Well, Let's again see how close I can get to the bottomless pit, and if Doron will kick me into it again.
I interpreted that line or scratch on the Venn diagram as Doron's Non-Locality/Locality Linkage.
Pure relation. Not a geometric object, not an additional range of elements, not an additional locality.
Doron replied that the line is a geometric object, but it is "non-composed," meaning it has no separable content.
It's his Line of Non-Locality that represents Qualitative Infinity.
That it's not purely relation, not the Relating Linkage as I thought,
but an Infinity Doron intends to mathematize, pushes me close to the edge of the pit.
But be that as it may, I am moved to comment again on the intent of that line.
If Doron had merely intended "Non-Locality" to be a super class, an infinite class that embraces and includes all sets, all contents, his better expression would be the all embracing class of everything with its circumference at infinity, and including all sets.
This however terms the Infinite into a locality and a container.
Non-Locality then becomes a super locality.
Scratch that!
Nestling sets within Russian Doll class containers is "local-only" manipulation.
He wants to think outside the boxes within boxes.
The scratch isn't an act of inclusion. It's exclusion as well and at the same time, as far as classes go. It steps outside thinking in terms of common classification.
Of course it's difficult to communicate, especially to an adult, letting go of linear thinking and wandering beyond the boundaries of classification.
But it's a losing battle for Doron, because he has chosen to try incorporating it into Mathematics and talk about it using Mathematical terms and objects.
Everybody here is bound to take every word he says within the assumptions and contexts of the kind of linear, logical, class thinking math does with all those terms. Add to that that he often using them metaphorically to express qualities, and disaster follows.
I really have no quarrel against non-linear thinking. It's a part of what our amazing in spite of emotional obstacles brains do.
Doron wants to bring linear and non-linear thinking under the same roof with the same language.
It's tough though. All those mathematical terms and objects assume linear thinking in progress.
For ordinary business, Organic Mathematics lets you proceed as usual summing up things by classes.
But it's in the mathmatizing of certain qualitative concepts that math as we know it gutted.
Qualitative Infinity vs Mathematical Infinity.
Qualitatively speaking no set is "complete." it's always a finite locality, a fragment in the face of The Infinite.
The Real Line symbolizes The Infinite, so cannot be said to be composed of elements or individual numbers. (Getting painfully close to falling over the edge here because he calls it the line of real numbers.) So Analytic Geometry upon which much of Modern mathematics is based is verboten.
The mathematical consistency that allows .99999999 ........ to equal 1 is smashed.
Of course there are mathematicians who have taken Lars Von Trier sorts of approaches, but all of them are doing local-only, linear, context dependent, deductive only, mathematics.
Only Doron is trying to express the "out of the box" in terms that ordinarily are only found in the box.
In ordinary language we often get out of the box via juxtapositions of incongruous metaphors.
I believe I can credit Doron with doing that in mathematical language.
Again, I get fall into that bottomless pit if I look to closely at the project,
For example what a "parallel" number is supposed to be, as opposed to a "serial" number.
Yes, the Relation/Element Linkage both creates quantities of common classes, and scratches their distinctions all at the same time.
(A scratch is non-composed.)
We have all asked Doron to create and define his own terminology so this confusion can be avoided, somewhat.
But really that's counterproductive for him, isn't it? Since he intends to break outside definitions?
It's better he just let us fall over the edge, or give us a solid nudge.
We keep mistakenly asking him for applications and formulas. (What we'd expect if this were math and science.)
But these things are all based on the manipulation of classes and local-only results.
Except for "serial" results OM has no such formulations. It's not how "complexity" is done.
I asked him how OM elucidates the process non-linear thinking.
Mostly there was no answer to this. It's not a logical process.
I seem to remember Doron saying there was no process to it.
It's not "serial."
Indeed! I get a non-serial observation, even if Doron's attempt to attach that to logic (which is damned serial) confuses me again and again.
But forget the confusion.
The fun is in jumping into the bottomless pit.
http://movieclips.com/watch/alice-in-wonderland-2010/down-the-rabbit-hole/