Counting the Moon: 32 in 945 days

One could ask “if I make a times table of 29.53059 days, what numbers of lunar months give a nearly whole number of days?”. In practice, the near anniversary of 37 lunar months and three solar years contains the number 32 which gives 945 days on a metrological photo study I made of Le Manio’s southern curb (kerb in UK) stones, where 32 lunar months in day-inches could be seen to be 944.97888 inches from the center of the sun gate. This finding would have allowed the lunar month to be approximated to high accuracy in the megalithic of 4000 BC as being 945/32 = 29.53125 days.

Silhouette of day-inch photo survey after 2010 Spring Equinox Quantification of the Quadrilateral.

One can see above that the stone numbered 32 from the Sun Gate is exactly 32/36 of the three lunar years of day-inch counting found indexed in the southern curb to the east (point X). The flat top of stone 36 hosts the end of 36 lunar months (point Q) while the end of stone 37 locates the end of three solar years (point Q’). If that point is the end of a rope fixed at point P, then arcing that point Q’ to the north will strike the dressed edge of point R, thus forming Robin Heath’s proposed Lunation Triangle within the quadrilateral as,

points P – Q – R !

In this way, the numerical signage of the Southern Curb matches the use of day-inch counting over three years while providing the geometrical form of the lunation triangle which is itself half of the simpler geometry of a 4 by 1 rectangle.

The key additional result shows that 32 lunar months were found to be, by the builders (and then myself), equal to 945 days (try searching this site for 945 and 32 to find more about this key discovery). Many important numerical results flow from this.

Counting the Moon: Two equals 59 days

Above: Title Slide of my 2015 Lecture

Counting the lunar month has a deep history, reaching right into prehistory. Firstly, how does one find a phenomenon that gives a whole number of days. Its actual length is now known to be 29.53059 days, and to give a whole number just two lunar months gives 59 days, leaving just 1.8 days too little. But never mind, for the stone age this looks promising but how can one observe the moon at a fixed point and which phase is best to count.

Within a day, before or after the full moon, the Moon looks pretty full, changing little and offering no decisive moment between to count between two full moons. For this reason, a few prehistoric bones give clues to their method which involved counting days with some mark representing the Moon’s phase. This led to the sickle/cresent marks to left “(” or right “)” and between these a round mark “O” and dashes of dark or invisible moon “-“. These are what Alexander Marshack saw in the Albard Plaque, carved on a flat bone from a midden:

Figure 1 (left) Alexander Marshack investigating marked bones in Europe and a crucial interpretation of a 30,000 year old bone as a double lunar month of counting. From my 2015 lecture in Glastonbury about my work prior to Sacred Number and the Lords of Time in 2014.

Marshack demonstrated plausible evidence that consecutive day marks were used in the stone age, stylised to indicate lunar phase within a pattern recognizing that two lunar months formed a recurrent structure in time in a whole number of days, namely 58 days. The utility of the calendric device was that the cycle could be visualized as a whole, making the plaque an icon of both knowledge and meaning. This could be shared but also gave the possessor of this small bone, a power to predict when hunting is possible in lighter nights the light cycle of the moon. In addition, the moon’s phase locates the location of the sun and how many hours were left before the dawn. The bone was an overview of a daily process during most of which the moon is visible by night and day.

In following posts I look at many other ways to count the month, based on longer counts and also look at where in the lunar phases one can best start and stop counting.

You may like to watch my lecture at Megalithomania
(which starts with an ad you may skip).

Inside Time

There are two things we can count in this world, one is the number of objects on the Earth and the other is the number of time periods between events in the Sky.

photo: The Moon, with Jupiter and Mars, on 11th January 2018. (see end for interpretation)

Objects are counted in an extensive way, from one to an almost infinite number, the count extending with each addition (or multiplication) of a population.

Time periods appear similar but in fact they emanate from measurable recurrences, such as phases of the moon, and these derive from the behaviour of celestial objects as they divide into each other.

For instance, the unit called the day is created by the rotation of the earth relative to the Sun and the lunar month by its orbit around the Earth relative to the Sun, and so on.

Thus, time originally came from the sky. Furthermore, it largely came from the zodiacal band of stars surrounding the Earth within which the planets, Sun and Moon progress eastwards. The Earth’s own orbital motion is superimposed upon those of the other planets and the inner planets (Mercury and Venus) also appear to orbit a Sun that appears to orbit the Earth once a year.

The zodiacal band is naturally divided up into a number of constellations or stars and about three thousand years ago it became popular to follow the Sun throughout the year into 12 constellations whilst the Moon tends to create 27 or 28 stars (nakshatras) where the Moon might sit on a given evening. When the moon is illuminated by the sun, the primordial month has 29 1/2 days and twelve such in less than a year hence perhaps first defining the 12-ness of our months within the year.

