Sacred numbers within metrologically-quantified geometries.
It would require 3 and a bit diameters to wrap around the circle – the ratio of 3 and a bit diameters to the perimeter is known as “Pi”, notated by the Greek symbol “π”. Half of the diameter, from the circle’s center to its edge, is named its radius.
Continue reading “Geometry 1: π”This paper proposes that an unfamiliar type of circumpolar astronomy was practiced by the time Le Menec was built, around 4000 BCE. This observatory enabled the rotation of the earth and ecliptic location of eastern and western horizons to be known in real time, by observing stellar motion by night and solar motion by day. This method avoided stellar extinction angles by measuring the circular motion of a circumpolar marker star as a range in azimuth, which could then be equated with the diameter of a suitably calibrated observatory circle. The advent of day-inch counting and simple geometrical calculators, already found at Le Manio’s Quadrilateral, enabled the articulation of large time periods within Carnac’s megalithic monuments, the Western Alignments being revealed to be a study of moonrises during half of the moon’s nodal period. Le Menec’s Type 1 egg is found to be a time-factored model of the moon’s orbit relative to the earth’s rotation. This interpretation of Le Menec finds that key stones have survived and that the gaps seen in the cromlech’s walls were an essential part of its symbolic language, guiding contemporary visitors as to how its purpose was to be interpreted within the pre-literate megalithic culture.
Two key lengths are found at Le Manio and Le Menec: The first, of 4 eclipse years is a day-inch count of the Octon eclipse cycle; the second is a four solar year count that, with the first, forms a triangle, marked clearly by stones at Le Menec. The principles worked out at Le Manio appear fully developed in Le Menec’s western cromlech, including the use of an 8 eclipse year day-inch count, consequently forming a diameter of 3400 megalithic inches which equals in number the days in half a nodal period. The scaling of the Western Alignments is found to be 17 days per metre, a scaling naturally produced by the diagonal of a triple square geometrical construction. A single sloping length on the top of the central stone initiating row 9, indicates a single lunar orbit at 17 days per metre, a length of 1.607 metres. This control of time counting within geometrical structures reveals that almost all of Le Menec’s western cromlech and alignments express a necessary form, so as to represent a megalithic study of (a) circumpolar time as having 365 time units, (b) the moon’s orbit as having 82 times 122 of those units and (c) the variations of successive moonrises over most of a lunar nodal period of 18.6 solar years.
appended to
Sacred Number and the Origin of Civilisation
There used to be an interest in metrology – the Ancient Science of Measures – especially when studying ancient monuments. However the information revealed from sites often became mixed with the religious ideas of the researcher leading to coding systems such as those of Pyramidology and Gematria. The general effect has been that metrology, outside of modern engineering uses, has been left unconsidered by modern scientific archaeology.
Continue reading “A Brief Introduction to Ancient Metrology (2006)”
Ad Quadratum is a convenient and profound technique in which continuous scaling of size can be given to square shapes, either from a centre or periphery. The differences in scale are multiples of the square root
of two [sqrt(2)] between two types of square: cardinal (flat) and diamond (pointed).
In reviewing some ancient notes of mine, I came across an interesting comparison between the Golden Mean (Phi) and PI. They are more interesting in reverse:
A phi square (area: 2.618, side: 1.618) has grown in area relative to a unit square by the amount (area: 0.618) plus the rectangle (area:1 ). This reveals the role of phi’s reciprocal square (area: 0.384) in being the reciprocal of the reciprocal so that in product they return the unity (area: 1).
The ratios of ancient metrology emerged from the Megalithic innovations of count&compare: counting time as length and comparing lengths as the longest sides of right triangles. To compare two lengths in this way, one can take a longer rope length and lay it out (say East-West), starting at the beginning of the shorter rope length, using a stake in the ground to fix those ends together.
The longer rope end is then moved to form an angle to the shorter, on the ground, whilst keeping the longer rope straight. The Right triangle will be formed when the longer rope’s end points exactly to the North of the shorter rope end. But to do that one needs to be able to form a right angle at the shorter rope’s end. The classic proposal (from Robin Heath) is to form the simplest Pythagorean triangle with sides {3 4 5} at the rope’s end. One tool for this could then have been the romantic knotted belt of a Druid, whose 13 equally spaced knots could define 12 equal intervals. Holding the 5th knot, 8th knot and the starting and ending knots together automatically generates that triangle sides{3 4 5}.
