RE: Dr. Dick's work:
"What I said was that there must exist a function F such that for all valid collections of data (data which obey the rules) the statement F = 0 is capable of enforcing the rule. Central to this statement is the fact that one is working with an open ended collection of imaginary entities: see Aurino's point # i ..."
Yes: what you have is effectively a "floating zero"; add a new interaction and you get a new floating zero. It is the web of interactions that makes the structure.
Thus the structure appears to be a whole lot of conections between different zeroes. It is like a mandelbrot set, the more interactions you add, the deeper you probe into your initial zero.
It's like a fantastic creation being constructed inside zero!
Weird, but it's a bit like there are all these perspectives on a vacuum. A structure is being created out of a vacuum, out of nothing. A real structure that is something. But what really is the zero? It is the quiet region, where something IS. So the zero is where the real something is at rest?
After all, where something IS; everything else ISN'T (except Existence and the something).
F is constrained to zero effect so-to-speak; but not F is zero itself. F is quiet in a zone.
"...I meant that the "rule" F=0 could be so written." Exactly right. It's like a "floating zero"; and of course a summation of delta functions is a way of doing this.
"If one includes the probability of observing a particular set of data in the analysis,..."
Probability is a kind of density. A structure built of connections between relative zeroes is being discussed it appears. In such a structure your rule F will have no density at values other than "floating zero" (or relativistic, quantised zero".
It appears to me that a new entity or structure appears where i meets j; thus i cannot equal j because their meeting creates something new. Space-time for example. Time itself is being created here it appears. And space. So Dr. Dick is consistent when he later says that "events have dimensions".
"The indices are indicators as to which argument we are referring to." Very curious. The number of traffic jams being summed?
Note: a straight line deceleration traffic jam: deceleration is like subtracting unknown data; the jam accelerates beyond its stationary (floating zero) phase...like adding unknown data?
This is like the narrowing (deceleration) of a definition, the quiet phase where a definition meets another definition crossing its path (the superposed at right angles deceleration-acceleration traffic jam), followed by the acceleration path of the definition (broadening).
When you track a definition's path through a meeting of two other definitions, you have what I found to be an actual curved path with superposed traffic jams at right angles.
When I take the summation of a meeting of a car in each jam, tracking that superposition of cars; and I rotate that curved path to get a straight line: I am preparing the new superposed-chosen-car-pair for a meeting with a new definition.
The mystery of Dr. Dick's comments re: cause and effect starts to unravel; the structure being created is so NEW that cause and effect can take on a rather different perspective, they colour the new structure metaphorically speaking, rather than make it.
Internet place closing....more later.