This is a work in progress, helpful in understanding what has become a quite complex set of ideas, based on the work of others and now required to explain how the megalithic monuments were conducting a form of exact science by counting and analyzing the lengths of time between recurring celestial events.
This work is done within a strong cultural consensus that it was not until the Ancient Near East and other civilizations that exact sciences became at all possible, due to their innovation of the arithmetic numeracy that would lead eventually to modern science.
The process of understanding rescues significant aspects of the late stone age which our culture does not expect to exist, starting with their astronomical work and continuing with their metrological numeracy. I have had to learn on the job and can only help others do the same, should they see some truth in this work. It is a work of imagination and visualization which the stone age demonstrated in their art and artifacts.
Table of Contents

Introduction
 before Matrix of Creation (2002 & 4)
 before Sacred Number and the Origins of Civilization (2007)
 before Precessional Time and the Evolution of Consciousness (2011)
 before Sacred Number and the Lords of Time (2014)
 before Harmonic Origins of the World (2018)
 before Sacred Geometry: Language of the Angels (2021)
Introduction
Organizing ideas are the supercategory of Meaning in that, once they are grasped, whatever you do is informed by that Idea. This is different to the standard model of science where such biases are glossed over even though every scientists has organizing ideas but they are often only visible in what a person cannot see, because of the organizing ideas are at work in the background, in what we choose to see.
As I mentioned in my last post, science has sort of caught up with this in the work of Thomas Kuhn who coined the term paradigm to describe the process whereby scientists might change their organizing ideas but do this subject to a due process, much argument and finally, a paradigm shift (see above graphic)
This explains how waves of new worldviews that have swept over science. However, my own work cannot yet join with science because many of my organizing ideas are absent from both the standard model of science, and that of history.
Most of my work is about the megalithic, a prehistoric movement of near worldwide manifestations of large stone monuments. And the organizing ideas in this working list will be according to how my work has developed in time, since 1992. Because the megalithic people were astronomers, I am concerned with what they found in the sky that our own astronomy cannot see.
I had many previous organizing ideas, such as the teachings of Gurdjieff and Bennett, the precessional lore of Hamlet’s Mill, the astronomy of star groups and star names, the significance of etymology and comparative religion and degrees in electrical engineering, system science and computing.
before Matrix of Creation (2002 & 4)
You can read my Introduction here.
1. The Geometry of the Right Triangle (1992)
In 1992, my brother shared an astronomical geometry which he called the Lunation TriangleThe rightangled triangle within which the lengths of the two longer sides are the relative proportions of the solar and lunar years., which for him was the {5 12 13}, found as the Station Stone rectangle at Stonehenge, having sides 5 and 12 of a unit length 8 megalithic yards, all rectangles being made up of two identical contraflow triangles with a common hypotenuse. He noticed the 5 side could be divided into 3 parts below and 2 leftover, above. If an intermediate hypotenuse was formed to the base of 12, from the 3:2 point, it would be 12.368 units long. This is the number of lunar months in a solar year whilst 12 is the number of months in a lunar year. The fractional part of 0.368 is 7/19 months, so that in 19 years (the MetonicGreek: The continuous 19 year recurrence of the moon's phase and location amongst the stars. period), there are a whole number of 235 lunar months, bringing the sun and moon into a complex (in the mathematical sense) yet neardeterministic ensemble of repeated manifestations which are then tantamount to a calendar of their joint behavior as a whole – all linked to the illumination, by the sun, of the moon, seen as its phases during a lunar month. And of course I now see the significance of this in the light of all my organizing ideas, such that the harmonization of two or more things is a manifestation of wholeness, when phenomena are viewed as to their holistic nature.
