats that feed me, and nothing else.
  14. Mar 16, 2007 #13
    I also am an engineer. I also use math to solve my problems, but I also see in math a very elegant and beautiful art form. It is the most abstract and austere form of beauty.
  15. Mar 16, 2007 #14
    Well, if you have a math that is usefull to me, then I'll use it. Otherwise, I wont touch it. Its useless to me, as an engineer. As an engineer, we dont use theoretical mathematics.
  16. Mar 16, 2007 #15
    Then you shall be a follower, like the hundreth and one sheep in a flock, which is not all bad as the first hundred may be destined for slaughter and the remainder only shorn for their coats...at least until the next year.
  17. Mar 16, 2007 #16
    :rolleyes: ..................o-kayyyy........this is a bunch of nonsense, but whatever.
    Last edited: Mar 16, 2007
  18. Mar 16, 2007 #17
    Talking about outsourcing at least in the USA. If one ccan employ some Pakistani or Indian engineer with an IQ of 160 for less than the costs of a USA countertype for twice the $$ and 2/3 rds the IQ, I'd be trying to think outside the box. Advanced math can help.
  19. Mar 16, 2007 #18
    Who cares if his IQ is 160, your paying him pennies on the dollar to what you would have to pay me. Its not because hes so much smarter than me, its because hes so much cheaper.

    Don't confuse advanced math, with formal math. We have math classes 'for scientists and engineers'. Those are NOT the same as math classes for MATH majors.
  20. Mar 16, 2007 #19


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    Since you don't say what you mean, I can only guess. So it's your fault if this has nothing to do with what you meant. :tongue:

    In any pursuit, you need people who look for new useful things, and people who use the useful things we already have. You can't make progress without both kinds of people.
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