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The primary focus of this notebook was achieved. We derived and analyzed a Potential Impact equation for individual data pieces upon the Directionals. We already knew from prior research that Directionals are based upon a combination of Raveled Data, i.e., Directionals = Ä(Raveling). Thus we started by looking at the potential impact of individual Data upon the Ravelings. We found that with each added raveling, Q, that the immediate potential impact, potential impact, was divided by D, the Decay Factor. We also found that the number of separations, R, from the Now, R=0, determined how many times that the data was scaled, i.e., multiplied by K=(D-1)/D. Finally we found that the number of times each element was used in the Raveling was based upon a combinatorial relationship between Q, the number of Ravelings and R the number of separations from XN, the Now. We then discovered that each time a Raveled number was used that it had the same potential impact on the Directional as every other Raveled number. A general equation for the potential impact of an individual piece of Data fell right out of all these discoveries. Thus we reached our destination.
But we met some interesting characters along the way. First we found that Q, the number of times the data is raveled, is a dimensional number. An analysis of its elements yields multi-dimensional tetrahedrons. Because of the symmetry of these structures, R, the degree of separation, and Q have a symmetric relation in the enumeration of elements. Because of this Q & R, together, form a bi-multi-dimensional system. We also saw that the dimensional organization of the number of elements could also be used as a scaling diagram. In looking at the scaling diagrams we found that each element was used the total number of possible routes based upon R and Q, their sum being a constant.
A few of our proofs were based upon parallels with Pascal's triangle. Because of the connection between the Binomial expansion and Pascal's triangle, we binomialized the Seed Equation and came up with Raveled numbers in a different form. Prior we used circle terminology based upon the N of XN, the number of samples. Raveling N once gave us the Decaying Average. In this new manifestation based on square terminology, the number of samples, N, becomes insignificant. The only relevant element becomes the degrees of separation, R, from the Now.
In binomializing the Seed Equation, we found that Raveled numbers behave like positive integers. When they are multiplied externally, they are added internally. When Raveled numbers are taken to a power externally, it is like multiplying them internally by the power. However Raveled numbers cannot be added externally without quite a bit of algebraic mumbo jumbo. Another unusual aspect of Raveled numbers is that they contain traces of all that went before and then into non-existence. These weird numbers, which extend from existence back into non-existence, are also dimensional in nature. The number of elements in a Raveling can be represented by a multi-dimensional tetrahedron. The potential impact of each of these elements can be represented as a multi-dimensional spiral cube. Each additional Raveling adds another dimension onto the tetrahedron or onto the cube. When Raveled Numbers are combined binomially, they add Dimensions, Q, and degrees of Separation, R, simultaneously. Q and R are so integrally linked that only a single line of Ravelings goes into making each Directional. Each individual Raveling connects up with one and only one Directional. Finally Raveled numbers are unitary numbers, i.e., each Raveled number that goes into making a Directional has the exact same potential impact.
Where have we been? We've come through a very long tunnel. It has been dark but we've uncovered some treasures. We've emerged on the other side of the mountain after so many adventures that we can barely remember why we entered the cave in the first place. Were we running away from boredom or were we attracted to a curious light inside the cavern? Upon pursuing the light did we find enlightenment? Or did we instead find that the light was only a mirror reflecting the true light. Upon changing direction in pursuing the one true light, we found that this too was only a mirror reflecting the true light. Before we knew it, pursuing the reflections of reflections of reflections deep into the cavern, we were lost. But we had gone so far; we couldn't go back even if we wanted to. So we decided to keep going. There was really nothing else for us to do. After many more reflections of reflections we saw what seemed to be the true light of the Sun. We ran excitedly ahead thinking that we had found our way back. But instead realized that we had gone all the way through the mountain. We were on the other side. How do we get back? We have been so thoroughly changed that we can never go back and step in the same stream twice.