The Real Pascal Triangle

The hidden structure of Pascal's Triangle.

This week I was looking into the logic of the mathematical triangle of Blaise Pascal.
That triangle was already discovered before him by some others, like the Chinese Yang Hui and the Persian Omar Khayyam, but in the west we still call it the Pascal Triangle. For the Buddhists and Hindus the triangle represents the Mount Semeru or Mount Meru. For them that abstract sacred mountain contains the Whole and it's combinations, and is the center of the Universe.

When we see the traditional triangle we should ask also: Where do the "ones" come from? It is not enough to say: We have to start somewhere.

Here is my analysis.
I use my proper "pelastratic" logic. In this logic there is a single dynamic background membrane which is indivisible, thus cannot be cut in pieces or cannot be broken. This membrane surface has not any additional structure, except it's proper entity. This membrane represents neutral energy. That neutral energy is not manifested yet in any form, therefor we call it "Zero Field". Tesla called such background: The Field of Force.
By a pelastration - a penetration - of one local part of that membrane by another part of that membrane, a new zone is created where these two part co-exist. That's a holon. The holon "unit" is in fact a UNION. This holon contains the active - penetrating - part in its center , call it the father, where this central part is covered by the passive part, call it the mother. The holon is the child. The child contains a part of the father and the mother. The child has structure: one layer of the father and two layers of the mother.



We can show this action in a diagram, where the membrane is presented with the sign of infinity (which are connected zero's). From infinity we can receive two zero's, one will be active and one will be passive. Or one will be minus and the other will be plus. Or we can call them a and b. Or we can call them yin and yang. By a pelastration these two parts of infinity, the two zero's, become a new "unit" (our holon).



If we call this holon a space unit we can say that the space unit is structurally composed of neutral passive dynamics and neutral active dynamics. So neutral dynamics has the potency to create space.

What if we project this approach on the Pascal's Triangle?
Then we see that the real Pascal triangle looks like this:



Next to the line with the "ones" is a line with the parents of each 1, and these parents are part of the infinity. This new presentation of the Pascal triangle gives the full mathematical reality. Of course stating that 0 + 0 = 1 is a very strange approach. This new Pascal triangle makes it easy to understand the so called "Zero Point Energy", promoted by researchers like Hal Puthoff, when they try to explain phenomena like virtual particles, the Casimir effect or Bose-Einstein condensates. In my opinion they should speak about Zero Field Energy.

Remarkable is that each "1" is separated from the others, thus has at least one vacuum space between them.

What does this means in mathematical sense?
Next image shows the powering in the real Pascal Triangle. In this case I use instead of two zero's, the letters a and b like in algebra.
The gray zones are areas where the combinations are made. They doesn't involve new "units". You can see how the algebraic formulas are build up by combined units (new unions).



I postulate the existence of a single neutral background field (a membrane) that acts as a "zero field energy system" which creates by a simple penetration different type of holons, which can have several presentations, like numbers, fundamental particals.