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.

Relative absolutes

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

Going back to the Egyptian concept of Ma'at [ Wallis Budge, "Gods of the Egyptians" Vol I and 2 ] and the Pythagoreans [ Prindle. Weber, and Schmidt "In Mathematical Circles" ] 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 architectual 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

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. Arithmetric and Geometric series, and other methods of rating proportionate expansion or contraction ccould 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.

Law and Order

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

* Howard W. Eves Section:Book reference after author|Year=1969|Title=:"In Mathematical Circles" |Publisher=Prindle. Weber, and Schmidt|ID=ISBN 87150-056-8

* Lucas N. H. Bunt, Phillip S.Jones, Jack D. Bedient Section:Book reference after author|Year=1976|Title=The Historical Roots of Elementary Mathematics|Publisher=Dover|ID=ISBN 0486255638 Includes references to a Days Journey and a Days Sail

* H Arthur KleinSection:Book reference after author|Year=1976|Title=The World of Measurements |Publisher=Simon and Schuster|ID=Includes references to a Days Journey and a Days Sail

* Francis H. MoffittSection:Book reference after author|Year=1987|Title=Surveying|Publisher=Harper & Row|ID=ISBN 0060445548

* VitruviusSection:Book reference after author|Year=1960|Title=The Ten Books on Architecture|Publisher=Dover|ID=

* Claudias PtolemySection:Book reference after author|Year=1991|Title=The Geography|Publisher=Dover|ID=ISBN 048626896
* 25. HerodotusSection:Book reference after author|Year=1952|Title=The History|Publisher=William Brown|ID=

* Michael GrantSection:Book reference after author|Year=1987|Title=The Rise of the Greeks |Publisher=Charles Scribners Sons|ID=

* R. A. CordingleySection:Book reference after author|Year=1951|Title=Norman's Parallel of the Orders of Architecture|Publisher=Alex Trianti Ltd|ID=

* H Johnathan Riley SmithSection:Book reference after author|Year=1990|Title=The Atlas of the Crusades place names in Canaan during the crusades
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* H.W. KochSection:Book reference after author|Year=1978|Title=Medieval Warfare|Publisher=Prentice Hall|ID=ISBN 0135736005

* William H McNeil and Jean W Sedlar, Section:Book reference after author|Year=1962|Title=The Ancient Near East|Publisher=OUP|ID=ISBN

* Andrew George, Section:Book reference after author|Year=2000|Title=The Epic of Gillgamesh|Publisher=Penguin|ID=ISBN No14-044721-0

* James B. Pritchard, Section:Book reference after author|Year=1968|Title=The Ancient Near East|Publisher=OUP|ID=ISBN

* Shaika Haya Ali Al Khalifa and Michael Rice, Section:Book reference after author|Year=1986|Title=Bahrain through the Ages|Publisher=KPI|ID=ISBN 071030112-x

* Dr. Muhammed Abdul Nayeem, Section:Book reference after author|Year=1990|Title=Prehistory and Protohistory of the Arabian Peninsula|Publisher=Hyderabad|ID=ISBN

* Michael RoafSection:Book reference after author|Year=1990|Title=Cultural Atlas of Mesopotamia and the Ancient Near East|Publisher=Equinox|ID=ISBN 0-8160-2218-6

* Nicholas Awde and Putros SamanoSection:Book reference after author|Year=1986|Title=The Arabic Alphabet|Publisher=Billing & Sons Ltd.|ID=ISBN 0863560350

* Gerard HermSection:Book reference after author|Year=1975|Title=The Phoenicians|Publisher=William Morrow^ Co. Inc.|ID=ISBN 0-688-02908-6

* GardinerSection:Book reference after author|Year=1990|Title=Egyptian Grammar|Publisher=Griffith Institute|ID=ISBN 0900416351

* Antonio Loprieno Section:Book reference after author|Year=1995|Title=Ancient Egyptian|Publisher=CUP|ID=ISBN 0-521-44849-2

* Michael RiceSection:Book reference after author|Year=1990|Title=Egypt's Making|Publisher=Routledge|ID=ISBN 0-415-06454-6

* GillingsSection:Book reference after author|Year=1972|Title=Mathematics in the time of the Pharoahs|Publisher=MIT Press|ID=ISBN 0262070456

* Somers Clarke and R. EnglebachSection:Book reference after author|Year=1990|Title=Ancient Egyptian Construction and Architecture|Publisher=Dover|ID=ISBN 0486264858

* Marie-Loise Thomsen, Section:Book reference after author|Year=1984|Title=Mesopotamia 10 The Sumerian Language |Publisher=Academic Press|ID=ISBN 87-500-3654-8

* Silvia LuraghiSection:Book reference after author|Year=1990|Title=Old Hittite Sentence Structure|Publisher=Routledge|ID=ISBN 0415047358

* J. P. MallorySection:Book reference after author|Year=1989|Title=In Search of the Indo Europeans |Publisher=Thames and Hudson|ID=ISBN 050027616-1

* Anne H. GrotonSection:Book reference after author|Year=1995|Title=From Alpha to Omega|Publisher=Focus Information group|ID=ISBN 0941051382

* HinesSection:Book reference after author|Year=1981|Title=Our Latin Heritage|Publisher=Harcourt Brace|ID=ISBN 0153894687

Footnotes