Appendix # 123456789101112 131415Chronicle

Appendix XIII:


Visualization is an idea that would seem to refer to an "in-sight" kind of "seeing" and not a seeing we usually or easily do with eyes open. Be it with eyes open or closed, observation and visualization should be considered interchangeable ideas. A method of visualizing "geometric space" draws " point, line and plane" on a paper or screen surface, and these are often mistaken for "one" or "two" dimensional objects.

That objectification on the screen is an illusion at several levels. For one, the molecules or photons used to compose the image, be they graphite (pencil lead) or light, arise in the indivisible three-dimensional realm of more space than you can imagine where at that microcosmic level, a so-called 2-dimensional surface has no meaning, because you're referring to a layer of 3-dimensional molecules.

A putting together of discrete dimension to make up the 3rd dimension is not possible. Even holograms, 3-D movies, are not made of discrete dimensions. I can schematically indicate "height, width, and depth," but that arbitrary abstraction or separation is more about measurement of "distances," not to be confused semantically with the idea of dimensions.

One presumes all distinctions to be real if the mind can map them. In that manner, duality arises out of what is otherwise a singularity and at-once-ment or oneness. Although one has navigated duality long before metaspheric mapping came along, it is metaspheric perspective or metasphere that provides the sphere through which to observe the geometer's generatrix and thus the singularity from which is arises.

"Mathematics is in this respect psychedelic." Is a curious phrase in G. Spenser-Brown's notes to his book, coming as it does after the following: "A recognizable aspect of the advancement of mathematics consists in the advancement of the consciousness of what we are doing, whereby the covert becomes overt." Or simpler said: Whereby the closed is opened or the hidden is revealed.  

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