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Wednesday, May 25, 2011

Zero is NOT equal to Zero

Its a long time since I have blogged about mathematics. Dont worry though, these are simple thoughts.

So what I want to talk about today is zero. We have been taught since childhood that Zero is a great number (invented by Indians no less, hence all the pride). Granted. We were taught that arithmetic was able to leap ahead because we gained the capacity to express large numbers using zero at the end (10, 100, etc.). So far so good.

But if we dig deeper, the function of zero which allows us to use a base-10 system is what we call 'Positional Notation' (see the link to understand better). In fact this Positional Notation applies for all other base systems as well. My grouse is, why the hell did the ancient Indians use the number Zero (as in, nil) as the positional notation instead of a brand new symbol - say, x? I (with my limited mathematical faculties, admittedly) don't see any reason why it makes sense for the Positional Notation to be equal to the number Nil. Lets see how things could have looked otherwise.

100 could be represented as 1xx
105 as 1x5
50 - 40 = 10 as 5x - 4x = 1x
50 - 50 = 0 as 5x - 5x = 0
(Here finally the zero appears in its true role - that of poverty - instead of masquerading as a multiplier, a giver of power!)

I continue to think: is there perhaps some mathematical reason why the positional notation needs to be the number nought? Perhaps 2^0? But the zero here is the number zero, not the positional notation. Cant think of anything else.

If I am right about this, then I am forced to conclude that the ancient Indians simply had an amazing sense of humor. They made a zero, the lack of something, a scarcity, a poverty, a failure, into the most important digit in math!

Pictured: Chanakya