Dear Chidi,
Thanks for writing a very interesting essay. I'll pick out a few things to remark on:
You say "conversely, the observable is definable strictly only in inverse-observer values...". That's worth contemplating. For example, James Putnam objects to the vagueness and circularity of the force definition F = ma whereby force is defined in terms of mass and mass is defined in terms of force (assuming acceleration is measurable.) If instead one rationalizes forces to dimensionless ratios, the mass becomes inverse acceleration m~1/a. I've played around with this in a number of key equations and everything seems to work [as one would expect, but one must always check.] I'm not sure that this is analogous to your statement, I only point it out to note there's value in such statements.
You also mention Peano's (and Noether's) notion of "the constant". I tend to think that physics is based around the notion of "the invariant", with energy being the prime invariant. Likewise your position that 'observer' implies superposition of natural unit and natural limit is intriguing. It also requires cogitation. In your endnotes you specifically note "this function of being at once the unit-and-limit is the essential utility of such as Planck's constant h, Newton's G, and Einstein's c." You then map this into the term "observer". As I said this requires cogitation.
I view information as what is stored following a threshold crossing which changes ('in'-forms) a physical structure. Until this threshold crossing and consequent change of physical structure occurs, there is only energy flow. Information "emerges" in "structure" or "context".
Once one "standardizes" such thresholds (as in silicon electronic gates) then one can construct 'logic gates' and connect these in simple structures to accept sequential inputs and produce binary (or other) coded outputs. This 'counter' circuit is the hardware implementation of Peano's Axioms, and it really doesn't matter whether the counter is implemented in DNA, silicon, or neural networks -- numbers result. Kronecker attributed these natural numbers to God and claimed that all other math is the work of man.
You seem to have something like this threshold in mind when you attempt to derive the "action potential" of 55 mV. I'm unsure whether you attach significance to this value, or simply to its function. You follow this with "the observable-ness of a number as a thing represented by the successor function of Peano's Axioms...". Again, I'm uncertain of your final point being made, but I would note that I elsewhere present the counter as the essential basis of physics, both in instrumentation and as creation-annihilation summation-of-particles counter in QED.
In summary, you've taken some very high-level abstractions, and, as far as I can tell, attempted to raise the level of abstraction. You tie this into specific numbers in a way that I do not understand. Your complete picture is impossible to understand in one or two readings, but some of your statements are worthy of reflection. I think you have covered too much ground, in a very unorthodox way, to accomplish in nine pages what you hope to accomplish. I would suggest that you pick a few key points and try to make them clear to an "average" physicist [whatever that may be.] Your point about the observer and the observable being inverse is fascinating, but I believe you will lose most people by going too far, too fast.
I hope this comment is useful to you.
Best,
Edwin Eugene Klingman
