Category: Prehistoric

5000-2000 BC: Quantifying astronomical time and geophysical space, using alignment, counting and geometry.

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.

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Counting Days and Lunar Months

Megalithic astronomy achieved far more than modern studies of their astronomy have thought possible. The role of the megalithic in seeding the later religious ideas, of subsequent civilizations, has therefore caused ancient religions to be seen as having no objective basis, and to be considered works of human imagination alone. To correct for this wrong perception and realize what ancient stories were actually about, a number of hybrid disciplines need to be recreated for the modern day. Astronomy, for example, needs to be related to whole number numeracy by seeing the metrological and geometrical possibilities possible to the (Stone Age) megalithic “monuments” and the heritage of later ancient buildings. When this is done, as I and other have, the conclusion is clear, that the megalithic understood not just the time cycles of the sun and moon but also those of the planets and the longer periods of “great time”, though counting time periods in terms of the smaller time periods such as the day and month. As this work proceeded many surprising results emerge hinging on whole number ratios.

My six books, written over twenty years, demonstrate that the planetary system constitutes a special type of system governed by relatively small numbers, the geocentric planets expressing invariant properties of the number field, especially harmony. And I suggest that modern astronomy may find that extraterrestrial intelligence exists on planetary systems similar to our own, in this numerical form given to time on earth, as a prerequisite for the complexity of the biosphere. The use of numbers for counting time in the megalithic, was therefore a further key process in the acquisition of important frameworks of meaning, attributed to civilization. And this is why my last book came to be called Sacred Geometry: Language of the Angels.

This significance of numbers to the cosmic process cannot be found until one tries to form an astronomy of time rather than of space. This appears true because the structuring of the world has more to do with the framework numbers provide in the fitting of “things” in space than the modern notion of cause and effect governed by laws, rather than by dimensionality. This can be illustrated by what types of things a framework enables, that cannot be achieved without that framework being extant.

As the megalithic counting of days and months developed, a whole tradition of geometry and numerical ratios were revealed to the prehistoric astronomers, as built in to the time body of geocentric astronomy. Alignments are found, centred upon megalithic observatories, to the horizon events of solsticial and equinoctal sunrises and setting, or to the lunar maximum and minimum standstills. The counting between successive events gave the length of time cycles. Only when one learns what the events are and their duration in days of their cycles, can a megalithic site can be properly interpreted as having counted time cycles, using a constant unit of length representing a day, or a month, to reveal a number of days or months within each cycle.

For exampe, Alexander Thom, a top engineer of the 20th century, noticed alignments between megaliths to lunar maximum events on the horizon, occurring every 18.618 solar years. He was once asked, what happened if the sky was cloudy and you missed the alignment. His response was the ancient astronomers must wait over eighteen years for another maximum; but Thom had not seen that counting between events, using a growing length of equal units per day allowed observatories to use counts between similar events and that this glued the whole enterprise of megalithic astronomy together.

And what we call the megalithic period, in some areas lasted millennia so that an enormous intellectual tradition based upon the numbers of time remains lost to the modern world unless one recognizes that, in the counting of time, lay a doorway into a large numerical scheme perfectly preserved within the planetary system itself. The heavy planetary bodies, orbiting the Sun and as seen from the Earth, are constant in their orbits and their consequent synods, with each other and the Earth. Whatever they are is frozen in eternity whilst this is experienced within time, as our present moment. The design of Time and the evolution of intelligence are therefore an artifact of a higher intelligence than our own, to which the ancient religions sought to connect, in one way or another.

But if one cannot recognize the significance of ancient time counting, then prehistory will be populated with mysteries and rather primitive ancestors.

Counting Days

A good example of counting days in a long cycle emerges from the fact that the nodal period of 18.618 years is 6800 days. It is obviously easier to have counted the days between a lunar maximum standstill and the next, and this means that, exactly halfway through the counting (3400 days) the lunar minimum will occur. It would be noticed that 17 divides into 6800 days to give seventeen periods of 400 days. And 400 days is very close to 399 days of the Jupiter synod, if one can count that between Jupiter’s loops against the stars as the earth “undertakes” the giant planet. So a 400 day-inch rope could be counted along seventeen times.

