above: The human essence class related to four other classes in

J.G. Bennett’s *Gurdjieff: Making a New World*. Appendix II. page 290.

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 the human intelligence, this based upon this Universal Will 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 *only possible* to participate in the intelligence behind the world, through a transformation into an Individuality, creative according their own pattern harmonious with the universal.

***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.

Will is not something one does. Rather, it is a participation of one’s being with Will. This creates a transformational action of Will within a human that is receptive to it (rather than merely assertive on their own account). We are born able, through our unique pattern, to participate in our own understanding of the meaning that is this world. In this, numbers are more than data: they form **structures of will** which do not rely on complexity and are therefore directly intelligible for an intelligent lifeform, enabling **what to do**, by seeing more deeply what is in the present moment. For example, number is the foundation of that universal invariance: the Present Moment of selfhood*.

The myth of a philosopher’s stone presents a challenge, to find the “stone” itself which we shall see is probably *the numerically favorable environment upon the earth*. The stone has been rendered invisible to modern humans by our functional science of infinite complexity, also called instrumental determinism. This has downgraded human expectations to being a walk-on part, an unintentional result of evolution, by natural selection, of intelligent life. To think otherwise it is necessary to see what is not complex about the sky, which is a designed phenomenon related to Life on Earth. Once-upon-a-time, the stone age understood the sky in this *right way*, the way it had been *designed to be read by us*, corresponding with the way intelligent life was intended to be, on a habitable planet with a large moon.

#### Geocentric Numbers in the Sky

Our pre-digested meanings are those of modern science. Whilst accurate they cannot be trusted in the spiritual sense, if one is to continue looking at phenomena rather than at their preformed conceptual wrapper. Numbers in themselves are these days largely ignored except by mathematicians who, loving puzzles, have yet largely failed to query the megaliths* but, if or when anyone might say the megaliths had a technical purpose, this has annoyed most archaeologists, who live by the spade and not by the ancient number sciences.

Fred Hoyle, Hawkins, Alexander Thom, Merritt and others all found something new in Stonehenge but still failed to explore stone age numeracy as well as the numeracy of metrology. Rather, they assumed measures unlike our own were used, yet the megaliths would continue to have no meaning “above ground”, except as vaguely ritualistic venues in loose synchronization with a primitive calendar.

Numbers are not abstract once incarnated within Existence. In their manifestations as measurements, they have today become abstracted due to our notation and how we transform them using arithmetic, using a positional notation based upon powers of two and five {10}, called the decimal system* (https://en.wikipedia.org/wiki/Decimal). The so-called ordinal numbers {1 2 3 4 5 6 7 8 9 10 …etc.} are then *no longer visually ordinal* due to the form in which they are written, number-by-number, from right-to-left {ones, tens, hundreds, thousands …} * (the reversal of the left-to-right of western languages). Positional notation awaited the invention of zero, standing for *no powers of ten*, as in 10 (one ten plus no units). But zero is not a number or, for that matter, a starting point in the development of number and, with the declaring of zero, to occupy the inevitable spaces in base-10 notation, there came a loss of ordinality as a distance from 1.

Before the advance of decimal notation, groups within the ancient world had seen that everything came from one. By 3000BC, the Sumerian then Old Babylonian civilization, saw the number 60 perfect as a positional base since 60 has so many harmonious numbers as its factors {3 4 5}, the numbers of the first Pythagorean triangle’s side lengths. Sixty *was* the god Anu, of the “middle path”, who formed a trinity with Fifty {50}, Enlil* (who would flood humanity to destroy it) and Forty {40} who was Ea-Enki, the god of the waters. Anu presided over the Equatorial stars, Enlil over those of the North and Ea-Enki over those of the South. In their positional notation, the Sumerians might leave a space instead of a zero, calling Sixty, “the Big One”. So, the Sumerians were resisting the concept of zero as a number and instead left a space. And because 60 was seen as also being ONE, 60 was seen as the most harmonious division of ONE using only the first three prime numbers {3 4 5}.

#### How do numbers “create”?

These days we are encouraged to think that everything comes from zero in the form of a big bang, and the zeros in our decimal notation have the unfortunate implication that nothing is a number, “raining on the parade” of ordinal numbers, Nothing usurping One {1} as the start of the world of number. The Big Bang, vacuum energy, background temperature, and so on, see the physical world springing from a quantum mechanical nothingness or from inconceivable prior situations where, perhaps two strings (within string theory) briefly touched each other.

In what follows we will nevertheless *need to use decimal numbers *in their position notation, to express ordinal numbers while remembering they have no positional order apart from their algorithmic order as an infinite series in which each number is an increment, by one, from the previous number; a process starting with one and leading to the birth of two, the first number.

Whole (or integer) numbers are only seen clearly when definedby

(a)* their distance from One (their numerical value) and*

*(b) their distance from one another (their difference).*

In the Will that manifested the Universe, *zero did not exist* and numerical meaning was to be a function of distances between numbers!

Zero is unnecessary due to the first true number {2} of doubling; Two’s distance from one is one and in the definition of doubling and the octave, the distance from a smaller number doubled to a number double it, is the distance of the smaller number from One. This “strange type of arithmetic” *(EGM) is seen in the behaviour of a musical string as, in that kind of resonator, half of the string merely provides the basis for the subsequent numerical division of its second half, to make musical notes – as in a guitar where the whole string provides low do and the frets when pressed then define higher notes up to high do (half way) and beyond, through shortening the string.

This suggests that a tonal framework was given to the creation by Gurdjieff’s Universal Will, within which many inner and outer connections can then most easily arise within octaves, to

- overcome the mere functionality of complexity,
- enable Will to come into being,
- equip the venue of life with musical harmony and
- make the transformation of Life more likely.

Harmony is most explicit as musical harmony, in which vibrations arise through the ratios between wave*lengths* which are the very same distance functions of ordinal numbers, separated by a common unit 1.

Take the number three, which is 3/2 larger than two. Like all ordinal numbers, succeeding and preceding numbers differ by plus or minus one respectively, and the most basic musical tuning emerges from the very earliest six numbers to form Just intonation, whose scales within melodic music result as a sequence of three small intervals {9/8 10/9 16/15}, two tones and a semitone. Between one and those numbers {8 9 10 15 16} are the first six numbers {1 2 3 4 5 6}* (note absence of seven between these sets), whose five ratios {1/2 2/3 3/4 4/5 5/6} provide any octave doubling with a superstructure for the melodic tone-semitone sequences; their combined interdivision, directly realizes (*in their wake*) the tones and semitones of modal music.

We will see that the medium for such a music of the spheres was both the relationship of the sun and planets to the Moon and Earth, but this manifested quite literally in the lunar months and years, when counted.

Coming soon: *The Musical Octaves of Gurdjieff’s Worlds*