Walter,
Very interesting essay. I found some quite brilliant and important analysis analysis which appears to have been missed by most. Also very well written, set out and argued. Yet at I understand your conclusions I could not agree less!
First points of agreement; Almost all of it! But including particularly; "it makes sense to define a set-specific frame of reference.", Exclusion, the LT, binary rotation, and also the "rich internal structure," (which is completely denied by QM in particle terms!), etc.
But I suggest Bohr's description, however correct and meaningful inside his 'box', completely missed an important matter, so leaving QM as a 'cop out'; I suggest it's the recognition that;
If we can find out and understand more we can then 'say' more!!
I noticed your question to Joseph brenner; "Can we find an universal logical principle that "explains" all kinds of information about the physical world?" I propose Yes. And I appreciate your blog view; "Of course, we may give these logical (binary) structures, together with their numerical values that they show in certain experiments, the name "Nature". But then this is merely a definition." if you mean they only 'represent' not pretend to 'BE' the physical world.
But is not a simple rotating dipole a binary system? Does it not then describe a torus not a 3-sphere in time? and then when also in axial motion through another (semantic if you wish) frame, not describe a smooth path of a (double) helix?
That is one of the 'rich structures' I've tried to falsify, and the only one I've failed with as it just keeps proving it's power. Perhaps you may help?
If you allow recursion to decode the 'noise' between binary 0,1 systems in line with Godel's n-valued ('fuzzy') logic and Bayesian distributions (between 0 and 1), then I agree an orbiting binary system (orbital angular momentum) is the key, but otherwise I suggest you are closing yourself in Bohr's box by suggesting; "Beyond this level, there is no further information. The physics of binary information, therefore, marks the ultimate basis of physics."
Might that not condemn us to our limited understanding forever?
Do perhaps read my essay before responding. Do respond there. It also has foundations in the last two years. The links in the 1st blog shows how the helix produces a smooth cosine curve in 2D, and the experimental evidence of a charge orbital (I also derive the LT direct from a physical mechanism elsewhere).
Very best wishes, and very well written. No essay here is 'complete'.
Peter