As far as the evolution of the Indian thought system is concerned, zero has been as much a mathematical concept as a spiritual one. The whole philosophy of Buddha is based on sunyata, nothingness. By the way the Sanskrit word for zero is sunya. When the philosophy, spirituality and mathematical use of zero was at its zenith in India, their western counterparts wondered how can nothing be something.
In India of the vedic age, there was no distinction between religion and science. A highly developed form of mathematics was used to place various temples in the geography of India and to construct individual temples. The Garbhagriha – sanctum sanctorum – was the sunya griha where for a moment the mind of the pilgrim went blank.
In eastern philosophy, existence was conceived as the paradox of being and nothingness. Buddha’s view was that the whole existence is a great void, it is all empty and nothingness. Then came Shankara who said there is fullness in everything.
While ‘nothingness’ was the basis of a rebellious religion and philosophy, ‘nothing’ was the starting point in the evolution of mathematics.
To make things simple, and from a mathematical point of view, let me divide all mathematics into three categories.
First of all, is the logical sequential common sense mathematics where two plus two is four. It has tremendous use in our day to day affairs. All scientific progress and commercial transactions are based on this. This is the mathematics that we learn as a part of curriculum in our educational institutions. Let us call it the logical mathematics.
Secondly, there is this mathematics of the group dynamics or for simplicity let us call it the dynamic mathematics. There is a proverb in Hindi –Ek aur ek gyarah – one plus one becomes eleven. According to the logical mathematics if one person does x amount of work in a day and another does y amount of work in a day, then both will do x+y amount of work. However according to dynamic mathematics both will do much more than x+y amount of work. Whenever two people work together they create a third force in the form of group dynamics or synergy that adds something to the total output. Of course if this third force is negative, then the total output will be less than the sum of individual outputs. If two people are able to lift a stone to a height of one meter it does not mean that one person will be able to lift it to a height of half a meter. One person may not be able to lift it at all. When a bird flies with its flock in a formation it uses less energy than it would do for the same distance if it flew individually. The synergy among the birds is such that even a sick bird that can hardly fly is carried along once it is a part of the formation.
Then, there is the mathematics of the transcendental or the mathematics of the mystical experience. Most of us are familiar with the first declaration of the Ishavasya Upanishad – Purnamadah purnamidam purnat purna mudachyate. Purnashya purnamadaya purnamevavashishyate. That is whole, and this also is whole. For only the whole is born out of the whole; And when the whole is taken from the whole, the remainder is whole.
This sloka attempts to describe the mystical experience of the ultimate reality. It is beyond logic. One has to transcend logic to get a glimpse of such mystical experience. Along with the illogical concept of zero, when some western logicians came across such declarations, they thought that the eastern seers who composed the Upanishads were lunatics.
Even though it is difficult to understand this sloka with our logical mind some indications can be given. Now water can be divided but not liquidity. When a jug of water is taken out from a bucket full of water the quality of liquidity is neither improved nor downgraded.
Or let us take another example. There is a rose plant. We cut a branch and plant it at another place where it grows into a plant again. When we cut a live plant what we are actually taking out is the tree-ness or the essence of the tree. However the tree-ness or the essence of the first tree remains whole at the same time the new branch also grows into a whole tree. We cannot say that by cutting the earlier tree the wholeness in either has been affected.
To make things simpler (or, more confusing), substitute the ‘purna’ in the above sloka with zero. Now you have something to argue with the logician, who has at least accepted the concept of zero i.e something is possible out of nothing.
To make things the simplest, meditate with Buddha or listen to Shankar’s Bhajagovindam. You will realise the nothingness of everything either way.