Paired opposites

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.

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

Paired opposites in rates of increase and decrease

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.

References

• 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. 
• Herodotus. The History. William Brown. 1952. 
• Michael Grant (1987). The Rise of the Greeks. Charles Scribners Sons. 
• R. A. Cordingley (1951). Norman's Parallel of the Orders of Architecture. Alex Trianti Ltd. 
• H Johnathan Riley Smith (1990). The Atlas of the Crusades place names in Canaan during the crusades. Swanston. ISBN 0-7230-0361-0. 
• H.W. Koch (1978). Medieval Warfare. Prentice Hall. ISBN 0-13-573600-5. 
• William H McNeil and Jean W Sedlar (1962). The Ancient Near East. OUP. 
• Andrew George (2000). The Epic of Gillgamesh. Penguin. ISBN 0-14-044721-0. 
• James B. Pritchard (1968). The Ancient Near East. OUP. 
• Shaika Haya Ali Al Khalifa and Michael Rice (1986). Bahrain through the Ages. KPI. ISBN 0-7103-0112-X. 
• Dr. Muhammed Abdul Nayeem (1990). Prehistory and Protohistory of the Arabian Peninsula. Hyderabad. 
• Michael Roaf (1990). Cultural Atlas of Mesopotamia and the Ancient Near East. Equinox. ISBN 0-8160-2218-6. 
• Nicholas Awde and Putros Samano (1986). The Arabic Alphabet. Billing & Sons Ltd. ISBN 0-86356-035-0. 
• Gerard Herm (1975). The Phoenicians. William Morrow^ Co. Inc. ISBN 0-688-02908-6. 
• Gardiner (1990). Egyptian Grammar. Griffith Institute. ISBN 0-900416-35-1. 
• Antonio Loprieno (1995). Ancient Egyptian. CUP. ISBN 0-521-44849-2. 
• Michael Rice (1990). Egypt's Making. Routledge. ISBN 0-415-06454-6. 
• Gillings (1972). Mathematics in the time of the Pharaohs. MIT Press. ISBN 0-262-07045-6. 
• Somers Clarke and R. Englebach (1990). Ancient Egyptian Construction and Architecture. Dover. ISBN 0-486-26485-8. 
• Marie-Loise Thomsen (1984). Mesopotamia 10 The Sumerian Language. Academic Press. ISBN 87-500-3654-8. 
• Silvia Luraghi (1990). Old Hittite Sentence Structure. Routledge. ISBN 0-415-04735-8. 
• J. P. Mallory (1989). In Search of the Indo Europeans. Thames and Hudson. ISBN 0-500-27616-1. 
• Anne H. Groton (1995). From Alpha to Omega. Focus Information group. ISBN 0-941051-38-2. 
• Hines (1981). Our Latin Heritage. Harcourt Brace. ISBN 0-15-389468-7. 

Footnotes