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Thank you so much for your reply!

Two points, quickly: 1) Information theory is used in molecular biology to discern meaning between molecules and their environment. Shannon did not concern himself with this, but this is one of the applications of his theory and useful in drug design, sequence comparisons, etc.
2) The simplistic "Where successful communications occur in nature, there is life." is not helpful at all for the fringes where the difficulty arises. By this definition, prions are alive (they are pieces of protein) and self-organizing automata are alive.

I certainly agree with your first point! The second however I thought I had already addressed in post 498 to which you were replying; that, and your mentioning of “self-organizing automata” are good indications that we are speaking past each other.

Self-organizing complexity (aka cellular automata) is a mathematical model proposed by von Neumann which is applicable to a wide range of disciplines – much like the Shannon mathematical model for communications. Self-organizing complexity may be useful in describing how complexity arose in natural systems – living or non-living. It is also very handy for designing artificial intelligence. It is not however “alive” in our four dimensions if space/time – it is, simply put, a mathematical structure with a wide range of application - like various geometries.

Math and the physical world are images of one another. Wigner called this the “unreasonable effectiveness of math”. Max Tegmark's Level IV theory proposed that existents in four dimensional space/time are mathematical structures in parallel universes. "Why pi?" asks Barrow, etc. Most recently we have seen this unreasonable effectiveness in physical dualities and mirror images of string theory.

Stephen Wolfram was so taken back by the broad applicability of von Neumann’s theory, that he proposed A New Kind of Science based on it. And today, Kolmogorov complexity and algorithmic information theory is also causing a kind of sea change in our view of the physical world and abstractions thereof.

We ought never to be surprised when a mathematical theory fits the physical world hand-in-glove. A prime example is when Einstein needed to describe his theory of general relativity he was able to literally pull Riemannian geometry off-the-shelf. That particular application of his geometry was surely not the intention of the mathematician.

Likewise with Shannon’s mathematical theory of communications. It was not formulated to define life which occurs in nature. But it is amazingly effective in making a bright line distinction between life and non-life/death:

Where successful communications occur in nature, there is life. When there is no successful communications in nature there is death or non-life.

Biochemical characterizations lack this purity or elegance – leaving viruses and prions and dormant life cycle phases outside the definition of life and thus an argument against evolution, centering on their lack of autonomy rather than their function. In the Shannon model, viruses etc. are part of the communication for good or ill (noise, etc.) and life cycle phases are moot, as in a spore which remains communicative in dormancy (anthrax for instance remaining dormant until breathed, and then changing states).

At the root, the biologist/chemist worldview is fundamentally different from a mathematician’s. The mathematician looks for structures. The absence of universality is a weakness in a model. In fact, to a mathematician, the absence of evidence is evidence of absence. Not so with the biologist whose theories can span geologic time frames with many absences of evidence.

Likewise, in looking at abiogenesis – the biologist/chemist focuses on the physical components – primordial soup v primordial pizza and the ilk. The mathematician, on the other hand, looks for the rise of information [Shannon, the successful communication itself], autonomy, semiosis and complexity.

And here, in looking for that which distinguishes life from non-life/death – when both consist of the same “stuff” – the biologist/chemist approach is characterization, the mathematician’s approach is mathematical structure. Hence, the difficulty in our making a “connection.” Perhaps we ought to quit trying?