The "Truth" about Arithmos
The nets of mosaics used by the greeks and promcipally Euclid in book7 of his Stoikeioon, which we gaily and wrongly identify as number, are in fact Platonic Forms/Ideals. The key aspect of Book 7 is the introduction and exposition of an Algorithm which i have called Euclids Algorithm which serve to lay out the combinatorial sequence rules which define the Arithmoi in all their forms and relationships combinaorially. The so ca;;ed 4 opperations are in fact combinatorial rules governing the creation of multiple forms from these arithmoi or indeed from the essential and fundamental
Euclids algorithm is the very definition of these so calle operations, and they are therfore procedural processes or steps in a combinatorial algorithm. That we should sing and dance and twirl about while doing this algorithm is without doubt the most neglected part of this study! of Eudoxuian proportion theory, and the first step in alienating students from the intended apprehension of the heavens.
The music of the spheres, their harmonies and their chords are Pythagoras's encoding of this synaesthetic relationship with our neurology and our experiential continuum. Fundamentally all our concepts rely on tautology for identification beccuse everything we experiemce is ideation. The concept of substance is the tautological identification of our internal ideation with external stimulii.
There is much I want to coherently write about the Arithmoi and their fundamental nature, but fate may not permit me. Time and again thoughts I have written have been lost to the "aether"! I strongly accept that there is a time for everything, and I may not be the one to cohere these things into written form.
Writing is in any case inappropriate as Arithmoi is an experience of a mosaic, and Arithmoi are the most beautiful mosaics we have created.
I am going to attempt to link to a video by Randy Powell in which the recreation of an Arithmos from a gem atrial system is demonstrated. The series of videos in fact starts with the mistaken codification we call number, and revere as mystical instead of obscuring and mystifying, and ends up, by a bit of sleight of mouth and hand with one of many fundamental Arithmoi . This one happens to be the torus, but there are many others.
Russ Griess takes the basic claim and "figures it out" literally.
These mosaics are the platonic and Euclidean Arithmoi, not the numbers or numerals rather that clutter the forms. As you can see it does not form a torus naturally, and what russ was not looking for was how the spires he identifies in the 4 th video form the 3d torus.
The torus and the sphere are formed only when the object is fractalised. That is instead of the regular , uniform scale russ uses to explore the shapes of the Arithmoi, a freer fractal scale and paradigm is utilised. Without a doubt, fractal iterative relationships underpin the morphology of our experiential continuum. As theoreticians we need to stop deriving models from uniformity and start expositing in terms of iterative fractality.
To apprehend that the Arithmoi are a fractal spaciometrical model is the first thing. To free ones mind of " number" and fill it with ourselves interacting iteratively and dynamically with space to perceive and generate the most beautiful fractal experiences.