Month: June 2022

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,

Book: Matrix of Creation

Sacred numbers arose from ancient man’s observation of the heavens, and represent the secrets of cosmic proportion and alignment. The ancients understood that the ripeness of the natural world is the perfection of ratio and that the planetary system–and time itself–is a creation of number. We have forgotten what our ancestors once knew: that numbers and their properties create the forms of the world.

A Mexican Triple Square at Teotihuacan

image: Ricardo David Sánchez for Wikipedia 

This article is from June 2012 on my past Matrix of Creation site where it was read 548 times at the time of last backup. It led to another article and so I repeat it here.

The late Hugh Harleston Jr revealed the famous Mexican pyramids at Teotihuacan as being the manifestation of a very advanced megalithic culture, the Olmec as a root culture for New World Megalithism of Mexico and South America (that led to the Maya nearly a millennium later, the Aztec and the Inca) . The Teoti city-building culture started around 200 BCE but it is not exactly clear when the great city started to be built or what it represented. However, Carnac’s megalithic geometries, its day-inch counting within monuments and evident use of circumpolar astronomy suggests important new clues in the interpretation of this sacred city’s design.

So I will open a new thread here to look at the Teotihuacas and the Maya. What better way to start than by immediately identifying the more formal part of the city as following the outline of a triple square, the geometry that in the old world linked the solar year to the eclipse year. Harleston’s web site had a very detailed site plan encoded in special units, called STUs or Hunabs which themselves appear derived from the metre but are also very close to the an Egyptian double royal cubits in length, in its Standard Geographical form (using John Neal’s classification). Harleston’s actual length for the Hunab is exactly the twelfth root of two metres, but that is another story.

Figure 1 Harleston’s time map view of Teotihuacan using his established unit measure of 1.0594 metres, based upon many distances between designed points in the complex. Note that the diagonal of the triple square passes through the two large pyramids that dominate the site, generally called Pyramid of the Sun and the Pyramind of the Moon. The triple square has been offset to the North to run through the end of the northerly viewing platforms of the plaza terminating the “solar highway” before the Pyramid of the Moon. [taken from Mayan Treasure]

The triple square is shown defining North with its diagonal but the sides follow the bearing of the “solar highway” (sometimes also known as The Path of the Dead), which is about fifteen and a half degrees east of north rather than the 18.43 degrees of a triple squares diagonal. However the diagonal runs through the two pyramids west of north by about three degrees minus two minutes even though the diagonal was NOT made to point directly North for reasons that may emerge. Instead, the principle axis of the triple square could be pointing to a circumpolar star at maximum eastern elongation and in fact, the behaviour of circumpolar stars could be responsible for the wide range of alignments found in Mexican pyramids over many centuries.

In the case of Teotihuacan, the triple square eems to point at the ex-pole star Thurban around 168 BCE, which could therefore be the date of foundation for the building of the city, since all else proceeds from this alignment of the road. Thurban, in this epoch, was rapidly moving away from the pole due to the precession of the north pole (and equinoxes), from its “reign” as the pole star when the Great Pyramid was built at Giza, whose northern “air shaft” pointed to Thurban. What could be happening is that when megalithism is practiced between 10-20 degrees latitude, the residual circumpolar region is shrunk but can nonetheless form part of the symbolic astronomy towards which megalithic structures are defined.

The long road structure at Teotihuacan pointed directly towards
the maximum elongation of Thurban to the east, in 170 BCE.

Figure 2 The Google Earth view of Teotihucan’s “ceremonial complex”, showing how its triple square pointed towards the circumpolar star Thurban in the epoch 170 BCE. The most significant astronomical reason for using a triple square is to represent the Metonic and Saros periods as a day count so that the pyramids of the Sun and Moon then lie on the metonic period of nineteen solar years whilst the triple square is both oriented to Thurban whilst signifying the controlling periodicity for Eclipses which is nineteen eclipse years. The day length of 0.365 metres would then point to the division of one day into 365 parts, a division quite natural for circumpolar astronomy with 365 days in a year.

At Lochmariaquer, the triple square pointing north was employed to count time in day-inches and even though the units seem different, the subject of such counts are the relations found between the solar and eclipse year. The epitome of this is found in the completing cycle of the sun and moon over nineteen years, called the Metonic period. The Saros period that dominates eclipse phenomena is nineteen eclipse years long, the difference between 19 eclipse years and 19 solar years exactly one lunar year of twelve lunar months.

Figure 3 The north facing triple square at Locmariaquer used the Tumulus d’Er Grah to mark a day-inch count for the Saros period, leaving an implicit metonic period count to the direct north.

Figure 3 The north facing triple square at Locmariaquer used the Tumulus d’Er Grah to mark a day-inch count for the Saros period, leaving an implicit metonic period count to the direct north.

