2014.11.25.The "Uni" in Uniinfo, just a little

Tree vs. Loop
People are scared of loop ==> convert everything into trees:
 * Tree: can be embedded in to line ==> 1D, specified by 2 points, "normal" order
 * Loop: must be specified by 3 points, cyclic order ==> 1D in 2D
 * Convert "cross links": Route the link Cr(B1-->C3) back up through the common ancestor A: Cr = Up(B1-->A).Down(A-->C3).
 * But the true leaves are identical and just like the true root ==> They are exactly only one ==> Loopback!

The Unity & The Singularity
==> The Unity and the singularity are one.
 * Unity: At the true "root" or the "universe" level, what does the (parent) arrow point to? It must point to the root itself! Eg. Top type in type system, top cat in category system.
 * Singularity: Every true "leaf" or "unit" is a crossing point of the 2 complementaries. Eg. extension >< intension, form >< content, interface >< implementation.

Tree vs. Loop again

 * Tree = Hard Formalism: 2 points are clearly ordered and form a line with 2 infinite ends.
 * Loop = Soft Formalism (Uniinfo): Relations between 2 points are bi-directional --> The 3rd point comes in, to make clear the order and to unify them, not to extend them (to a plane) but to join the 2 ends of the line, to form a loop!

The order of 3 basic elements in Uniinfo
History:
 * From JAIST, the "Diff axiom" of science had always haunted me. Got back home, (in the bathroom, on the toilet,) the name "Uniinfo" came to me. Someday (check my blog for the accurate date) I decided to formalize Uniinfo, and the first axiom was obiously "Axiom of Separation (Diff Axiom)" even with a symbol associated, an arrow, in the bathroom on the toilet again. Just right after the arrow appeared, still sitting on the toilet seat (maybe changed position[posture]), I saw something must be there before the arrow... something which without it, the arrow cannot be there... I saw the existence of the arrow itself as a circle, thus the second axiom came was "Axiom of Existence" but labeled number 0 to stand before the Axiom number 1.
 * Later on, I had found almost everything can be categorized with that 2 symbols circle & arrow. However, just like the 2 digits 0 & 1, they were good only for information representation (categorization, classification), never enough for knowledge representation and absolutely helpless for completing a universal system, just like what Gödel's Incompleteness Theorems say. Then a quest for the third element began and had extended for years before the last symbol was nailed down as an equals sign. If the first 2 elements were named before assigning symbols to them, then the third element had been called merely "the third element/axiom" even after being associated with the equals sign. Eventually one day as I wrote a post onto Facebook, the name for it came as "Axiom of Unification"!
 * (Bonus:) "Axioms" or "elements" or anything else? I don't want to use the name "axiom" because of the "hard formalist" sense. The first 2 can be "elements", like yin/yang, 0/1, but the 3rd is much like a "law" than an "element" though. So one day I decided to call these 3 primary stuff "presuppositions"(abbrev. "presup") or simply "premises"(vi. "tiền đề"), which focus on the content over the form, and be relative rather than absolute, i.e. there are many other triplets out there to be taken as a basis.

So, the 1st, 2nd and 3rd presups are numbered 1, 0, and 3, respectively! Tonight I've seen a torus structure of that three, in the bathroom on the toilet again :D
 * Let put the three on Ox axis
 * --> The 2nd presup and its number 0 are shadows of the circle on Oxy plane (centered at number 1).
 * --> The 1st presup is a vector in Oz axis which extrudes the circle on Oxy out to a pipe.
 * --> The 3rd presup unifies the first two by bending the pipe toward number 3 to form a torus.