Hi Dr. Dick,
I very much appreciate the depth of your reply.
Although I have read your explanation in the previous post and thought about it; precise mapping of what you did there has to be done later.
But off the top of my head; I do not recall you saying in your chapter one, the bit about filling up the number of entries in those groups so that each group had the same number of entries. That step seems to be missing from the paper.
And of course, if one adds a '5' to say a (5,5,6); and also adds a '6' to a (5,5,5); discounting the order of entries; such unknown data additions have gone and made those two groups identical!
And if step one you add a '3' to a (2,2) group; and add a '3' to a (2,7) group; O.K. they are still different. But should additional unknown data additions be made in step two; say add a '7' to the now (2,2,3) group; and add a '2' to the now (2,7,3) group: if order doesn't count:
the two groups have gone from being unique; still unique after one step of adding unknown data; to being identical after two steps of unknown data addition! (2,2,3,7) and (2,7,3,2).
Just a little side-point here: adding unknown data is a tricky business! Since it is unknown; it could be making your groups more identical.
Which is why I guess you say by definition enough is added to make them unique. But can it be proven that it is logically possible to always do that?
Well, ultimately to exist is to be unique; so with the whole Universe at your disposal; if these things are even identifiable they must be abe to be unique.
Another side point; reality can not be fully represented. The real thing always has that which is unique to itself; representation is generalisation apparently. Ultimately things are what they are.
Short of time just now, but some brief comments:
Heisenberg's matrix mechanics; Schrodinger's wave mechanics: "That is very true; but they were both stated very precisely in the language of mathematics!"
I probably can state my self-swallowing set that may do all your system does (and I think IS your system) very precisely in the language of mathematics!
Quote: A: "It was open to several interpretations!"
D: "That is possible; but I believe there is only one interpretation which is internally consistent with everything I said and with the conventional understanding of the mathematical relations expressed. I did and do expect the reader to be familiar with serious mathematics."
Comment: That may be, but it could be like a maze trying to find that one interpretation! As there may be many interpretations available till the last 't' is crossed and the last "i" dotted.
I know what a function is; I maintain that you may be assuming a bit too much re: what path even an expert reader takes through your work.
Quote: "if A is a function of B, that means that if you know B and you know the function, you also know A." Of course I know that, that was inherent in my post. As I said, I can re-write my breakthrough in precise math language. There appears to be some divergence in approach; will take time to demonstrate exactly what is going on.
I have had a paper copy of your work for a long time; but I do not have typing speed! (Re: internet posting).
Re: Feynman: I think it was in a book "Six Easy Pieces". I'll have to check it. But as I recall: many experts were working for a long time on a particularly difficult problem. Lots of math involved. Now as I recall, the experts couldn't figure this puzzle out. But Feynman got the answer, very directly; the math could be bypassed, it wasn't needed. Maybe not even to prove the result. I'm not Feynman, but I might succede in doing something like that; it is possible.
Aurino once noted that the difficulty of infinite 3s in the expression 0.333333 disapears when you use base 3. So paradoxes can be artifacts of the way we look at things. They can vanish in the light of a new perspective.
"They believe their world view is well defended by their successes (those successes being judged from the perspective of their world view. I prove, quite conclusively, that their position is completely unsupported."
I think you are missing something: while their beliefs might be shown to be self-fulfilling prophesies; they remain responsible for the pattern match-ups they make.
If you match "Zeus" with "thunder"; that is your match. The thing with pattern matching, is to be logically consistent over all matches; to avoid double-booking; to avoid contradictions.
Quote: "Essentially, you want to use my work as support for your world view when it is in fact support for no world view at all."
But "support for no world-view" looks mighty like "maximum freedom" doesn't it? Freedom to match patterns as you wish, to create what matches you want? So long as you are logically consistent?
And isn't that my world view? Freedom (no constraints, letting be, love); Existence (non-contradiction, uniqueness); the conscious love of Existence. Your "minimum surface" becomes mine, doesn't it?
RE: difference between "knowable" and "unknowable"; no time now but might I ask ever wondered how water was turned into wine?
Consider: no assumptions; reality being created right now.
All your data might be there at the start; "nesting" occurs when transitions occur between different perspectives on that data.
Quote: "The central point of my paper is that most all of science is a made up story (how the tiger got its spots) the only advantage of the scientific story is that it is at least internally self consistent (most of it anyway)."
That does not present a difficulty; if one considers everything is constructed out of conscious love of Existence.