I am glad i waited, (or was i fated?) until this time to explore symmetry.
My youthful disdain has given way to the appreciation of the lightest of touches being significant to the point of being of infinite force!
It is like when the most delicate of spices drives the commodity markets of an entire 3 continents, and the common place we call salt was worth the labour of a man for a week!
Precious things in ordinary forms , as invisible as dust in the air until illuminated by a beam of light, and then found to be everywhere in such abundance as to equate to a force of nature!
That the smallest invisibles, the viruses should shape the zoology of 'life"promoting species,demoting other species, and layinf apparently dormant in the DNA and RNA of every lifeform we know.And these constructs do nothing of their own, but in concert with the other proteins in Enzymatic "controlled" action and reaction conforming other chemicals through conformation to the life processes of a unified entity of trillions!
"I" had originally started to consider the connection with The Logos Response, summetria being so rich a description that i thought i might equate it to the Logos response.
But symmetry is a perception not an active manipulating response, so i did not equate it,but it is so close!It is the closenes of a mirror as one arises out of the other!
Shunyasutras and arithmoi possess symmetria because their boundaries are "cut" from space, but only by relativistic motion, and a density distribution wave effect. Such a standing wave of density distribution holds error in its dreadful symmetria!
The power of E=mc2 is that it is Residual, Resident within a form. It represents the ceasless motion of internal symmetries!
I was going to write more on rotational motion and gravity through axial angular momentum/ acceleration torquing space along an axis, with the torque axes twisting off to infinity at the speed of light, thus explaining radiative energy etc. Gravity was going to be the epiphenomenal effect of the mesh of torque axes in space. This mesh was to be like churned up bubbling water, a foam that did not support the denser forms as well as smoother space. Hence denser objects moved in trochoidal paths around even denser objects.
Had i done so i woukd have left out the rich assonance that symmetria brings to the exposition.
My plan had been to remove the obstacle of he centre of mass and the centre of gravity, by replacing them with the centre of density and the centre of rotational symmetry. It struck me then, and perhaps gave me pause that all things move around and relative to a centre of rotational symmetry.
The notion of mirror symmetry arrived in me after a long exploration of what is misleading in complex number arithmetic.
The two came together when i read Mandelbrot's explanation while working on the programming for a polar mandelbrot. He used the easily recognisable greek word summetria, and it struck a harmonious and unifying chord, resonating with Eudoxus and the Pythagorean search for unity.
There is no basis for unity.
Then Brahmagupta, misunderstood, gave a yoked relationship for unities and this tied shunya forever into my conception, not as nothing, but as everything… and therefore nothing!
The making of distinctions, the mental cleaving of shunya to form the shunyasutras is an act that creates summetria. And summetria is fractal in every sense of the word, and understood by the Greeks as a design principle for architecture. In the Renaissance Italian artists were very excited by symmetria, and Albrecht Duerrer made several trips to study with them before writing his 5 books on art and measurement.
In his study Duerrer came away with the firm conviction that the trochoids were the explanatory symmetry of nature.
Why then, did i not get the importance of symmetry in my early childhood maths lessons! Because my teachers did not know, the scientists at the time did not know, the mathematicians at the time were too wrapped up in their abstractions, everybody and every one was out to make a name for themselves, and ditched the knowledge of centuries of apprehension of " the cosmos"
If it had not been for Benoit Mandelbrot, we would not have reconnected with our past information resources and continued the research and play there, not in the arid arizonian areas of abstraction!
We have a deep a rich vein to "mine" and it tis the trigonometric ratios. Already Cotes De Moivre Napier, Brahmagupta to name but a few ha e added to it. Many Arabic and Persian scholars have added to it and we too can extend it and its utility to our modern needs. The trig formulae on the unit circle are the defining symmetry, but there is a symmetry of the spiral we need to fully explore as in ratios and logarithms.
I am tempted o think of the hypebolic sin as beginning that process, but i have yet to verify it.
So the symmeria of "the self" seems an odd topic to draw attention to. but it underlies all greek understanding of symmetria. "Man is the measure of all things!"
As grandiose as that sounds it is ultimately a cry for an anthropomorphic scale to all our architecture , art and design concepts, and by extension our apprehension of the universe!
But now our internal symmetry informs us on the construction of identity! For "i" might otherwise be called "we" but for linguistic convention!
Our study of microbes reveals a chemical signal which gives all bacteria in a symmetria ( see how the notion underlies all our set and group theoretic structures quite naturally!!) a sense of "quorum". That is being a group, a combine, a cybernetically linked system, a gathering, a commonality etc, etc.. in short a symmetria. Shorter still from a perception viewpoint a "we".
The quorum chemical gives rise to the identity "we". It is but a slip of the perceptual tongue to become "i" in relation to all other "we".