Paired opposites

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Paired opposites are an ancient, pre-Socratic method of establishing thesis, antithesis and synthesis in terms of a standard for what is right and proper in natural philosophy.

Relative absolutes[edit]

From the very beginnings absolutes are named as gods and paired opposites taken as consorts light and darkness are associated with relative absolutes such as air, earth, fire and water, whose noun based relational synthesis gives birth to new ranges of adjective and adverbial qualitative paired opposites.

Egyptian goddess "Geb", from the Greenfield papyrus.jpg

Where for example, power and wisdom give birth to justice, we have a qualitative rather than strictly scalar synthesis. Paired adjectives and adverbs implying a change in state toward for example wetness or dryness are further expanded through their relative absolutes to be conditional or dependent on a process of becoming or changing towards a well ordered balance.

Going back to the Egyptian concept of Ma'at [1] and the Pythagoreans [2] there is an idea that what is beautiful and pleasing should be proportionate to a standard and with the Greeks the expansion on that idea that the more general and formulaic the standards the better. This idea that there should be beauty and elegance evidenced by a skillful composition of well understood elements underlies mathematics in general and in a sense all the modulors of design as well. The idea is that what makes proportions pleasing to humans in categories such as the architecture of buildings music, art, and mathematical proofs is their being scaled down to dimensions humans can relate to and scaled up through distances humans can travel as a procession of revelations which may sometimes invoke closure, or glimpses of views that go beyond any encompassing framework and thus suggest to the observer that there is something more besides, invoking wonder and awe.

The classical standards are a series of paired opposites designed to expand the dimensional constraints of the harmony and proportion. In the Greek ideal Vitruvius addresses they are similarity, difference, motion, rest, number, sequence and consequence.

These are incorporated in good architectural design as philosophical categorization; what similarity is of the essence that makes it what it is, and what difference is it that makes it not something else? Is the size of a column or an arch related just to the structural load it bears or more broadly to the presence and purpose of the space itself?

The standard of motion originally referred to encompassing change but has now been expanded to buildings whose kinetic mechanisms may actually determine change depend upon harmonies of wind, humidity, temperature, sound, light, time of day or night, and previous cycles of change.

The stability of the architectural standard of the universal set of proportions references the totality of the built environment so that even as it changes it does so in an ongoing and continuous process that can be measured, weighed, and judged as to its orderly harmony.

Sacred geometry has the same arrangement of elements found in compositions of music and nature at its finest incorporating light and shadow, sound and silence, texture and smoothness, mass and airy lightness, as in a forest glade where the leaves move gently on the wind or a sparkle of metal catches the eye as a ripple of water on a pond.

Paired opposites in the proportions of units[edit]

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

Paired opposites in rates of increase and decrease[edit]

The concept of balance vs chaos can be thought of as particle vs wave. The particle minimizes change even when in motion. The wave accentuates change by increasing or decreasing. Relative change may result in one dimension increasing as another decreases or one rate of change increasing as another decreases.

Law and order[edit]

As the natural order of things gives rise to consensus as to what is right and proper and what is by contrast wrong, evil, or bad; societally, mathematically, philosophically and scientifically it becomes necessary to establish standards and orders of magnitude by which something may be evaluated as in or out of tolerance

References[edit]

  • Howard W. Eves (1969). In Mathematical Circles. Prindle. Weber, and Schmidt. ISBN 0-87150-056-6. 
  • Bunt, Lucas N. H.; Jones, Phillip S.; Bedient, Jack D. (1976). The Historical Roots of Elementary Mathematics. Dover. ISBN 0-486-25563-8.  Includes references to a Days Journey and a Days Sail
  • H Arthur Klein (1976). The World of Measurements. Simon and Schuster.  Includes references to a Days Journey and a Days Sail
  • Francis H. Moffitt (1987). Surveying. Harper & Row. ISBN 0-06-044554-8. 
  • Vitruvius (1960). The Ten Books on Architecture. Translated by Morris H. Morgan. Dover. 
  • Ptolemy, Claudias (1991). The Geography. Dover. ISBN 0-486-26896-9. 
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  • Michael Rice (1990). Egypt's Making. Routledge. ISBN 0-415-06454-6. 
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  • Silvia Luraghi (1990). Old Hittite Sentence Structure. Routledge. ISBN 0-415-04735-8. 
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  • Hines (1981). Our Latin Heritage. Harcourt Brace. ISBN 0-15-389468-7. 

Footnotes[edit]

  1. ^ Wallis Budge, Gods of the Egyptians Vol I and 2
  2. ^ Prindle. Weber, and Schmidt In Mathematical Circles