Fractal Scaling Relationships.
Eulers clock arithmetics, the logarithmic base and the modulo( n) arithmetics and equivalence classes or cofactor groupsj, sets, rings are all tautologically identifiable as the same, experience of congruency or similarity.
Any model I make is dependent on a collection of Metrons. The Metrons may appear to be incoherent because dynamically they are unstable, but where a dynamical stability exists, this is the same as saying a fractal coherence or similarity exists at different scales. This is also known as the experience of internal and external harmony.
Because we experience space as magnitudes which we quantise the collection of quanta either adhere and fit( Artois) or they don't(perisos) , and using Euclids algorithm we can derive a common measure or one close to( perisos). The difference in the process or algorithm in these 2 cases is the definition of commenurability or in commenurability, otherwise known as finite or infinite process. To reduce this difference to clock arithmetics is a wonderful Eulerian tool of making plain this fundamental distinction. Because of it Euler in effect demonstrates that concepts of magnitude are if fervent to concepts of quantisation of magnitude.
In fact this distinction was drawn irst by the Inin mathematicians, and Brahmagupta invokes it in his famous but forgotten discussions on Shunya. His students and followers in attempting to explain the terminology created a division in the minds of some who did not understand the Euclidean algorithms on which his notation is based.
To cut it short, Hamilton in deriving his rules of arithmetic of the imaginaries in the theory of couples simply states that the symbol 0 to be called zero would be used to denote the origin for quantised magnitudes, but for arithmetic scalars an additional restriction would be imposed that limits the short hand mnemonic rules for division. The limit was put in place to minimise the mental jerk of falling out of conjugacy into wholeness.
Since then, many have abided by the rule without understanding, and consequently Shunya has been confusingly given the meaning nothingness, when in fact it means fullness of potential, wholeness oneness etc of everything. Shunya is everything.
The use of the circle to represent everything and therefore infinite process is a direct use of the symbol of Shunya O which is also formed in different ways with the fingers. It can also symbolise by these fingers ultimate perfection.
The infinite process of Euclids algorithm is the process of iterative fractalisation or discretisation. The Indians derived from this process the continuos reciprocal, or fraction notation, which is just going round the Shunya symbol, the quantised or coordinated circle as many times as one wishes.
The formalism of the Vedic numerals into 9 distinctions is fascinating but based on this Shunya circle. Once you know that you may in fact use any collection of symbols or marks. The key to the system you are encoding is the symbol of Shunya with the symbols around the edges. From this all codes and encoding and ciphers and cipher ism is derived.
Of course any closed form will do and so squares, triangles pentagons etc may be used as symbols for encoding. Perfection or complete Harmony is experience only when there is rotational symmetry. Few realise that this system is the same system for Bombellis conjugate and adjusted numerals, which Wallis and Newton intuitively formulated as the imaginary arithmetics, which Cotes and then Euler related to circular area, but which De Moivre completely formulated as the roots of unity theorems, part of the inner workings of the logarithmic trigonometry of spherical trigonometry and spherical geometry, better described as the Gematria of Astrology and the fundamental combinatorics for the sphere.
The use of Shunya by sages in all these ways was obscured or even hidden from the general view, firstly because public education is in fact a relatively "new" idea! Jesus comments about secret things or even occult things being hosted from the roof tops is not a mystical retrenchment and exposition of dark secrets, but an appeal for a public education system to raise the level of awareness of all. It was not a new appeal even in Jesus day. Plato Academy and the Greek gymnasia were a step in this direction, and it has taken over 3000 years to come to any meaningful fulfilment!
The Children of Shunya, therefore underpin the very philosophies of quantisation of magnitudes as experience. These sequences of this fundamental Euclidean algorithm fractalise our spaciometrical experience and give a structure to scaling and scalers as factorisation structures of forms. But they also encapture the dynamic equilibrium called or experienced as form, and how these forms shift relative to each other in growth and motion.
The seemingly static forms, the revered ideals are in fact coherence forms of dynamic relations. Rotational symmetry is the chief way these forms are experienced. But they are rare as perfection. What we experience are varying degrees of advancement( growt ) or deterioration(destruction) but always, always Heracltian change. The perfect circle is in fact a very special form of spiral.
Shunya as the symbol of everything is in fact a spiral when formed with the fingers. Everything grows and or decays, nothing remains in this ceaseless field of rotational motion fields, the ultimate field of fractals at all scales.