Paired opposites

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 arithmetically, 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

Paired opposites are used as poetic diction meaning "everything". Common phrases incorporated paired opposites in English include "all creatures great and small," "working for the man every night and day," "more things in heaven and Earth" "searching high and low" "in sickness and in health". In Greek literature, Homer uses the device when he lets Telemachus say, "I know all things, the good and the evil" (Od.20:309-10).[1] The same phrase is used in Hebrew in text of Genesis, referring to the Tree of the knowledge of good and evil.[1][2][3]

In quantum mechanics, as well as some fields of mathematics, conjugate variables are a form of paired opposites, in which knowledge of one precludes knowledge of the other. A standard example is the relation between position (x) and momentum (p), which can be expressed in terms of the uncertainty principle as ${\displaystyle \Delta p\Delta x\geq \hbar }$.

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