## Diary Notes

#### Grids of Squares & Flattened Circles

There is a common approach in ancient building based upon the establishment of a grid of squares, as a framework for the geometrical construction of buildings, from stone circles to Egyptian and Greek temples, to Roman and Orthodox Basilicas, and to Gothic and Enlightenment buildings, plus in Indian temples. Just as one builds foundations, all that is inside a building is controlled by numerical ideas. I have therefore published some work I did to show how flattened circle, in megalithic times, could have used what came to be Egyptian methods for laying out building works and to not always depend on the ropes and stakes of the free style geometrical construction which led to analytical geometry, compass and straight edge.

#### Peat Fires revealing Rock Art

There have been a number of large peat moor fires in England and one of these in North Yorkshire revealed a few megalithic sites. I have republished my own interpretation of a significant pattern made on a major flat stone as part of an egg-shaped stone circle. The egg can be seen in the work of Alexander Thom as based on the near-Pythagorean triangle with sides {17 17 24.0416}. When Thom’s plan is laid over that of the excavation (Rock Art and Ritual by Brian Smith and Alan Walker), one can see there is a close fit to the excavated site. When the egg is expanded to fit the line drawn by the excavators, the units of the geometry are 1/2 foot (6 inches) so that 17 = 102 inches (8.5 feet), 24 = 144 inches (12 feet) and 12 = 72 inches (6 feet), possible by overlaying different plans, one with the scale shown!

Geometry of the stone egg where the rock art was found on one of its stones. Note the alignment of the egg’s axes to the cardinality of the sun’s solstice extremes at that latitude.

#### Chalk Drums to generate pi

When I joined the Prehistoric Society for a year, an article about megalithic chalk drums being found with strange decoration which may depict PI, since their diameter allows rolling them to count out a given type of foot measure. This may be why some are not carved because they were heavily used while others could have been metrological standards, not as rods but as cylinders that do not required end-to-end counting but continuous counting, providing one can count!

#### Angkor Wat as west-facing observatory

I have been doing work on Angkor Wat, something I never got around to after a first introductory post about nested squares there. Both Lords of Time and Language of the Angels were to have included it. Eleanor Mannikka, spent 20 years on a numerical analysis of its architecture and there is an amazing set of French plans by G. Nafilyan. I looked at the temple as an observatory, since it looks west as aligned towards the sun and moon setting on the horizon, which appears to have been part of its intended use. Settings are easier to work with that risings, since there is plenty of warning of settings as sun or moon slowly travel every day towards the western horizon.

## Angkor Wat: Observatory of the Moon and Sun

above: Front side of the main complex by Kheng Vungvuthy for Wikipedia

In her book on Angkor Wat, the Cambodian Hindu-style temple complex, Eleanor Mannikka found an architectural unit in use, of 10/7 feet, a cubit of 20/21 feet (itself an outlier of the Roman module of 24/25 feet, at 125/126 of the 0.96 root Roman foot).

She began to find counted lengths of this unit, as symbols of the astronomical periods (such as 27 29 33) and of the great Yuga time periods proposed within Vedic mythology. Hence Mannikka’s title of Angkor Wat: Time, Space, and Kingship (1996). Whilst the temple was built by the Khymer’s greatest king, their foundation myth indicates the kingly line was adopted by a matriarchal goddess tradition.

#### Numerically Symbolic Monuments

Interpreting a monument using its metrology can be contentious. For example, in the megalithic period the established position has been that there was no metrological tradition and, to be found proposing one can cause your work to be ignored if not exiled from peer-reviewed journals, as was eventually the case with Prof. Alexander Thom.

At Teotihuacan, Japanese professor Saburo Sugiyama proposed an architectural unit of 83 centimeters was used, since the monumental complex would then clearly have numbers of these units corresponding to significant celestial periods, as if periods had been counted out within the City: the eclipse half year of 173 days at the Moon Pyramid, the Tzolkin of 260 days at the Sun Pyramid, and the Venus synod of 584 days at the Quetzalcoatl pyramid’s compound. More such day lengths and a well-known harmonic matrix were also seen in my Harmonic Origins of the World.

Sugiyama did not reply to my message that his Teotihuacan Measuring Unit of 0.83 meters was the 2.72 foot length of Thom’s megalithic yard, implying some connection between Olmec/Maya Mexico and megalithic Europe. This was probably not welcome. Wikipedia’s editors of the “Megalithic Yard” page also objected to my mentioning this since it was I that had noticed this correspondence.

