Ancient cultures knew about sacred geometry reflected in nature and derived their individual measures of length from it. Many ancient writings suggest that this knowledge was given to mankind by god(s). The ‘Gods’ of certain cultures could be early post-flood founders a few generations after Noah. In Egypt, building overseers required the Royal Egyptian Cubit to be calibrated against a precision standard at regular intervals. Failure to do so was punishable by death. This extreme respect for the royal cubit indicates an important legacy, like a standard handed down from the ‘Gods’.
According to the “Secrets of the Great Pyramid” (by L. Stecchini) the Egyptian measures of length, originating from at least the 3rd millennium BC, were directly derived from the circumference of the earth with an amazing accuracy. On page 346, his claim is that the Egyptian measurement was equal to 40,075,000 meters, which compared to the International Spheroid of 40,076,596 meters gives an error of 0.004%. No consideration seems to be made to the question of, on purely technical and procedural grounds, how the early Egyptians, in defining their cubit, could have achieved a degree of accuracy that to our current knowledge can only be achieved with very sophisticated equipment and techniques.
Note: Egyptians calculated polar radius as 12,000,000 Royal Cubits (of 0.525 m per cubit) which is equivalent of 6300 km (modern value for the polar radius of the Earth is 6,357km)
The Sacred Cubit (aka Royal Cubit) was used in constructing buildings and monuments and in surveying in ancient Egypt. Royal Cubit consists of 28 units, digits ( 7 palms of 4 digits). The names of divisions of royal cubit may suggest anatomical origin, however the division numbers indicate astronomical origin of the cubit (7 days per week, 28 days lunar calendar, 4 weeks per lunar month)…
Note: Here is an interesting connection between modern and ancient units of length with astronomy and geodesy: 1 foot = 12 inches, 1 mile = 5280 feet = 63,360 inches = 4800 Sumerian Feet = 3200 Sumerian Cubits.
There is great confusion today concerning metrology, the history of measurement systems around the world. Beyond the child’s tales of the “foot” deriving from some king’s foot, measurement was actually part of a sacred system of knowledge established in prehistory and based on timeless truths seen in the harmony of the cosmos. Standards of measure were everywhere framed upon never-changing principles of number, in particular, the interplay of natural tension between ten and twelve, and the dimensions of the turning Earth. Except for the survival of the English system in the U.S., most other traditional systems of measurement worldwide have succumbed to the “easy” and modern, but inferior “metric” system, which uses only ten, is divorced from nature and the human scale, and requires its users to conform to the measuring tools themselves, not to the nature of the objects measured, as was traditionally done.
The Cosmological Diagram (The New Jerusalem Diagram)
The Sacred Geometric Community has fallen short of the grand prize, the New Jerusalem and her fullness of purpose, they have at least seen, especially through the apostolic efforts of John Michell, the suburbs of the Holy City and from this afar view have come imminently close to her profound and universal meaning; and certainly by framing their quests for universal understanding and sustainable social systems in terms of the Celestial City (or as in Plato’s case, Magnesia). Their approach to the City Whose Builder and Maker is God (even though that “god” is NOT the One of revelation and authority held by their antagonists amongst the aforesaid monotheists), as we all, is seen through a glass darkly but, nevertheless, they are searching to unlock the mystery of the New Jerusalem and to confirm their findings through geodetic discovery.
Another version of the NJ Diagram is Magical Seal of Solomon.
In Medieval Jewish, Christian and Islamic legends, the Seal of Solomon was a magical signet ring said to have been possessed by King Solomon, which variously gave him the power to command demons, genies (or jinni), or to speak with animals. In some versions the seal was made of brass and iron, carved with the Name of God, and set with four jewels. In later versions the ring simply bore the symbol now called the Star of David (hexagram), often within a circle, usually with the two triangles interlaced rather than intersecting.
