It is as they say, "an Eternal Verity…"
The Fractal nature of an iterative computational consciousness awareness and experience of "reality" is just so. Whenever i peer into the vastness of the universe, as opposed to the Kosmos, whenever i press my face against the mirroe of Shuya i find a pont reflected, a region by region reflection of myself" The universe to me necessarily has a human face.
The Greeks, protagonists par excellence describe this in a comparable way: they developed the notion of Anthropos, that is the upward reaching sentient entity, the upright walking, the erect running, the skyward looking consciousness. the defier of the gods! The protagonists to the gods who would not bow down on the face, who would not islam, submit, who would engage in agonia and competition with the gods on equal terms, and if not. then "****@#¡" you gods!
To the irratinality of the gods, the uncaring distant unpredictable cruel and discompassionate actions, they declared the antidote: Rationality. Above all hings Anthropos would annihilate and do battle with the irratinal gods with rationality. the goal was Kosmos! Perfect peaceful order, annihilating the influence of the gods, discovering the laws that both god and man had to abide by; wresting control of the perfect world from himan and divne influence from rational anthropos and crazy irrational theoi and revealing the underlying perfect orde of all things that Greek philosophers bekieved was underlying Everything.
So Eudoxus and Pythagoras hid the irratinal immesaurable by unities values behind the brilliant and eternal proportional theory, and created and hid the wonderful fractal universe they were so afraid of. And bit by bit Eudoxus was able through these means to push back the irrationality of the gods and reveal the Kosmos that he and Pythagoras so passionately believed was there.
Gradually a sphere of glass confined the Kosmos from the irrational crazy gods on the other side, and year by year the sphere was extended further and further in "perfect" peaceful order.
That was the theory. In practice cracks began to appear the further they extended the Kosmos, but by killing off or otherwise sidelining any who opposed them they kept the illusion for a thousand years, or rather Their followers did. And what amixed bunch they were. They included the grrek scholars from all religious persuasions, a cross section of societies intelligentsia, both rational and mystical or religious. The notion of Anthropos was watered down to suit or beefed up to provide a defense.
However, on the world stage, Buddha in greek inspired india had already developed an essentially fractal philosophy, and before him in antiquity the magi had already devised the same in a level s of heaven conception, which was taken up and transmitted to scientists of all ages via gnosticism, incliding Indian scientists. So 2 views existed and depended on whether you wanted to fight the gods or have no gods or any mixture in between.
The meta physics of the fractal universe answers the question who made the gods. The metaphysics of those who fight the gods seeks a just and perfect order that both combatants live in, and by whose rules both must abide. It dismisse the obvious question as pragmatically irrelevant, which of course it appears to be so. That is until you start to look at the very very small, the world that Eudoxus and Pythogoras tried to hide away behind proportional theory and equivalence relations of unity, and avoidance of approximation and neusis. Rational thought alone was the ideal, and indeed it served well the rich and the powerful who had others to engage in the necessary pragmatics of engaging with reality.
Reality, according to raionalism is too messy to be fundamental, until you look through a microscope at greater and greater magnification.
Rationaliy and irrationality combine to make perfect order! That was the plan, and it is logically plausible except what is the annihilation product?
Only the Indians and Buddha had an answer. The answer is Shunya. Not perfect order but infinite potential.
After thousands of years copying nature and aggregating to measure and playing games of chance Brahmagupta managed to ask the question: what are we doing?
His answer as an astronomer and astrologer was: exploring the things from shunya!
Everything comes from shunya and returns to shunya, but how? The answer he saw in his reflection in a mirror pool . For every 1 there is a mirror 1. And 1 aggregates with the mirror 1 to give shunya.
Brahmagupta was influenced not only by greek thought, Brahman thought, but also Chinese thought. His contribution was a synthesis of all of these with shunya.
Shunya means " fullness". The symbol is o for the void full of potential. Everyone who read his sidhanta understood it as infinity. Those who did not took it to mean 0 zero. The confusion exists to this day. Brahmagupta was advising on the infinite void, and what he said was it was full of perpetual motion. And all things had a mirror object that returned them to the void.
Meanwhile the symbol could be used to show when something was complete or full.
