It is in this nature of direction as dimension as qualitative we observe three fundamental qualitative polar duals of up/down, right/left and forwards/backwards. These duals synthesize as third element, resulting in the triad of vertex, amplitude, and depth.

It may be observed that:

1)These duals exists through inversion, and as inverted manifest a positive and negative nature. Up is generally viewed as positive with down being negative. Right is generally viewed as positive with left being negative. Forwards is generally viewed as positive while backwards is viewed as negative.

2)These duals, while inversely proportional, manifests as 1 dimension as direction and in these respects maintain an equality.

a.Up/down, left/right and forwards/backwards are all the same direction when viewed relativisitically. For example, “A” may lead to “B” as “up”, and “B” may lead to “A” as “down” however invert the perspective and “B” equals “up” and “A” equals “down”. This act of inversion implies moving points of observation and in these respects are not stable.

b.The same applies for vertex, amplitude and depth. As vertex can only be observed relative to amplitude and/or depth, amplitude can only be observed relative to vertex and/or depth, and depth can only be observed relative to vertex and/or amplitude.

c. When viewed as stable points up/down, left/right and forwards/backwards are merely approximations. For example, “A” may lead to “B” as “up”, and “B” may lead to “A” as “down” however they are merely approximates of eachother through the line as 2 points. In these respects “A” and “B” manifest vertex as an approximation as both “up” and “down”.

d. The same applies for vertex, amplitude and depth. As vertex can only be observed as an approximate of amplitude and/or depth, amplitude can only be observed as an approximate of vertex and/or depth, and depth can only be observed as an approximate of vertex and/or amplitude. As approximates, they are merely extension of “direction” as 1.

e. These inverse duals are expressed through relational movement and as approximate extensions of structural points. In these respects these duals maintain a neutral element as dimensional limit.

f. As these duals are directions, in themselves, they are simultaneously possible dimensional limits, as no-limit, considering that direction manifests through ad-infinitum centers.

3) The third element of synthesis through these polar duals results in dimension, as direction, being the ratio or proportion itself. The vertex is the medial dimension of up/down, amplitude is the medial dimension of left/right and depth is the medial dimension of forwards/backwards. As medial dimensions vertex, amplitude and depth as 3 dimensions as 1 dimension and 1 dimension in 3. In these respects vertex, amplitude and depth are boundaries that give form as limit.

4) Ratios, or proportions, are dimensional boundaries in themselves and dimension, boundary and direction may be viewed as synonyms who approximate nature is a result of language problems. Direction exists as the boundary of space as space itself and dimensional limits are the foundations of space, with possible dimensional limits being neither space nor not space.

## Direction as Proportion

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