the spirals on a torus

[benpadiah]

Now, I would like to take a moment to compare some self-evident facts that we can observe in nature. I am not going to claim to have invented any of these things, as I hear doing so results in bad karma.

It is a self-evident fact, for example, that the seven basic colours of the spectrum of light (red, orange, yellow, green, blue, indigo, violet in order) can be mapped onto the surface of a torus, or hypersphere, in only one way, such that each of the seven colours occupies the same area on the surface of the shape.



Now, once these colours have been mapped onto the surface of the torus, we see that the outline between each of the mapped areas forms a spiral that wraps around the surface of the hypersphere.



The spiral that outlines the seven coulour spectrum is, and this also is a completely self-evident fact and was not "invented" by any human hands, is a "phi" spiral.



Now, this "phi" spiral revolves AROUND the circumference of the torus (clockwise or counterclockwise) depending upon the rotation THROUGH the centre of the torus (outward from centre or inward toward centre, respectively) of the seven coloured areas mapped onto its surface.



In other words, the "phi" spiral revolves around the circmference as a MEASUREMENT of the surface of the torus. It MEASURES the fourth-dimensionality of this shape by MOVING, that is, it changes over time, and is therefore, like the clock, a means of measuring the passage of the fourth dimension.

However, this MEASUREMENT is only of the SURFACE of the torus, measuring the revolution from the circumference (seen from above) to the centre. This is a measurement of AREA, that is, of the combined seven areas of the mapped colour spectrum.

However, what if we measure the VOLUME of the torus, that is, the interior of the rotating radii of the hyersphere? Just as the "phi" spiral REVOLVES as it measures the SURFACE AREA, so too do we need a measurement device for the ROTATION of the INTERIOR VOLUME.

We know that, as the "phi" spiral "revolves" around the "top" and "bottom" of the hypersphere, so too, when we look at the torus from the "side" we see there is "rotation" of each radius, "right" or "left." Thus, just as the "revolution" of the "phi" spiral tells us about the external surface area, so too can the rotation of these radii tell us about the internal volume.

Now, when the "phi" spiral is revolving "clockwise" it means the torus is rotating "outward." When the "phi" spiral is revolving "counterclockwise" it means the torus is rotating "inward." But, just as the "top" rotates "inward" while the "bottom" rotates "otward," yet there are not two phi spirals, only one continuous spiral measuring the external area, so, even though there are two radii "sides" that rotate "clockwise" or "counterclockwise" respectively, there are not two different spirals, one for each radius, one moving "clockwise" while the other moves "counterclockwise," but only one cntinuous spiral measuring the internal volume.

So, we have "phi" measuring the outside, and another, single and continuous, spiral measuring the inside. I call this spiral "pi" for short hand, but the spiral I mean when I refer to this spiral as "pi" is really the "spiral mirabilis" derived from "e," the so-called "natural number." I have found that by dividing "phi" (1.1618) by "pi" (3.14) and adding one, you arrive at 1.37, which is the same as the so-called "natural" number. Therefore "e" would equal the combined "phi" (exterior) and "pi" (interior) spirals. This would mean that, if "phi" was both clockwise and counterclockwise, and "pi" was both counterclockwise and clockwise, as in the torus, then the "natural" spiral would be equal to the combination of their motions, that is, would be the sum of their spin, expressable mathematically as e=phi/pi.

All of these observations arise from self-evident facts of nature. None of them is my own personal invention, nor, I would posit, the "invention" of anyone other than the Creator of this universe, God. Therefore, please feel at utter liberty to discuss these ideas with no worry that I will oppose your applications of them. We are free here, and we are equal.

My own personal applications of this model, the "phi/pi" spiral model for the measurement of the fourth dimension and the hypershapes that exist therein, form the basis for my cosmological diagrams that I included with my published book, "the Metaphysician's Desk Reference." On my website, you can find these diagrams on the MPDR diagrams page:

http://www.benpadiah.com/MPDR_diagrams.html

although you might want to start at figure 5 and work backwards from there toward Tau sub Tau.

In the "Meatphysicans' Desk Reference," I discuss at great length the ubiquitousness throughout the universe of the torus shape and the phi/pi measurement method thereof. I have found that this shape pertains most directly to the propagation of energy, such as gravity, and of higher-order forms, such as tachyons.

I would be interested to hear your opinions on these subjects.

-Jon
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