Cosmology ... and Catalan numbers.

GROWTH OF NUMBERS (as Holons, each with specific layers).
The REAL PASCAL TRIANGLE (with hidden information)

Next two images show the causal diagram of how the membrane can couple locally in unique sub-sets. The second image is dynamic.




	You can see in next Pascal Triangle that each Catalan number is the sum of specific Pascal numbers. The Catalan numbers occupy all Pascal numbers except the middle row and the rows of ones.

	What is the logic behind the difference in layering? The direction of a pelastration (membrane penetration) creates different membrane combinations in holons. Which holon is active and which is passive determinates the number of layers. You can check this in next image which shows only two steps of coupling. On the right the holon 2 pelastrates a new part of the membrane, creating that way the (child) holon 3A with 5 layers. On the left the holon 2 is pelastrated by a part of the membrane, creating that way the (child) holon 3B which has 7 layers.

When we combine this new information we can state that till now we had a wrong idea about the real Pascal Triangle. From the understanding that there is one background field (which Tesla called: The Field of Force) that we call the membrane, we say that there is infinite neutral energy, called the Zero Field Energy. Puthoff calls it wrongly the Zero Point Energy. The zero field energy (ZFE) can create locally holons. These holons can be seen as abstract units in mathematical sense, also energetically as entangled dynamic forces, also as spaces in cosmology and as fundamental particles. When we put this general idea in a diagram which will relate to the Pascal's Triangle we get this images:

This external addition to the Pascal's Triangle gives us new information about the hidden structure of the triangle. The traditional Pascal's Triangle is in fact compressed. Between each "one" there should be at least one empty zone, which represents the isolation between each "unit". This is clear in next "mathematical analysis" of the Pascal Triangle.

back to numbers

Riemann Space