polyshapes

[Jonathan Barlow Gee]

Each original IDEA is a shard from the transfinite ideal meta-form. Every THOUGHT is attacked from all sides by countless alternative perspectives. All EMOTIONS occur simultaneously as scalar wavelengths in a planar field.

POSTULATE:

if the functions of "Psi" (ESP potential) are graphed onto geometric forms as diagrammatic lattices, then their sum yields multi-dimensional results. 

FORMULA:

if "idea" is mapped onto the corner-points of a "meta-form" object, and "thought" is mapped onto the edges of same, and "emotion" onto the faces of same, then patterns form; thus:

a tetrahedron = 4 ideas, 4 thoughts and 4 emotions.

an octahedron = 6 ideas, 12 thoughts and 8 emotions.

a cube = 8 ideas, 12 thoughts and 6 emotions.

an icosahedron = 12 ideas, 30 thoughts and 20 emotions.

a dodecahedron = 20 ideas, 30 thoughts and 12 emotions.

these patterns also occur in non-3rd dimensional forms as well.

EXPLICATION:

The combination of all "actual" motions for all "meta-forms" made of "psi" energy moving amidst and often through one another amounts to the experience of this limitless energy field as our own mental egos. Our own neural networks are only sieves filtering out static and rendering more exact psi-energy, temporal ellipses in their wake. The combination of all "possible" meta-forms of psi and all their "possible" trajectories provides the "inductive" cosmological set, and "deduction" reduces this from infinitude to an apprehensible scale. The result is the perception of "psi" energy in phases within the singularity-well of "ego" as "ideas," "thoughts" and "emotions."

There are various ways to define what constitutes an "ideal form" in any dimension. For example: if one begins with the "zero dimension" of one corner-point, and proceeds next to the two types of 1-dimensional extension of such a point: the straight line and the semi-circular arc. However, these lower dimensions are not usually included in the list of "ideal forms," which begins, most commonly with 2-dimensional, planar faces, in the form of the three regular polygons (triangle, square, pentagon). However, the circle, comprised of a single completed arc, can also be counted as a shape at this stage, as the sphere can be in three-dimensions, although it is usually excluded. In 3-dimensions, the "ideal forms" are the regular polyhedra: the tetrahedron (or simplex) of 4 triangles, the octahedron (or orthoplex) of 8 triangles, the cube (or hexahedron) of 6 squares, the icosahedron of 20 triangles and the dodecahedron of 12 pentagons. In 4-space these have corresponding geometrical forms as well; there are 6 "4-space" regular polytopes: the 5-cell (hyper-tetrahedron), the 8-cell (tesseract), the 16-cell (hyper-octahedron), the 24-cell (self-dual), the 120-cell (4-d icosahedron) and the 600-cell (4-dodecahedron). The circle and sphere also have a correspondent 4th spatial dimensional form, the torus or hypersphere. In all dimensions greater than 4, only 3 types of "meta-form" ideal shapes exist; these are extensions of patterns formed in the first three 3-d solids: the simplex (hyper-tetrahedron), the orthoplex (hyper-icosahedron) and the tesseract (hypercube). Therefore, in the 5 extra-spatial dimensions from the 5th through the 10th dimension, there are only 15 "ideal forms."

To assemble the 5 "ideal forms" in 3-dimensions, and do so each one at a time, one would only need as many components (corners, edges and faces) as the largest / most complex of the solid forms - in 3-dimensions this being the dodecahedron of 20 corners, 30 edges and 12 pentagonal faces; in 4-dimensions the 600-cell of 120 corners, 720 edges, 1200 faces and 600 solid shapes. However, if you wanted to assemble all of the solids in all of the dimensions simultaneously, one would require 190 components (50 corners, 90 edges and 50 faces) in 3-dimensions, and 49990 elements (773 corners, 1362 edges, 2082 faces and 773 solid "cells") in 4-dimensions. Thus, for all the "ideal forms" in both 3 and 4 spatial dimensions to be all assembled one next to the other in a line would require 5180 parts (823 corners, 1452 edges, 2132 faces and 773 solid "cell" shapes). The total of all these parts assembled into shapes along this line, however, is only 11 "ideal forms" in the 3rd and 4th dimensions, excluding the sphere and torus.

To assemble the 15 "ideal forms" in the 5th through the 10th spatial dimensions, and do so each one at a time, one would only need as many components (corners, edges and faces) as the largest / most complex of the "meta-forms" - in 10 dimensions this being the hypercube of 59,048 components). However, if you wanted to assemble all of these meta-solids in all of the dimensions from 5 thru 10 simultaneously, one would require a total of 4,020 components for the "simplex" model (the "hyper-tetrahedron"), 88,446 components for the "tesseract" model (the "hyper-cube") and 88,446 components alike for the "orthoplex" or "cross polytope" (the "hyper-octahedron"). This means, to assemble these 15 shapes altogether would require a total of 180,912 components to complete.

To assemble 1 each of the 26 "ideal forms" in the first 10 dimensions, one would therefore need 186,092 components.