Month: June 2022

The 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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The Fourfold Nature of Eclipses

The previous post ended with a sacred geometrical diagram expressing the eclipse year as circumference and four anomalous months as its diameter. The circle itself showed an out-square of side length 4, a number which then divides the square into sixteen. If the diameter of the circle is 4 units then the circumference must be 4 times π (pi) implying that the eclipse year has fallen into a relationship with the anomalous month, defined by the moon’s distance but visually by manifest in the size of the moon’s disc – from the point of view of the naked eye astronomy of the megalithic.

In this article I want to share an interesting and likely way in which this relationship could have been reconciled using the primary geometry of π, that is the equal perimeter model of a square and a circle, in which an inner circle of 11 units has an out-square whose perimeter is, when pi is 22/7, 44.

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The Strange Design of Eclipses

We all know about solar eclipses but they are rarely seen, since the shadow of the moon (at one of its two orbital nodes) creates a cone of darkness which only covers a small part of the earth’s surface which travels from west to east, taking hours. For the megalithic to have pinned their knowledge of eclipses to solar eclipses, they would have instead studied the more commonly seen eclipse (again at a node), the lunar eclipse which occurs when the earth stands between the sun and the moon and the large shadow of the earth envelopes a large portion of the moon’s surface, as the moon passes through our planet’s shadow.

This phenomenon of eclipses is the result of many co-incidences:

Firstly, if the orbit of the moon ran along the ecliptic: there would be a solar eclipse and a lunar eclipse in each of its orbits, which are 27 and 1/3 days long.

Secondly, if the moon’s orbit was longer or shorter, the angular size of the sun would not be very similar. The moon’s orbit is not circular but elliptical so that, at different points in the lunar orbit the moon is larger, at other points smaller in angular size than the sun. This is most visible with solar eclipses where some are full or total eclipses, and others eclipse less than the whole solar disc, called annular eclipses.

Thirdly, the ecliptic shape of the moon’s orbit is deformed by gravitational forces such as the bulge of the earth, the sun and planets so that its major axis rotates. When the moon is furthest away (at apogee), its disc exceeds that of the sun. And when the moon is nearest to the earth (at perigee), its disc is smaller than that of the sun. This type of progression is called the precession of the lunar orbit where the major axis travels in the same direction as the sun and moon. This contrasts with the precession of the lunar nodes which also rotate (see later).

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The Fourfold Nature of Sun and Moon

A previous post explained the anatomy of the primary celestial cycles of the Sun and Moon. The “resting” part of these cycles are the winter solstice (opposite the summer solstice which was today) and the dark moon (which is coming in a week, after the waning half moon day before yesterday). In the resting phase, the cosmological origin is traditionally found, containing all that is to manifest but that is not yet expressed. In this respect, the Big Bang is the equivalent for modern thinking, as the origin of the entire visible and invisible universe seen via modern instrumentation and discoveries.

Life is somehow connected with our large Moon, without which there could have been no living planet. The form of life appears influenced by the moon and its conjunctions with different planets. And without (a) the tides, (b) the tectonic plates supporting continents, and (c) the tilt and spin of the earth; the earth would be static rather than actively supporting the necessary rhythms of Life. A primordial collision created these features of our earth and moon, since the cyclic archetypes provide an essential framework for living beings, to which their bodies are synchronized through circadian and behavioral rhythms.

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Time and the Midpoints of the Sun and Moon

Our two luminaries, the sun and moon, share a similar form-in-time, as the seasonal year and the monthly phases of the moon. The form they share is of two extremes of opposite character, and two midpoints between these.

The Solar Extremes: At the solar extremes, the sun rises high in midsummer day and rises to a much lower point in midwinter day, extreme points at which the sun moves very slowly day-by-day these hence called solstices from the Latin, “sun stands still”.

The Lunar Extremes: These are the full moon, meaning its face is completely illuminated by the sun, and the dark moon, when the moon stands by and in front of the sun and so its face is not illuminated but during a rare solar eclipse, the dark disk of the moon can be seen slowly crossing the sun’s face since the moon moves 12.368 times faster than the sun that defines each day.

The Solar Midpoints: These occur when the sun rises exactly east and sets directly west, everywhere on the earth. These moments are called Equinox because the length of the day then equals (in Latin: “equi”) and the length of the night (in Latin, “nox”). In the year these two equinoxes are called Spring, when light and heat from the sun are growing (waxing), and Autumn, when light and heat are diminishing (waning).

The Lunar Midpoints: Like the sun, these are exactly between its extremes, when exactly half the moon’s face is illuminated. In the morning, as the full moon approaches the sun, its gibbous (less-than-circular) face is waning until it reaches the point of half illumination by the sun. In contrast, the dark moon reappears as a crescent moon, pulling away from the sun setting in the evening.

