Zero and cognitive factors

I write about a topic of which I am very largely ignorant but which nevertheless seems interesting.

The overall question is: to what extent is our concept of zero shaped by religious, philosophical or metaphysical considerations and to what extent is it based on our mathematical sense.

The question came to me after attending a very interesting lecture/discussion on Indian mathematics given by Dr. George Gheverghese Joseph as part of the Royal Society’s 350th Anniversary celebrations.

As I understand it, the concept of zero was developed in India in the Vedic period, which stretched from the second millennium to the 6th century BC.

It is strongly related to a concept called Sunya which means nothingness, emptiness, void, while Sunyata refers to “emptying the mind of all impressions”, presumably to achieve peace.

It is a concept that has been used to describe an important aspect of the arts, namely the capacity to realize the void and represent it, while within the context of Sunya, architecture is also related to the void – “It is not walls that make a building but the emptiness”.

Is there, one wonders, any relation between the concept of zero and these almost philosophical and quasi-religious views about emptying the mind to achieve peace?

The view held by the Vedic mathematicians is that the number zero, being no number at all, is the necessary condition for the existence of all numbers.

But our view of zero, unlike our view of other numbers, seems to have evolved. In the 19th century, division by 0 was considered to be a meaningless operation, while it is viewed differently today. It is indeed critical in computational operations.

But zero is apparently also linked to very large numbers, indeed to infinity, a question that fascinated the ancient Indian mathematicians, whereas the ancient Greeks, apparently, had a horror of large numbers and infinity, preferring finite geometrical representations.

All of which would seem to suggest that the number zero, unlike natural numbers, is one that is open to other influences and open also to conceptual modifications. Perhaps this is also true of infinity.

It is worth thinking about in the context of the mathematical brain.