November 12, 2012

De-mystifying Mathematics (Part 3) – Concept of zero

We discussed in the previous post on the need to create a representation for non-existent values in the placeholder system of writing numbers. Using blank spaces may make it ambiguous as blanks are also used for separating words and numbers. We can create another symbol for this – so what is the big deal? Let us say we represented it by ‘0’ and called it ‘nothing’.

The problem arises in the definition of this symbol and its value. As we are talking about counting as the basic need, what does nothing mean? All other symbols 1 to 9 are countable. You understand what 1 apple means or 7 chairs mean. But what does nothing mean? Is ‘no apples’ the same as ‘no chairs’?

If you had just one apple on the table and took that away – you would be left with ‘no apples’. You will also be left with ‘no oranges’ or ‘no plates’. How do I deal with this symbol in basic calculations?

These are the types of questions that plagued mathematicians in Middle East and Western world even as late as 10th century. The more you think of it as a mystic symbol, the more confusing it may get. The Indian cultures had already embraced the concept of nothingness and it was an integral aspect of the spiritual traditions. ‘Shunya’ (the nothingness) and ‘Anant’ (the infinite) were easily understood and talked about in this part of the world.

The earliest documented references to this numerical symbol go back to around 5th century AD. This was the time when not only the numerical representations, but also the rules governing the usage and calculations came into existence. Rules explaining addition, subtraction, multiplication with zero were laid down and understood.

We are not sure if these existed before that time as there is no documentary evidence available so far. Even after this advancement, it took a few hundred years before the rest of the world understood and accepted this notation. The journey from ‘Shunya’ to ‘Sifr’ to ‘Zephyr’/ ‘Cipher’ to ‘Zero’ was a long one across continents and centuries…

Many great mathematicians and physicists have commented on this in the past. One of the best descriptions is by the French mathematician Pierre Simon Laplace who wrote:

“It is India that gave us the ingenious method of expressing all numbers by the means of ten symbols, each symbol receiving a value of position, as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit, but its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions, and we shall appreciate the grandeur of this achievement when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest minds produced by antiquity.”

To be able to fully appreciate the contribution of ‘Zero’ in today’s context, imagine writing numbers without the zero and placeholder system. Imagine no binary system and hence no electronics, no computer, no TV, no mobiles! On a lighter note, this is the mathematical representation of the spiritual truth – everything has come from nothingness :-)

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