

News: DNA of Prime Numbers!
The Prime numbers are in fact composed by numbers on two rows, one starting at 5 + 6+6+6+... and the second starting at 7 +6+6+6+6+..... After elimination by other sequences only prime numbers stay! We can speak of the DNA of prime numbers.You can find more on this on this new webpage (in Dutch)
On Numbers and their pelastrations.
Millions of mathematicians, engineers, businessmen, teachers, use numbers to calculate. Our society and knowledge is partly based on them. They make it possible to communicate exactly "quantity","value" and are used in various fields such as in formulas, computing, meters, etc.. A lot of people also use them in metaphysical systems (religion, kabbal, numerology, prediction, ...). We all believe that numbers can not be questioned. Why should we ... all works fine.
But a strange thing happens when we analyze integers with the pelastration concept. It seems that numbers can have a extra value or quality. So 5 is not always 5 (because 2+3 has a different number of layers then 3+2), due to the orientation. This means that the active tube will determinate the outcome. It depends from the point of view of the observer. Will we count the layers or will we count the tubes? We humans  only seeing the results  have access only to the observed reality: the effect of the layers. But mathematically it's interesting to do some logic exercises. But only noncommutative mathematics make sense in looking to cosmological physics.
When we pelastrate a (active) tube through another (passive) tube one or more extra layers are 'added' to the passing tube. So 'value' is added. Only for the resonant observer there is significance. That added value may be completely different from the acting tube. Still there will be interaction. Two phenomena are combined (pelastrated) for a given time. For the nonresonant observer there is however no causal relation. There is just an observed fact seen as a new unity that appears. But that new unity is a subset created by parent holons.
Here some points/thoughts.
Remarks:
(1)In our additions we always start with the active (impact) tube.
(2) We postulate that the polarity switches in the skinlayer when the outer layer of the impact tube has the same polarity as the polarity of the receptive tube.
(3)In this exercise we start from the condition that the impact tube will pelastrate all layers of the receptive tube.


The basic tube pelastrates itself.
Polarity of one is +, and polarity of 2 become negative.
There is a metaphysic tradition to say that 1 is the father and 2 is the mother. 3 will be the child. What brings number 3? 
Analysis of further pelastrations through the basic tube [1(+)].
Result: traditional polarity switch is still valid.

NUMBER 3:
When we make 2() pelastrate through 1(+) the 3 becomes positive again. BUT when we pelatrate 1(+) through 2() we see a different numbers of layers and in that situation the outer layer of three is negative! This means that 2+1= 3(+) but 1+2=3().


We can say that the child (3) can be male or female! Valid! 
NUMBER 4:
Since there are two types of 3 there will be more combinations to come to 4. Below image shows that brings us 5 layered number fours (from which two have identical layers, the red and yellow 4), thus 4 types. 

NUMBER 5: Here we have  of course  more combinations. Seven different type of 7's with a different number of layers. But they still all all 14 unique since they have an layer history. 

Can you image how many combinations a composed number like 26 has?
;)
Just by combinating these 4's and 5's you have already 60 unique combinations.
Now this type of unique combinations reached by pelastrations (creating unique holons) is exactly the combinations shown by the CATALAN numbers. The Catalan numbers (1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, ...), named after Eugène Charles Catalan (18141894), arise in a number of problems in combinatorics.
So we can say: All generations till 3 have 5 ways to pelastrate, All generations till 4 have 14 ways to pelastrate, etc.
You can find more on Catalan Numbers and Combination trees on next link and on: http://mathworld.wolfram.com/CatalanNumber.html
It start to become also interesting when we look to the relationship between those Catalan numbers and Pascal's triangle. Different from the known relationship we found that for each Catalan number an unique exclusive set of numbers of Pascal's triangle is used. Check next image.
(click on the image to have a larger image covering the Catalan numbers till 58,786)
You can see the TOP 1 as being the complete set, and all following lines are levels of subsets. In each hexagon is mentioned the number of combinations (number of subsets with a unique layer combination) that are possible with the previous subsets. The descending outer hexagones with 1 represent the local subset parts of the nonbreakable membrane. The next diagonal row becomes more complex, and so on. We see also that there is an irregular distribution (i.e. orange = 14 = 4 + 10). When we analyze this in the previous sheet on the number 5 we find that there are 4 combinations of 3 with 2, and 10 combinations of 1 with 4, and that confirms the 4 and 10 found in the Pascal Triangle. Isn't this amazing?
This insight confirms again the noncommutative origine and hidden structure of the Universe(s).
In category theory the Catalan numbers receive now a lot of attention, i.e. from John Baez. Here is a link to a pdffile (3.5 Mb) on a lecture he gave in fall 2003. From about page 75 is starts on Catalans.

In our knowledge system it will be preferable (or more easy) to say that the numbers of layers make the correct value, independent from the number of tubes/membranes. But we know now that there is another way ... too ... on cosmological level. When we bring each catalan number to power 2 we get all pelastration combinations possible by those unique holons, on that level of generation, and this gives us all new unique combination of the next generation on which we much add the combinations of all previous generations. This giant growth of combinations explains the fantastic complexity of our worlds of interacting dimensions. And all comes from one membrane that is locally restructured by pelastrations.
This unique layering is explained in two eBooks that you can download from the pdfpage (with all newest developments).

On the right is an animated image that shows the membrane  which has almost infinite parts  will start local combinations.The first step is when two parts of the membrane couple and create the first holon (2). Then the membrane and the first holon have two ways to couple; 1 > 2, or 2> 1. This are the 3A and 3B holons. But 2 can also pelastrate itself: 2>2. We call that the new holon 4E. There will be 4 holons created in the next step by coupling of 3A and 3B with 1. 


Something else: The pelastration of numbers gives also some other analytic fun when they are projected on a spiral. On level 1 (through one) with potential pelastration in next available tubes some numbers can only be reached by a pelastration through one: 2, 3, 5, 9, 17, ...


... thats all is for now ... but these short abstract analysis shows that the pelastrational concept can introduce "qualities" in the strange and fascinating world of numbers. 

Nice quote of Edward Edinger (Ego and Archetype): "The number one as the first and original number is strictly speaking not a number at all. One as unity and totality exists prior to the awareness of numbers which requires a capacity to distinguish between separate discrete entities. Thus, one symbolically corresponds to the uroboros state prior to creation and the separation of things. Two is the first real number." 

