Re: We believe in design

On 5/31/05, Pim van Meurs <pimvanmeurs@yahoo.com> wrote:
>
> Iain Strachan wrote:
>
>
>
> So ... to return back to my original point - if the space of viable
> phenotypes were densely populated (designed that way as Glenn said in his
> article) so there were caverns of viability connected by viable paths, then
> evolutionary search can work, and indeed the neutrality idea would improve
> the efficiency of that search by spreading out over neutral networks. But if
> this were not the case, then as I see it, neutrality doesn't have much
> effect - it won't change a space that is sparsely populated with viable
> organisms into a viable one - only make a densely populated one more rapidly
> searchable.
>
>
> Neutrality is the essential feature which links 'caverns' of viablity by
> viable paths, that's the whole issue. The whole issue of evolvability is how
> evolution can evolve a genotype-phenotype mapping. Combine this with scale
> free systems which can be explained by duplication and preferential
> attachment and you have some very powerful mechanisms to explain why
> evolution has been successful.
>
Pim,

I don't mean to sound rude, but I think you've missed my point. I agree
wholeheartedly that neutrality and populating neutral networks will work on
a 2-dimensional example - I was thinking in 2-dimensions when I dreamt up
the S-P-Q idea. But I remain wholly unconvinced for high dimensional search
spaces. Read up about the "curse of dimensionality" at
http://www.faqs.org/faqs/ai-faq/neural-nets/part2/section-13.html .

A populated "neutral network" does indeed connect up disparate regions of
feasible space in the 2-D diagrams that were given in your link (
http://www2.informatik.uni-wuerzburg.de/staff/ebner/research/evolvability2/evolvability.html)

but in high dimensional space you are going to need exponentially more
points on your neutral network (growing exponentially with dimension) in
order for it to find those elusive connections. My original idea behind the
S-P-Q formulation was to assist in global optimization. A GA can get stuck
in a local optimum - a phenomenon known as "premature convergence", where
the population becomes unevolvable because it has to come down from the
optimum before it can get better. Having the neutral bits that could later
be switched in allowed it to make sudden jumps to very distant parts of
phenotype space. But if these disparate parts are in 100 dimensional space
(and 100 parameters is a small optimisation problem for the kind of work I'm
in), then the curse of dimension will make it vanishingly unlikely that you
will find it. In 2-D space you can get to all the corners with four points,
but in 100-D space you need 2^100 = 10^30 points - not even feasible on
planet earth, I think.

I'll need to think more about "free-scale" systems before I can comment, but
I am finding this conversation quite stimulating.

Cheers,
Iain
Received on Tue May 31 03:04:14 2005