Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

On G.H. Hardy's Comment

  1. Apr 13, 2010 #1
    Who maintains a more objective view of reality - a mathematician or a physicist?
    I might have laughed this off , but I'm bewildered by G.H. Hardy's views (who was a mathematician).
    I'll present an excerpt from his book , 'A Mathematician's Apology' (The most relevant paragraphs can be found at

    "..... I went on to say that neither physicists nor philosophers
    have ever given any convincing account of what "physical reality"
    is, or of how the physicist passes, from the confused mass of
    fact or sensation with which he starts, to the construction of the
    objects which he calls "real". Thus we cannot be said to know
    what the subject-matter of physics is ; but this need not prevent
    us from understanding roughly what a physicist is trying to do. It
    is plain that he is trying to correlate the incoherent body of crude
    facts confronting him with some definite and orderly scheme of
    abstract relations, the kind of scheme which he can borrow
    only from mathematics.
    A mathematician, on the other hand, is working with his own
    mathematical reality. Of this reality, as I explained in § 22, I take
    a "realistic" and not an "idealistic" view. At any rate (and this was
    my main point) this realistic view is much more plausible of
    mathematical than of physical reality, because mathematical
    objects are so much more what they seem. A chair or a star is not
    in the least like what it seems to be ; the more we think of it, the
    fuzzier its outlines become in the haze of sensations which surrounds
    it ; but "2" or "317" has nothing to do with sensation, and its properties
    stand out the more clearly the more closely we scrutinize it. It may
    be that modern physics fits best into some framework of idealistic
    philosophy---I don't believe it, but there are eminent physicists who
    say so. Pure mathematics, on the other hand, seems to me a rock
    on which all idealism founders: 317 is a prime, not because we think
    so, or because our minds are shaped in one way rather than another,
    but *because it is so*, because mathematical reality is built that way."

    Back in 1922, some physicists (and mathematicians too)found this provocative. Please share your views.
  2. jcsd
  3. Apr 13, 2010 #2


    User Avatar
    Science Advisor

    Well, provocative in which way? Please explain your opinion of it.
  4. Apr 13, 2010 #3


    User Avatar
    Homework Helper
    Gold Member

    Sure, for philosophy as for everything else, perhaps more than everything else, the student should make an effort to advance some idea of his own. As for everything else, more than for everything else, he should be prepared for strong criticism. Firstly from people who might know more about it that the student, secondly from people who know nothing about it and don't want to know but have strong opinions on it and are sure the student is wasting his and everyone's time because it's philosophy. He might as well get used to this reaction as it is a view he will hear in the future when he is outside academia. He might as well get used to this reaction as it is a view he will hear in the near future when he is inside academia.

    That said I always had me doots about this statement by Hardy. He is contrasting idealism, thinking that everything is in the mind, with an out-there reality independent of us I think. Well I suppose you could call humans (who else?) deciding to assemble a hundred pebbles or whatever, then another hundred then another hundred then another ten then five (or equivalent) then finding they can arrange them in a couple of ways in a regularly spaced thing they have invented and call a rectangle but that if they add another two stones they can't make a regular rectangle using them all in any way, I suppose you could call that a fact about the reality of a universe outside themselves. Well you could argue it and you would have to. I don't dispute that it's objective. Once they have made the rules of this game they can't get 317 as rectangle in it without cheating. Another objective fact is that they don't know this beforehand, at least not in the general case. But that's a fact about them, not really about much else. They worry about their not knowing beforehand, and try to find a way to do so; in the past they have found such ways for similar things that were not obvious (to them - again, who else?) which is an inspiring story (to them). Everything here seems to be about them and their thoughts, not some 'external reality'.
  5. Apr 13, 2010 #4
    Its an old argument.... goes back to the ancient greeks.... who saw geometry as perfect, and anyway it was much more predictable than everyday life, which seemed much more chaotic.

    Mathematics starts with definitions and a syntax. You can really start anywhere, but then you look for the implications of your assumptions. If you model your mathematics on the external world, then you can use it to predict what will occur.

    A theorem may seem very solid ground for a mathematician, but even mathematicians need to eat, sleep and take a dump every now and then. The reality of experience is solid.... just in a different way.

    People always see the world through their specialty. Mathmaticians see the world as numbers, Doctors as an organism, and mechanics as a vehicle. We all have our prejudices.... our constructed reality.
  6. Apr 23, 2010 #5


    User Avatar
    Gold Member

    A mathematician has a more objective view of our reality.
    A Physicist is trapped by observation.

    Mathematics is a finer kind of physics.
  7. Apr 25, 2010 #6


    User Avatar
    Science Advisor

    At large scales, pressure and temperature are a "sharp" things.

    At smaller scales, they are "fuzzy" things, just like Hardy says.

    In physics, this is modelled by the macrostates on a large scale being emergent from coarse-graining over microstates at a smaller scale.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook