Are you familiar with Godel's mathematical proof of God? There are other such 'proofs' of God that I see having a great deal of parallel with Dick's work. First you set a few mathematical definitions that mean something with relation to the world (e.g., reality, God, etc), and then you do the math, and whoala... you make deductive conclusions from these definitions. The problem is that they don't mean anything in terms of the world. They are just "fun with math" teasers that raise the eyebrow and make us laugh.
***As you know, Harv, I supported your suggestion that we use 'R1' as the symbol denoting Dick's arbitrary "set of numbers". But, as you have consistently failed to see, such a choice makes no difference in the results of Dick's formal development. It only makes a difference in how people interpret his results, and what he says, if they haven't put in sufficient effort in trying to understand the formal result.***
Okay, I accept that as it is. But, like the term 'God' in Godel's mathematical definition, it's meaning is at best murky with regard to the real world. In fact, the meaning is so murky that one shouldn't even make statements about the real world based on such a mathematical work. Dick should completely drop his critique of science, his work has almost nothing to do with science or the limitations of science. Using terms like 'reality' or 'God' is just "fun with mathematics" and does not from what I can tell provide any significant insight for those serious about studying the philosophy of science. You could just as well interpret God as a Goose or Reality ('R1') as Soup.
***As for Monday morning quarterbacking - You are pretty demanding, Harv. Dick stumbled on his fundamental equation after a considerable amount of work and in his opinion at that time, he thought it was remarkable that such a set of formal constraints could be found on an arbitrary set of numbers. If we stop the clock there, and if I imagine that I were told of that result, I am sure that I would tell him the same thing I tell him now. I would say, "Dick, I'm no expert, but from what I know, I think you have discovered a new theorem of Probability Theory!" But, I wasn't there then. If you were there then, Harv, you would ask him, "Dick, do those constraints tell us the rules of football?" Dick would say, "Well, ...no.", and you would dismiss his result with a polite snort.***
I dismiss any interpretative work of mathematics as it applies to the real world UNLESS it provides predictive applications. A body of work might provide a good explanative account of our experimental findings, but without evidence that testable predictions are forthcoming (e.g., chaos theory, quantum cosmology), then it is not science. All we can do is stand around and gaga at the theorem wondering what it means.
***Start the clock again. Five years or so after that discovery, and after five years or so of work on that differential equation, Dick was able to find solutions to his equation which turned out to be most of the laws of Physics (The rules of football, baseball, and soccer). Now, you come along and ask him "But what about Basketball? And what about the scores of next week's games?"***
Here I think you have it wrong Paul. The equations of physics that we currently have are all seen as - at best - an approximation to something deeper to what is happening in nature. For example, Einstein's equations are a global approximation perhaps of a quantum theory of gravity that has yet to be understood. If Dick's model only produces the higher approximations, but not the more primitive statements that is hiding under the surface of those equations, then any explanatory merit of his work is severly questionable. It is not so different had Dick modeled Kepler's laws without any reference to Newton's laws, or quantum laws, etc. If Dick has come across something FUNDAMENTAL, then why doesn't produce FUNDAMENTAL results? Why does it produce results that happen to match 20th century physics, versus 21st century physics, or 22nd century physics, and so on. Why does it give absolutely no indication that there is any physics beyond 20th century physics?
***To make that last point a little clearer, Harv, consider difference in the level of difficulty between these two questions: (1) What are the factors of 28,203? and (2) Is 237 a factor of 28,203? It is pretty clear that the monday morning help you get from (2) makes (1) a whole lot easier.***
Generally this is backward to how one should expect things to head if one is truly dealing with fundamental definitions that produce our physics equations. That is, if you truly stumbled upon fundamental first principles from which to extract physics, you'd expect to see that such a work would work from the fundamental end toward the higher and higher approximation end of the spectrum. After you've continued to extract all of the most fundamental implications, you'd finally reach higher approximations - which presumably would eventually stumble upon our current physics. To first stumble upon our current physics (or physics 40 years old), suggests strongly that you are not working from any fundamental end of the spectrum, but simply phrasing the first principles in such a manner that you obtain our current physics.
I am not surprised at all that this can happen. Current physics thinks in terms of wave equations, symmetries, etc. It is this kind of thinking that limits us even though it has produced the kind of effective science that we have in our knowledge banks. The next generation of science might have to stop thinking in terms of wave equations and symmetries (etc) if they are to advance our view of nature. Perhaps just thinking in those future terms will mean the ability to easily produce those physics results from first principles. For example, let's say that the next generation of physicists think in terms of category theory and certain kinds of categorical transformations. If you set the initial conditions of your 'first principles' stage in that guise, it is perhaps possible to produce the future expected quantum theory of gravity. Of course, such a future 'Dick' will only be fulling themselves in the manner similar that the current Dick is doing. Hopefully that 'Dick' will be more polite as they do it.
***My response is that it is time to pass the baton. Dick is an old man. He should be credited for what he has done and he should be relieved by a set of young, energetic, mathematicians and physicists who should step up and carry on that new work.***
No need to worry. There will always be those seeking to produce our scientific knowledge from first principles. It's in our nature.
Warm regards, Harv