More Thoughts on Entropy

Early in our courtship Mrs ERJ and I had a serious discussion.  We were both sure that the other was wrong and felt that it was important that the other be "straightened out."

The question regarded the definition of heterogeneous/homogeneous.

We were both right.  We determined that the concept is NOT scale invariant.  One cannot discuss whether a population is homogeneous or heterogeneous without first defining the size of the sample.

Picture courtesy Marcella Jones

At a metropolitan level, a homogeneous population would be as if every subpopulation were put in a blender and buzzed together.  This is similar to what happens in the military (as a branch or service)...especially when there is a draft that inductees cannot "buy" out of.  Each branch of the service is large enough that it is rational to speak in terms of "percentages".  Any random group of 1000 will look very similar to any other random group of 1000.

At the metropolitan level a heterogeneous population would be a city that has a distinct "Chinatown", Little Italy, a Harlem/Watts neighborhood, a  geographically distinct middle-Eastern enclave; perhaps with various religious groups clustered within walking distance of specific centers-of-worship.

At a platoon level or smaller, the unit is heterogeneous.  The lens is able to discern individuals at this level.  It does not make sense to speak about 14% of a group of the group is 50 individuals or fewer.  We are talking about an integer: 7, or 10 individuals or 3 individuals.

The small group (classroom, workplace) netted from a "heterogeneous" city would likely be "homogeneous" in composition.  Most of the classroom would be Asian, Italian, African-American...depending on the neighborhood the sample was drawn from.

The best ending of an argument is when we can both agree that we were both right.

Entropy

The Sage of Eaton Rapids mentioned that "entropy" had been used as an argument against evolution.  The contention was that "evolution" suggested that more species are created on that exploit the trophic cascades in ever finer steps.  That (evolution) suggested that entropy (disorder) is decreasing.

Depending on how finely one focuses...this can be seen as increasing order (at the level where individuals are discerned) or no increase in order (at the population level).  One can also argue that species go extinct so there is little guarantee that differentiation will ALWAYS increase over all time spans.

Finally, consider that proposal that none of these life forms that appear "new" or "novel" really are at the DNA or Kreb's Cycle level. 

So I cannot state whether I believe that "entropy" supports, refutes or is neutral with regard to the topic of "evolution". 

I can definitively state that I learn far more drinking coffee with a bunch of retired guys than I would by watching network TV.