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Things may be quite singular. My life is quite singular. But when they are not, they are one of the following list:
To me, these, and even the singular itself, are basic types of ineluctable "three-dimensional-ism". Perhaps I should say: it appears to me that everything is effectively described in three dimensions. In fact, it is possible that, if it's knowable, it's three-dimensional. But please understand that "three-dimensions" may be perceptually rather subjective. Examples of the listed categories:
Dimensions are handy tools to develop. Anything describable analytically crosses a spectrum of dimensions within any informative description. Interestingly, I don't find myself able to identify anything that is singly, one specific dimension. Singular things, like life, seem to accumulate dimension after dimension. A singular thing seems, in simple terms, huge: energy, time, multiplicity, existence, love, death, happiness, reason, potential, sentience, editing, gifts, observance . . . Presence presents presents. How's that for singularly one-two-three dimensional? I have a presentiment that this was sent previously to you, dear gentle reader. Take it as you will and please forgive me this paragraph's tropism.
The Euler/Pascal "cube" of power series relationships described and graphed in these web pages tends to emphasize and support both the reality of apparent power levels as well as the confusion of power levels. The nice "3D" layout of the relationships is a nice three dimensional logic. Furthermore, a 3-dimensional graph of Pythagorean triples and their shells adds insight to all logical paths that lead from a2 + b2 to c2.
One more observation on singular realities: assume an "x to an infinite power". Take the positive integers and work out the x-to-the-infinite-power accumulation series using the sieve procedure for accumulating powers. The first accumulation from positive integers is triangular #s, the next, tetrahedral #s, the next pentatope #s, etc., line after line, infinitely summed infinitely, (which is Pascal's Triangle, theoretically). The only power value of x that we ever would come close to is: 1. (We know that 1^n = 1 in every power-of-n that is not infinite.) But do you see how we could never finally sum to "1" due to an initial lack of culling; due to the lack of the original, missing positive integer in the first series of positive integers? There will be no arrival to x = 1 for "x to the infinite power". Infinity sounds singular to me . . . |
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