It had become indian practice to use simple strokes for names, and to count in tens so as to reuse the same strokes. Thus the world recognised the first decimal system in India, mainly because they put shunya in a full space to indicate the need to go into the next space to the left. Shunya meant "full" so everything had to go into the bigger container.
Amongst these and other things Brahmagupta promoted the Indian rhythmical structures for counting and aggregation,and the ratios for the right triangle called by the Arabs the sine or cove due to another mistake.
Brahmagupta was the father of the directed magnitudes and how to aggregate them. He formalised mirror smmetry in the structure of later geometries. He advised structures for aggregating that gradually changed the world.
Bombelli asked the question: how do we use the new ideas in geometry?
His answer was to popularise arabic algebra in common speech. In so doing he found a simple rule for employing the geometric mean to directed magnitudes. He made a little ditty identical to Brahmagupta's except he extended it to deal with geometric means. His algebra showed everyone how to get the best out of the new methods and how to aggregate with them. He also began to detail certain symmetries in directed numbers and certain standard techniques.
It was finally Hamilton who took all the advances in trigonometry including logarithms, and all the work done on the geometric means of directed numbers and demonstrated that they formed a complete algebra like arithmetic. In doing so he created the field of set or group algebras, the field of scalars, vectors, versors, and complex magnitudes. The beginnings of every form of tensor algebra, and vector algebra. Every familiar vector operation is derived from Hamiltons work.He even uilises matrix formats.
Hamilton thus made a huge shift to our understanding of aggregation and aggregation structures. Directed magnitudes had to be aggregated algebraically , not by arithmetic. This invariably meant that aggregation was governed by geometrical concerns, as Brahmagupta had advised from the start. Shunya governs all aggregation.
George Boole asked: what are we thinking when we interact with reality? He started with 0 and 1. These were his symbols for any thinking that involved distinctions. He was not symmetrical in his theory so he introduced negate. This was a flip algorithm and he began to show patterns in decisions that had these dimensions. He showed that aggregation structures were governed by our thinking rules even on a simplistic level. We did not just copy nature we negated nature to get an "answer" sometimes.He reduced our aggregation structures to negate, conjunct,disjunct.
Our aggregation structures needed to be thoroughly tested as Hamilton had done with his algebra.
Finally Cantor, developing general notions into a set theory for " numbers" opened the floodgate on a welter of investigations into the very foundations of our aggregate structuring. Suddenly what we had done for thousands of years was found lacking in rigour, and potentially misleading. Everything Needed to be reconstructed from the ground up.Cantor reduced our aggregation structures to a version of Booles: union,intersect,and exterior to. The geometrical nature of our aggregation structures and rules were laid out in diagram form for all to see, and for the blind geometers to understand by symbolic manipulation.
By the time of Cantor mathematics was well and truely distinguishing itself from science, pushing toward what? No one knew, but some tried to steer it into academic harbours like philosophy. The attempt failed.
Now mathematics stands alone and lonely on its own serving all its former bed fellows, but not subject to any of them.
In the meantime under its baleful eye a new "science" grew called computer science. `it seemed to be a natural companion to mathematics, but some disdainful mathematicians wanted to keep it a boy, even a toy boy! But look at it now! It is akin to a god!
Mathematics now serves computer science and computing technology. This is its natural home. This is where all our realisation and angst about aggregation structures has found an answer and a technological representation. This is where it all comes together, the Logos Response, the Language contribution and derivation, the contribution to grammar, syntax, the iteration, the convolution, the ratios and particularly the trigonometric ratios extended by Napierian logarithms ,the computation aids, the geometry, the graphical interfaces, the underlying numerical representation in a digital code based on boolean algebras, and varying logarithmic bases…The ceaseless rotation of things from shunya, the rotational expansion and reflection in a point-like region, all meet in this subject and have meaning and realisation in technology or in code.
To get to here we have witnessed some pretty strange thinking. But it has always been simple, no mateer how hard the maths guys wanted to make it. It is and always has been a conversation about spaciometry, about how we measure shunya, about what unities we use and what aggregation structures we employ. The goal of measuring is to apprehend shunya, and in part to comprehend shunya.
We will return to shunya, She will not come to us. Like a mirror in Shunya we will see our mirror likeness appear just before we transform. There is only fullness in shunya, not annihilation.