Paired Opposites in The Proportions of Units
Scalar ranges and coordinate systems are paired opposites within sets. Incorporating dimensions of positive and negative numbers and exponents, or expanding x,y and z coordinates, by adding a fourth dimension of time allows a resolution of position relative to the standard of the scale which is often taken as 0,0,0,0 with additional dimensions added as referential scales are expanded from space and time to mass and energy.
Ancient systems frequently scaled their degree of opposition by rate of increase or rate of decrease. Linear increase was enhanced by doubling systems. An acceleration in the rate of increase or decrease could be analyzed arithmetrically, geometrically, or through a wide range of other numerical and physical analysis. Arithmetic and geometric series, and other methods of rating proportionate expansion or contraction could be thought of as convergent or divergent toward a position.
Though unit quantities were first defined by spatial dimensions, and then expanded by adding coordinates of time, the weight or mass a given spatial dimension could contain was also considered and even in antiquity, conditions under which the standard would be established such as at a given temperature, distance from sea level, or density were added.
Rates of change over time were then considered as either indexes of production or depletion
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