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.

In Search of the Miraculous* had an 11-fold “Diagram of Everything Living” (shown above), in which the Universal Will for the universe was represented by an equilateral triangle within a circle (top left). The triangle expresses the equal division of the circle into three parts, and it is only through seeing the parts of Gurdjieff’s cosmology, in that book of lectures and (differently) in his later writings (and other sources) that one can arrive at a simple explanation for this triangle inside a circle (see section X), which also figures in his famous Enneagram (see below). The two circles demonstrate doubling in size, using the triangle which expresses division of both circles into three parts, which in Just intonation are three large intervals {4/3 5/4 6/5} which together equal 2. The important point here is that all the notes of an octave are related by the rational distances between the numerators and denominators of ratios, thus automatically increasing the relatedness of an octave’s parts, at whatever scale. This is what the ordinal numbers achieve from the very outset, of their seemingly primitive ordinality {1 2 3 4 5 6}, which leads to an intense and well-behaved type of relatedness. By the number 24, the octave of eight notes appears and, within this octave and the next {24 48 96}, seven modal scales emerge, from each interval of the major diatonic, in order (section 2.8).

In recent centuries, alternative voices to science have been talking about this sort of phenomenology. The European School of philosophers, pursued phenomenology rather than rational introspection. From Wolfgang Goethe (1749 – 1832) onwards, they wee discovering that science was not, in principle, a participation of the human senses in understanding the world but rather had become the application of instrumentality instead of the natural senses (next section). Moments of scientific genius, discovering new mathematical laws of nature, are remarkably not focused on how they were achieved, but on what they revealed within the physical world (as a technology to create a human “good”, exploiting new understandings of nature to explain then control nature). This change of focus had collapsed the original genius of a participatory moment, in which the fundamental process of understanding for its own sake, is a part of the world understanding the world. The problem was dramatized in Goethe’s Sorcerer’s Apprentice, where an apprentice magically tinkered disastrously with the world of his Master.  Phenomenology lacks the apparent usefulness that science provides since it seeks to understands the world rather than control it. In seeking to control the world, the world soon comes to control what the human world is like and what humans, now a world, want to do.

The failure to understand the world in the right way, on an individual level, suppresses the human destiny for which nature and the whole universe was probably created. It is easily done, to revert to a life where the world no longer participates within us but we benefit from the exploitation of parts of the physical world. The meaning of the world becomes our description of it, rather than the world’s meaningful action through human beings. It is therefore true to say that today we use numbers but don’t understand them* (in their pychoactive role of expressing meaning in the world) as the manifestation of the Universal Will for this universe. Holding to this is useful when wishing to understand the ancient number sciences, as they must have originally got their insights by looking towards the being of numbers as the native framework of the Universe. Numbers are, for example, made up of prime numbers, just as we think atoms are made of subatomic particles such as protons, neutrons and electrons.

Numbers can be explained as a tool for the universe-creating Will. The will of numbers is that, within the creation, “even God cannot beat an ace with a deuce [that is, a two]”

<EN> I do not remember which of us was first to remember a well-known, though not very respectful school story, in which we at once saw an illustration of this law. The story is about an over-aged student of a seminary who, at a final examination, does not understand the idea of God’s omnipotence.

‘Well, give me an example of something that the Lord cannot do,” said the examining bishop. “It won’t take long to do that, your Eminence,” answered the seminarist. “Everyone knows that even the Lord himself cannot beat the ace of trumps with the ordinary deuce.” Nothing could be more clear.

Ouspensky, In Search of the Miraculous, page 95

That is, numbers are a foundational set of rules based upon their distances from each other, in a single dimension or rather, in any direction away from one. This is perhaps why the strings of string theory are numerical and, in manifestation, how long chains of DNA proteins determine living forms. Numbers must be obeyed for the universe to be actual. Our world appears as we think it is and, the facticity behind material causes lurks within phenomena as more than a cause-and-effect “explanation” using physical laws. One can return to the notion that nature has provided, through numbers, shortcuts between numbers which, in the physical world, can connect things of a similar sort together, in a special way that means that the connection of the whole to the parts remains intact within phenomena.

The question is, how could numbers have created the context for a Living Planet and be knowable to human beings without an instrumentality other than the sensorium made up of senses + intelligence.

Phenomenology as an Act of Will