Monday, March 06, 2006

Verbogeometry -- Installment VI --- Prismatic Structures

2.5. Prismatic Structures in Verbogeometry: Notice that 'barren and infertile' is a complex antonym and 'fertile and infertile' is a simple antonym as previously defined. This is interesting because we can see that there exists in verbogeometry a geometric construction where a line expressed as a simple antonym is normal (90 degrees) to a plane containing all of the complex antonyms related to the line which is expressing the simple antonym. To illustrate this idea lets look again at the relationship between the simple antonyms 'fertile' and 'infertile' and the synonyms 'barren', 'fruitless', 'unproductive', 'sterile', 'impotent' which reside on the plane that is normal (90 degrees) to the line created by the simple antonyms. Furthermore you can draw lines from all of the synonyms back to the complex antonym 'fertile'. (See figure 19)

Figure 19.

This idea also lends itself to prismatic structures where we have a group of parallel simple antonyms whose endpoints construct polygonal faces on two parallel synonym-planes. (See figure 19) Example: Let us define one synonym plane containing the words 'pleased', 'content', 'affected', 'satisfied', 'enchanted' and 'sympathetic'. The other plane contains the following simple antonyms for the previous group of synonyms: 'displeased', 'discontent', 'disaffected', 'dissatisfied', 'disenchanted' and 'unsympathetic'. Due to the synonyms of one plane have corresponding simple antonyms which create lines 90 degrees from the synonym-plane then the simple antonyms are synonyms of each other and reside on their own individual synonym plane and because the lines are 90 degrees to each other the planes must be parallel. The former verbiage is a lot easier to understand visually (See figure 20)

Figure 20.

On a side note: Everything that we have been talking about up to this point has been viewed in Euclidian space. Not much time has been spent exploring verbogeometry outside of Euclidian space. However, I see that there can be a lot more thought evolving models of verbogeometry in other spaces. For example, Instead of viewing antonyms and all the varying meanings spread out across a number-line, we may think of the antonyms as magnetic dipoles. Furthermore, all the varying meaning between them is analogous to a magnetic flux. Yet again, another view may be looking at the antonyms residing at the endpoints of a major axis of a three dimensional ellipsoid and the varying meanings reside on the surface of the ellipsoid. (See figure 21)

Figure 21.

Figure 22 shows an ellipsoidal flux-like paradigm for the previous prismatic structure. (See figure 20)

Figure 22.

Figure23 shows an unlabeled side view

Figure 23.

It may be easier to see the ellipse structure if it was wireframe (See figure 24)

Figure 24.

Figure 25 shows 5 parallel word axes in a wireframe structure

Figure 25.

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