Phenomenology of Zero

May 21 2008  | Views 142 |  Comments  (0) Leave a Comment
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Zero

The Dark and Un-fathomable



“Prior to the Dasarajna war,” the stranger begins. “One had no real use of something like, say: a ‘‘0’ (zero), It has no real value, for example, there are no ‘0’ (zero) horses, no ‘0’ (zero) revenue, no one ever goes to buy ‘0’ (zero) mangoes, in fact it makes no difference, and contributes nothing to our daily lives.
Most cultures prior to the war either counted using a unary or a binary system, for example a series of 1 makes many. The Egyptian in fact had a highly evolved unary system known as sign-value notation.
Some cultures count by 2’s, they have no system of numbers beyond 2’s, thus 3 would be 2 plus 1 and 4 would be 2 plus 2, 5 would be 2 plus 2 plus1 and so forth. There are many cultures that still count by 3’s or via a ternary system, there are no numbers beyond 3‘s, thus 4 would be 3 plus 1, so on and so forth. For the ternarians, our present day decimal system of 10’s would appear to be unnecessary cumbersome. Interestingly, the most widespread system in ancient times was the quinary or counting by fives and group of fives. Next to it was the senary or heximal system, but the most popular and widely followed among all these were the Germanic system that counted by 10’s, this was different from the Indian numerical as the Germanic system had no sense of the ‘0’ (zero).

In ancient times the most successful was the Sumerian sexagesimal positional numbering system of 60’s. Even today we count our seconds, minutes, hours in 60’s. Though the Sumerian system used ‘0’ (zero), they to had no conceptual sense as to what ‘0’ (zero) stood for in the scheme of things. The Sumerian system were further qualified by 10’s and 12’s. In some villages of France, they still use a vigesimal system. None of these systems had any need of ‘0’ (zero)’s.
The Greeks evolved the Egyptian system of 5‘s, 10’s, 50’s, 100‘s, 500’s by replacing the Egyptian symbols with Ionic alphabets, where each number from 1 to 9 were assigned a separate Greek alphabet, this was repeated for 10 to 90 and further 100 to 900, thus making a total of 27 symbols. This gave them a certain edge, for example: writing the number 87 in an Egyptian system would require 15 symbols, the Greek required only two. The Romans would digress back to an Egyptian like numerical and the Greek system would ultimately be lost to the Europeans who would end up using the cumbersome Roman numerical.
For complex astronomical calculations the Greek freely borrowed from the Sumerian sexagesimal positional numbering system thus introducing ‘0’ (zero)’s. But even the Greeks had no conceptual understanding of the ‘0’ (zero). The Greek worldview had no use of them. They would calculate using the Sumerian system and once done, they would then simply translate the result back into their own.

‘0’ (zero) is a dangerous number, It has uncanny proprieties, it does not behave like rational numbers do. It flouts the very ordering of ratio. Neither addition or subtraction, nor multiplication, nor division behave as they are supposed to. Without the conceptual understanding of the ‘0’ (zero), the Greeks kept tumbling into insurmountable paradoxes. For example, the Zeno’s paradox arise because his inherited sense making, or referential and conceptual framework lacked all mathematical and conceptual sense of ‘0’ (zero); introduce ‘0’ (zero) and his paradoxes cease to be paradoxical. But there are no easy ways to introduce a new conceptual sense, infact, it is almost impossible and demands a slow poetic unfoldment within the very skin of ones received world, that is within the mercurial folds of ones own-most language. It demands a complete transformation of the body from its inside, a change in the very perspective, which meant the destruction of the collective ways the Greek psyche had overtime come to experience and pose things. But nothing could be worse and deadly than the irrational powers of ‘0’ (zero), and Irrationals were poping up everywhere in their calculations, but the Greeks did not believe in the reality of the Irrational, especially ‘0’ (zero), which held within its indefinable definition (as the irrational never terminate, or repeat) a very dangerous and explosive power.

The Greeks believed that all numbers were in some sense deeply connected with the real world, and if irrational numbers exist as did the rational numbers, then their counterparts were sure to show up in the real world, which according to their world picture was simply impossible, cause it meant that reason and rationality were some how broken and this meant both human nature as well as nature herself had an irrational side to it. Which meant that if we could never come around to define rationally who we are, we will never be able to understand our ‘self’ in an ordered and rational way, which also meant that we would never ever be able to attain a full understanding of our world. It also meant that the world in some sense has no implicit meaning, and existence was after all only a play of appearances, and this meant that the universe had no underlying reality beyond this play (of appearances). This frightened the wits out of the Greeks and instead of accommodating this uncanny and unpredictable side of reality, they ended up suppressing and banning all references that suggested or hinted about their existence. …and they did this with a xenophobic zeal, in fact Pythagoras even declared that none such thing ever exists, and if such a thing ever showed up, then, they did so because they had somehow failed to apply the right method of calculation, which meant that it was just a matter of time before one would find the right one and the anomaly would cease once and for all. But the irrational kept showing up everywhere, and refused to be exorcized away.

It was one Hippasus who came up with a working proof and having done so had to pay with his dear life for having proven that their existence were after all provable as was any of the other rational number, and as Pythagoras could not disapprove his findings nor accept them, he had him punished by drowning. Accepting his proof meant destroying the very belief in a perfect and elegant universe. A universe that was supposed to be a handiwork of Divine reason, the word of God.

The Romans picked it up from the Greeks and via them this ancient prejudice found its way into the middle ages, and in essence the Christian West. Like the Greeks, the Church had no real use of it, in fact unlike the Greek before them, they feared it even more, as it threatened the very Idea of Divine creation and hinted about the irrational at the very heart of Godhead. This was unacceptable.

Mathematically ‘0’ (zero) is nothing and everything, point instant and infinity, it was this dual nature that was unacceptable to the Christian Europe. So dangerous was this ‘Idea’ of ‘0’ (zero), that Giordano Bruno would be burnt at the stake as a heretic. Though all this was to change in the age of enlightenment, still, somehow, this ancient prejudice would seep in and become the dominant bias of modernity. We don’t have to look for it in the torn pages of history, rather it is here, right under our roof; In this so called, ‘rigor’ of our professor through which the irrationals are filtered out.
And behind this demand for pure value independent rigor I contend, lies an ancient bias, a prejudice, a fanatic and frantic attempt to control, normalize, thematise, synchronize all things different and antithetic -to its own typical and technical way of thinking.”

“Coming back to Yama and Yami” The stranger continues, “He ‘one’s many‘, lords ratio and time, she zeros and nothings, plays with counterfactuals and irrationals, he regulates and orders, where as she hides within her womb, the power to shatter ‘ratio‘, to turn it mad, and to vaporize time, into a point eternity. She wholes, nonlocals, He separates, locals, she grants healing and he disease, but it is through them, these binary twins, that the world weaves its fabric. And thus, in spite of Yama’s contentions, their fates arrive entwined and their paths remain forever entangled.
Two task they bear, two paths they sketch, bheda and abheda, thus their gaze guide all things living.”

Extracted from: Dasarajna ‘Battle of the Ten Kings’ (a vedic fantasia)

© RajivMudgal., all rights reserved.

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