Over a 20 year period, Eleanor Mannikka found a numbers that were symbolic** or actual long counts of the solar and lunar years. In her thesis, these numbers were embodied as a ritual background for visiting pilgrims, whose steps corresponded to numbers – the megalithic yard being a metrological step of 2.5 feet. Her eventual counts emerged by a protocol that skipped thresholds, ran beyond, or started before a threshold, the counts were being human walkways but also excellent surfaces for doing accurate metrology.

**Her rule-based system that revealed numbers may well be a later function of the eventual monument, made to correspond with the numbers found in Hindu epic stories, since these are lavishly illustrated within extensive bas-reliefs, visible to pilgrims, depicting major Hindu myths. Statues of the gods punctuate the building’s many walkways to express the Indian practice of parikrama, of circumnavigating holy sites (such as around Mount Kailash or the great dome of Sanchi).

#### The Temple as AN Observatory

The symbolic use of numbers could only have become established through cosmic measurement in which astronomy (before our own) counted the actual numbers of days or months between repeating cycles of celestial alignment, and the differences and ratios between these. That is, ancient symbolic numbers originated in the Sky, where number-laden events measured in days or months generate whole numbers that were only then held to be sacred. One might think Angkor Wat too recent to have been constructed to suit this ancient sort of astronomical work. But the temple’s explicit orientation, to the west, was suited to just that. This made the temple perfect for observing and counting all sorts of time-counts, repeating measurements made millennia before using megalithic monuments.

That is, Angkor Wat is a current-era megalithic monument to the sky gods, these illustrated using the famous tableau of Vedic and later Indian myths.

The sun and moon set to the west**, each having a maximum range north or south of west. The sun at winter and summer solstice defines a fixed range within the solar year, depending on the latitude of a given site. In contrast, the Moon ranges over the horizon when setting over one orbital period of 27 1/3rd days. However, the moons orbit is skew to the sun’s path (ecliptic) so that the moon rises above and below, except at its nodes where eclipses can take place. These nodes move backwards so that the moon’s range on the horizon expands and contracts over 18.618 solar years.

**Looking west is very convenient since the sun or moon approach the horizon rather than suddenly appearing as they do in the east.

As a consequence, there are seven key points on the western horizon, the maximum standstill to north and south, the minimum standstill to north and south, the solstice extremes of the sun in summer (North) and winter (South), plus the equinox sunrise**. It is possible to calculate these alignments for the virtually flat terrain of Cambodia as in Figure 2.

**The Equinox sunset is a very exact point to measure since the sun appears to move rapidly on the horizon, between sunsets.

Figure 2 The alignments of Sun and Moon to the west (Left) around 1000 CE at the latitude of Angkor Wat using the Processing.org framework.

The notion of alignments seems to throw light upon the highly specific elements of Angkor Wat (see figure 3), if these alignments were viewed from the north eastern and south eastern corners of the raised temple enclosure.

Figure 3 Viewing the alignments of Sun and Moon, to the west (on Left), from the eastern corners.

There is a natural north-south symmetry, where the alignments to the solstice cross in the pream cruciform (see figure 4). The punctuation of the towers of the temple, seen from the eastern corners, would provide landmarks to calibrate the movement of (a) the sun in the year and (b) the moon within the lunar orbit, as the 18.6 year nodal movement expands and contracts the lunar range.

Figure 4 The Alignments seen within the plan of the temple complex.

The cruciform terrace outside the walls and nine fold cruciform within, could relate to the crossings of alignment and the periodicity of these cycles which would be countable in days using units of length.

The maximum moon alignments near 1000 BCE were 30 north and south or west, and one can plot those alignments over a flat Cambodia to the boundaries with Thailand which are, in contrast, significantly mountainous (see dark green areas at end of yellow alignments in Figure 5.

#### Parallels with the Megalithic near Carnac

The basic idea of such an observatory is a stone square instead of a stone circle. Alignments can be built-in, between back-sight observation points and fore-sight marker stones, marking the horizon location of an extreme event such as solstice. An observatory location can also look to an horizon event for which a distinct natural feature exists on the horizon, from that location. The stone perimeters of Carnac, called cromlechs, are various shapes but at Kerlescan, the cromlech is a rounded square, where the western perimeter is concave towards the east. That is, it faced rising events on the eastern horizon instead of setting events to the west.

Otherwise, the “setup” is conducive to the observation of the sun and moon possible at Angkor Wat. Below I show how the observatory could work for the epoch 4000 BCE. The red lines are solar extremes and green lines are lunar maximum and minimum extremes. Equinoctial events at Spring and Autumn complete the inherently seven-fold nature of such phenomena.

## 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.