Search for “lunation triangle“
2. The Normalization of Right Triangles (1994)
If one takes the excess of 0.368 (7/19) lunar months and divides this into the two longer lengths, the base of 12 and the diagonal above it of 12.368, then the triangle reveals its invariance structure, its “normal” form of 32.6: 33.6. The excess of 0.368 has been divided by itself to become the number one, that is 1 unit that is the natural unit. Every right triangle has a single normalised form of N:N+1, and in this case N = 32.6. Because the megalithic was forced to attend to numbers as lengths, then the difference in the two lengths led naturally to the notion of metrologyThe application of units of length to problems of measurement, design, comparison or calculation.. At Le Manio, where inches were used to count days over three years, the excess was 32.625 (32 + 5/8th”) inches and there was as yet no foot of 12 inches. By using the excess to then count lunar months, over three years, the excess was (what we now call) a yard of 36 inches so that, one foot of 12 inches was then the excess per solar yearFrom Earth: the time in which the sun moves once around the Zodiac, now known to be caused by the orbital period of the Earth around the Sun.. From this foot, the later metrology based upon variations of the English footThe standard prehistoric foot (of 12 inches) representing a unity from which all other foot measures came to be formed, as rational fractions of the foot, a fact hidden within our historical metrology [Neal, 2000]. was used, enabling simultaneous division and multiplication of any measurement in order to create rationality of measurements whilst also recognizing that specific numbers and ratios between time counts were regulating planetary time. see Ancient Metrology below .
Search: “N:N+1“.
3. The Numbers of the Planetary Matrix (1999)
The organizing idea of normalized Right Triangles, with sides whose counted lengths were the years of the sun and the moon, could also be applied to the geocentric cycles of the planets upon the stellar tapestry of the sky, and the visual phenomena of both the inner planets that move with the sun, and outer planets which loop when opposite the sun, with the earth inbetween. The units of measure used to count time evolved from counting the sun and moon but now the eclipticThe path of the Sun through the sky along which eclipses of sun and moon can occur, traditionally divided into the 365¼ parts of the solar year, each part then a DAY in angle rather than time. path of the planets became the focus rather than the horizon. However both of these were seen as circular so that these years of planetary motion (called synodicThe recurring time cycle of a given celestial phenomenon seen from the Earth.) were soon found to have integer lownumber resonances, or to express Fibonacci (Golden Mean) or musical ratios. The most telling are Venus which is locked into having five synods in eight solar years, Jupiter having two synods in 27 lunar months (a tone of 9/8) and Saturn having five synods in 64 lunar months (a semitone of 16/15).
Search = “planetary“
4. World Myths based upon Astronomy (2001)
At this point it became clear that this work on the megalithic was revealing the detail behind what Hamlet’s Mill had only glimpsed:
“Over many years I searched for where myth and science join. … Number gave the key. Way back in time, before writing was even invented, it was measures and counting that provided the armature, the frame on which the rich texture of real myth was to grow.”
Professor Giorgio de Santillana. Hamlet’s Mill, 1978.
Ancient texts have a peculiar association with numbers and with heavenly characters such as gods. Stories were the means for an oral society to store their knowledge about the sky amongst other things. The myth of Hephaistos (the smith) and Aphrodite are proto typical in that both were born through parthenogenesis (unnaturally) ways as a virgin birth to Hera, or Aphrodite from Zeus’s head. The megalithic work with the numbers of astronomical time seemed to provide a new key, from original findings appearing to have framed ancient stories in one way or another, in wonderful, creative allusions.
Search = “myth”.
before Sacred Number and the Origins of Civilization (2007)
5. Ancient Metrology as postMegalithic (2004)
Metrology has, in the last centuries, had a checkered career since academics have not been expecting the megalithic to have invented what became a single worldwide tradition for the civilizations of the ancient world. John Michell communicated the ancientness of it (AM 1983) by showing longer and shorter versions of ancient foot modules (of many geographic attributions) whilst his coworker John Neal saw that the ratios between these microvariations (of 176/175Ratio crucial to maintaining integers (see geometry lesson 2) between radii and circumference of a circle, and crucial to the microvariation of foot modules in ancient metrology. and 441/440) were all linked into modules that, at their root, were feet linked to the Greek module (of one foot) through small rational fractions such as 10/9 Assyrian, 32/35 Iberian, 24/25 Roman, 21/20 Persian, 8/7 Royal, 7/6 Russian – to name but a few. As usual, the ability to interrogate monuments and the celestial time periods in a new way, ancient metrology can be seen as an evolving reality – this best put in Heath 2021, in chapter 1 and appendix 2.
Search = “ancient metrology”.
