Re: We believe in design

Iain Strachan wrote:

>
>
> On 5/31/05, *Pim van Meurs* <pimvanmeurs@yahoo.com
> <mailto: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
> <http://www2.informatik.uni-wuerzburg.de/staff/ebner/research/evolvability2/evolvability.html>
> )
>
Again, that we can envision a 2-dimensional solution much easier than
higher dimensions may make it harder to accept that neutrality works in
higher dimensions.

> 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.
>
Neutrality surely can lead to appearance of stasis while the genotype
'diffuses' until it reaches new possibilities. Stasis followed by rapid
evolution (punctuated equilibria like...) is what we also observe in the
fossil record for instance or even in simulation runs. There are some
good examples for RNA space.

> I'll need to think more about "free-scale" systems before I can
> comment, but I am finding this conversation quite stimulating.
Received on Tue May 31 10:33:11 2005