: > 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"?
Given the following fitness landscape, where higher points on the
vertical axis represents higher levels of fitness:
B
A /\
/\ / \---------
/ \-----/
--------/
--------------------------------
0 N
A replicator (or algorithim, or whatever) is "stuck" if it
gets fooled into thinking that some point other than B is
maximum fitness. A replicator (or algorithm, or whatever)
is _not_ "stuck" when it reaches B, even if it stays at B
forever. At B, no further improvements are possible.
Here's an algorithm that would get stuck at A:
BEGIN STUCK
Begin at 0.
If the loction 1 space to the right is the same fitness or more fit
than the current location move 1 space to the right, otherwise stay
where you're at.
END STUCK
Here's the basic idea behind evolution's "algorithm":
BEGIN EVOLVE
Begin at a random location.
Select a random location and move there.
Repeat EVOLVE
END EVOLVE
Notice that even if the replicator reaches B, evolution will move
it off B and back again.
EVOLVE is a simplified version of evolution. Evolution doesn't
move beings around the fitness landscape, rather it moves their
descendents around. Also, it kills off critters that land in
an area too low on the vertical axis.
Kenneth Boyd presented the problem where the fitness landscape was
such that a jump from A to any other point with acceptable fitness
was too big to make with a single mutation. My point was that
evolution can make a big jump by what's equivlent to combining
several jumps at once.
: 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?
I don't think so.
1] There are many different fitness landscape (eco-systems).
2] I'm not saying that because of evolution everything is at point
B on the fitness landscape. I'm saying that evolution will never
get stuck at A. It will visit A, but it won't get stuck there.
A Very Minor Point: ad infinitum means "endlessly", not "infinite".
Evolution is not infinite, but it is endless.
-- David Leeper dleeper@gte.net Homo Deus http://home1.gte.net/dleeper/index.htm 1 + 1 != 2 http://home1.gte.net/dleeper/CMath.html