To them the “geometric construction” of the New Jerusalem presents cosmological realities which govern the universe – a universe numerically understood far more by the “ancients” who have left us a testament in their objects and writings to these realities whereby John’s vision of the Holy City is the culmination of all their most vivid aspirations; to wit, the elaborate geometric configurations from the New Jerusalem Diagram to intriguing planetary measurements of circles, squares, triangles, polygons of all sorts which provide immediate connectivity between earth and heaven’s realms – as well as those earthly objects of antiquity which replicate the heavenly dimensions of Paradise, and all within the context, preservation and accuracies of antiquity:
“Another relic of the archaic tradition that produced these divisions of time is our present system of measurement by units of feet, furlongs, and miles, with the acre as the unit of land measuring. Those measures, which are still found the most convenient today, were canonized and held sacred, because not only do they relate both to the human and to the astronomical scales, expressing the unity between macrocosm and microcosm, but they bring out the same numbers in the dimensions of the solar system as were given to the units of time.” — Dimensions of Paradise, Michell, p. 117.
One of the foremost metrologists of Teotihuacán is, without equivocation, Dr. Hugh Harleston Jr., who during the late 1960s and 1970s measured this “ritual city” from a “…unified geometrical composition whose intervals are clearly defined, and Harleston was soon able to establish the basic unit of measure in its dimensions. This proved to be a unit of 1.0594 meters, which Harleston called the Standard Teotihuacán Unit (STU) or Hunab after the Mayan word, adopted by the Aztecs, for Measure. He also recognized the geodetic significance of that unit: 1.0594063 meters is equivalent to the ‘Jewish rod’ of 3.4757485 ft., the same unit which represents the width of the Stonehenge lintels, a six-millionth part of the earth’s polar radius and one part in 37,800,000 of its mean circumference.” (Ref. The New View Over Atlantis, Dr. John Michell, 1995, p. 131).
Also: “Harleston says of Teotihuacan’s builders: ‘When they draw a line, they’re telling you an area. When they draw an area, they’re telling you a volume. When they put volume, they’re telling you time.”
Geodesy and geodetic placement of “sacred sites” of ancient origins has long been affirmatively suspect – especially, the Great Pyramid of Giza. Geodesy involves a fundamental understanding of plane or solid geometry, astronomy relative to latitude and longitude with latitude of more recent vintage since ships-clock (cir. 1540) came into vogue. These geodetic or geometric relationships both on earth and in the heavens are a frequent haunt of pagans and occultists and of novel interest to science – though science with its unfortunate proliferation of skeptic is apt to go off into “metric tangents” and miss out on all the “fun!”“For quite some time researchers have been documenting the astronomical alignments of ancient archaeological and megalithic stone sites all over the world. But discovery of their geodesic alignment has been more recent. Geodesy refers to the theory and practice of surveying to determine the position of specific points on Earth’s surface. It is distinguished from plane surveying in that it deals with areas whose dimensions are so great that the curvature of the Earth must be taken into account. Geometric geodesy involves the creation of a mathematical model of Earth, while physical geodesy studies Earth’s gravity field. The discovery of the precise alignment of Mayan sites along the 90th parallel is significant because it demonstrates that the Maya were aware of Earth’s curvature and knew the advanced formulas used in geodesy.
Note: Carl Munck, archaeocryptographer, introduces an ancient Pyramid Matrix, in which ancient monuments – across the globe – encode their exact positions with respect to latitude and longitude. The science of decoding these monuments is called archaeocryptography. For latitude, ancient monuments were referenced to the same (modern) equator. For longitude, these monuments were referenced to a former Giza, Egypt Prime Meridian – discovered by Munck – that ran from pole to pole across the Great Pyramid.
PS1 The Forgotten Harmonical Science of the Bible
Note: The following segment is from “The forgotten harmonical science of the Bible” by Ernest G. McClain
“…but thou hast ordered all things in measure and number and weight” — Wisdom of Solomon 11:20 (1611 King James Bible)
Biblical creation “by measure, number and weight” required God to possess a fluency in arithmetic not always shared by the faithful. And so Bible arithmetic of the first millennium BC eventually became incomprehensible.
Today much of the astronomy, arithmetic, and music attributed to Classical Greece is documented to Semitic Babylon in the second millennium B.C. Mesopotamian fluency in calculation–in the age of Abraham, Isaac, and Jacob–already was 3000 years ahead of 16th century AD Europe. Babylonian exile in the sixth century BC made accessible to the Jews anything not already known.
