Numbers, Constants and Phenomenology

  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.

We have seen that the early numbers define the world of musical harmony but other important patterns arise within the ordinal numbers such as,

  • the Fibonacci approximations to the Golden Mean (phi = 1.618),
  • the Exponential constant (e = 2.718, the megalithic yard), from which trigonometry of the circle arises naturally,
  • the radial geometrical constant, (pi = 3.1416) as approximated by rational fractions {π = 22/7 25/8 63/20 864/275} and
  • the triangular progressions of square roots, as another development of the early numbers (in space) as geometry, also approximated by rational* numbers (rational meaning “integer numbers that can form mundane ratios”).

The transcendent (or irrational) ratio constants * (first mentioned in the Preface) are the visible after-effects of the creation of time and space. They must be part of the framework conditions for Existence, these also creating harmonic phenomenon that are not transcendent; these relying instead (as stated) on the distance functions of ordinal numbers: their distance from one and their relative distance from each other, lying beneath the surface of the ordinal numbers. Ordinality, to modern thought a universal algorithm for such distances, explains or defines what is harmonious in the physical world and in what way. Significant distance relations, such as those found in the early ordinal numbers, must then be repeated at ever greater doubling, tripling and so on {1 2 3 4 5 6} => {45 90 135 180 225 270}, where units can be scaled up by any number to become the larger structures, within any greater micro-cosmos. This is especially seen within ancient number science and its primary context of octave doubling, where what lies within octaves vis-à-vis scales and octaves within octaves, requires the right amount of up-scaling, as in the cosmology of Will (and not of Being), presented by G.I. Gurdjieff from 1917 onwards.

The illusion of number is that one can never penetrate the ubiquitous unitary distance of 1, the unity which becomes the ordinals which are so many exact assemblies of one; and of their ratios, so that one is not a number nor a transcendent ratio but rather is Number is the primordial Thing: a transcendent wholeness, found in every unit that causes relatedness through intermediate distance, or proximity. One is like Leibnitz’s Monads applied to the cosmic enterprise of universe building, as a fully quantified Whole and its Parts.

“The Absolute, that is, the state of things when the All constitutes one Whole, is, as it were, the primordial state of things, out of which, by division and differentiation, arises the diversity of the phenomena observed by us.”

Gurdjieff. In Search of the Miraculous page 76.
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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.

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”.

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.

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