Oct 13, 2012
Poly-metric Relations Approach to Understand the Fourth Dimension
Yool, G.R. (1998) strived to delve into the relationships that exist between families of dimensions and specific polyhedrons, as well as the geography of those polyhedrons with respect to specific dimensions within the family by, to some extent, examining both where relationships exist and where they do not exist between processes within “mensonnomy” and the processes exhibited by the polyhedrons.
However, he found that there are few differences, inclining the belief, as with extraneous data in other sources, that either the absence of relationship is a matter of misjudgment of variables or more likely a lack of understanding or recognition of all the processes involved.
Yool, G.R. (1998) began to minimize mathematics and thoroughly explained to allow the common reader to understand and visualize without being a mathematician; and for the convenience of the reader, the sections are ordered by the family of dimensions being discussed.
According to him, the families and their polyhedrons (with number of faces in parentheses) are:
Holistical Sphere (1)- 1 Dimension Holistic,
Paralogical Tetrahedron (4) -2 Dimensions Time,
Axiological Octahedron (8)-3 Dimensions Matter,
Locustical Hexahedron/Cube (6)-4 Dimensions Space,
Metaphysical Dodecahedron (12)-5 Dimensions Energy,
Antithetical Icosahedron (20)-6 Dimensions Definitive
Further, he explained that anything that can be measured, added or increased may also be subtracted from, reduced or decreased; this sounds remarkably profound and obvious; accordingly, if it is not stated however, it is easily neglected.
This rule is perhaps the most important, as it indicates the potential of a dimension. It is also of extreme importance when applied to time, whose tradition of being mono-directional is discarded in mensonnomy.
Yool, G.R. (1998) claimed that every dimension has, at minimum, a potential of two values, one positive the other negative. The Potential of other dimensions may cause a family to exhibit greater Potential values as a function of the contributing dimensions.
Two or more dimensions may comprise a plane with two times the vertices as there are dimensions on that plane; and the total number of vertices of a polyhedron representing a family of dimensions is equal to the potential times the number of dimensions in one period of the family.
Two, three and four dimensions may be represented as having ninety degree (right) angles from each other; a complex plane consists of two or more angles where one or more dimensions use a complex number to differentiate them from another dimension or group of dimensions, providing means to represent those dimensions two dimensionally and to show mathematical relationships between the dimensions involved.
Further, he elaborated that complex planes intersect at right angles which become eccentric respecting the complex angles of each plane; connecting dimensional vertices with the fewest edges yields a regular polyhedron.
The dodecahedron (12 faces) is a cross between the tetrahedron (4 faces) and octahedron (8 faces), whose sum of faces, potentials, and number of dimensions involved coincide.
He added that Einstein's energy equation applies as modified by the dimensional transform to the tetrahedron, octahedron, hexahedron, and dodecahedron, specifically to number of faces, angular multipliers, and row values; and when isolated to one side yield the sphere.
Treating the faces of the dodecahedron as vertices, connected with the fewest possible edges yields the icosahedron (20 faces); the functions of dimension families provide direct relationships with values on the icosahedron.
The relations, respecting eccentricity, are at right angles from each other; while the Locus family provides the topology system for all the dimensions, as well as values from which the regular polyhedrons are constructed, limited and defined.
He claimed that per these rules, we can easily follow a logical sequence through the first four families of dimensions, and then with some ambiguity the next two families.
Yool, G.R. (1998) finally resulted the following kinds of relationship:
The relation between Holistic and the Sphere:
“Of the polyhedrons, the sphere's application is perhaps the most ambiguous. With regard to the Holistic, it is presented as both infinitely vast and infinitely small. Neither case is actually contradictory, though one may tend to think a vast difference exists between a singularity (a sphere with no dimension) and a sphere with infinite dimension. Even more baffling is the idea that the sphere can have an infinitely negative dimension. This is a consequence of rule #1: anything that can be measured or added to may also be subtracted from. The sphere, no matter the human value applied thereto, is a unit sphere, meaning any dimension may be applied, but that the root dimension (radius) is one. This is supported by the row and column values, which provide D0 = 1.”
The relation between Time and the Tetrahedron:
“Time and antitime provide crossing dimensions, each with positive and negative values. Because each belongs to a separate relation, we know these dimensions are at right angles from each other.
Also, because they belong to separate relations, they are likewise polarized by spatial planes, each having two dimensions.
Time thus exists in two separate two dimensional spaces, each at a right angle from the other.
Rather than a simple cross as with traditional Cartesian/Euclidean two dimensional space, two dimensional time is twisted (see figure) like a mobius cut off before it begins its circuit back to the beginning.
It is highly likely this analogy goes the distance, allowing these dimensions to complete the transitions into each other when one approaches its maxima and the other approaches zero. We will not explore that possibility here. Our chief interest here is its relationship to the tetrahedron”
Yool, G.R. (1998) concluded that if this brings up a cosmology issue, many argue that stars and planets are formed from dust clouds, while celestial bodies certainly absorb dust and particles from space, this is by no means their primary source of naissance.
He suggested that we may observe in our own planet not just the expansion, but the observations of the heavy, molten core and our atomic energy sources.
If the universe began with the bang and bodies formed from the dust, then why would our planet be expanding under its own power?
The amount of mass Earth accumulates each day from space is stunning, but insignificant compared to its own growth from within; likewise, black holes are young while quasars are immensely old.
Yool, G.R., 1998, The Unified Field Theory: Chapter 9--Polymetric Relations