The common factor between the midpoints of both sun and moon is that this is when time begins, in the sense that, at two equinoxes and at the two half-moons, (a) the sun’s daily sunrise on the horizon is moving fastest and (b) The sun’s illumination of the moon is changing most quickly. In both cases, this allowed the megalithic to accurately start and finish their counting of these time cycles of the year and the month. In both cases, midpoints could most accurately define the day on which an event occurred.

The following post takes this further.

The Integration of the Megalithic Yard

Above is a proposed geometric relation between Thom’s megalithic yard (2.72 feet), the royal cubit (1.72 feet) and the remen (1.2 feet). Alexander Thom’s estimate for it based on decades of work was refined from 2.72 to 2.722 feet at Avebury. If the origins of it are astronomical, then its value emerges from the Metonic period of 19 years which is 235 lunar months, making its value 19/7 feet or more accurately 2.715428571 (19008/7000) feet and this makes it 2.7 feet x 176/175 within ancient metrology. Another astronomical derivation is found at Le Manio as the difference between three lunar and three solar years, when counted in day-inches as 32 + 5/8th inches which is 2.71875 (87/32) feet. The megalithic yard of Thom’s first appraisal, of 2.72, probably arose from its megalithic rod (MR) of 6.8 feet since, the Nodal Period of the moon’s nodes take 6800 days which in feet would be 1000 MR. For a fuller explanation see my the appendix of my Language of the Angels book and my discussions of the Cumbrian stone circle, called Seascale by Thom and the only known example of a Type D flattened circle.

One can see that the Megalithic Yard is a tale of many variations, some of which might not consider how or why the megalithic might have come to adopt such a yard. I have come to trust simple integers and ratios to guide me to a possible megalithic pathway. To demonstrate, the above megalithic yard at Le Manio, of 32.625 inches is 29/32 of the English yard, and 32 lunar months (at Le Manio Quadrilateral) is 29 AMY. Such simple rationics is explored here.

My 2012 Post below discusses John Neal’s view of the megalithic yard
drawing on his ancient metrology.

John Neal makes a masterful job of considering the megalithic yard in the context of historical metrology, a metrology that he has managed to forge into a single conceptual scheme in which measures known to history from different lands all inter-relate.

Neal’s book, All Done With Mirrors, is one of the most fundamental and significant contributions to the late megalithic and ancient world understanding of numbers but to read it is no easy matter since he takes no prisoners and fully expects readers to resolve through calculation what he does not explicitly state. This makes his approach different to mine in which I try to present as easily a possible aids to the visualisation and registration of a pattern of facts. However, neither approach can really substitute for what one has to do for oneself in order to understand and John gave his “Secret Academy” idea the catch line “We can’t give it away” because of the often deafening silence with which his work is met.

The aim here is to give some workings based on Neal’s book, to give others a taste of what lies beneath what is written and also to further my own interests in the Megalithic Yard. Thom’s lack of metrological background led to both an original approach but also a disconnect to what is known about historical metrology. One particular mystery is how measures appear to have propagated unchanged across millennia.

Neal says on page 47:

Thom made a comparison of his Megalithic Yard with only one other known unit of measurement. This was the Spanish vara, the pre-metric measurement of Iberia, its value 2.7425 feet. Related measurements to the vara survive all over the Americas wherever the Spanish settled, from Peru to Texas. Although the vara is exactly one of the lengths of the m.y. the fact that it is divided into three feet makes this relationship uncertain. These feet are thought to be Roman but this belief is also unlikely, and they would appear to be related to the earlier Etruscan-Mycenaean units. This is a good example of an intermediate measure being thought to be related because of a similarity in length, and illustrates the importance of considering the sub-divisions when sourcing a measure.

How units of measure are divided and aggregated follows strict rules. If these rules did not exist then the system of metrology would have no inner structure as a system. We don’t expect measures to follow rules because today we simply measure things, and do everything else as a calculation following on from that. Metrology is an “ology” because it is a system of calculation that was used for building ancient structures when only limited calculation was possible.

Thus Neal can talk about the ancestry of the megalithic yard because the forensic tools are available through the system of metrology, in which a yard has three feet but that places the foot at close to the limits for a foot, at just over 0.9 feet, for the vara which would then be a yard of near Assyrian feet (9/10 feet). The Roman foot is far greater at 24/25 or 0.96 feet. A Mycenean foot would be 15/16 of the Roman which is in the region of 0.91 feet but the compounding to two errors, that the vara is a yard and that the Roman is its foot is the sort of confusion that only an exact metrology can ever recover from.