All celestial cycles recur and this has formed our notion of eternity, that the sky world is made up of cyclic time rather than extensive time – every year being the same cycle seen again but then numbered so that they can be referred to as to when something happened in the past. The intensive reality above our heads is the polar opposite of extensive counting of time we see in History where numbered years and days within named months provide an unbroken continuum of time and famous people are said to have made history through their actions at a given date.

Whilst on Earth we might measure feet or meters between objects, above we effectively measure angles and angular rates to arrive at a synthesis between intensive and extensive time we call a calendar, an inevitable necessity for an organised civilization. And the moon and then the sun gave rise to the early calendars that naturally led to the arising of history as a human phenomenon. The oldest myths were connected to the sky, and were less than historical because the language of the sky had not been formalized in a way we would recognize.

Myths speak of eternal patterns that repeat rather than of existential events, on earth. The sun, moon and planets were seen as gods whose generative functions were hailed as emerging from their interactions with each other.

It has been widely assumed that “primitive” thought was premature, fantasizing planetary gods out of thin air with an as yet unripened grasp on logic and reason. But a simpler explanation, for the equation of planets with super beings, was their finding of special numbers linking the planetary cycles when these were counted and compared. This quantification of celestial time evolved from knowing the days in a year and a month, into a running calendar – of various sorts. The Maya Long Count is an example where numbers could interact through week lengths of 13 and 20 days to give a sacred calendar of 260 days whilst in historical times the 7 day week emerged, tied to Saturnian time. In this way, a calendar could add weeks adapted to societal events such as having a market every Tuesday.

This is a big subject where we have all the sky data but do not spend time understanding it. In the past, the sky was our constant companion between few man-made spaces. The sky sits within the horizon and so was like a primordial cave for humans and, the sky became an early teacher through its phenomena.

Jupiter and the Lunar Year

The lunar month is like the common denominator of what happens inside time. The sun illuminates the phases of the moon during its month so that, the month combines the movements of the moon and the sun to form a synthetic (combined) period of 29 1/2 days and twelve of these months fit inside the solar year as the lunar year of 12 1/3rd months (354.367 days). Jupiter has its own relationship to the sun in that, when the sun is opposite the moon, Jupiter describes a loop amongst the stars, and strangely there are 13 1/2 lunar months between loops (Jupiter’s synodic period of 398.88 days). 13 1/2 months divided by 12 months is the ratio 9/8, a musical whole tone.

But in the image above, of Jupiter and the Moon, the moon would be full if Jupiter was going to loop (as earth “overtakes” Jupiter on the “inside lane” – the planets inspiring ancient racetracks). Mars is another “outer planet” which loops in the same way and so Mars is also not looping.

But without understanding these matters, the picture cannot be understood. The phase of moon shows where the sun is. The planets have been in conjunction. If Venus had been present, then it has a 4/3 ratio to Mars but has to remain close to the sun to appear first as an evening star, then a morning star, in a cycle 8/5 years (584 days) long compared to Mars synod (between loops) of 780 days. Less accurate than Jupiter to the Lunar year, by a day. This is what I mean by being inside time, where all the celestial bodies have relationships to one another, when these are seen by us from earth.

This is how I started, with my first book Matrix of Creation. The musical ratios and their entrance into ancient stories was explored in Harmonic Origins of the Earth. How ancient humans counted time was discussed in Lords of Time and a unified treatment made in Language of the Angels. Used alongside archaeology, more can be understood about the prehistoric and early civilizations since astronomy was the first real subject for the human race.

Chartres 2: the harmony in its towers

In the previous post, the difference in height of the two towers was seen to have an exoteric and an esoteric meaning. Exoterically, the taller tower is sometimes called the sun tower, probably because the globe at its top (below its cross) is about 365 feet-as-days (hence representing the sun and its year). From this fact, the lower tower was considered lunar , since the lunar year is “not as long” and so less high. However, one must go to the top of the cross on the lower tower to achieve the height of 354.367 feet-as-days (hence representing the moon and its year).

This article presents a deeper meaning, that the difference in the full heights of the two towers represents the musical intervals of the synods of Saturn and Jupiter, relative to the lunar year: cunningly encoded within the full height of the solar tower as the Saturn synod of 378 feet-as-days, which is 16/15 of the lunar year. To have made the taller tower higher, to achieve the Jupiter synod, was impractical so that, instead, Jupiter was symbolized by the lunar year of 12 lunar months while Saturn was 12 “months” of 28 days, the 336-foot high globe of the moon tower, as shown below.

The two towers have a deeper meaning regarding the two gas planets Jupiter and Saturn, representing their synods to the lunar year. These musical intervals of 9/8 (tone = Jupiter) and 16/15 (semitone = Saturn), are different by 132/128, the ratio of the cross relative to the lunar tower.

