Hi,
I've been away, computer time is limited now.
I'm hoping at least smartguy will see what is going on here.
I have not fully unravelled this due to lack of time to pull apart a detailed post Dr. Dick wrote.
But here is some clues as to what is becoming revealed:
Dr. Dick set out to write a generalised model. It is already known that Hamiltonian mechanics is a rather generalised form of analysis. Dr. Dick appears to have taken this further.
Now, Dr. Dick was reportedly surprised when "physics dropped out" of his analysis.
If "physics" is the "rabbit" which Dr. Dick pulled out of the "hat" (his paper): the 64 million dollar question is:
Did he put the rabbit in the hat first?!!!!!!
At last I have uncovered increasingly precise evidence that he did!
How did he do that?
Consider: the technique of "adding arrows" (probability amplitudes) described by Richard Feynman in his book on Quantum electrodynamics
involves considering every way an event can happen.
Consider: what is "number".
Example: 10.
10 what? Surely whether it is 10 elephants, or 10 ducks; number implies "category". Instead of "elephant". or "duck", the GENERALISED category is called "ten". Is that argument sound? That "number" is "categorization?
What matter if you say "10 elephants" (elephant-category), or 10 ducks (duck category)? Is not the very act of COUNTING the act of CATEGORISING?
10 "ten label" category? Is that O.K.? Am I missing something?
To talk of "number" is to talk of "category"?
Let us take some sets of numbers:
(5,5,5,6) (5,5,5,6) (1238,2) (1238,3) (5,5,5,6,2)
Now, to make each set unique (different from the others); how do you do that?
Well, I can not add a 2 to one of the two (5,5,5,6) sets to make it different from the other such set. (note: ORDER of the set contents is not being considered, only the contents).
Why not? Because it would make it have the same contents as the (5,5,5,6,2) set.
So my choice of "unknown data" that I am allowed to add to any one set is restricted by the nature of the contents of every other set. Further, even after adding some acceptable "unknown data" to a particular set; I must take into account the new restriction that the new pattern places on my choices of what I add to the others.
So this process of "adding unknown data" to make each set different involves taking into account every way data can be added to my collection of sets; they must all have data-additions chosen so as to be complementary to each other so as not to upset the requirement that each set at the end of that process will be different.
If you consider "an event" as the appearance of all the sets being different; then "every way an event can happen" is integral to the complementarity requirements of this process of "adding unknown data" to make each set unique.
Kind of looks like QED is the "rabbit being put in the hat" right where Dr. Dick establishes his technique of adding unknown data so that his sets of numbers all look unique!?
Now, if each set is still unique even after one item is removed; you seem to get two complementary "webs" linked by any item in any set.
The added data must be complementary along all possible comparison paths that connect the sets individually.
If I add a 3 to (1238,2) and then add a 2 to (1238,3) they contain the same numbers. So my additions of data must be complementary. In this case these sets were already diferent. But if I had several (1238) sets, I have to add something to each of them to make them different.
But I can not choose any data to add. Because I already have a (1238,2) set and a (1238,3) set; I must not add a 2 or a 3 to any of my (1238) sets as that would give the same contents in such a set as are in sets I already have.
The deep requirement of complementarity across all sets to which data is added to achieve uniqueness; involves an "all paths considered process" reminiscent of the technique of quantum electrodynamics, surely?
The rabbit being put in the hat? This does not detract from Dr. Dick's discovery; but sheds light on what is going on in QED.
Dr. Dick appears to have gone beyond the genarilsed coordinates of Hamiltonian mechanics to a more general system that matches QED.
Whatever data you add to one of his sets of numbers must be complementary to whatever data you add to each other set.
Now, Dr. Dick writes of adding additional "unknown data" such that you can subtract one entry from any set and it is still unique.
Again, these additional additions of set-entries (numbers) must be in harmony with the contents you already have in the sets. Deep complementarity rules apply.
Now you have two ways to compare every set. Interesting to note that the minimum requirement of a "rule" that determines a set contents is that there are two ways (the "rule" way and at least one no-rule way).
Consider (1238,2) add content-item '8' so have set contents (1238,2,8). Then minus any item and it is still unique means options (1238,2), (1238,8) and (2,8) must all be unique (I subtracted a different item each example).
But if I had another set (1238,2,5) I'm in trouble because subtract any item from that; say subtract 5; and you get (1238,2) which is the same as one of my options above.
So the adding of additional "unknown data" such that any 1 item may be subtracted from any set contents; yet it still contains a unique pattern of numbers (order nor considered); this may require further adjustments to the permitted added-data in the first stage of "adding unknown data".
Actually it becomes apparent that a "minimum path" or "least action" type principle is at work here in this delicate juggling. This "cute little trick" that Dr. Dick has discovered does seem to have quite stunning consequences!
I think it might be describable as "musical chairs, join the dots, known the difference"; or the child's ryhme about a row of teddy bears in a bed where "and the little one said "roll over". And they all rolled over and one fell out and the little one said "roll over". And they all rolled over and one fell out and the litle one said "roll over". And they all rolled over....."
Subtract an item from one set; any way you do that, the resulting set contents must be different from all the others afterwards.
Musical chairs: change one here, all the others synchronised to stay different.
Consider:
Instead of using specific numbers as the set contents, one could use letters.
take set with contents just (a).
Now try set (a) with set (b) in your collection.
They are unique, no problem.
Now try this:
(a) and (b) and (a). Two sets with an 'a' only in them; want to make them look different?
So add a 'b' to the contents of one of them.
Now have sets (a), (b), (a,b). All unique.
Now take away any item: take away 'b' from the set (a,b) uh oh it now looks like the other (a) set.
So it isn't still unique as Dr. Dick requires.
Seems we have a rule here: no set of two items (or numbers) may have an item (number) in common with a set of one item (number) only; because if you subtract the uncommon item from the two-items set it becomes the same looking contents as the one item set.
In general form:
no set of n items may have 'n-1 items' in common with a set of n-1 items, because if you subtract the single uncommon item your two sets look the same.
This analysis could be continued to work out each complementarity-rule implicit in Dr. Dick's procedure of: add unknown data to make each set appear unique even after any item subtracted from any set.
The above is only a partial investigation of Dr. Dick's procedure.
-dolphin |