At Locmariaquer (circa. 4500 BCE), its tumulus ended, in similar fashion, one Saros period from the starting point at Er Grah and this can be equated with the length of the triple square at Teotihuacan, making the diagonal equal to the length of the Metonic period of nineteen years. At this scaling, each day would be 365 millimetres long – showing how large megalithic monuments have to be if each millimeter is to represent just the four minutes that it takes for the earth’s rotation to catch up with the sun’s movement in a day, on the ecliptic.

The parallelism between Lochmariaquer and Teotihucan is striking as a mode of astronomical symbolism that naturally makes monuments of different epochs a unique statement within a continuing tradition that is best called Megalithism. Megalithism has its roots in astronomical symbolism and rituals strongly tied to astronomical periods, many of which have been sublimated or dropped within modern calendars.

Chapter 9: Quetzalcoatl’s Brave New World of Harmonic Origins of the World describes some of the number sciences of the Olmec and their derivative New World civilizations.

Introduction to my book Harmonic Origins of the World

Over the last seven thousand years, hunter-gathering humans have been transformed into the “modern” norms of citizens (city dwellers) through a series of metamorphoses during which the intellect developed ever-larger descriptions of the world. Past civilizations and even some tribal groups have left wonders in their wake, a result of uncanny skills – mental and physical – which, being hard to repeat today, cannot be considered primitive. Buildings such as Stonehenge and the Great Pyramid of Giza are felt anomalous, because of the mathematics implied by their construction. Our notational mathematics only arose much later and so, a different maths must have preceded ours.

We have also inherited texts from ancient times. Spoken language evolved before there was any writing with which to create texts. Writing developed in three main ways: (1) Pictographic writing evolved into hieroglyphs, like those of Egyptian texts, carved on stone or inked onto papyrus, (2) the Sumerians used cross-hatched lines on clay tablets, to make symbols representing the syllables within speech. Cuneiform allowed the many languages of the ancient Near East to be recorded, since all spoken language is made of syllables, (3) the Phoenicians developed the alphabet, which was perfected in Iron Age Greece through identifying more phonemes, including the vowels. The Greek language enabled individual writers to think new thoughts through writing down their ideas; a new habit that competed with information passed down through the oral tradition. Ironically though, writing down oral stories allowed their survival, as the oral tradition became more-or-less extinct. And surviving oral texts give otherwise missing insights into the intellectual life behind prehistoric monuments.

Continue reading “Introduction to my book Harmonic Origins of the World”

Introduction to my book Sacred Number and the Lords of Time

Modern mathematical science deals in precise measurements accurate to many decimal places. Simple integers rarely appear. the trend has recently been toward reforming our units of measure to get away from specific objects of reference and base them on universal physical properties. in ancient times people tried much the same thing, but, not having an arithmetical system, they used whole numbers of the same length (the inch) to measure astronomical time (the day). then, using geometry, they created their first objective measure, a megalithic yard, which expressed the difference between the solar and lunar year.

Their idea of sticking to whole numbers remains part of our number theory and, as Leopold Kronecker famously said, “God created the natural numbers, all else is the work of man.” The natural numbers or integers carry with them a sense of unity and design as to how they interact with one another. As symbols these number relationships affect the physical world and this suggests they provided a fundamental creative fabric for the universe. the constructions made by megalithic people present such a view. The monuments could only reflect a “heavenly pattern” (“as above, so below”) because the fabric of abstract whole number relationships appears to have been employed in a later weaving of planetary time cycles, which were then seen as the work of some god or gods (the demiurge) who surrounded the earth with numerical time ratios.

Continue reading “Introduction to my book Sacred Number and the Lords of Time”

Introduction to my first book, Matrix of Creation

My first book interprets the planetary system through pure number. The numbers involved in this interpretation are surprisingly simple and will be accessible to anyone holding a basic arithmetic education. From this approach we have gained substantial new insights into the realm of mythology, religious thought and what have become known as the Traditional Arts. We show that the solar system evolved from pure number and can no longer be thought of as an accident of nature.

It is also no coincidence that this work lies poised between the realm of mathematics and the world before numeracy. In the ancient world, numbers assumed god-like powers that were continually creating the world through stable numerical relationships. The core of this ancient science developed such a view naturally through simple astronomical observations, by counting events and regular movements in the night sky. This science was then artic­ulated as mythological stories, calendars, sacred geometry, musical theory and monumental architecture, such as the Great Pyramid and Stonehenge.

These artefacts, found in all ancient cultures, have remained obscure to the modern world because modern science has become too sophisticated to see the simple celestial relationships which demonstrate that the planetary system, including the Sun and Moon, hold to a particular design.

Continue reading “Introduction to my first book, Matrix of Creation”