Re: Order from chaos - according to New Mexicans for Science and Reason

Thanks for the responses. As no YEC/ID'er on the list has responded,
here are my thoughts as someone sympathetic to ID but not a YEC.

I sent the link about the Sierpinski Gasket generated by random means
to a YEC colleague of mine, who wasn't fazed by it. (Sorry, the claim
in the article that it's the "Creationist's worst nightmare" doesn't
seem to be justified).

Instead, he pointed out interestingly that the function isn't as
ordered as it seems. It appears to generate the fractal as a by
product of the screen resolution. The point is that each iteration of
the algorithm enters the next higher order of Sierpinski Gasket. At
each order N (level of recursion) there are 3^N points, of which only
_one_ is sampled, so after a few dozen iterations, you are in fact
sampling the higher order gaskets extremely sparsely. The appearance
of order is that the "rounding error" introduced by screen resolution
makes them all collapse onto one of restricted order.

The next point is that the pattern is pre-defined at the start without
the aid of randomness. We know that if a point is on the Gasket, then
the next one will be also _whatever_ the choice of next vertex. The
random selection is only needed to get a good coverage of the space so
we can see the full pattern. Non-random ordering will not show all
the pattern. For example if you restict the choice to only two
vertices, the pattern collapses to a straight line.

A better way to understand what the randomness does is to imagine a
slightly different random algorithm that generates the gasket where
eventuall _all_ points up to a given order of gasket are visited. To
do this, we generate, say 1000 rows of Pascal's triangle. This is a
stack of 500500 points. Then we successively generate random numbers
in the range 1..500500 and examine the corresponding number in the
triangle. If it's an odd number we draw a dot at the corresponding
location on the screen. If the random number generator is truly
random, then we shall eventually generate all the numbers between 1
and 500500 and have drawn dots for all the odd numbers in Pascal's
triangle. The odd numbers lie on the Gasket.

It's easy, then to see what the randomness does - it's like a magic
paint brush that flicks paint at the canvas, which only sticks to the
odd numbers. In doing so, all we have done is to uncover the pattern
that was designed in from the start. Contrast this with the algorithm
where we colour the dot in irrespective of the value, and we get a
solid filled triangle.

It seems to me that the authors of the NMSR web-page would have you
believe that the randomness + ordering principle have generated
something complex (a fractal), whereas the demonstration would not be
so impressive if it just produced a solid triangle, which is simple.

My response to this is that the two are just the same (by the
paintbrush flicking analogy), and in any case, the fractal really
isn't as complex as it seems, because it is built up recursively and
contains many copies of itself (self-similarity). By contrast,
something like a molecular motor does not exhibit self-similarity - it
has many _different_ parts that all work together.

Another website that had a Java applet of the SG on it claimed that
the randomness was necessary to generate the pattern. This is only
true if you select one vertex at random each time. If, however you
select all three vertices, generate the mid points of all three, and
then apply the same procedure in a recursive fashion to the three new
points, traversing a "3-tree" of possibilities, then you will generate
the gasket deterministically without the need for a random number
generator.

In summary - the complexity (or not as may be) is programmed in from
the start - a fixed target, and all you need is a means of hitting
enough of the points to show the pattern. To this end a random number
generator that generates a uniform distribution is all that is needed.

Iain.

On Sat, 26 Feb 2005 10:54:08 -0700, Terry M. Gray
<grayt@lamar.colostate.edu> wrote:
> Iain,
>
> In general, I'm sympathetic with these arguments. See Loren Haarsma's
> and my chapter in Perspectives on an Evolving Creation entitled
> "Complexity, Self-Complexity, and Design".
>
> In my presentations "against" ID I mention two methods of producing
> "irreducibly complex" structures by some kind of natural evolutionary
> process (not necessarily Darwinian): pre-adaptation (or exaptation or
> coopting or whatever you want to call it) and self-organization.
>
> As a theist, who is ultimately a creationist, I affirm that the
> "laws" of complexity and self-organization are created "laws" just
> like all other regularities of nature. As with other laws, the
> atheist argues that that is just the way the world is--i.e. there is
> no creator, sustainer God who gives the universe its behaviors and
> properties. To the atheist there is no need to explain where these
> laws come from.
>
> But this is the great debate and science doesn't solve it. Science
> can be built on either foundation: this is the way things are, period
> or God made things to have these properties. Either way, however, the
> world works the same for the atheist and the theist, thus we can
> teach and practice the same science.
>
> The questions of *ultimate* behavior, purpose, and meaning is a
> theological question. And this is where I think the debate should
> occur--at the philosophical/theological level and NOT about the
> science. Let the scientists wrangle about the details, but when they
> step over the line and start doing theology and philosophy, we need
> to call them to task.
>
> TG
>
>
> >The skeptic website "New Mexicans for Science and Reason" give the
> >following web page to debunk creationist claims that order cannot
> >arise out of a random process:
> >
> >http://www.nmsr.org/digdudle.htm
> >
> >It describes how a complex fractal pattern, known as a *Sierpinski
> >gasket*, can arise from a random process plus a simple ordering rule.
> >A quickbasic program they give to produce the pattern is less than 400
> >keystrokes. They suggest you should send it to your creationist
> >friends and it will "drive them nuts", and furthermore that the
> >Sierpinski Gasket is the creationist's worst nightmare.
> >
> >Without revealing what I think of the argument, I'd be interested to
> >hear from list members of different persuasions what they think of the
> >argument presented by NMSR.
> >
> >If you're a creationist or ID person, how would you debunk this
> >argument? On the face of it, randomness and an ordering rule produce
> >order out of chaos, akin to random mutation plus natural selection.
> >
> >If you're a TE, or otherwise, do you think this is a convincing
> >argument that can be used against creationism/ID?
> >
> >If you're Vernon, you'll no doubt be amused to see that the N=1
> >Sierpinski gasket appears to be identical to your triangle-in-triangle
> >pattern from the Genesis 1:1 numerics!
> >
> >[ Aside. A very cute way to produce Sierpinski Gasket patterns is
> >from Pascal's triangle, which can be found on the Java applet at this
> >page: http://www.math.ohio-state.edu/~btk/Pascal/ . Unfortunately
> >this does not involve random processes so cannot be used to argue
> >against creationists].
> >
> >Iain Strachan
> >
> >--
> >-----------
> >There are 3 types of people in the world.
> >Those who can count and those who can't.
> >-----------
>
> --
> _________________
> Terry M. Gray, Ph.D., Computer Support Scientist
> Chemistry Department, Colorado State University
> Fort Collins, Colorado 80523
> grayt@lamar.colostate.edu http://www.chm.colostate.edu/~grayt/
> phone: 970-491-7003 fax: 970-491-1801
>

-- 
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There are 3 types of people in the world.
Those who can count and those who can't.
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