With help of Philo of Alexandria I am reading Divine prescience as pre-scientific musical insight encoded in tribal mythology. Biblical emphasis on twelve sons as eponymous ancestors of twelve tribes who build an altar of twelve stones concerns twelve idealized “boundary markers” in a cyclic octave needed for Davidic musicology. The pattern was long symbolized in the concentric circles of the Babylonian astrolabe, adjusted monthly to correlate the watches with the varying lengths of day and night. Figure 2 strips all star data from van der Waerden’s reconstruction, and converts his base-60 water-clock weights (for full watches in the outer circle, and half and quarter watches in the inner circles) to base 10 arithmetic.
The astrolabe’s naked geometry and simple arithmetical doubling expose the idealist mind set which guided the evolution of Chaldaean sciences — converted to priestly ritual by Jewish ingenuity. Twelve ideal months of 30 fictitious days were superimposed on the heavens, and the ratio of longest night to shortest day, known to be about 3:2, was computed as 2:1, so that only music offered a “manipulable” example which conformed to these rounded measures.
Concentric circles anticipate Ezekiel’s “wheel in a wheel” as the throne of heaven. Within each circle maxima and minima water clock weights of 2:1 anticipate the ratio of cyclic octaves. But equal weight differences between successive months (reversing at the solstices in months III and IX) had to give way to proportional differences between successive semitones when this geometry was applied to music. Rational tonal arithmetic, cleverly mimed by Ezekiel, could anticipate this conceptual equality only via a slight but cumulative excess or deficiency, for in a cyclic octave of ratio 1:2 all equal divisions are defined by irrationals. Thus the Holy Land of a spiritual Israel had to be conquered conceptually in intricate warfare between the excess of primordial “giants” (products of 3) and the deficiency of human “weaklings” (products of 5) among rational numbers, and “weaklings” won only with Divine help in circumventing the lack of real number. Bible narrative brilliantly allegorizes every aspect of Diophantine approximation to modern Equal Temperament, and it does so with exhausting respect for numerical detail–making the Bible a priceless repository of tuning lore and its elementary number theory. The “unhewn” stones of Jewish altars are integers, meaning the natural or counting numbers to which harmonical theory normally was restricted, although its calculation demanded great fluency with reciprocal fractions. From the perspective of any reference pitch all integers except 2n necessarily “sinned” by “missing the mark” to some degree because octave doubling imposed, a priori, a universal matrix (“womb”) tied to integral powers of 2. Problems arose immediately with division into 2 equal parts (requiring the square root of 2) and 3 parts (requiring the cube root of 2).
Sensory intuition always fails at some level of arithmetical subtlety where least noticeable differences create a Platonic “no man’s land” of uncertainty. Greek, Jewish, and Chinese cultures are unanimous in accepting the comma of 80:81 as its convenient normative value. It is the difference between a “giant” wholetone of 8:9 (worth 204 cents in modern logarithmic measure) and a “human weakling” of 9:10 (worth only 190). They are approximations to the sixth root of 2 worth 200 cents, the value necessary to divide an octave 1:2 into six equal parts. How Davidic tuning theory reconciles this conflict becomes the central focus of Bible allegory And in the sixth century BC only God could have solved this problem numerically–although any geometer could map results to his own satisfaction for the astrolabe pointed the way.
For musician/philosophers of Philo’s temperament, tuning theory may always have been a contest in the soul between the potential tyranny of masculine intellection, considered mankind’s very highest power, and the relative benevolence of our feminine sensorium, where least noticeable differences create some measure of perceptual tolerance. Wisdom required a congenial mating between our own masculine concepts and feminine percepts, and sometimes rewarded it with the experience of transcendent beauty in “out of the body” adventures like Philo enjoyed when listening to the antiphonal singing of segregated sexes in his Alexandrine synagogue. I am trying here to articulate Bible harmonics in Philo’s spirit while paying closer attention to its computational logic.