> > 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.
> Easy!
> Local maxima: points where the gradient of the evaluation function for
> relative survival is 0, and all local orthonormal frames have the
> survival function decreasing on all basis vectors. [This is a fancy way
> of saying 'locally optimal solutions that Natural selection ends up at'.]
>
> 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.
Also, in the real world, the fitness landscape is not static.
-- David Leeper dleeper@gte.net Homo Deus http://home1.gte.net/dleeper/index.htm 1 + 1 != 2 http://home1.gte.net/dleeper/CMath.html