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.

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.

Continue reading “The Fourfold Nature of Sun and Moon”

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.

Geometry 6: the Geometrical AMY

By 2016 it was already obvious that the lunar month (in days) and the PMY, AMY and yard (in inches) had peculiar relationships involving the ratio 32/29, shown above. This can now be explained as a manifestation of day-inch counting and the unusual numerical properties of the solar and lunar year, when seen using day-inch counting.

It is hard to imagine that the English foot arose from any other process than day-inch counting; to resolve the excess of the solar year over the lunar year, in three years – the near-anniversary of sun and moon. This created the Proto Megalithic Yard (PMY) of 32.625 day-inches as the difference.

Figure 1 The three solar year count’s geometrical demonstration of the excess in length of 3 solar years over 3 lunar years as the 32.625 day-inch PMY.

A strange property of N:N+1 right triangles can then transform this PMY into the English foot, when counting over a single lunar and solar year using the PMY to count months.

The metrological explanation

If one divides the three-year excess (here, the PMY) into the base then N, the normalized base of the N:N+1 triangle. In the case of the sun and moon, N is very nearly 32.625, so that the lunar to solar years are closely in the ratio 32.625:33.625. Because of this, if one counts 

  • months instead of days,
  • using the three-year excess (i.e. the PMY) to stand for the lunar month,
  • over a single year,

the excess becomes, quite unexpectedly, the reciprocal of the PMY;

One has effectively normalized the solar year as 12.368 PMYs long. This single year difference, of 0.368 lunar months cancels with the PMY; the 0.36827 lunar months becoming 12.0147 inches. Were the true Astronomical Megalithic Yard (AMY of 32.585 inches) used, instead of the PMY, the foot of 12 inches would result. Indeed, this is the AMYs definition, as being the N (normalizing value) of 32.585 inches long, unique to the sun-moon cycle. The AMY only becomes clear, in feet, after completion of 19 solar years. This Metonic anniversary of sun and moon over 235 lunar months, is exactly 7 lunar months larger than 19 lunar years (228 months).

But this is all seen using the arithmetical methods of ancient metrology, which did not exist in the megalithic circa 4000BC. Our numeracy can divide the 1063.1 day-inches by 32.625 day-inches, to reveal the AMY as 32.585 inches long, but the megalithic could not. Any attempt to resolve the AMY in the megalithic, using a day-inch technology***, without arithmetical processes, could not resolve the AMY over 3 years as it is a mere 40 thousandths of an inch smaller than the PMY. So arithmetic provides us with an explanation, but prevents us from explaining how the megalithic came to have a value for the AMY; only visible over long itineraries requiring awkward processes to divide using factorization. However, by exploiting the coincidences of number built in to the lunar and solar years, geometry could oblige. 

***One can safely assume the early megalithic resolved
eighths or tenths of an inch when counting day-inches.

The geometrical explanation

In proposing the AMY was properly quantified, in the similarly early megalithic cultures of Carnac in France and the Preselis in Wales, one must turn to a geometrical method

  1. One clue is that the yard of 3 feet (36 inches) is exactly 32/29ths of the PMY. This shows itself in the fact that 32 PMYs equal 29 yards.
  2. Another clue is that the lunar month had been quantified (at Le Manio) by finding 32 months equalled 945 day-inches. By inference, the lunar month is therefore 945 day-inches divided by 32 or 945/32 (29.53125) day-inches – very close to our present knowledge of 29.53059 days.

From point 1, one can geometrically express any length that is 32 relative to another of 29, using the right triangle (29,32). And from point 2, since the 945 day period is 32 lunar months, as a length it will be in the ratio 29 to 32 to a length 32 PMYs long, the triangle’s hypotenuse.

Point 1 also means that 32 PMY (of 32.625 inches) will equal 1044 inches, which must also be 29 x 36 inches, and 29 yards hence handily divides the 32 side of the {29 32} right triangle into 29 portions equal to a yard on that side. One can then “mirror the right triangle about its 29-side so as to be able to draw 29 parallel lines between the two, mirrored, 32-sides, as shown in figure 1. The 945 day-inch 29-side which already equals 32 lunar months (in day-inches), now has 29 megalithic yards in that length, which are then an AMY of 945/29 day-inches!

Figure The 29:32 relationship of the PMY to the yard as 32 PMY = 29 yards whilst 32 lunar months (945 days) is 29 AMY.

