Hi Dr. Dick,
Thank you; I appreciate your detailed explanation.
I am away quite a bit these days, so there are delays in responding.
Just clarifying the deal you offered me:
Your rules were that we must discuss the issues one line at a time.
In my defense: I focused specifically on understanding equations 1.1, 1.2, then 1.3.
I'm sure you are aware that Heisenberg's matrix mechanics and Schrodinger's wave mechanics turned out to be different views of the same thing.
I put it to you: it is possible there exist other ways of looking at the subject your paper addresses, that accurately map the same phenomenon you investigated.
Now; in your post above you have given a level of detail that was glossed over in your paper. Your paper was vague! It was open to several interpretations!
What is good about your reply here is the increase in precision! Any difficulty I have with mathematics tends inevitably to be: the ommission of steps in mathematical presentation.
Now; it is possible that as a trained mathematician you assume your audience are travelling the same "path" as you are. So certain steps are ommited as you assume your audience is jumping those bits with you. But it may be a good thing if your audience is not doing so; as it may be better if your EXACT thinking path is made VERY explicit.
Now: you did say that you thought I was rushing ahead without the necessary foundation in mathematics. I do not think you are saying I need to get a degree in math to even follow the first three equations, or chap. 1. What kind of subject-matter text should I have consulted?
If my level of mathematical understanding is perceived by you to be "too low"; that is sad but understandable that you do not wish to explain it at that level. It is sad because surely any closing the door might be postponed by you till at least there is mutual understanding of the first three equations. I can not afford the money it would cost me to go through your whole paper at "a very low level", if it costs as much internet time as the first 3 equations have.
But I would like to reach clarity on those 3.
In my defense: I could follow your explanation of the Dirac delta function you gave to me re: Yanniru's approach to that. I can prove that if you like.
In my defense: it has been said of Richard Feynman, that he could bypass whole complicated mathematical processes and get straight to the key in something intuitively. That is: there is more than one path from A to B. Your paper may get from A to B; but there may be much simpler paths from A to B.
I am rather shocked if you didn't get my "breakthrough". It will take me some time to follow the detail in your post.
It will be interesting to see if, and how, this detail you posted here creates a divergence between your path and my interpretation. It will be interesting to see if I can map your detail exactly into my breakthrough.
Please do not give up; let us see if there can be a reconciliation of views.
I think the kind of explanation you have given here is what is missing from your paper. If your paper is as good as it claims; I see value in making your thought path very precisely defined in at least the opening equations.
Before I try and figure out the detail in your post; I will leave you again with my alleged breakthrough (that may unravel your whole paper?)
(Consider also this: if your present explanation diverges significantly from what I thought you were saying; I invite you to approach the following as if it were something fresh, to be considered on its own merits. That is, suppose a system as I describe here. It is the anatomy of a self-swallowing set. And it does work, doesn't it? It does what your paper claims to do; doesn't it?)(And Yanniru may have yet another system that works?).
you conclude by 1.3 that the pattern rule is "no rule" for:
a set of special-rule-generated-data that either includes 2 items of unknown arbitrary unique data, but lacks an item of special-rule-generated-data;
or: includes all special-rule-generated-data plus one unique arbitrary unknown data; but lacks the other arbitrary unique unknown data.
The lacking data is known by default from the special-rule; or is one of the two added unknown data.
(One wonders if "uniqueness" means one can hardly call the unknown data "unknown")
Now, suppose he were to take this little model that has a "tracking program" tagged on.
This tracking (with unknown data tag-ons) has
so far isolated one special-rule-item into a system that has no rule other than the adding of unique unknown (tracer) data.
You could nest this cute little idea over and over couldn't you? All the way down to the last unknown special-rule-generated bit of data!
And look what you got: a beautiful logical construct that is "built of nothing (its rule is: NO rule other than NESTING and adding these tracer unknown data each NESTING.)
Yet this construct HAS CONVERTED the special-data-rule into an astonishing format: a format constructed from specially NESTED, SEQUENCED, additions of "tracer" unknown data items!
So any special-data-generating-rule can be fitted into this beautiful logical construct!?
Which makes it common ground for communication? And having converted a mystery into this format, we ...what? We make up our own rule? I mean, anything can fit this, can it?
Or we figure there is no rule, but notice the construct itself; which reduces to NON-CONTRADICTION and CONSCIOUSNESS (nesting?) and LOVE (letting BE; no unnecessary constraints?)
You know, that would figure wouldn't it... QED...that would be there wouldn't it...and the rest of physics?
Thank you very much for your time,