To achieve this, the lunar tower had to be built shorter by 135/128 so that the top of its cross could ride 354.367 feet-as-days (of the lunar year), from the base, and the cross could then represent the ratio, 135/128 in height, between the two intervals the synods make with the lunar year.

The globe is at 336 feet-as-days, which is 12 times 28 days, a month belonging to the Saturnian year of the Goddess culture recorded in Greek Myth, whilst we know the Cathedral was a major shrine to the Goddess and Child found in the Crypt beneath this rebuilt upper form of the Cathedral. In Hesiod’s cosmogony, from the Archaic period, Saturn was the previous ruler over the sky, a culture which kept patriarchal cultural norms at bay*. Zeus-Jupiter was suppressed by the Goddess culture’s view of time and its year of 364 days, of exactly 52 (7-day) weeks.

That the archaic month of 28 days, times 135/128, is accurately the lunar month of 29.53 days, suggests a combined influence of the outer planets on the Moon’s synodic period with the Sun of 29.53 days.

NEXT: design of the west façade

*see my forthcoming Sacred Geometry in Ancient Goddess Cultures.

Interpreting Chartres
  1. the cosmic coding of its towers in height
  2. the harmony in its towers
  3. design of the west façade

Yet to come: the design of the Rose Window.

Numbers of a Living Planet: Preface

The image above is Kurma avatara of Vishnu, below Mount Mandara, with Vasuki wrapped around it, during Samudra Manthana, the churning of the ocean of milk. ca 1870. Wikipedia.

  1. Preface
  2. Primacy of low whole numbers
  3. Why numbers manifest living planets
  4. Numbers, Constants and Phenomenology
  5. Phenomenology as an Act of Will

Please enjoy the text below which is ©2023 Richard Heath: all rights reserved.

It is impossible to talk of a creation outside of the time and space of Existence, though from it, other dimensions can be inferred such as an “Eternity” visible in the invariances of numbers and structures. It is this higher dimensionality that leads to

  1. The recurrence of celestial time periods,
  2. The mental powers to recognise manifested patterns,
  3. The use of spatial geometries of alignment,
  4. The numerate counting of time,
  5. A phenomenology which is neither factual nor imaginary.

The quantification and qualification of Existence, adequately conducted, reveals harmonious structures within time and space, especially in the spacetime of our planetary system, when this system is as seen from our planet. The harmonious nature of our planetary system helped the late stone age to develop a large numerical and geometrical model of the world through counting astronomical recurrences. This model, which shaped ancient texts, implies that solar systems may have an inherent intelligence which makes them harmonious.

Harmony in a planetary system must therefore employ invariances already present in the number field, by exploiting the recurrent orbital interactions between planets and large Moons, this in a connected set of three-body problems. Before our exact sciences and instruments, prehistoric naked-eye astronomers could understand the planetary world by counting the duration of planetary time cycles: the subject my books explore. Through counted lengths of time, the megalithic age came to understand the invariances of the number field and so evolve an early and distinct type of numeracy. This numeracy lived on as the basis for the ancient Mysteries of the early civilizations, embodied in their Temples and in the Pythagorean approach to ordinal numbers and geometries, expressing the “number field” in two or three dimensions, areas and volumes. (see Sacred Geometry: Language of the Angels for an introduction to this)

That is, this early human numeracy naturally manifests within the maths governing rotational systems, this involving key transcendental* constants such as π, these regulating what is actually possible, mathematically, within dynamic planetary systems that are gravitational attractors of each other: these constants include pi {π}, √-1 {i}, e, and phi {φ}.  The first three { π, √-1, e} are surprisingly well-organized rotational frameworks making the behaviour of vectors relatively simple using geometry. For example, the lunar year of twelve lunar months has become strongly resonant with the two outer gas giants, Jupiter and Saturn. The Golden Mean (or Phi {φ})1 can be approximated by orbital ratios between planets through exploiting the Fibonacci number series2, most visibly in the orbital recurrence of Venus and the Earth, seen in the 8/5 {1.6} relationship of its synod* to the solar year. Phi φ is also expressed in living forms of growth, since growth is often based upon the present size of a living body and what it has previously eaten.  Fibonacci ratios are ideally suited to creating the “strange attractors” which can create stable patterns out of otherwise chaotic orbital interactions.

1 My use of curly braces is borrowed from a stricter world of set notation. It offers an ability to place groups of numbers, symbols and other non-grammatical element next to their grammatical context.

2 The series reinvented by Fibonacci uses addition of two previous number to create the next number. His version of that algorithm is {0 1 1 2 3 5 8 13 21 34 55 and so on}. These numbers are found within natural form of life, where such numbers can be generated from two previous states or when two counter rotating spirals of seeds will fill the surface of an egg shape with maximum packing. More on this later.

