Sounds like my cue for another attempted explanation of what Doron's about.
I can't resist the puzzle.
And I don't mind chucking up another false answer.
It's the journey, you know.
Yes, I hear you, "Give it up, Apathia. There’s no answer to this puzzle!"
You're very likely right.
No answer except of the sort of the sound of one hand clapping.
"Friend Vrs. Enemy"
Doron says that our existence as a species is at steak, because we continue to categorize people.
One is in the "set" of Friend. Another in the "set" of enemy. And there's no overlap.
Setting a person as exclusively a member of a category, localizes that person.
But there is an aspect of us, indispensable to being a person that isn't "local."
That is that you are a "distinct" (another important Doron word) individual whose relation to categories is such as to be both within and without them.
First of all, before analyzing you into a category identity, you are just who you are.
Doron feels science misses this important aspect of our being and forever wants to make us localized objects of analysis that are identified by restrictive categories.
What is to be done to rescue our humanity from this death?
Doron's answer: rework, retool mathematics (since it's the language of science), so that it involves as well the non-local distinctiveness of things being primarily just what they are in their own distinct light.
So, he sets out to give numbers that same respect.
Enter the Organic Numbers ("organic being used here in contrast to analytical numbers), where a number has not only the "serial," analytic aspect that we are accustomed to, but also has that "parallel" existence outside being counted. It's sitting within/without prior to being some sum or difference.
Doron's fractal diagrams set out the various combos of these aspects, each combo being an Organic Number.
It's his way of bringing that essential, outside, independent, distinct, transcendent selfhood into a conceptual framework.
This is by means of the fractal combos.
To be way over simple (but not much off the mark),
here's "friend" and "enemy."
Applying the "non-local" to these categories, we find a person, not merely a friend or an enemy, but there are combos such as "friend-enemy" or "enemy-friend," or "friend-friend." ("friend-enemy-friend" would be to much fracturing for this particular, except the ongoing fracturing practically deconstructs the whole business.)
That's pretty much the program.
The question than becomes: is this actually how we deal cognitively with the relationship between the individual and the collective?
Add to that the question: Does treating the concept of number in this way humanize mathematic cognition?
Now everyone asks Doron (and I did for a long time till I saw it wasn't in his intention):
given this new system of number, what mathematical results can be derived?
And can you use it to reconstruct the theorems we use in everyday practical and scientific mathematics.
Doron's not going there.
In fact we are expecting him to do something that isn't in the Organic Math agenda, except in the restricted "serial," step by step department.
In his broader notion of non-locality, such analytic approaches as if-then deduction, and use of the Law of Contradiction are too restrictive to grasp the intuition of number being prior to serial counting. How many is merely a restricted aspect of a thing or things that can stand alone outside the count.
He's content with showing his underlying bridgework between the Local and the Non-Local. It's not about proofs and theorems as we know them, especially when the tools of deduction are cleared off the table.
Making a conceptual framework of what is beyond concept is the business of Metaphysics of the old school.
Doron, uses mathematical language and terms metaphysically,
OK, if the disclaimer is made up front.
Otherwise, it can’t but look like gibberish, when you’re expecting deductive mathematics.
