Nope ;-)
> this question is I think a good illustration of a
> point I was trying to make earlier. Armed only with
> the words order and disorder how is one to decide
> which of these is more orderly. I'm going to say
> that the two groups which cannot interbreed is
> less orderly since this represents a case of greater
> diversity and that order decreases as diversity
> increases. Ron might say the opposite and herein
> lies the problem with the word game approach. What
> appears orderly to one person may appear disorderly
> to another.
Excellent point. I think the intuitive notions of 'order'
and 'disorder' can be good guides, and compose valid conceptual
material for trying to figure stuff out, but they are indeed
fuzzy in meaning, and often non-transferable. :-) I have to
say that my intuition about this is pretty clouded. I don't
see it necessarily the way you spell it out (although I can
see the logic in it). I don't really see it the other way,
either. Pretty indefinite, just as you said...
[lots of entropies]
Fer sher. Some of which are designed to try to apply to
biological systems (with mixed success).
[Tierra measures]
Some of these experiments are pretty exciting. I
waded through a large part of the One True Book of
the complexity people (that Santa Fe publication on
the subject with papers by everybody in the field).
Ray's simulations were in there somewhere.
> The entropy referred to above has the same form as the
> thermodynamic and Shannon entropies, i.e. it is the
> negative sum of p log(p). In this case p refers to
> the proportion of the total community occupied by
> each genotype. Ray points out that this entropy is
> a measure of the diversity of the community. To explain
> why this is the case, consider first the case where
> there are 100 genotypes but only one of these occurs
> say 80% of the time. This would correspond to low
> diversity and also, according to the formula
> - sum [p log(p)], to low entropy. The case of highest
> diversity, and also highest entropy, would be where
> all possibilities occurred at the same frequency.
>
> Thus, increasing diversity leads to increasing entropy.
Makes sense, and its an interesting measure, but I'm not
sure any kind of second law would apply! In fact, there were
periods in Ray's simulations when the *reverse* applied!
Of course, many evolutionary simulations of natural selection
produce decreases in this measure. I have done a bit of
work with genetic algorithms, and there the whole idea is
to start with a maximally entropic (by this measure) 'ecosystem,'
and have the trajectory be towards one where one particular
problem-solving 'genotype' dominates. Obviously this is a lot
different than the real world, but there are real ecosystems
where it happens--the phenomenon of kudzu in the south for
instance :-).
[...]
> So, here we have scientific proof that diversity leads
> to disorder. This is based on one of the most fundamental
> laws of science, the second law of thermodynamics.
> Yet, our science-ignorant dilbert politicians keep
> insisting on increasing the diversity of our society.
> It is no wonder our schools are in such bad shape and
> that crime is rampant in our streets.
The Chickens Are Restless!!!!
:-) :-)
-Greg