Neal continues:

Why he [Thom] did not analyze the Megalithic Yard in terms of what was already very well known of ancient metrology, must remain a mystery. And why, after the Megalithic Yard becoming the most scrutinized measure in the history of measure, nobody else has succeeded in doing so, is an even greater mystery. The very simple fact of the matter is, that if as Thom claimed from the beginning, the Megalithic Yard has 40 sub-divisions, then it is not a “yard” but a double remen [1.25], or 2 and 1/2 feet, and the “megalithic inch” is a digit! If the Megalithic Yard is taken to be 2.7272 feet, which is within Thom’s parameters for the value, the megalithic inch is .06818 feet, which is well within the range of the digits of all known ancient measurements. 16 of these digits are therefore one megalithic foot of 1.0909 English feet. This is a well-known measurement in ancient metrology, sometimes referred to as the Ptolemaic foot, and mistakenly, as the Drusian foot. His “fathom” of 2 m.y. is the historically well-known intermediate measurement, of a pace of 5 feet. Then, his “megalithic rod” [6.8 feet] is 6.25 Ptolemaic feet, which is also a measure known in antiquity as being 100th part of a furlong of 625ft or 1/8th part of the 5,000ft mile. The megalithic measures are not, therefore, peculiar to what is accepted as the megalithic arena, but are perfectly integrated with measuring systems found throughout the ancient world.

One should realize here that Neal is using the word “ancient” in an unquantified way because he believes metrology and other sciences of the numerical arts were inherited by the megalithic – a position that I question since there is no evidence for it. The megalithic could have generated a science of metrology in its earliest phase which then evolved into the greater system of many types of feet (Neal’s modules) since the older megalithic monuments have not been well studied – the British monuments being from a later phase. The early burial mounds, if found to have employed this fuller system, would prove Neal’s thesis. he continues,

Furthermore, the methods whereby Thom discovered [his megalithic measures], namely by careful surveys and comparisons, are the time honoured methods pioneered by Petrie and in no way are they a mistaken interpretation of the evidence, or invention.

The pattern of metrology comes in the ratios between types of unit. If a different foot is used these patterns remain constant and when metrology is used to analyse monuments then it this grammar of its usage that has remained invariant. This may seem to be geeky nonsense until metrology is resolved as a system within which the apparent babel of metrological signals become a direct communication from the past. Neal does not make this any easier by delivering a masterly analysis that prerequires most of the structural understandings to be in place.

Doth this profit a man? And is it simply a specialist field? For sure, by now, like Neal I am something of a specialist. It is true that no older language than metrology, other than language itself, has come down from such antiquity. If there is a truth behind claims (like mine) that the number sciences were sacred and contain mysteries concerning the spiritual world, metrology could be a philosopher’s stone. But when and how?

It is also true that this system of prehistoric thought is now a very powerful forensic tool for recovering their intended meaning of ancient sites and the types of measure found might reveal lines of metrological transmission in the ancient world. Anyone interested needs to apply it in practice.

This excerpt was first published on matrixofcreation.co.uk in 2012

Postscript

The only problem in adopting Neal’s full structure for ancient metrology is that it bears upon the type of metrological knowledge of the size and shape of the Earth, that lies behind the form of the Great Pyramid and other ancient buildings. But I have since seen, from the point of view of early megalithic astronomy, a much freer use of the ordinal numbers {1 2 3 4 5 6 7 8 9… etc} was applied to counts of astronomical time, using simple geometries of circles and right triangles within which a simpler metrology arose, as explained in Sacred Geometry: Language of the Angels. Another problem with Neal’s metrological grid of “Earth ratios” is that the modular range becomes so filled with versions of each foot that a given measurement can give one a false identification upon which a false interpretation or dead end can defeat the process.

This means that, earlier than the late megalithic, one is studying primitive ratios between astronomical measurements. This is clear at Crucuno Dolmen to Rectangle, where the month was coded as 27 feet but the day was the root Iberian foot of 32/35 feet. From this can be deduced an accurate approximation of the lunar month as 27 feet divided by 32 and multiplied by 35 giving 29.53 125 (27 x 35/ 32) Iberian feet. When one multiplies this month by 32 (the denominator) the result is 945 so that 945 days equals 32 lunar months. It is therefore true that the original three lunar year count (leading to the megalithic yard) is 36 months, two lunar years 24 months and two Jupiter synods are 27 lunar months. This forms a limiting octave of {18 24 27 36} which became Plato’s World Soul in his Timaeus cosmogony 6:8::9:12 only tripled [do1 fa sol do2} (see my Harmonic Origins of the World). From this the megalithic can be seen to naturally lead finding 27 lunar months between three loops of Jupiter, so that one Jupiter synod is 13.5 (27/2) months. Hence my reconstruction of the Pythagorean Music of the Spheres, as a mystery garnered from the megalithic.