The Knowing of Time by the Megalithic

The human viewpoint is from the day being lived through and, as weeks and months pass, the larger phenomenon of the year moves the sun in the sky causing seasons. Time to us is stored as a calendar or year diary, and the human present moment conceives of a whole week, a whole month or a whole year. Initially, the stone age had a very rudimentary calendar, the early megalith builders counting the moon over two months as taking around 59 days, giving them the beginning of an astronomy based upon time events on the horizon, at the rising or setting of the moon or sun. Having counted time, only then could formerly unnoticed facts start to emerge, for example the variation of (a) sun rise and setting in the year on the horizon (b) the similar variations in moon rise and set over many years, (c) the geocentric periods of the planets between oppositions to the sun, and (d) the regularity between the periods when eclipses take place. These were the major types of time measured by megalithic astronomy.

The categories of astronomical time most visible to the megalithic were also four-fold as: 1. the day, 2. the month, 3. the year, and 4. cycles longer than the year (long counts).

The day therefore became the first megalithic counter, and there is evidence that the inch was the first unit of length ever used to count days.

In the stone age the month was counted using a tally of uneven strokes or signs, sometimes representing the lunar phase as a symbol, on a bone or stone, and without using a constant unit of measure to represent the day.

Once the tally ran on, into one or more lunar or solar years, then the problem of what numbers were would become central as was, how to read numbers within a length. The innovation of a standard inch (or digit) large numbers, such as the solar year of 365 days, became storable on a non-elastic rope that could then be further studied.

The 365 days in he solar year was daunting, but counting months in pairs, as 59 day-inch lengths of rope, allowed the astronomers to more easily visualize six of these ropes end-to-end, leaving a bit left over, on the solar year rope, of 10 to 11 days. Another way to look at the year would then be as 12 full months and a fraction of a month. This new way of seeing months was crucial in seeing the year of 365 days as also, a smaller number of about 12 and one third months.

Twelve “moons” lie within the solar year, plus some days.

And this is where it would have become obvious that, one third of a month in one year adds up, visually, to a full month after three years. This was the beginning of their numerical thinking, or rationality, based upon counting lengths of time; and this involved all the four types of time:

  1. the day to count,
  2. the month length to reduce the number of days in the day count,
  3. the solar year as something which leaves a fraction of a month over and finally,
  4. the visual insight that three of those fractions will become a whole month after three full solar years, that is, within a long count greater than the year.

To help one understand this form of astronomy, these four types of time can be organized using the systematic structure called a tetrad, to show how the activity of megalithic astronomy was an organization of will around these four types of time.

J.G. Bennett’s version of Aristotle’s tetrad.

The vertical pair of terms gives the context for astronomical time on a rotating planet, the GROUND of night and a day, for which there is a sky with visible planetary cycles which only the tetrad can reveal as the GOAL. The horizontal pair of terms make it possible to comprehend the cosmic patterns of time through the mediation of the lunar month (the INSTRUMENT), created by a combination of the lunar orbit illuminated by the Sun during the year, which gave DIRECTION. Arguably, a stone age culture could never have studied astronomical time without Moon and Sun offering this early aggregate unit of the month, then enabling insights of long periods, longer than the solar year.

The author (in 2010) at Le Manio Quadrilateral
where megalithic day-inch counting is clearly indicated after a theodolite survey,
over three years of its southern curb (to the left) of 36-37 stones.

The Manio Quadrilateral near Carnac demonstrates day-inch counting so well that it may itself have been a teaching object or “stone textbook” for the megalithic culture there, since it must have been an oral culture with no writing or numeracy like our own. After more than a decade, the case for this and many further megalithic innovations, in how they could calculate using rational fractions of a foot, allowed my latest book to attempt a first historical account of megalithic influences upon later history including sacred building design and the use of numbers as sacred within ancient literature.

The “output” of the solar count over three years is seen at the Manio Quadrilateral as a new aggregate measure called the Megalithic Yard (MY) of 32.625 (“32 and five eighths”), the solar excess over three lunar years (of 36 months). Repeating the count using the new MY unit, to count in months-per-megalithic yard, gave a longer excess of three feet (36 inches), so that the excess of the solar year over the lunar could then be known as a new unit in the history of the world, exactly one English foot. It was probably the creation of the English foot, that became the root of metrology throughout the ancient and historical world, up until the present.

The southern curb (bottom) used stones to loosely represent months from point P while, in inches, the distance to point Q’ was three solar years.

This theme will be continued in this way to explore how the long counts of Sun, Moon, and Planets, were resolved by the megalithic once this activity of counting was applied, the story told in my latest book.

Counting Perimeters

above: a slide from my lecture at Megalithomania in 2015

We know that some paleolithic marks counted in days the moon’s illuminations, which over two cycles equal 59 day-marks. This paved the way for the megalithic monuments that studied the stars by pointing to the sky on the horizon; at the sun and moon rising to the east and setting in the west. It was natural then to them to see the 12 lunar months (6 x 59 = 354 day-marks) within the seasonal year (about 1/3 of a month longer than 12) between successive high summers or high winters.

Lunar eclipses only occur between full moons and so they fitted perfectly the counting of the repetitions of the lunar eclipses as following a fixed pattern, around six months apart (actually 5.869 months, ideally 173.3 day-marks apart). The accuracy of successive eclipse seasons to the lunar month can then improve over longer counts so that, after 47 lunar months, one can expect an eclipse to have occurred about one and a half days earlier. This appears to be the reason for the distance between the megalithic monuments of Crucuno, its dolmen and and its rectangle, which enabled simultaneous counting of days as Iberian feet and months as 27 foot units, at the very end of the Stone Age.

