Category: Autumn 2024

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How Geometries transformed Time Counts into Circles

Above: example of the geometry that can generate one or more circles,
equal to a linear time count, in the counting units explained below.

It is clear, one so-called “sacred” geometry was in fact a completely pragmatic method in which the fourfold nature of astronomical day and month counts allowed the circularization of counts, once made, and also the transmission of radius ropes able to make metrological metrological circles in other places, without repeating the counting process. This “Equal Perimeter” geometry (see also this tag list) could be applied to any linear time count, through dividing it by pi = 22/7, using the geometry itself. This would lead to a square and a circle, each having a perimeter equal to the linear day count, in whatever units.

And in two previous posts (this one and that one) it was known that orbital cycles tend towards fourfold-ness. We now know this is because orbits are dynamic systems where potential and kinetic energy are cycled by deform the orbit from circular into an ellipse. Once an orbit is elliptical, the distance from the gravitational centre will express potential energy and the orbital speed of say, the Moon, will express the kinetic energy but the total amount of each energy combined will remain constant, unless disturbed from outside.

In the megalithic, the primary example of a fourfold geometry governs the duration of the lunar year and solar year, as found at Le Manio Quadrilateral survey (2010) and predicted (1998) by Robin Heath in his Lunation Triangle with base equal to 12 lunar months and the third side one quarter of that. Three divides into 12 to give 4 equal unit-squares and the triangle can then be seen as doubled within a four-square rectangle, as two contraflow triangles where the hypotenuse now a diagonal of the rectangle.

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Quantification of Eclipse Cycles

Following on from the last post:
Given the many sub-cycles found in the Moon’s behavior, and the angle of its orbit to the Ecliptic, one would expect the eclipse phenomenon to be erratic or random but in fact eclipses repeat quite reliably over relatively fixed periods that were quantified symbolically by megalithic astronomy, within monuments and by the “sacred” numbers and geometries which encapsulate eclipse cycles, as with many other cycles.

An eclipse cycle repeats, to greater or lesser degree of accuracy, over an integer number of days or months. And because of a lack of conventional arithmetic or notation like our own in the megalithic, the practical representation of a cycle would be a raw count of days or months, using uniform measures, which could then be interpreted by them using (a) the rational fractions of whole unit metrology, (b) the factorization of a measured length by counting within using measuring rods or (c) using right-triangles or half-rectangles, which naturally present trigonometrical ratios; to compare different time cycles.

The Eclipse Year

The solar year (365.242 days) is longer than the lunar year of 12 lunar months (354.367 days) and we know that these, when counted in day-inches, gave the megalithic their yard of 32.625 (32 and 5/8) inches and that, by counting months in megalithic yards over one year, the English foot (of 12 inches) was instead the excess over a single lunar year of the solar year, of 12.368 lunar months. 0.368 in our notation is 7/19 and the megalithic yard is close to 19/7 feet so that counting in months cancels the fraction to leave one foot.

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Geometry 5: Easy application of numerical ratios

above: Le Manio Quadrilateral

This series is about how the megalithic, which had no written numbers or arithmetic, could process numbers, counted as “lengths of days”, using geometries and factorization.

My thanks to Dan Palmateer of Nova Scotia
for his graphics and dialogue for this series.

The last lesson showed how right triangles are at home within circles, having a diameter equal to their longest side whereupon their right angle sits upon the circumference. The two shorter sides sit upon either end of the diameter (Fig. 1a). Another approach (Fig. 1b) is to make the next longest side a radius, so creating a smaller circle in which some of the longest side is outside the circle. This arrangement forces the third side to be tangent to the radius of the new circle because of the right angle between the shorter sides. The scale of the circle is obviously larger in the second case.

Figure 1 (a) Right triangle within a circle, (b) Making a tangent from a radius. diagram of Dan Palmateer.

Figure 1 (a) Right triangle within a circle, (b) Making a tangent from a radius.

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Sacred Latitudes of the West

The post explores the geodetic concept of “Sacred Latitudes” and “Michael lines,” tracing historical and religious significance along these lines. It discusses saints’ locations, Columbus’s explorations, Templar disappearances, and maritime traditions. The narrative links these geographic lines to cultural, spiritual, and historical events, suggesting deeper connections in European and New World history.

above: the symmetrical Mary line of Europe to the Michael line (see figure) which correlated with places of significance to Mary. first published on Sunday, 19 September 2010

Adventures in Geodetic Imagination

At the heart of my second book, Sacred Number and the Origins of Civilization, lay the story of the Secret Men of the North, which followed the west-to-east path of a European Michael line (see figure 6), in the sense of the original invasion of the Middle East by northern Christianity, during the Crusades; ostensibly to re-take Jerusalem from a world of Islam that was itself invading Europe, from Spain, Sicily and the Levant.

Whilst working on a continuation of such a geodetic story, the concept of Sacred Latitudes emerged in which parallels of latitude might have some psycho-historical relevance, based on the original insight that, in the last century, “manifestations of Mary” have emerged, first in Garabandal in Spain and recently in Medjugorje, in Bosnia, that are on exactly the same line of latitude, 43 degrees and 12 minutes (43.2 degrees) (this brought to my attention by the late John D. Kirby’s studies of “Mary places”. He had organized tours from the UK to Medjugorje: see youTube video at end.)

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Tetraktys as plan of planetary harmony and the four Elements

Figure 1 The elimination of 5 as a factor in the harmonic mountain for 36 lunar years, resolved using matrix units of one tenth of a month and the limit 360 units.

In a previous post I explored the astronomical matrix presented in The Harmonic Origins of the World with a view to reducing the harmonic between outer planets and the lunar year to a single harmonic register of Pythagorean fifths. This became possible when the 32 lunar month period was realized to be exactly 945 days but then that this, by the nature of Ernest McClain’s harmonic mountains (figure 1) must be 5/4 of two Saturn synods.

Using the lowest limit of 18 lunar months, the commensurability of the lunar year (12) with Saturn (12.8) and Jupiter (13.5) was “cleared” using tenths of a month, revealing Plato’s World Soul register of 6:8::9:12 but shifted just a fifth to 9:12::13.5:18, perhaps revealing why the Olmec and later Maya employed an 18 month “supplementary” calendar after some of their long counts.

By doubling the limit from 18 to three lunar years (36) the 13.5 is cleared to the 27 lunar months of two Jupiter synods, the lunar year must be doubled (24) and the 32 lunar month period is naturally within the register of figure 1 whilst 5/2 Saturn synods (2.5) must also complete in that period of 32 lunar months.

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