6. Calculation using Powers of Prime Numbers {2 3 5 7 11} (c. 2002)
The metrology of my first book used the measures commonly available, like the foot, yard megalithc yard yet in meeting John Michell and John Neal on Lundy Island, it was obvious that Michell’s book Ancient Metrology was a good starting point. Travelling by air, I used the time to deconstruct the measures he was working with, that were, for each historicalgeographical foot, like the Roman, Greek, Persian, Royal, etc, each having two variations (Tropical and Northern, 175th part larger), in which primes were being exchanged between the original foot (e.g. 21/20 feet which is 3 x 7/4 x 5) and 176/175 (which is 16 x 11/ 25 x 7). Obviously with the twos, four reduces 16 to 4, the 25 becomes 125, the sevens and an eleven s added to give 3 x 4 x 11/125 which is 132/125 = 1.056 feet which I now know is the natural foot of the mean earth degree from 5152 degrees. This Northern measure then has the southern variant which Michell associated with Ethiopia at 1011 degrees. This eventually plays out in my posts on the Great Pyramid. I have started pulling back work on prime calculation and am developing types of notation of this. In essence, one is cancelling the primes when two fractions are multiplied in a simultaneous multiplying and dividing. The importance of this to megalithic studies only comes when one accepts that when numbers were lengths and not symbols, before the advent of a functional arithmetic, one could divide into a length to establish whether a prime in the set {2 3 5 7 11} divided into it exactly.
7. Counting Time in dayinches (2009)
It may seem obvious that my brother and I had seen time as lengths since the lunation triangle had numeric lengths of its longer sides (and 3rd sides) but, for some reason, we had not unified the notion of metrology and astronomical time except in that monuments symbolized time through number. In different ways, we both came to realize the practical import of monuments, that their representation of time as length was part of the counting of time. We had been “finding the cheese but failing to recognize the milk that made it”[Bortoft]. I began looking for monuments that were counting time with units rather than as symbols, after a holiday in Crete in a replacement hotel. That same summer, my brother accidentally came across a monument we had both seen in 2007, armed with a theodolite. The angle shown by a theodolite from a “sun gate” to a far stone edge was that of the lunation triangle relative to a kerb of stones: the Le Manio Quadrilateral. A simple survey using a long tapes revealed the length of the solar year in three inch units. Returning in 2010, to survey the monument, it became obvious that the actual count was over three years, in the dayinches I was looking for. Rather than a numerical symbol of the sun and moon, this was an actual counting, along the summer solsticeThe extreme points of sunrise and sunset in the year. In midwinter the sun is to the south of the celestial equator (the reverse in the southern hemisphere) and in midsummer the sun is north of that equator, which is above the geographical Equator). sun {3 4 5} triangle angle. The inch then appeared to have been the first unit of length, deployed to count in this way. In French the inch is a pouce or thumb’s width when pressed down.
Search = “counting time”.
2010: Reentrant Circles to Simulate the Ecliptic
The counted length of time in a line between similar celestial events can be made round to then represent the reality of angular motion around the Earth as the Centre. AT that point, a count of four solar years in 4 x 365.25 days equals 1461 and this made into a circle allows one to count days equal to 4 units so that the one left over is then the quarter day the earth takes after 365, to complete its orbit around the sun. That is, a 4year count in say dayinches could be used to create a counter simulation for a single solar year.
At Le Manio in Brittany, there are both 3 and 4 year counts diagonally across the rectangular monument but also evidence for an 82stone circle which would allow the lunar orbit to have been counted by moving a moon marker three stones every day since 82/3 is close to the 27.32122 day average period of the lunar orbit, again around the earth though tilted 5 degrees to the sun.
At Stonehenge, the Aubrey Circle of 56 post holes, once bluestones, has been interpreted to be a combined simulator of sun, moon and lunar nodes that indeed works to for example predict eclipses by tracking the nodes on the ecliptic since sun and moon on a node at the same time usually equals an eclipse event.
Search = “simulation”.
Text to follow.
2011: Sidereal Tracking of the Circumpolar Sky
Search = “circumpolar”.
Text to follow.
before Precessional Time and the Evolution of Consciousness (2011)
2012?: Ring Composition
Search = “ring composition”.
See my third Book Precessional Time and the Evolution of Consciousness
Text to follow.
2014:
before Sacred Number and the Lords of Time (2014)
before Harmonic Origins of the World (2018)
before Sacred Geometry: Language of the Angels (2021)