> At David M's suggestion I found this stuffed in the back of my
> mail box:
>
> David Leeper said:
> > > > 2) If you imagine the mind as a landscape of peaks and valleys and mutations
> > > > occuring which randomly move the replicators around the landscape, can you
> > > > see how it is impossible to get stuck in a local optimum? Mutations are
> > > > random, they don't seek out global or local optima, they just move their
> > > > replicators around randomly.
> > > If the mutations don't go far enough, they will wipe before finding any
> > > nearby [improved] local maximum.
> > Evolution is sneakier (is that a word?) than this. It'll mutate the
> > replicators and throw a new beast at the problem. If that doesn't work
> > it'll try again with another beast, and another, and another.
> > Here's the secret. Not all mutation cause a change in the phenotype
> > of the replicator. Mutations occur and the beast remains at the same
> > spot on the fitness landscape. But _collections_ of "useless" mutations
> > can combine to create a valuable mutation (See Gould on this topic).
> > This combination creates a big jump that no single mutation can do by
> > itself. Evolution can continue this process ad infinitum until it finally
> > gets out. Evolution never gets stuck.
>
> If you have an infinite amount of time, how do you define "getting
> stuck"? That aside, isn't the diversity of life sort of evidence
> for the fact that species get stuck? If every mutation found the
> absolute maximum in fitness space, everything would evolve to the
> same phenotype wouldn't it?
The last sentence assumes that the species all exist in the same
fitness-space. I don't think that's clearly true; my snap conjecture
would be: NOT! The problem is that the fitness-space of a species has at
least part of its geometry/evalution function dictated by what other
species are in the system. A 2-species strong-competition model is
rather dramatic in this respect; either species in isolation can hold
equilibrium [until conditions change!], but superimposing both species
will almost surely [there is a practically-impossibly chance that both
species survive indefinitely, but almost any perturbation will shift the
system to the normal case] cause one of them to die out, even though it
is technically the same physical environment.
I remember a physics professor (sitting in on/teaching the course I'm
taking on General Relativity this semester) working me over on how I
could NOT use the same proper time coordinates for two different
particles in Classical General Relativity; each particle has its own
proper time measurements, and it makes no sense to mix measurements from
two different particles.
The above may be a similar situation.
=====
Going backwards, if the change due to selective pressure goes
unmeasurable, then the species may look "stuck" even when it isn't. This
allows an effective definition of "getting stuck" on medium-term time scales.
As far as I'm concerned, "infinite amount of time" is equivalent to
"steady-state universe". If one has that, there are no inherent problems
with biological evolution--the speciation problem is implicitly solved.
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/ Towards the conversion of data into information....
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/ Kenneth Boyd
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