Very good Paul! Food for thought. Excellent reply. Little time now so really quickly:
Here's a puzzle for Dr. Dick:
Take an English dictionary. Make a new version that is identical except there is a backwards-shaped "E" at the end of every word.
Both Dictionaries still describe the same system of inter-word definition relationships right?
You could have dozens of dictionaries all describing the same "word-universe".
Take a bit of data: "a". Probability of finding "a" at "a" is 1.
Take a bit of data "a" and add a bit of data "b". Probability of finding "a" among all alternatives:
alternatives: "a" , "b" , "ab" , "ba" is 0.25
Add another bit of data "c".
Probability of finding "a" in all alternatives:
alternatives: "a" , "b" , "ab" , "ba" , "c" , "ac" , "ca" , "bc" , "cb" , "abc" , "acb" , "cba" , "cab" , "bac" , "bca" , so probability of finding an "a" in all the alternatives is 1 in 15.
(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")
In the above model, I can talk of the probability of finding a specific subset (say "cab") in an examined set (say "b" , "bac" , "ac" , "cab" ) lifted from this set of alternative perspectives (alternative networks of the possible patterns (explanations!) formable from the data letters.
If I calculated all the possible combinations of my initial list (a combination might be:
"ab" + "abc" + "c" + "bac" for example, I could give you a probability of finding a specific combination like the "examined set" I gave.
I could also give a probability for finding a specific "observation" in that specific examined set (observation example say: "bac" + "b").
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.
Back to your reply:
I agree that 3 dots may look different according to perspective; what I'm saying is that there are certain laws about 3 dots: they can only look like 1, 2, or 3 dots (some perspectives might place one dot in front of another). The "flexi-pattern" if you like, of 3-dots, is not a concept. It's a base ingredient from which concepts and different viewpoints can be built.
(Of course it is a concept from outside this postulated (conceptulized) dot-based universe)
"Triangle" has objective existence as "a way the dots might be viewed". "Mind" has existence as a particular view of a particular minded (noticed) perspective.
Conservation of pattern: yes O.K. to introduce "memory" here; but one may simply say that if another 3 dots beside the first 3 goes through a change from a line-shape to a right-angle shape, while all the while the first group look like an equilateral triangle shape; you may say that from this particular viewpoint your first group conserved their pattern while the neighbour went through changes.
"Memory" occured because you memorised the relationship ("equilateral triangle" beside "line"); and compared that with the relationship ("equilateral triangle" beside "right-angle triangle").
Notice the "self reference" of "equilateral triangle" to "equilateral triangle"; thus like a self-awareness or self-consciousness of the equilateral triangle as compared to its neighbouring pattern. What I'm saying is that to detect that a pattern has held constant with respect to another pattern, requires self-reference of the pattern to itself.
"continuity per changes" just means that the first 3 dots might stay continuously as an equilateral triangle while its neighbour 3 dots go through dozens of changing arrangements.
So you can imagine the equilateral triangle keeps checking itself is still an equilateral triangle; while all these different arrangements take place among its neighbour 3-dots. Not so blub-blub-blub now?
I am regarding the dots rather as minds themselves, as capable of being aware of how many dots are in their own pattern and how that can appear to other viewpoints; and how a neighbouring pattern of dots may appear to them.
Sorry I'm out of time to "un-ramble" this better.