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Eugene Wigner's take on math's role in natural science

  1. Mar 29, 2012 #1
    An excerpt from The Unreasonable Effectiveness of Mathematics in the Natural Sciences
    by Eugene Wigner

    "There is a story about two friends, who were classmates in high school, talking about their
    jobs. One of them became a statistician and was working on population trends. He showed a
    reprint to his former classmate. The reprint started, as usual, with the Gaussian distribution
    and the statistician explained to his former classmate the meaning of the symbols for the actual
    population, for the average population, and so on. His classmate was a bit incredulous and was
    not quite sure whether the statistician was pulling his leg. “How can you know that?” was
    his query. “And what is this symbol here?” “Oh,” said the statistician, “this is pi.” “What
    is that?” “The ratio of the circumference of the circle to its diameter.” “Well, now you are
    pushing your joke too far,” said the classmate, “surely the population has nothing to do with
    the circumference of the circle.” Naturally, we are inclined to smile about the simplicity of
    the classmate’s approach. Nevertheless, when I heard this story, I had to admit to an eerie
    feeling because, surely, the reaction of the classmate betrayed only plain common sense. I
    was even more confused when, not many days later, someone came to me and expressed his
    bewilderment2 with the fact that we make a rather narrow selection when choosing the data
    on which we test our theories. “How do we know that, if we made a theory which focuses its
    attention on phenomena we disregard and disregards some of the phenomena now commanding
    our attention, that we could not build another theory which has little in common with the
    present one but which, nevertheless, explains just as many phenomena as the present theory?”
    It has to be admitted that we have no definite evidence that there is no such theory.
    The preceding two stories illustrate the two main points which are the subjects of the present
    discourse. The first point is that mathematical concepts turn up in entirely unexpected connections.
    Moreover, they often permit an unexpectedly close and accurate description of the
    phenomena in these connections. Secondly, just because of this circumstance, and because we
    do not understand the reasons of their usefulness, we cannot know whether a theory formulated
    in terms of mathematical concepts is uniquely appropriate. We are in a position similar to that
    of a man who was provided with a bunch of keys and who, having to open several doors in succession,
    always hit on the right key on the first or second trial. He became skeptical concerning
    the uniqueness of the coordination between keys and doors."

    So we dont understand why math works?

    Also just curious what exactly does pi have to do with the population (distribution)?

    LINK: http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
     
  2. jcsd
  3. Apr 1, 2012 #2
    That's a really thought-provoking question. Different people have different answers, and there seems to be no general consensus. A partial explanation is that we actually develop mathematics ourselves in order to describe the natural world. In other words, it works because we make it work. But this argument fails as a complete explanation, because there are still mathematical patterns present within the natural world. We don't just come up with math out of the blue--we base it off of the mathematical language in nature. So the question becomes, Where do those patterns in nature come from? Again, different people have different answers. I for one find the best option is to refer to an intelligent and all-powerful Creator...we can trust that math will work because God created the universe in an ordered, mathematical way.

    But yeah, I'd like to hear others' thoughts as well.
     
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