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