One can see how the Maya came to their Long Counting by merging all of their knowledge of cycles and letting them play out from a known starting point, hence creating a single calendar representing the geocentric planetary as a whole. Using that one can also go back in time and forward, to predict sky events.

Before the study of great time day-inch counting was developed by 4000 BCE to quantify the invariance between the sun and the moon , from which an integrated calendar could be created (or reconstructed from previous counting exercises) at Le Manio near Carnac Brittany – and also see geometry lesson 5. This explains how Robin Heath’s Lunation Triangle, implied by Stonehnege’s Standing Stone Rectangle, came into the megalithic vernacular by counting three solar and lunar years and comparing these, geometrically within right angled triangles, which are both trigonometric structures (relating to the circle) and proportional calculators in the metrological sense.

The three year triangle creates an excess of three solar years over the three lunar years, equal to the megalithic yard (MY) of 32.625 (32 and 5/8ths) day-inches which I call the Proto MY (see appendix 2 of Language of the Angels).

I made a film about this about ten years ago. Poor sound and picture quality for nowadays, but it gives interesting details of a possible cosmic “design”.

Counting Months

By counting in inches per day, 32 +5/8 day-inches is the excess, of 2.718 feet, a megalithic yard. This led to the idea of counting months using the new unit of lengths and, counting the twelve lunar months (24 half months) the remains of the solar year became an english foot, somewhat defining the foot of 12 inches as a new standard unit. To recap, using day-inches created an solar excess over 3 years of the megalithic yard and then counting a single year using megalithic yards generated the English foot.

If we allow the megalithic astronomers to have pondered such a sequence then the world of time seems to be giving new unit when counting using a simpler unit: inches per day giving the megalithic yard and megalithic yards per month giving the foot as the excess over a solar year. It was as if counting time was generating significant set of measures, some we still use today: the inch and foot. This continuity between the megalithic period, the ancient world and the modern world of measure implies that measures of length have a very long history of at least 6000 years! It also means that the ancient world somehow got these measures from the megalithic astronomers from whence, classical writings and historical discoveries show that civilized building practices built these measures into often sacred buildings so that religion were specuations based upon the measures and findings of megalithic astronomy.

When counting in months, many longer cycles are seen to recur over an integer number. The eclipse cycle called Saros, 10 days over 18 years long, is 223 lunar months because the sun and moon are conjunct at a solar eclipse at one of the two lunar nodes whilst, at a lunar eclipse, they must be on opposite sides of the earth. This makes the integer number of “moons” in that case.

In 19 solar year, there are 235 lunar months and 254 lunar orbits, because the number of lunar months in a single year is 12 and 7/19 lunar months so that after 19 years, seven extra lunar months is the excess over 19 x 12 (=228) lunar months and 228 + 7 = 235.

There are also 13 plus 7/19 lunar orbits in that period so that 19 x 13 (=247) orbits plus (again) seven more equals 254 orbits in 19 years, a period called the Metonic. And since, after (any) 19 year period, the orbits and the months are all integer, almost identical celestial circumstances repeat (continuously) over 19 years. That is all the permutations, patterns, or behaviors, are continuously expressed within nineteen years, over the Metonic period. In this sense “there is nothing new under the Sun” (Ecclesiastes 1:9).

One can count all sorts of celestial recurrence using measures to arrive at a strong tradition of sacred numbers and geometry pre-existing the historical period and informs its characteristic religious thinking. After my first book on the astronomy, I wrote Sacred Number and the Origins of Civilization for this reason. The megalithic and religious use of numbers was then explored in Sacred Number and the Lords of Time.

I had also found the lunar month was in musical harmonic resonance with the outer planets and even the other planets too in Harmonic Origins of the World – where I also had to explore rudimentary musical realities as these are also numerical. My latest, Sacred Geometry: Language of the Angels,