Re: loose ends

From: George Murphy (gmurphy@raex.com)
Date: Sun Aug 03 2003 - 19:50:38 EDT

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    Glenn Morton wrote:
    >
    > George wrote:
    >
    > > Simplicity isn't the issue. There isn't even a complicated
    > >formula or
    > >prescription for generating primes. The formula for the Bernoulli
    > >numbers, e.g., is a
    > >good deal more involved than that for the Fibonacci sequence
    > >(Bn = (2n)!Z(2n)/2^(2n-1)*pi^2n, where Z is the zeta function) but
    > >it's a formula into
    > >which you (or a computer) can plug n = 1,2, 3 .. and generate as
    > >many as you wish.
    > >The sieve doesn't work that way. What you're doing with it is
    > >seeing if n is prime by
    > >checking multiples of all the integers up to n-1 & if none of them
    > >is n then n is prime.
    > >
    >
    > At the risk of pedantry, why isn't the seive a 'prescription' for generating
    > primes? It may not be very elegant, or even efficient, it may take a long
    > time, but it is a prescription, isn't it?
    >
    > I would suggest this: we have different definitions of 'formula' and
    > 'prescription'. Within the confines our our individual definitions, we are
    > both right. The seive is a formula or prescription in the sense that it is
    > "a set of algebraic symbols expressing a mathematical fact, principle, rule,
    > etc;" or a recursivly applied prescription. But we are getting to the point
    > of pedantry here. I would argue that the seive is a recursive formula
    > every bit as much as is the recursive formula for Fibonacci.
    >
    > I think our definition debate is a side show. The more important issue is
    > below:
    >
    > In the context of ID, is there really any difference in specifying the seive
    > as a generator of specificity rather than specifying Fibonacci's formula in
    > your sense of the word? If Dembski received a message from Mars which
    > counted in the Fibonacci sequence, doesn't that have structure? Can't that
    > be the intended message?
    >
    > As for what is an isn't a formula, you can have the last word. But I am
    > interested in why Fibonacci wouldn't be a specifiable message.

    Glenn -
            I'm not just out for pedantry either - though I've been known to do that - & was
    going to try to turn to a similar question.
            There are natural processes that generate some of well-defined sequences which
    can be generated by the type of formula that I've spoken of. E.g., a source of waves
    can be thought of as "generating" a sequence related to the zeroes of appropriate
    oscillatory functions (sines & cosines &c). For the primes, however, I just can't think
    of any plausible natural process that would carry out the sieve procedure.
    (I realize that this isn't a proof!)
            The Fibonacci numbers do show up in patterns of leaves, seashells, &c. Does
    anyone know why they do - i.e., the natural processes that produce those patterns? IF
    we knew that & IF part of a Fibonacci sequence could be considered a specifiable message
    then we would have a clear counterexample to the claim that such messages can be
    produced only by intelligent design (in the ID sense). But those are significant IFs.

                                                            Shalom,
                                                            George
                            

    -- 
    George L. Murphy
    gmurphy@raex.com
    http://web.raex.com/~gmurphy/
    


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