Home Science Page Data Stream Momentum Directionals Root Beings The Experiment

We first gave the Reader a touch of Root Being language. In the past section we explored the algebra of Root Beings. In the process we introduced some different types of these Beings. Now let us look at how these Root Beings, seeing how they behave under different Circumstances. As mentioned we will confine our study to Fourth Order Root Beings. In the section we will show the Reader some pictures of our Root children.

Let us begin with the True Root Beings, those creatures that approach the True Root under any Circumstance.

We mentioned that the starting point or seed had virtually no influence upon the ultimate destination of our Root Beings. Let us look at this phenomenon graphically, in order to visualize our mental constructs. In this way we will also see how pictures of our True Root Beings and how they behave, accomplishing multiple tasks simultaneously.

Let us see what effect different seeds, i.e. Circumstances, have upon our True Root Beings. We could print out and analyze a chart documenting this feature of our Root Beings. Instead we will show a picture, which says much more. On the following page there are two graphs. In the top graph all of the seeds are zero, while in the bottom graph, the seeds alternate between positive and negative trillion. Unless one looks very carefully at the two graphs, one cant find any differences. The lines were so stable that we didnt have to move any labels in changing from one graph to the other.

Basically each line represents the difference between five different F Series and their respective Roots. From top to bottom the F Series represent approximations of the square, cube, 4th, 5th, and 6th Root of 1000 over 100 iterations. We notice that while there are small individual differences in the lines that they all are approaching the proper Root and at a very similar speed. From these graphs it is easy to see that no matter whether our F series starts at zeros or plus and minus trillion, it has virtually no influence upon the speed that the Root is approached. To be more specific, after 100 iterations each of the F Series is just as close to their destination, the Root, no matter if the seeds are zeros or trillions, and of course, any other number in between these values. These graphs establish beyond a reasonable doubt that the starting point or seed has no effect upon the speed at which our Root Beings pursue their Destiny, the True Root.

There are a few other noteworthy features of these Root Being that are apparent from the graphs. First, the higher the Root of the F Series the quicker the approach to their Destiny. While there are local differences in this result, globally the result is quite apparent. After 100 iterations the square Root is only within a tenth of its Destiny, while the cube Root is closer by four orders of magnitude, while the 4th Root is closer than the third by three orders of magnitude and the 5th is closer than the 4th by about one order of magnitude, as is the 6th than the 5th. Thus the F Series for the 6th Root is 10 orders of magnitude closer to the True Root than the F Series for the 2nd Root, i.e. the square Root, after 100 iterations.

Second the approach to the Destiny is globally consistent while locally erratic. While it would be easy to draw a straight line through the elements of any of our F Series, connecting most of the elements in a straight line, there are elements that jump off the line above or below, further away from the goal or much closer than any of the elements surrounding it. The approach is in no way consistently linear, (i.e. linear from our exponential perspective).

Below is a graph of the differences between the F Series for the Cube and 6th Root and Real Root minus One. (This is same graph as above except it has arrow lines and leaves out the other Root Series.) While this graph expresses all the differences positively, actually many of the differences are negative. (These could not be expressed logarithmically so we turned them all positive.) This differs significantly from decimal fractions, which only approach their goal linearly from below.

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