I am applying communications ideas to
your question. If you will respond, then
maybe we can make progress.
1) You have a great deal of practice on this topic regarding Dr. Dick's paper. The most recent
post contains a fairly direct approach to
discerning its degree of readiness as a tool.
Question: Will you please parse out a few steps?
Without deleting anything, please add a few MORE transitional sub-topic sentences announcing the significance of each paragraph.
2) A few questions about your words and phrases:
"try to figure this out:"
Shall I look for errors, or terms needing more precise definition, or what?
"Dr. D. has a set of: arbitrary sized groups each of arbitrary numbers."
By "arbitrary," do we mean "randomly selected?"
"He wants the members of his set of "observations" (groups of numbers) to be free to be smaller or larger than each other or to be "identical" to each other.
(In actual fact, if something is "plural", it is already a series of unique items, or you couldn't talk of "many" at all)."
I do not see the point of connection between those two paragraphs.
"He adds so-called "unknown data" to each observation to allow for the possibility that some are smaller than others or some look the same as others within the limits of his view. But he overlooks? that his so-called "unknown data" must be complementary to what is in his sets."
a) Were these unknowns added before, or after, the sequence of "observations" was put in their sequence?
b) If the unknowns are added before the sequencing, we have less of a problem. The other choice, "after," says we have added an unknown to an unknown and changed the sequence...and we now do not know what the sequence has become.
"E.g. if you have two observations: (5,5,5,5) and (5,5,5,5) you might add a 6 to the first one so you get (5,5,5,5,6). But if you already had somewhere a (5,5,5,5,6) then you have just gone and muddled your supposedly newly-uniquely identified observation with one of your others."
Could you explain it with U=unknown and the sequence as U1-1, U2-1, U3-1, U4-1
where the first number tells the sequence and
the number after the hyphen tells which version
of the sequence we mean? For example, if you add another unknown to U2-1, it will aways be U-2
which we could call U-2a for (Unknown2 with added unknown)?
And you could describe the new sequence after adding unknowns. If what I have just said seems incomplete to you, please tell me where.
Then I would understand better what you meant.
"Any rule must involve either a unique order or many possible orders but leaving at least one order free."
What is the significance of "at least one order free?" Is it to provide an exception case?