Comparing the two AMYs and their necessary origins

Using a modern calculator, 945 divided by the PMY actually gives 28.9655 PMY and not 29, so that 945 inches requires a unit slightly smaller than the PMY and 945/29 gives the result as 32.586 inches, which length one could call the geometrical AMY. This AMY is 30625/30624 of the AMY in ancient metrology which is arrived at as 2.7 feet times 176/175 equal to 32.585142857 inches. By implication therefore, the ancient AMY is the root Drusian step whose formula is 19.008/7 feet whilst the first AMY was resolved by the megalithic to be 945/29 inches.

This geometrical AMY (gAMY?) obviously hailed from the world of day-inch counting, which preceded the ancient arithmetical metrology which was based upon fractions of the English foot. The gAMY is 32/29 of the lunar month of 29.53125 (945/32) day-inches, since 945/32 inches × 32/29 is 945/29 inches.

Using ancient metrology to interpret the earliest megalithic monuments may be questionable in the absence of a highly civilised source which had, in an even greater antiquity, provided it; from an “Atlantis”. In contrast, the monumental record of the megalithic suggests that geometrical methods were in active development and involved less sophisticated metrology, on a step-by-step basis.  From this arose the English foot which, being twelve times larger than the inch, could provide the more versatile metrology of fractional feet, to provide a pre-arithmetical mechanism, to solve numerical problems through geometrical re-scaling. This foot based, fractional metrology then developed into the ancient metrology of Neal and Michell, which itself survived to become our historical metrology [Petrie and Berriman].

The two types of AMY, geometrical and the metrological, though not identical are practically indistinguishable; the AMY being just over one thousandths of an inch larger. The geometrical AMY (945/29 inches) is shown, by figure 2, to be geometrically resolvable, and so must have preceded the metrological AMY, itself only 40 thousandths of an inch less than the PMY.

The two AMYs, effectively identical, reveal a developmental history starting with day-inch counting, and division of 945 inches by 29 was made easy by exploiting the alternative factorisation of 32 PMV as 36 × 29 yards using geometry. The AMY of ancient metrology was the necessary rationalization of 945/29 inches into the foot- based system.

Bibliography for Ancient Metrology

  1. Berriman, A. E. Historical Metrology. London: J. M. Dent and Sons, 1953.
  2. Heath, Robin, and John Michell. Lost Science of Measuring the Earth: Discovering the Sacred Geometry of the Ancients. Kempton, Ill.: Adventures Unlimited Press, 2006. Reprint edition of The Measure of Albion.
  3. Michell, John. Ancient Metrology. Bristol, England: Pentacle Press, 1981.
  4. Neal, John. All Done with Mirrors. London: Secret Academy, 2000.
  5. —-. Ancient Metrology. Vol. 1, A Numerical Code—Metrological Continuity in Neolithic, Bronze, and Iron Age Europe. Glastonbury, England: Squeeze, 2016 – read 1.6 Pi and the World.
  6. —-. Ancient Metrology. Vol. 2, The Geographic Correlation—Arabian, Egyptian, and Chinese Metrology. Glastonbury, England: Squeeze, 2017.
  7. Petri, W. M. Flinders. Inductive Metrology. 1877. Reprint, Cambridge: Cambridge University Press, 2013.

pdf: Synchronicity of Day and Year with the Lunar Orbit

This document was prepared by Richard Heath as a letter for Nature magazine and submitted on 14th April 1994 but remained unpublished. For readers of the Matrix of Creation (2nd ed, Inner Traditions Press, 2004) it marks the discovery of a unit of time proposed and named the Chronon, as being 1/10000th of the Moon’s orbit and also the difference between the sidereal and tropical day of the Earth. The paper also documents a discovery made, with Robin Heath, later to be documented in his books: that one can divide up the solar year by its excess over the eclipse year to reveal an 18.618:19.618 ratio between these years, and many other interesting numerical facts not mentioned in this place. The puzzle here is a connection between the rotation of the Earth, the solar year and the precession of the Moon’s orbit which (a) may be explainable by science (b) appears to have puzzled Megalithic astronomers and (c) should puzzle us today.

Fibonacci in Jupiter’s 12-fold Heaven

The Fibonacci series is an ideal pattern, widely found within living systems, in which the present magnitude or location of something is the product of two previous magnitudes or locations of it. The next magnitude will again be the sum of the last two magnitudes in what is, an algorithmic pattern producing approximation to the Golden Mean (designated by the Greek letter φ,’phi’). As the series gets larger, the ratio (or proportion) between successive magnitudes will better approximate the irrational value of φ = 1.618033 … – which has an unlimited fractional part whilst the virtue of the Fibonacci numbers within the Series is that they are integers forming rational fractions.

Jupiter taken by the Wide Field Hubble Telescope by NASA, ESA, and A. Simon (Goddard Space Flight Center)
Continue reading “Fibonacci in Jupiter’s 12-fold Heaven”