Conrad,
thank you very much for your interest.
I do understand your concern and your aim of „Finding Meaning" as the title of your essay says. Information appears as inextricably linked with meaning. In this light, it had confused and dismayed me over a long time that what Shannon ended up with is not more than a mathematical formula telling how to compute a number. Maybe I gave up hope then and became too radical, but I am not sure. It has happened over history of science that entities whose existence had appeared as undisputable turned out as misconceptions.
I well agree that length, mass, charge, spin etc. are different. But aren't they quantum numbers alltogether (what regards the first two, some explanatory discussion would be necessary)? And doesn't the existence of quantum numbers „mean" that there are associated symmetries, eventually hopefully reckognized as one single symmetry comprising all of them? Physic appears to me as very homogeneous at the basic level - everything is in terms of symmetries, and any symmetry corresponds to a mathematical group / algebra. This is the case even for theories looking so much different as General Relativity and quantum physics do. Starting from the U(1) group, electric charge is immediately defined without necessary reference to any other physical entity. But I agree that the discovery of charge exactly went the way you discribe: the concepts of length, velocity and force were necessary. The situation is even more intricate: physics hardly will be able to comprehend the entirety of our world - like the aspects associated with Picasso. The only way out I found is pragmatism, thus considering oneself satisfied with what can realistically be achieved at this point in time.
For such price paid, we possibIy will get something back. I elaborated on this in a paper, which I did not refer to because it still may have some flaws. But in the light of your post, yesterday I put the most recent version on my personal website. At the introduction you find a reference to Keith Devlin's book „Logic and Information", while in the second section I discuss „the Enigma of Information":
http://magnific.at/r0g/loads/law7.pdf
One can say without exaggeration that information has remained a mystery. Devlin starts his book with a metapher. He compares us Information-age people with a blacksmith living in the Iron-age. While being very skillful in handling information, we may have no idea of what it actually is. This influenced me strongly and eventually I came to the conjecture that there exists no other meaning - semanticity - than that of numbers. The implication would be a self-consistency relation: nature would encode nothing but its number of degrees of freedom - what only consumes logarithmically few such degrees of freedom. This leaves a vast room for redundancies, what not only explains why there are laws of nature, rather even gives a quantitative measure.
I have to apologize in advance if I do not quickly respond to further posts. But I need time for reflection to have at least some chance of avoiding bad logic mistakes in my argumentation.
Gerald