I'm amazed at what is happening here. Dick said to Paul that his model wasn't about the process of communication; but "describes a universal way of perceiving the result of any communication. That is, it provides us with a universal foundation of concepts against which any specific communication can be analysed!"
(If you do not know the story of "Harry Potter And The Philosopher's Stone", maybe best not to read the paragraph following where I quote you as it gives the punchline of the book/ movie.)
"We'll we have to focus on what we can communicate, but we cannot be so naive that we fully understand the meaning behind any particular message."
Here you are actually stating the premise of Dr. Dick's paper! You then set out to do what he tries to do, as you look for a universal (both parties can understand) way to analyse the result of his communication to you!
"Me and you are perfect examples. We spend a great deal of time miscommunicating with each other. It's not that either one of us are idiots, rather we simply have a totally different mindset that gives us quite different perspectives."
Brilliant! "totally different mindset" (result different from message communicated) ".....quite different perspectives"
Now you solve this:
Quoting: "The way I interpret incoming messages is vastly different than how you interpret those messages. Obviously we are interested in narrowing those differences by better communication, but we cannot be so naive to think that we will ever eliminate the sources for our misunderstanding."
This is incredible. My impression is that Dick's mathematical technique very much involves solving the same problem that you just solved by the same method: "narrowing those differences".
Narrowing those differences! Differences between two arbitrary sets of numbers as 'seen' by a third set of arbitrary numbers (or pair of sets).
I tried a basic by-example test some weeks ago of what would happen if I tried to find an arbitrary set of numbers (I wrote down some numbers) in another different sized arbitrary set and as 'viewed' by a third set. And it became intuitively apparant that physics patterns could appear this way from the techniques needed (reminiscent of Feynman's sum of histories); I just started narrowing the differences!
Only used adding and subtracting, the higher math though was 'visible' in the patterns.
And curious math-structures like physics laws seemed possible to appear (yet procedure was in principle maybe as simple as playing with lego blocks!)
O.K. maybe I'm jumping to conclusions here but I don't think so. It seems like "Harry Potter and The Philosopher's Stone".
If you know the story, it's like "the philosopher's stone" has been placed in the "mirror of Edelrid" by Prof. Dumbeldore (Dr. Dick!).
The mirror is the actual conversation between you and Dr. Dick! And with your comments about trying to understand the result of Dr. Dick's communication to you, and about "narrowing the differences"; it seems to me that "the philosopher's stone" has miraculously jumped out of the mirror and landed in your (Harry Potter's!) pocket! You may have just stated the key to Dr. Dick's paper!
Also; I agree with you that abstract concepts relate to tangible ones as evidenced by how children are taught mathematics.
And there is an analogy about imagining if your intelligence was like a telephone exchange operator who learns of the world only through wires. A philosophy book explains why the claim of human isolation from the tangible real world is false; in agreement with your comments on that.
I looked through physics material recently to see just how circular it was (like a dictionary); they addressed the circularity problem under the entry for "force"; ultimately they had to go back to a piece of matter in Paris called the standard kilogram (which is in a precise place); and a number of vibrations of a caesium atom (among other things).
I think it would be good if Dr.Dick could give an example of his model at work: just write down some actual arbitrary different sized numbers sets and show the technique (narrowing differences?) in operation.
Thanks Harv, Paul, Dr. Dick for ever more revealing insights evolving with this discussion.