You pump out a lot of food for thought for being short of time.
***Take a bit of data: "a". Probability of finding "a" at "a" is 1.***
I think referring to "a" at "a" is an error. It confuses the data "a" with the location where you might find it. It would be better to say, as you did in the next line, The probabiity of finding "a" among all the alternatives (when "a" is all we have) is 1. I think that's what you meant.
***(If I had ignored reverse patterns such as: list only "ab" but not "ba"; and continued to build this model of data aquisition and the probability of seeing a particular pattern of data, I suspect I find I am working with power series, partial diferentiation, and matrices as per Dr. Dick's "model of anything")***
I suspect that your suspicion wouldn't pan out. (But of course that is only a suspicion on my part.) I don't remember enough, and I haven't the time to check into it so I can't be sure. You might be right that what you describe would lead to a binomial series, or something like it, which is a power series, but your mention of partial differentiation and matrices is too sketchy to make much out of.
***Now, the reality modelling system I am hinting at here is automatically tautological, and my guess is it would turn out to explain QED, Relativity, gravitation even, along similar lines to Dr. Dick's system.
You are correct that you have only given us a hint at your reality modelling system. Your guess as to how it would turn out would be a lot better than mine, and I happen to agree with your guess. I suspect that you have some deep insight into some things the rest of us miss, Alan, and that you can see some vague connections to mathematical structures that you do not have a rigorous command of. Again, those are just more suspicions of mine. You either need to learn the math and proceed more slowly and methodically, or you need to find some math whiz who can take your hints and run with them.
***"Memory" occured because you memorised the relationship ("equilateral triangle" beside "line"); and compared that with the relationship ("equilateral triangle" beside "right-angle triangle").***
"you"? How did I get into the picture?
I don't know about you, but my interest in this whole subject is to explain in a believable way how reality came into existence in the first place. I think the evolution after that is fairly well understood so that is not so interesting to me.
The problems for a sensible explanation of the origin of everything, as I see them are:
1) to choose between two nonsensical alternatives: either reality got started from nothing, or there always was something. and
2) to explain consciousness in the face of a universe that seems to be nothing but unthinking particles bouncing around in fields of forces.
My choice is to posit that consciousness is fundamental and primordial. Whether it got started somehow, or whether it always existed, I have no opinion on, and I really don't care. Once that consciousness started creating universes, it wouldn't really matter. I am interested to know how a primordial mind could create universes.
So, to me, reality is this consciousness with its thoughts. That's it.
Now, in this thread, you suggested we consider the universe as consisting of a single dot. Okay. Then I say there can be no patterns or concepts if there is no mind or consciousness around to conceive of the patterns or concepts. In my scheme tho, I posit such a consciousness and say that there is no "place" for a dot to exist except in that conscious mind. So when you say, suppose the universe consists of a single dot, I say that the only way that can be is if the dot is the single thought of that conscious mind. Otherwise we can't talk about patterns or concepts at all.
Then, you come along and say ""Memory" occured because you memorised the relationship..."
Me??? I memorised the relationship?? Hardly. I don't remember being around when this universe got started. Of course, I don't really know what my consciousness is, so it might be part of that primordial consciousness. In fact, I believe it probably is. But to stay within the context of the hypothetical universe-of-three-dots, you have to leave me out of the picture.
Now, you say that a dot can be conscious of itself. Hmmmmmm. That doesn't make sense to me, unless again, you admit my picture of some existing consciousness, and the dots are simply figments of that conscious mind. Since that mind is all there is, that dot must be part of it, so it would make some kind of sense to say that the dot is aware of itself. I'll buy that. It means that reality is really an undifferentiated unity, viz. mind, but the thoughts entertained by that mind can change, thus leading to our obviously changing reality.
With that picture as a backdrop, we as humans know what kind of consistent mathematical structures can be derived from certain sets of definitions and axioms. Furthermore, we know that if you accept definitions and axioms that lead to our familiar concept of number, then there is an elaborate structure of inferences that are inescapable. Among those, as I believe Dick has proved, is that the behavior of probability density functions describing the probability of the existence of certain subsets of sets of numbers, is necessarily constrained to exhibit the laws of physics. So we get QM, QED, galaxies, elephants, and all the rest.
What remains to show, then, is the specific evolution of the thoughts of that mind, beginning perhaps with the thought of just one dot, to the universe we experience. And, I think that is the process you are sketching out for us. At least that is what it suggests to me.
To make a wild guess, I would bet (not too much) that if you did a rigorous development along the lines you suggest, that you would be able to infer many (or some) of the universal constants which give our universe its character, and that for those which couldn't be inferred and which would represent degrees of freedom for the creation of various types of universes, we can imagine that mind trying out various combinations until our universe was successfully born.
Such a "rigorous development" is w-a-y beyond me and my capabilities. But, as Aurino has reminded you, I did get the impression from someone, or something, while I was in an altered state in the dentist's chair, that if we worked on it, such a "rigorous development" was possible by human mathematicians. I think that would be a fantastic project for someone.
***Sorry I'm out of time to "un-ramble" this better.***
No problem; so am I. And I probably out-rambled you with this one.