Tag: prime numbers

Harmony of the Biblical Patriarchs

This extract from The Harmonic Origins of the World (p58-62) shows how what are taken to be arbitrary numbers, in the narrative of the Patriarchs, expressed knowledge of planetary resonances.

above: Diagram of the Bible code of “holy mountains”: Products of the powers of five upwards and of the powers of three across, each mountain within a limiting number if note D is {60, 120, 45, 180, 720} .

Female archetype Eve, “mother of all living,” becomes Abram’s wife Sarai. Childless, Abram was encouraged (by Sarai) to have first son Ishmael by concubine Hagar, but the Lord God (the mountain god whose number sums to 345) renames Sarai as Sarah and Abram as Abraham. At a miraculous 90 years of age she gives birth to Isaac (“he laughs”), then reportedly dies at 180 years old. It is harmonically relevant that (a) the giving of heh = 5 to both Sarah and Abraham elevates them from their former selves onto the second row, “stepping up” like the god Ea in Sumeria, and that (b) Adam’s number 45 has now been doubled to 90 and can form an octaval womb in which Isaac can be born, his life to then end at the doubling of Sarah’s 90 years to 180 years.

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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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Primacy of low whole numbers

  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.

What we call numbers start from one, and from this beginning all that is to follow in larger numbers is prefigured in each larger number. And yet, this prefigurement, in the extensive sense {1 2 3 4 5 6 7 etc.}, is completely invisible to our customary modern usage for numbers, as functional representations of quantity. That is, as the numbers are created one after another, from one {1}, a qualitative side of number is revealed that is structural in the sense of how one, or any later number, can be divided by another number to form a ratio. The early Egyptian approach was to add a series of unitary ratios to make up a vulgar* but rational fraction. This was, for them, already a religious observance of all numbers emerging from unity {1}.  The number zero {0} in current use represents the absence of a number which is a circle boundary with nothing inside. The circle manifesting {2} from a center {1} becomes the many {3 4 5 6 7 …}.

The number one manifests geometrically as the point (Skt “bindu”) but in potential it is the cosmological centre of later geometries, the unit from which all is measured and, in particular, the circle at infinity.

Two: Potential spaces

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π and the Megalithic Yard

The surveyor of megalithic monuments in Britain, Alexander Thom (1894 – 1985), thought the builders had a single measure called the Megalithic Yard which he found in the geometry of the monuments when these were based upon whole number geometries such as Pythagorean triangles. His first estimate was around 2.72 feet and his second and final was around 2.722 feet. I have found the two megalithic yards were sometimes 2.72 feet because the formula for 272/100 = 2.72 involved the prime number 17 as 8 x 17/ 100, and this enabled the lunar nodal period of 6800 days to be modelled and and the 33 year “solar hero” periods to be modelled, since these periods both involve the prime number 17 as a factor. In contrast, Thom’s final megalithic yard almost certainly conformed to ancient metrology within the Drusian module in which 2.7 feet times 126/125 equals 2.7216 feet, this within Thom’s error bars for his 2.722 feet as larger than 2.72 feet.

This suggests Thom was sampling more than one megalithic yard in different regions or employed for different uses. Neal [2000] found for Tom’s statistical data set having peaks corresponding to the steps of different modules and variations in ancient metrology, such as the Iberian with root 32/35 feet and the Sumerian with root 12/11 feet. It is only when you countenance the presence of prime numbers within metrological units that one breaks free of the inevitably weak state of proof as to what ancient units of measure actually were and, more importantly, why they were the exact values they were and further, how they came to be varied within their modules. However, the megalithic yard of 2.72 appears to outside the system in embodying the prime number 17 for the specific purpose of counting longer term periods which themselves embody that prime number.

The discipline of using only the first five primes {2 3 5 7 11} must have been accompanied by the perception that only if primes were dealt with could certain ends be served. This is crystal clear when we come to musical ratios in which the harmonic primes alone are used of {2 3 5} with an occasional “passenger” of the prime {7} as in 5040 which is 7 x 720, the harmonic constant.

Using 2.72 feet to count the Nodal Period

The first remarkable characteristic of 2.72 feet is that 8 x 17 in the numerator means that the approximation to π of 25/8 = 3.125 can, in (conceptually) multiplying a diameter, provide an image of 25 units on the circumference of a stone circle. For example a diameter of 2 MY would suggest 17 MY on the circumference, which is quite remarkable. Further to this, we know that the 6800 days of nodal cycle is factored as 17 x 400 and that the MY was shown (acceptably) to have been made up of 40 digits (in conformance to the general tradition within metrology that there are 16 digits per foot and 40 for a step of 2.5 feet, which a MY traditionally is). The circumference of 17 MY is then 17 x 40 digits which means that a diameter of 20 MY would give a circumference of 17 x 400 digits equalling 6800 digits as a countable circumference in digits per day.

This highlights how prime number factors played a role, in the absence of arithmetical methods, in solving the astronomical problems faced by the late stone age when counting time periods in days.

Working with Prime Numbers

Wikipedia diagram by David Eppstein :
This is an updated text from 2002, called “Finding the Perfect Ruler”

Any number with limited “significant digits” can be and should be expressed as a product of positive and negative powers of the prime numbers that make it up. For example, 23.413 and 234130 can both be expressed as an integer, 23413, multiplied or divided by powers of ten.

What Primes are

Primes are unique and any number must be prime itself or be the product of more than one prime. Having no factors, prime numbers are odd and cannot be even since the number 2 creates all the even numbers, meaning half of the ordinals are not prime once two, the first “number” as such, emerges.

Each number can divide one (or any other number) into that number of parts. In the case of three (fraction 1/3) only one in three higher ordinal numbers (every third after three) will have three in it and hence yield an integer when three divides it.

Four is the first repetition of two (fraction ½) but also the first square number, which introduces the first compound number, the geometry of squares and the notion of area.

Ancient World Maths and Written Language

The products of 2 and 3 give 6, 12, etc., and the perfect sexagesimal like 60, 360 were combined with 2 and 5, i.e. 10, to create the base 60, with 59 symbols and early ancient arithmetic, in the bronze age that followed the megalithic and Neolithic periods.

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