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Division by Infinity/Zero, Version 1:
Infinity Explained in Terms of the Relative



Equivalence

          Taken by itself, the word "is", as "isness", implies the broad expanse of the infinite beyond: transcendental being. But in normal usage, "is" is an exclusive attempt to equate singularities. It is the intellect failing to recognize the "big picture" by focusing on details. On the other hand, "is equivalent to", or any other version of "approximately equal to", overlooks differences in order to associate singular "things" by way of parallelism. It is completely opposite to the process of equality. The questions involved with equivalence are: how much difference can be overlooked and still maintain relevance; what is relevant; and how abstract or specific are we willing to go to expand or shrink the scope of relevance?
          Traditionally, we make a mistake every time we equate one thing with another. I suppose we get away with it provided we always assume that we are equating ideas or symbols and not things, because nothing in the relative is the same as anything else; everything is unique to some degree. But we can never be sure our thought about something doesn't also evolve or change into another thought ---- never remaining entirely the same over time. Strictly speaking, we would need to redefine our use of "is" when used in the course of normal conversation. The only thing that becomes, or is equatable to, something else is the degree to which things pertain to some quality. Presence or absence of a quality is the degree to which something is either full or empty of that quality. For most things, quality is relative. But when taken to extreme (and assuming we can match nature's ability to measure anything), presence or absence of a quality become their opposite. At this point, we reach nature's capacity, and our's as well, to distinguish differences ---- there is nothing else left to contrast. Only here is equality absolutely operable ---- all else is an approximated equivalence. This is the real world. Unfortunately, the unreal world of mathematics does not directly affect the real world so long as it is trying to equate mere numbers, symbols, or variables. The real world of numbered things are only as accurate as they are assumed to be ---- they are never as exact as we would like them to be. Not because nature lacks precision, but because all topics are relatable to something else and in the scheme of things all topics are brought to bear on integrating a contextual excuse for the existence of some "thing", or even some process (since in science's view, everything is a process: a verb, not a noun). This is where aesthetics jumps in: it associates equivalences in the relative and allows a broad range of styles to approximate them. Aesthetics deals with equivalence, not equality. Styles of approximation I will refer to elsewhere as harmonic systems of polynomial formality ---- there are infinitely many of these; as many as there are polynomials of integer coefficients in a single unknown. Additionally, there are infinitely many different versions of expressing a harmonic system, since approximation (using equivalence) is a trend towards equality and not a singular finality of it. Equality need only be pursued once in a while here and there, but equivalence is an ageless task. That is why Esoteric Research opens with the quote: Art is long, life is short. In a larger view, there should be infinitely various systems of mathematics to express aesthetics in, since all math is formulated using rules written in some prime base of Boolean logic ---- from one to infinity. But esoteric wisdom steps in at this point to put a lid on variety within our creation: there are only sixteen prime bases supporting logical systems of thought from the numbers one to fourty- seven. More on this later.
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Four Views of Infinity


          Division

Version 2