[Hajman]

My point is that B grows. And GA's are modeled after evolution theory, not the other way around. We know enough about evolution to understand that natural selection is icing on the cake. Developmental and structural constraints play a far larger role in what evolves. As of yet, those constraints are far too complex to model.

If B grows, it still fits into the set A<=B, and you still don't get Macro Evolution (in fact, the constraints become tighter). An infinite iterations of A<=B will still equal A<=B. If it's too complex to model, how do you know the model is valid? That's where I'm stumped. If Evolutionists can't model their own theory, how do they test it to see if it's even valid or not? (This isn't pointed to those that believe Historical Evolution is a theory, but rather to those that believe it's a fact).

-The Hajman-

[Nebullis]

If B grows, it still fits into the set A<=B, and you still don't get Macro Evolution (in fact, the constraints become tighter).

Ah, I see my notation doesn't follow yours. The output grows. And, as edsheppa points out, your final output is the current most evolved system, not the primitive protocell.

However, your rigid adherence to information theory and its current state of development as a final model for evolution is limiting. Life as information is a theory under construction. Darwinian theory can be modeled in a GA. But there's more to evolution than Darwinian theory. Following your last response to edsheppa (and I hope I'm not confusing the subject, as he's perfectly capable of explaining this himself) I want to point out that natural selection in real life works at the level of function unlike natural selection in a GA. When I mentioned constraints above, I meant by that constraints on the information that becomes available or accessible to selection. The most obvious constraints are structural and developmental.

As far as modeling these constraints, progress has been made on individual molecules such as RNA. Given a functioning RNA molecule, random mutations will yield a very limited number of RNA molecules with a new structure that could conceivably be functional and therefore selectable. Negative mutations never make it to a selectable endpoint. Most mutations are carried as neutral. They do not change the structure of the molecule and are carried along successive generations without selective influence. New mutations in subsequent generations eventually lead to either a deleterious endpoint, or a complete structural change. One that carries the organism through it's developmental pathway. Whether it is then carried through the population successfully is a matter of natural selection.

Technically put, natural selection (NS) acts on the topology of phenotype. The GA's are performing NS on the genotype. The phenotype determines the fitness landscape (there's your A) and the genotype-phenotype map determines B, not the genotype alone. With each new phenotypic change, the fitness landscape changes into a completely new space and thus A grows.