Through universal mathematical laws and constants, rotational and recurrent systems will effectively provide numerical shortcuts* (J.G. Bennett’s null-vectors) expressing Musical or Fibonacci ratios, and without those ratios being available, relationships within existence would be more complex, less synchronous, and truly accidental. Harmonic shortcuts have therefore given the planetary world a simplified mathematics when viewed from the surface of the earth, within the geocentric pattern of time. This synchronicity provided the stone age with a path towards a direct numerical understanding of time through phenomena (that is, a direct visual and countable phenomenology).

In this way, the megalithic cultures of prehistory found that the geocentric planetary system expressed numerical invariances (these already within the number field itself) thus making the time world of the sky unusually harmonious and intelligible. This contrasts with the now-popular modern notion that, while the solar system is a large and impressive structure, its origins come only from the mathematical laws of physics, these forever operating in a mechanical way. That is, the modern way-of-seeing planetary time is heliocentric and causal and this has hidden an ancient view, gained through the megalithic study of the phenomena in the sky using megaliths as large instruments with sightlines to the horizon events of sun and moon, to simply count of time-as-length and, evolve a very basic numeracy based upon numerical lengths (a metrology) and triangular geometries to compare lengths.

Megalithic methods employed the properties of circles, ellipses, squares, rectangles, and right triangles before the analytical geometry of Euclid, Greek math, or ancient near-eastern arithmetic. This was only possible because key parts of the mathematics of complex numbers, for example, are directly visible in the form of the right triangle and unit circle; as the natural form of two vectors: a length at a given angle (or direction) and another length at different angle gives access to ratios. A right triangle can therefore express two vectors of different length and differential angle, and this applies to a pair of average angular rates in the sky, without knowing the math or physics behind it all. If the two vectors are day-counts of time, then the right triangle can study their relationship in a very exact way. Such a triangle may also have been seen as the rectangle that encloses it, making the diagonal (vector), the hypotenuse of the triangular view.

The properties of the imaginary constant i (√-1) represents, through its properties, the rotation of a vector through 90 degrees. It is this that gives the right-angled triangle its trigonometric capacity to represent the relativity of two vector lengths. My early schoolroom discoveries concerning vectors in applied math classes, that right triangles can represent vectors of speed for example, was without any knowledge of the mathematical theory of vectors. This geometry enabled prehistorical astronomy to study the average planetary periods as vectors. That is, rotational vectors enabled the sky to be directly “read”, from the surface of the third planet, through simple day-counting, comparing counts with right triangles, and forming circular geometries of alignment to astronomical events found on the horizon; all without any of our later astronomical instrumentation, maths, or knowledge of physics.

Physics has not yet explained how the time constants between the planets came into a harmonious configuration, because it is unaware that this is the case. The mathematization of Nature, since the Renaissance, has hidden the harmonious view of geocentric planets and all preceding myths, cosmologies and beliefs were swept aside by the heliocentric world view (see Tragic Loss of Geocentric Arts and Sciences, also C.S. Lewis’s The Discarded Image).

The modern approach then emerged, of blind forces, physical laws and dynamic calculations. That is, while the simplifying power of universal constants is fully recognized by modern science (these having made maths simpler) the idea that these simplifications came to be directly reflected in the sky implies some kind of design and hence an intelligence associated with planetary formation.

Furthermore, modern way of seeing things cannot imagine that the megalithic could conducted an astronomy of vectors (using geometrical methods while not understanding why they worked) and that this empowered a simple but effective type of astronomy, without our mathematical or technical knowledge. This is an anachronistic procedural heresy for the history of Science and also for the present model of history, where science for us is the only science possible, evolving out of near-eastern civilization after the stone age ended.

Foundational myths of modern civilization are threatened by the notion that the world is somewhat designed by a higher intelligence. Until these subconscious conflicts of interest are overcome, prehistory will remain the prisoner of modernity where mysteries remain mysteries because we don’t wish to understand.

2. Primacy of low Whole Numbers

Astronomical Rock Art at Stoupe Brow, Fylingdales

first published 28 October 2016

I recently came across Rock Art and Ritual by Brian Smith and Alan Walker, (subtitled Interpreting the Prehistoric landscapes of the North York Moors. Stroud: History Press 2008. 38.). It tells the story: Following a wildfire of many square miles of the North Yorkshire Moors, thought ecologically devastating, those interested in its few decorated stones headed out to see how these antiquities had fared.

Background

Fire had revealed many more stones carrying rock art or in organised groups. An urgent archaeological effort would be required before the inevitable regrowth of vegetation.


Figure 1 Neolithic stone from Fylingdales Moor | Credit: Graham Lee, North York Moors National Park Authority.

A photo of one stone in particular attracted my attention, at a site called Stoupe Brow (a.k.a. Brow Moor) near Fylingdales, North Yorkshire.

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