Mutation would increase the algorithmic complexity up to a point. After that
the complexity would go up and down depending upon what mutation occurred.
Consider a 4-mer molecule. There are of the order of 256 different
permutations. Some of these are identical so the number is somewhat less.
There is maximum length of any algorithm which is needed to define the
sequence so there is a maximum algorithmic entropy. Assuming that any
nucleotide substitution raises the entropy of the universe by a similar
amount, there is no inherent difference in the entropy generated by aaaa or
actg. After you reach the maximum complexity, any further substitutions,
(mutations) will actually reduce the complexity of the chain. The only way to
increase the complexity further is by a copy mistake where an input atcg is
output as atcgtagc. From that point on, mutation will take the complexity to
higher levels. Stepwise, this mistake is not a majorincrease in entropy since
it can be generated by splitting t he double helix and taking the opposite
sides together end to end. Then comes the template determined reproduction of
a new other half of the helix. In this way, complexity and DNA length can be
increased without a large violation of the second law of thermodynamics. The
universe can easily tolerate small reductions of entropy in a stepwise fashion
but not large ones all at once.
In plants a similar type of process (a doubling of the amount of DNA) has b
een observed to create new species and is believed to have been the basis for
the formation of wheat, corn and many other useful plants. It is called
polyploidy. In one generation, a new species of plants is generated. There
is no gradual evolution of parent to daughter species.And the new species are
incapable of crossing with the parent.
I agree whole heartedly with your assessment of the initial conditions for
objects both in the Game of Life and in the REAL game of Life. I do have
problems seeing how the cell could form by itself. This doesn't mean that it
couldn't so I don't feel comfortable in using this as an evangelical argument.
My imagination is weak.
While the initial conditions certainly point to a creator, once created, life
has the capability to complexify according to the rules of the game that the
Creator set up. So with modern knowledge of iterative systems and
observations of how some species arise in nature today, I think we can
conclude that it is possible for a cell, operating on the God designed laws of
mathematics, chemistry and physics, is able to give rise to the life we see.
I would agree that we have only limited ability to do the inverse problem.
That is, look at a complex system and determine the rules. I could choose a
blown up picture of part of a Julia Set, and ask you to tell me the rules and
initial conditions and unless you are Karnac you wouldn't be able to do it and
neither would I. That is the weakness in modeling complex phenomena. We can
set an arbitrary set of rules and watch how those work, observe the
similarities between different sets of rules and draw conclusions from the
similarities. That is what I was trying to do with my models. It is the only
thing available today.
glenn