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I really have not had time to respond to this, but I am going to take a quick stab now before you all go to far afield. The Shannon-Weaver model is an idealization of more general theory that has utility for some types engineering, in the same way that most types of engineering use idealized Newtonian mechanics rather than theoretically correct physics since the errors in the model fall below the noise floor for engineering purposes if one assumes certain system parameters. Molecular biology and molecular machinery is well outside the parametric space in which the Shannon-Weaver assumptions give good results. In the Shannon-Weaver model, you list six elements. In the generalized theory, these are not only not independent from each other, there is no distinction between these elements. Cutting a single system into quasi-independent elements is probably the single most common engineering idealization, but one has to understand the limits of that idealization. A very common example of this is the distinction between "program" and "data" that is pervasive in computer science, a widely accepted distinction which has no theoretical basis and only exists for engineering convenience (and which will get you into trouble in some algorithm spaces).

DNA should not be treated as a "message" in a molecular system without making some assumptions that I do not think apply here, nor is it an element that can be legitimately treated as independent of the rest of the molecular machinery. The "message" that materializes is completely dependent on the context of the rest of the system/machinery, and the lack of functional independence for practical matters in real molecular systems makes the application of Shannon-Weaver doubtful. A simple example of this is that there are single machine code sequences for computers that are valid (and different) programs on wildly different machine architectures. The entire system determines the algorithm, not just some inextricable element that is arbitrarily determined to be "the program" or message.

Because of this, DNA only preserves state, not the algorithmic information of the system. Hypothetical transplantation of the DNA to another cellular system does NOT preserve the algorithmic information of the previous cellular system. Now, sufficiently similar systems may tend to converge on similar states (in biology, ones that don't will die), but that is really an accident of the configuration space and not at all required. My DNA is a bit of state that will usually converge on something stable in cells that are configured like mine, but it does not carry a message; there are plenty of contexts where my exact DNA will produce stable systems that are nothing remotely like me. Under the proper cellular contexts, my DNA would produce a living organism that looks like a slime mold. But for a lot of practical reasons, nature tends to put my DNA in system contexts that look similar to mine and so there are no slime molds with my DNA running around in the wild (that I know of anyway).

I want to comment upon tortoise's post #455, which I really liked because I actually had to sit and think about it a bit.

". . . DNA should not be treated as a 'message' in a molecular system without making some assumptions that I do not think apply here, nor is it an element that can be legitimately treated as independent of the rest of the molecular machinery. The 'message' that materializes is completely dependent on the context of the rest of the system/machinery, and the lack of functional independence for practical matters in real molecular systems makes the application of Shannon-Weaver doubtful. . . ."

In technical terms, the "message" in a molecular machine is "Messenger RNA," but this does not detract from the rest of what you posted. You are absolutely correct that -- whether you are speaking of either DNA or mRNA -- it cannot be treated independently of the rest of the molecular machinery because to do so would bring discussion of it -- within the context of an application of Shannon Information Theory -- to the discrete level, when what is actually being measured as the theory is applied is state within a continuous process. And on the application of Shannon-Weaver Information Theory being limited by this "lack of functional independence" I would say the real limitation is that Shannon-Weaver Information Theory applies to processes within a molecular machine, which is why state is measured, but it is of little value when dealing with either the product of those processes or the discrete elements that function within those processes.

"Because of this, DNA only preserves state, not the algorithmic information of the system. . . ." (underline emphasis mine)

AMEN brother! This is exactly the point about "Biological Information" that must be kept in mind in my opinion. To step outside of state is either to step into the semantics of the messages communicated or the discrete calculation of entropy, which is a value representing the range of choices in compiling an RNA "message." Shannon Information Theory may distinguish "life from non-life" and is relevant to a discussion of the origins of life in that it makes clear that an explanation must be given for the origins of state, but since it does not explain the complex processes under which life functions, the "algorithmic information" to which you refer tortoise, it cannot explain the "origin" or "rise" of "Biological Information" (Shannon Information) in biological systems. We must look elsewhere for that and, what is especially important for our discussion, we must look outside of mathematics.

I think that one of the most important quotes put up on the applicability of Shannon-Weaver Information Theory in this entire thread is the following one from Alamo-Girl's post #371:

"In spite of this dependence on the coordinate system the entropy concept is as important in the continuous case as the discrete case. This is due to the fact that the derived concepts of information rate and channel capacity depend on the difference of two entropies and this difference does not depend on the coordinate frame, each of the two terms being changed by the same amount." --- Claude Shannon, A Mathematical Theory of Communication, Part III, section 20, number 3

It is this distinction between discrete and continuous cases that makes state the focus of Shannon Information Theory as it is applied to molecular biology.

That was a great post tortoise!