Logical consistency requirements transform Dr. Dick's "unknown data" into known data. Try to define "moon" as "made of cheese" and still be logically consistent; and you end out using the word pattern "cheese" when you talk about "rock", I think.
Dr. Dick wrote:
"Since the only original mathematical relation I present is the fact that a sum over Dirac's delta functions of differences can be used together with invented data to constrain any given data to the values desired: i.e., that the rule F=0 is capable of expressing any rules on the knowable data desired, that must be the essence of the theorem.
The rest of the paper is essentially about possible application of the theorem. "
It is known that any function can be represented by a superposition of simple harmonic functions.
A delta function is an intersection of two simple harmonic functions.
So is Dr. Dick's math theorem now obvious?
A "rule" is a constrained path that gets you from 'A' to 'B' via function 'C'.
If you make visible all possible paths from 'A' to 'B'; any particularly constrained path that depicts a "rule" or "function" can of course be
expressed as a particularly constrained path.
If all paths are made of "comparing and matching paterns"; and all structured paths are represented by "comparing and matching two patterns; repeating this process in a particular ordered sequence (= how the brain works: multi-level pattern-comparison to give concept construction?); then the "rule" for your "constructed concept" can be mapped by the sum of delta functions (the ordered addition of pattern-intersections?).
Is "unknown data" a red herring? If the system works abstractly; it works with all imaginary data. If it can describe any path restriction in travelling through that data; then of course you can mix "real" and "imaginary data" and get some paths that restrict "real data" by using some "imaginary data"? As an abstract game.
Responsibility and logical consistency still separate truth from error. You might claim the moon is made of cheese; but must be logically consistent in what you match up with the sound "cheese"; no doubt your definition pattern-network for "cheese" will mimick the one for "rock".