"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. "
Yes, I meant "a" was all we have.
"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."
Yes, it is sketchy.
Differentiation just means differentiating a rate of change (e.g. speed of a car) from a rate of change (e.g. increase in speed of a car).
Partial differentiation just means hold other variables constant when you differentiate (e.g. find the increase in speed of a bug in the car, but ignore (hold as a constant) the bug's simultaneous crawling speed at right angles across the car-seat.) (You'll just get the car increase in speed, which is only a partial differentiation of the total bug speed change)
(So treat the bug and the car as one; which looks just like the MATCH of patterns you make when you make a DEFINITION)
When you define stuff, you ignore their relative movement, you integrate them.
When you now try to connect the components (e.g. bug, car) individually to their surroundings outside the integration (in this case outside the car), you partially differentiate those components (like: bug, car) from their surroundings if you continue to hold them together as one.
To EXPLAIN something is to show the linkages it has with other stuff.
When you try to explain (connect to the surroundings) one or other component (bug or car)
while still holding the bug and car together (as a sum), you are going to end out with only a partial differentiation of the bug or car as your explanation (your link of the bug or car to the other stuff).
Relativity is involved because one may assume either the bug crawls along the car seat, or the car seat crawls along under the bug.
From the point of view of a MATCH of "car" to "bug", of a combining (sum) of "car" and "bug"; that is from integrating "car" and "bug"; the linkages (the explanation) of "car" or "bug" to the other stuff will be a partial differentiating of "car", or of "bug", from the other stuff.
A "match" view is a 2-D view, or complex number perspective.
If a "concept" is a bunch of linked stuff; the linking of that bunch to other stuff (its "explanation") will be such that the "other stuff" will either map one-to-one wholly on to the bunch, or the other stuff will be made of bits that each only partially differentiates the bunch (concept) from the perspective of a bit within all the other stuff.
In other words: the concept "total acceleration of bug in car" is only partially differentiated from the sum "change in car speed + change in bug speed" from the particular view of "bug" within the overall viewpoint of "car + bug".
However this is all getting rather dizzy...
(I think I messed up in the clarity department above in places...no time to fix it now...)
Matrices turn up when you find you are writing up tables of combinations and permutations I guess.
"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."
Well if I had the money to use internet more I could go into detail of the math; I get the impression that it is not so difficult but I like to do "sub-math" simultaneously. Example: if you tell me you are "squaring" the sum of the other two sides in a triangle I like to have a picture of the visual fact of the squares. You can prove Pythagorus's theorem just by drawing the squares themselves.
I like my math to be "eyes wide open"; which requires exposing the inner foundations of math along the way.
Here's a thought: the computer has it easy? It gets all Dr. Dick's paper set out in simple binary steps of zeroes and ones; so clear even a machine can cope with it! But wait; it doesn't understand Tolstoy's "War and Peace" when you download it, does it? It doesn't know how to link all those lucid ones and zeroes, to all the other linkages out there.
"How did I get into the picture?" I was regarding you as "honorary dot" in the dot world.
"...to explain in a believable way how reality came into existence in the first place. "
Problem: what do you mean by "explain"?
A philosophy text says ultimately things just ARE (no explanation required as no more "something elses" in terms of which to explain or those "something elses" would be more ultimate)
Explanation always involves a wider context or network in terms of which things are explained. So "explanation" is about linking within networks of links (I call "join the dots". The array of possible ways of linking stuff seems to me like a whole lot of juggling: musical chairs).
"...came into existence": "came"? This implies "before and after". What if from one perspective their is no "before and after"; just eternal presence?
"2) to explain consciousness in the face of a universe that seems to be nothing but unthinking particles bouncing around in fields of forces."
Mankind is stuck with the fact that he THINKS of the alleged unthinking particles. He projects them from his thought and then says they might project him.
I was tending to regard "dot" as mind.
To figure it all out I think the thing to do is start at the end and work backwards.
The most basic and ultimate idea is EXISTENCE.
Any specific item that HAS existence (other than the very ISness of Existence) must have a boundary (at least distinguishing it from pure Existence).
Two or more items must have boundaries that separate them from each other; they are all distinguished by their very existence. So existence is the boundary.
The items may be seen as groups or combinations of various sorts, they may be grouped or summed or networked in various ways.
Any particular grouping must be logically consistent with the existence-boundary of the items in the grouping and those outside the grouping.
A grouping is a constraint; but opens a freedom (group activity). Just as a particular array of Chess pieces in a game constrains the pieces by the very specific nature of the grouping; but opens up freedoms of game-strategy available to such a group.
The creation of the universe unfolds as an explosion of new freedoms that open up with every new creation (new grouping) (new constraint).
The name of the game is creation, life, play.
This is along similar lines to Chris Langan's ideas on the interplay of constraints and freedoms; I'm not aware though that the model I started describing before of "all the alternatives open to a system as seen in 2-D from any particular jump between two alternatives" would give universe constants; but rather just show physics laws to be the structural defining laws of "explanation" in digital systems (i.e. obtaining Dr. Dick's paper).
I would be very intersted in your view on what is "explanation", what "knowable" means, and "unknowable" means, and "data" means, and what "definition" means, and what "logically consistent" means, and what "number" means, re: Dr. Dick's paper. I think the very act of clarifying these might generate Dr. Dick's findings at a sub-mathematical level!