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Monday, May 26, 2008
The Sunya Machina - Part I
The concept Sunya (zero) is a tantric machine. It sits at the root of arithmetic, a number that denotes paradox itself. Zero is the signature and symbol of something that does not exist and yet it could have or would have. Having zero mangoes means having no mangoes at all. And yet, despite the lack of mangoes, you do have something – a signifier of your lack.

In this way zero splits the continous flux of kala (time) into two channels – that which is, and that which isn't. It has now become customary to denote 'that which is' with the number '1' and that which isn't with '0'. Therefore, zero is a seed (and generator) – it necessitates the birth of 1. However, wherever there is difference (is/isn't), there must be a repetition. One is zero as seen from a Universe with one less dimension.

As soon as '1' takes birth, it usurps the not-being of '0' as a kind of 'being somewhere else' (in some other Universe) and sees it's own holographic reflection/repetition, giving rise to a duality instead of a union – the number 2.

Two is to be understood therefore as '1 more of that which we called 1 before' or 'both is and isn't are now here'. Even then, these three concepts above cannot by themselves describe all of existence – the superset of which they are merely subsets. That Superset, the Totality of Existence would consist of the following entities (and in brackets we have the symbols associated with each concept):

Totality of Existence (Kala) = That which isn't (0) + That which is (1) + That which is and isn't both(2) + The remaining cosmos (3).

The number 3 therefore denotes the final doubt of the Descriptor, the sign that even though he may have attempted to describe in exact terms universal phenomenon, there is something that will always be out of his grasp, because the Descriptor is a mere subset of that which is being described. Not only does the Sunya Machine obviate the next 3 terms, it generates all the numbers till infinity without the help of symbols like 4, 5, 6, 7, 8, 9. How does it do that?

The number line of integers from 0,1,2,3....and onwards to infinity is a kind of cellular automaton. Euclid proved long ago in the fundamental theorem of arithmetic that every natural number greater than 1 can be written as a unique product of prime numbers. The original section of the number line (0,1,2,3) is a conceptual machine that 'generates' the rest of the numbers as an output. Merely two unique symbols (0 and 1) are sufficient to represent all the numbers in binary, and number systems with a base greater than 2 are justified by their practical circumstance.

Abhijit Bhattacharjee's “polar place value number system” is a system based on his conjecture (the Bhattacharjee Conjecture) that any kind of number, even fractional number – can be expressed as additions or subtractions of powers of three. He has provided an algorithm in Pascal to calculate these factors for any given number. If proven rigorously by a mathematician who knows the jargon that is valid in academia, this finding could stand as a more profound observation than Euclid's fundamental theorem. Euclid showed that all numbers can be produced by prime numbers, but Bhattacharjee is trying to show that all numbers can be produced by the numbers upto 3. This is a significant reduction/compression in the algorithmic complexity of the number system. Marvin Minsky has written in an email to Abhijit that more mathematicians should take note of his work. Meagre doubts that one might have will be clarified only by a careful study of his Pascal algorithm.


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