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One of these days perhaps the likes of Adami will come up with something better in algorithmic information theory. But he's not there yet.

With all due respect, not bloody likely. Perhaps you should look into how algorithmic information theory fits into the broader spectrum of mathematics. I could actually interpret the above as suggesting that you have a very funny notion of what mathematics is and how it is structured.

Algorithmic information theory is the unifying great-grandfather theoretical construct of a huge swath of mathematics. You are trying to figure out and "solve" fundamental relationships that are already understood and proven, you just haven't figured that part out yet. You really do not understand algorithmic information theory -- "plain old, vanilla, information theory" is but a tiny facet of its scope.

As for Adami, he is doing nothing but applied mathematics -- there is no "new" fundamental theory anywhere there, certainly not a mathematical one. In fact, everything he does uses well-established vanilla algorithmic information theory that has been around for twenty plus years and is contained within its scope, including all the "quantum" stuff (which requires no novel treatment for the most part). How is it that you do not recognize this?

You call algorithmic information theory a “unifying great-grandfather theoretical construct of a huge swatch of mathematics” – but actually it is the unification of the fields of computer science and information theory. It is no father or grandfather but an after-the-fact unification.

Its pearl of great worth is Kolmogorov complexity, which is not that difficult to embrace – and, IMHO, not much more illuminating than von Neumann’s cellular automata for understanding biological complexity.

Algorithmic information theory (AIT) is the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously. The basic idea is to measure the complexity of an object by the size in bits of the smallest program for computing it. (G. J. Chaitin)

The grandfather here is Shannon’s theory (40’s) not Kolmogorov’s (60’s).

However, if you truly believe the Shannon model is no longer up to the task, you ought to contact the National Institute of Health and the various pharmaceuticals right away.

As for me, I'll stick with Shannon entropy on the forum rather than Kolmogorov entropy to measure information in biological systems (successful communication, life v non-life/death) and to convey the principles of information theory.