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But as I understand it, the accepted view is that some organism, probably single celled, had to appear first. The authors' point was that even the simplest possible organism would still have an enormously complex genetic structure.

That is not the accepted view, I think. It is entirely possibly for self-replicating compounds to exist that bear no resemblance whatsoever to single-celled organisms as we know them today. Simply acknowledging that possibility renders this article moot. Fine - we're not expected to believe that lightning flashed and a human crawled forth from the slime, instead we are supposed to believe that lightning flashed and a single-celled organism such as an amoeba crawled forth.

You are looking at the complexity of single-celled organisms as they exist now and assuming that the first self-replicating "creatures" were at least as complex - bearing analogous structures and such. That is not a requirement for evolutionary processes to occur. Other posters have discussed self-organizing systems - some of those posts might interest you.

In any case, this is all about abiogenesis, in the end, not evolution per se. Am I to assume that you have no objection then to evolution or natural selection, and that in fact your issues involve only abiogenesis?

Of course there is. Indeed, there is some 10 billion years of physical existence before organisms appeared. This is his whole point. Before organisms existed, what created the specific genetic sequence necessary to sustain that first organism?

Oh, I see. No, you misunderstand me. Natural selection is an effect of organisms living in an environment, any environment. To discuss natural selection in any other context is to abstract the effect away from the cause - it would be akin to discussing gravity with respect to a universe that had no physical bodies. Therefore, implicit in my discussion of natural selection is the assumption that there is an a environment, and an organism or organisms. "Before natural selection" would mean, I suppose, that you are really interested in a discussion of abiogenesis. As I said, others can discuss that probably better than I can. Just be aware that there is no requirement that the first self-replicating systems bear any resemblance whatsoever to contemporary organisms, and that there is a such thing as a self-organizing system.

"Am I to assume that you have no objection then to evolution or natural selection, and that in fact your issues involve only abiogenesis? "

The focus of my reply was to explain the orginal point made by the author; i.e., that he is referring to a process preceeding natural selection and the improbability of sufficiently complex genetic information appearing at that stage. I thought you misunderstood his point as you were focusing on processes occuring in the context of natural selection; where he wasn't.

As for your broader question above, a theory can be internally consistent, agree with all known observable phenomena, and still be incomplete. An elegant example is General Relativity. While it explains the vast majority of gravitational phenomenon, it fails to describe, for example, what happens to the fundamental metric tensor of G.R. (the meat and potatoes of G.R.) at the center of a black hole: The eigenvalue of the tensor approaches infinity as the singularity is approached, a physically meaningless result. It seems to me that if evolution is supposed to be the theory of genetic change over time, then the theory of evolution is incomplete if it cannot explain the origin of biologically meaningful b.p. sequences. Ergo, I do not have any reason to not believe that the process of natural selection is a reasonable mechanism for explaining some genetic change over time. But I have little or no evidence to convince me that it is sufficient to explain the genetic changes that occured from beginning to the present. So, I'm not sure I agree with your use of the term 'abiogenesis' as I'm not sure you can so safely decouple the emergence of biologically meaningful b.p. sequences from biology. Indeed, a process other than natural selection would have been necessary for that initial sequence, but whatever it was, by definition, it must have had distinctly biological implications in order that it:

1.) Be responsive to the selection pressures that were later levied upon it.

2.) Provide information sufficiently complex to guide the formation of some biological organism (before it existed!).

Your point is valid that we can debate how complex that organism must have been at its' simplest. That would, of course, drive the probability analysis.

I suspect, for the reasons alluded to above and for many other reasons, that evolution is largely correct in some of its' most basic assumptions, but that it fails as a complete theory of genetic change over time. That is, of course, stated with the qualifications of any honest amateur in the subject.

I've reviewed the mathematics the author is using and, formally speaking, his usage is valid. But what isn't clear is his application of it to physical systems. That requires a lot more brain power than math alone but I'll look at it this weekend (could take a while!).