Author: Richard Heath

Why numbers manifest living planets

above: The human essence class related to four other classes in J.G. Bennett’s Gurdjieff: Making a New World. Appendix II. page 290. This systematics presents the human essence class which eats the germinal essence of Life, but is “eaten” by cosmic individuality, the purpose of the universe. The range of human potential is from living like an animal to living like an angel or demiurge, then helping the cosmic process.

  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.

The human essence class is a new type of participation within the universe where the creation can form its own creative Will, in harmony with the will that creates the universe. The higher intelligences have a different relationship to the creation than human intelligence. It is based upon this Universal Will (to create the universe) which has manifested a world we can only experience from outside of it. And the creative tip of creation* is the universal life principle that led to the human world where it is possible to participate in the intelligence behind the world, through a  transformation into an Individuality, creative according their own pattern while harmonious with the universal will.

*creative tip: The evolving part of organic life is humanity. Humanity also has its evolving part but we will speak of this later; in the meantime we will take humanity as a whole. If humanity does not evolve it means that the evolution of organic life will stop and this in its turn will cause the growth of the ray of creation to stop. At the same time if humanity ceases to evolve it becomes useless from the point of view of the aims for which it was created and as such it may be destroyed. In this way the cessation of evolution may mean the destruction of humanity.

In Search of the Miraculous. P.D. Ouspensky. 306.
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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: 99 equals 8 years

Plan of Avebury showing the stone arrangement of the henge. 
Source: The Avebury Cycle Michael Dames (1977).

The principle of finding anniversaries appears promising when three solar years contain just over 37 (37.1) lunar months while three lunar years contain 36 lunar months and, if one then looks for a better anniversary, then one can move to the 8 year period which has two key features.

  1. The sun will appear on the horizon where it did 8 solar years ago because of the quarter day every solar year.
  2. The moon will be in the same phase (relative to the sun) after 99 lunar months.

This appears useful: by dividing the days in eight years (~ 2922 days) by 99 (having counted to 99 months by eight years) the resulting estimate for the lunar month is 29.514 days, out by just 23 minutes of our time.

Eight solar years was therefore an early calendar in which the solar year could be somewhat integrated by the lunar year. However, the lunar year was entrenched as a sacred calendar, for example in Archaic Greece. And it may be that when the Neolithic reached England in the Bronze Age that 99 stones were placed around the massive henge of Avebury so that eight solar years could be tracked in a seasonal calendar alongside 99 lunar months, 96 months constituting eight lunar years.

The three lunar months left over must then, divided by 8, give the solar excess over the lunar year as 3/8 = 0.375, whereas the actual excess is 0.368 lunar months or 5 hours less. In the previous post, two months the stone age could have been counted as 59 days, here 8 solar years could have been counted as 99 lunar months at Avebury. Through this, one would be homing in on knowing the solar excess per year (10.875 days) and the length of the lunar month, to more accuracy.

It is obvious that counting using whole months has not got enough resolution to catch an accurate result and so in the next post we must revert to counting days in inches, as was done at Le Manio around 4000 BC, over the 36/37 month anniversary at three solar years. It is important to grasp that while we have great functional mathematics, we are here using it to find out what the numeracy 3000-4000 BC could have intended or achieved within counts monumentalized geometrically as a stone monument that can store information.

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).

A House that is your Home

This graphic demonstrates how the inner geometry within numbers can point to significant aspects of Celestial Time or here Space regarding the relative sizes of the Earth and the Moon, namely 11 to 3 according to pi as 22/7.

In some ways one cannot understand numbers without giving them some kind of concrete form as with seeing them as a number of identical units. Sixteen units can make a square of side 4 since the square root of 16 is 4 and 6 is factorial 3 (3! = 1 x 2 x 3 and 1 + 2 + 3) which is triangular, so together they make 22, and if the triangle to placed on top of the square, like a house and its roof, then the house is 7 tall. If you want an accurate approximation to pi of 3.14159 … (pi is transcendental), the 22/7 is good and the house defines it.

This adds another mystery to this form of pi often used in the ancient world where numbers were best handled as whole numbers and ratios of these. This pi allows a circle of diameter 11 to be set within a square of side 11, whose perimeter is then 44. This can be seen in the diagram as made up of 16 yellow squares and 6 blue ones, centered on the circle and making 22 squares in all.

If one looks to the end of the 7th square, as a radius, then 22/7 will deliver the dashed circle (red) of circumference 22 and hence equal to the house number (16 +6 = 22) just 1.5 units beyond the first circle (green). This is called the equal perimeter geometry and a small circle radius 1.5, diameter 3, will “orbit” the inner green circle and the ratio between the circles is obviously 11 to 3, and this is exactly the ratio between the mean Earth and the Moon.

It was thought, by John Michell, that the model was well known in the megalithic since simple experiments in geometry, as above, delivers the relationship between a circle’s diameter and its circumference with very small whole numbers. My own work finds it is indeed prevalent within the design of later buildings, for example in domes, circular windows, and sacred pavements. If so, such buildings became sacred spaces as models of the Earth and moon. Many examples are explored and interpreted in my Sacred Geometry: Language of the Angels.

Advent of “House” Numbers

The oral world of early numeracy was rather like number theory, where numbers can be observed as being related to the geometries of square, triangle and hexagon. The Islamic world of the Sufis appears to have continued this form of numeracy.

A recent book about possible Platonic numeracy in the Quran, Plato and the Quran, suggests the numbers 3 to 9 were stated as a puzzle inviting both the addition and multiplication for seven consecutive numbers, to generate two significant numbers, 33 and 20160, where 33 reminds us of the solar hero period of 33 years and 20160 is twice 10080, the diameter of the equal perimeter model of the Earth and the Moon.

Many centuries later, an early poem of Sufi master Ahmad Yasavi, in present day Khazakhstan, expressed a similar additive formula; that one should add the numbers 4 to 8 together and, when done, this generates the number 22. Twenty two was important in the ancient world and was seen to form the geometry of the equal perimeter square side 11 and circle diameter 14, which, can represent the relative sizes of the Earth and Moon. The geometry is a manifestation of a useful approximation to pi, as 22/7 = 3 + 1/7 or 3.142857, instead of the transcendent number 3.14159 … .

If one looks at the sequence, there are four numbers starting with four and so part of 22 is here 4 x 4 = 16, a square number. In addition there are the added ones of enumeration.: 4 + 1 = 5 + 1 = 6 + 1 = 7. These add up to 1 + 2 +3 = 6, a triangular number which one famously sees in the Tetractys of 1 + 2 + 3 + 4, then usually expanding downwards from 1, and this then adding to 6 + 4 = 10.

The lesser triangle of 6 can sit on top of the square of 16 to equal 22 while looking like a house roof for the square. The whole structure is seven units tall and I am looking at calling this a house number, but perhaps it is known somewhere in the literature – please let me know.

  1. The first house number must be 5, a single 1 above 4 = 2 x 2.
  2. The second house must be 12, a triangle of 3 above 9 = 3 x 3.
  3. The fourth is 22.
  4. The fifth is 35, a triangle of 10 above the square of 25 = 5 x 5.
  5. The sixth is 51 , a triangle of 15 above the square of 36 = 6 x 6.

In each case, the triangle’s bottom row can be seen to share the top row of the house’s square and the triangular roof is most simply equilateral.

I wish happy celebration to my worldwide visitors, between the solstice and new calendar year; inviting you to see this “house number” as a “room” with a celestial “roof”.