Re: Re:Math applications; was Wheel of God

From: iain.strachan2 (
Date: Thu Aug 09 2001 - 16:41:55 EDT

  • Next message: george murphy: "Re: Math applications; was Wheel of God"

    David F. Siemens wrote:

    > As I see it, the problem from the empirical side is collecting enough
    > data on which a discipline can be based; on the theoretical, a system
    > that fits the observations, so that predictions can be made. This leads
    > to expansion and testing.

    As someone who works in the field of neural networks, pattern recognition
    and mathematical modelling, I am only too aware of the problem you mention!
    Collection of data is always the most costly, time consuming part of the
    operation, and there is never enough - you have to throw away half of it
    because data by nature is noisy. If you choose a model that is too complex,
    then it will "fit" the noise, and if you choose one that is too simple, it
    will not represent the underlying structure. This is known as the
    "Bias-Variance dilemma".

    However, this does not mean one should give up the struggle. Vernon's and
    Richard's models may appear arbitrary to some, but they are simplicity
    itself compared with some of the preposterous models I have seen advanced at
    some neural networks conferences. Twice I have seen a Professor whom I
    greatly respect stand up at a conference and ask the speaker something along
    the lines of "You have a model with 12,000 adjustable parameters, and you
    have about 20 data examples to fit the model. Does this worry you?". The
    depressing fact is that I have never seen an instance of him doing this
    where the speaker concerned has even understood the question.

    > is that the dead ends are not pursued and are soon forgotten. This type
    > of selectivity certainly functions in other areas of human recall. So I'm
    > not too surprised that our mathematics fit the world.

    You would appear to differ from Polkinghorne on this one. It's not a
    question necessarily of picking the maths to fit the world. When Abel
    Galois laid down what was to become the foundations of group theory, he had
    no idea that it was going to have direct relevance to particle physics and
    quantum theory, because those fields of science had not even been
    discovered. It really was just an "abstract free creation of the human
    mind". Maybe God's mind as well? Maths is full of peculiar facts that
    apparently have no relevance to nature. For example, the "Ramanujan
    constant" e^(pi*sqrt(163)), which differs from a 40 digit integer by
    around 10^-12. A coincidence? No, apparently there is a very deep reason,
    also, I understand, connected with group theory - who knows? maybe there is
    a physical relevance to this as well - but it started out as "just an
    interesting fact" in the abstract realm. It is this aspect - of the
    abstract ideas of the human mind turning out to fit the world, that
    Polkinghorne finds so amazing, and that he relates to the Logos/Creator.


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