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The Best Eclipse Cycle

The anniversary of the Octon (4 eclipse years in 47 lunar months) did not provide similar eclipses and so, by counting more than four, the other motions of the Moon could also form part of that anniversary. This is especially true of the anomalistic month, which changes the changes the apparent size of the Moon within its phase cycle, recreate the same type of lunar eclipse after nineteen eclipse years. This 18 year and 11 day period is now taken as the prime periodicity for understanding eclipse cycles, called the Saros period – known to the Babylonian . The earliest discovered historical record of what is known as the saros is by Chaldean (neo-Babylonian) astronomers in the last several centuries BC.

The number of full moons between lunar eclipses must be an integer number, and in 19 eclipse years there are a more accurate 223 lunar months than with the 47 of the Octon. This adds up to 6585.3 days but the counting of full moon’s is obviously ideal as yielding near-integer numbers of months.

We noted in a past post that the anomalistic month (or AM), regulating the moon’s size at full moon, has a geometrical relationship with eclipse year (or EY) in that: 4 AM x pi (of 3.1448) equals the 346.62 days of the eclipse year as the circumference. Therefore, in 19 EY the diameter of a circle of circumference 19 x 346.62 days must be 4 x 19 AM so that , 76 AM x pi equals 223 lunar months, while the number of AM in 223 lunar months must be 239; both 223 and 239 being prime numbers.

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Vectors in Prehistory 1

In previous posts, it has been shown how a linear count of time can form a square and circle of equal perimeter to a count. In this way three views of a time count, relative to a solar year count, showed the differences between counts that are (long-term average) differential angular motion between sun and the moon’s cycle of illumination. Set within a year circle, this was probably first achieved with reference to the difference between the lunar year of 12 months (29.53 days) and the solar year of 12 average solar months (30.43 days). Note that in prehistory, counts were over long periods so that their astronomy reflected averages rather than moment-to-moment motions known through modern calculations.

The solar year was a standard baseline for time counting (the ecliptic naturally viewed as 365.25 days-in-angle, due to solar daily motion, later standardized as our convenient 360 degrees). Solar and other years became reflected in the perimeters of many ancient square and circular buildings, and long periods were called super years, even the Great Year of Plato, of the precession of the equinoxes, traditionally 25920 years long! The Draconic year, in which the Moon’s nodes travel the ecliptic, backwards, is another case.

At Le Manio’s southern curb, the excess of the solar year over the lunar year, over 3 years, is 32.625 (32 and 5/8ths) day-inches, which is probably the first of many megalithic yards of around 2.72 feet, then developed for specific purposes (Appendix 2 of Language of the Angels). At Le Manio, the solar year count was shown above the southern curb, east of the “sun gate”, but many other counts were recorded within that curb, as a recording of many lengths, though the lunar year was the primary baseline and the 14 degree sightline above the curb aligned to the summer solstice sunrise.

Numbers-as-symbols, and arithmetic, did not exist. Instead, numbers-as-lengths, of constant units such as the inch, were generated as measurements of different types of year. To know a length without our numeric system required the finding of how a given number of units divided into a length, in an attempt to know the measurement through its observed factorization. This habit of factorization could start with the megalithic yard itself as having been naturally created from the sky, as Time. In this case, when the megalithic yard was divided into the three lunar year count of 1063.1 days, the result was 10.875 (10 and 7/8th) “times” 32.625 day-inches. which is one third of the megalithic yard, and is the number of day-inches of the excess for a single solar year.

The lunar year is the combined result of lunar motion, in its orbit, and solar motion along the ecliptic, of average of one day-in-angle per solar day. The lunar year is the completion of twelve cycles of the moon’s phases. The counting at Le Manio hinged upon the fact that, in three solar years there was a near-anniversary of 37.1 lunar months. This allowed the excess to be very close to the invariant form of the solar-lunar triangle which can be glimpsed for us by multiplying the lunar month (29.53059 days) by 32/29 to give 32.58548. (see also these posts tagged 32/29).

The excess of the solar year, in duration and hence in measured length, the 0.368 (7/19) lunar months (over 12), almost exactly equals the reciprocal of the megalithic yard (19/7 feet) so that, when lunar months are counted using megalithic yards, the excess becomes 12 inches which is 32/29 of 10.875 day-inches. From this it seems likely that the English foot and megalithic yard were generated, as naturally significant units, when day-inch counting was applied to the solar and lunar years.

The Manio Quadrilateral may have been like a textbook, a monumental expression of Megalithic understanding, originally built over the original site of that work or, carried from a different place in living memory. It presents all manner of powerful achievements, such as the accurate approximation of the lunar month as 29.53125 (945/32) days, the significance of the eclipse year, alignment to the solstice maximum and lunar minimum standstill, the whole number count over 4 years of 1461 days – then available as a model of the ecliptic, and a circular Octon simulator – and much else besides. This megalithic period preceded the English stone-circle culture initiated by Stonehenge 1 around 3000 BC but was somewhat contemporary with the Irish cairn and dolmen building culture. Metrology is presented near Carnac as a work-in-progress, based closely on astronomy rather than land measurement as such.

My work on the Megalithic tools-and-techniques can be read in my Lords of Time and in Language of the Angels, further considered as a tradition inherited by ancient world monumentalism. This post will be followed soon by more on vectors in prehistory.

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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