- Preface
- Primacy of low whole numbers
- Why numbers manifest living planets
- Numbers, Constants and Phenomenology
- 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.
Continue reading “Numbers, Constants and Phenomenology”“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.