Conrad,
I very much liked your exposé on Wheeler's ideas, especially your original take on measurement-processes presented in evolutionary terms. Your suggestion that "the process we call measurement -- including the communication of the results as the basis for setting up further measurements -- can also evolve through accidental selection" is brilliant! In this regard, have you read the essay by Prof. McHarris? Speaking of non-linear loops, he brings up the example of evolving computer programs, modeled on the principles that drive biological systems. The implications of these programs provocative results are very much in line with the body and the conclusion of your essay.
Until I read your essay, the undisputed truth of these statements never occurred to me: "There's no such thing as information without a context that actually defines it" and "in principle, any kind of measurement is possible only because other kinds of measurements have already been made" -- even though just a week ago I had a discussion with a friend in the course of which we decided that an individual had no meaning without the context of the whole (it's funny how we tend to overlook the truths that appear self-evident).
I like the predatory spin you give to the processes underlying reality setting up "information-traps" and your vision of "the world not only as a set of facts, but also as a web of many kinds of interaction contexts that trap those facts and make them observable, defining each in terms of other relevant facts, defined in other contexts". Together with your recursive definition of "measurement", this actually resonates very well with my essay where I propose that reality is a local phenomenon perpetually generated anew by recursive processes that capture the bits of info from their environment and output them transformed.
I could offer a slightly different spin on this: "For systems in this subnetwork, interactions that happen to fit its self-defining structure do define and communicate specific information, that contributes to contexts defining other information. Interactions that don't happen to fit this structure aren't physically eliminated; they're just irrelevant to the ongoing process". One could also view this in the context of harmonic oscillations and resonances (eloquently spoken of by Dr. Carolyn Devereux in her essay).
Regarding the "storage-mechanism available within quantum systems", I actually chanced upon an idea of such a storage while writing my essay but did not expand on it, because it was so novel to me. But it boils down to a definition of a quantum process as requiring --in order to run-- a certain set of input bits. And, say, a simple process needs 3 bits of input and it has already acquired 2. It can't run without the 3rd bit and so it idles, while the 2 bits already captured can be viewed as 'stored'. The moment the 3rd bits arrives, the process runs. Isn't this in line with the definition of a quantum? I had not yet a chance to explore this idea in more detail (the only thing that occurred to me since in this regard was a neuron, which waits for the action potential to build up until a certain threshold before firing -- if the proposed definition of a quantum process turns out to be valid, one could claim that the universe exists, literally, in the Head Of God lol)
I could argue though with your conclusion, "To me at least, it seems clear that the physical world is incomparably more powerful as an information-processing system than any kind of mathematics or computational logic." Have you looked at cellular automata? Prof. D'Ariano pursues this in his essay and Maria Carrillo-Ruiz speaks of the same in her very short essay. You wrote, "Of course, physicists don't necessarily imagine the world as computing itself in real time." -- actually, some do and mean exactly that when suggesting that 'the universe is a computer'.
"So whether or not we believe in mathematical miracles, this universe hardly looks like a system based on deterministic computation." -- indeed, instead it may be based on simple processes like cellular automata that, despite their inherent simplicity give rise to great complexity. In this regard, you may also like to read Jochen Szangolies' essay (if you have not already, of course), where he discusses Leibniz' idea that one can always find a mathematical formula describing any random distribution, like in an ink blot, which however does not prove that this distribution is governed by a 'mathematical law': "This means that there exists a law simpler than just listing all the facts, from which nevertheless all the facts can be derived." This description fits the concept of cellular automata very well.
Sorry for such a long post. I gotta run now.
Again, many thanks for your thought provoking, stimulating essay!
-Marina