While I am writing this, I am now in Singapore with my son Ken. I have attended the workshop on “Bright Dark Ages,” which is organized by the Institute of Southeast Asian Studies here. Their aim is to rethink what is known as the “Grand Question” posed by the work of British historian of science Joseph Needham. For those who may not know him already, Needham is widely known for his monumentally huge work on science and civilization in China. And the Grand Question here is why it is the case that, given the tremendous advances made by the Chinese civilization in matters of science and technology for the past millennia, modern science did not develop there.
Many of the participants debated and analyzed this question from many angles, but I won’t focus on this point here in this post. I would rather talk about one of the papers presented in the workshop on the numeral ‘zero.’ As is well known, zero originated in India around the Middle Ages. However, the author, George G Joseph from the UK, pointed out that the use of the concept “zero” was found in many other cultures which were contemporary or even older than India. For example, the Egyptian had the concept nfr, which means ‘beautiful’. This happened when the account sums up the costs and expenses of some transaction and found that the two were equal. So the word ‘nfr’ is written instead of a numeral.
Back to India, Joseph told us that the numeral ‘0’ originated from the Buddhist conception of “sunyata” or “emptiness.” So this was what perked up my attention. The idea is that from zero everything comes to be, and the zero is prevalent in anything and everything. I was immediately reminded of Nagarjuna’s dictum that emptiness gives rise to everything in the world, and that everything in the world resolves back to emptiness. Mathematics and reality are much more closer to each other than I thought previously.
So how did zero give rise to all other numbers? I don’t remember what Joseph said here in detail. Perhaps I have to look at his paper. But the idea is that without the zero, no mathematical computation that would give rise to more and more numbers than there are symbols for was not possible. If you have a symbol standing for a fixed number only, then you will have to have an infinite number of different symbols standing for an infinite number of numbers. That is certainly impossible. With zero, you can have the positional system of representing number, whereby the position a numeral is placed signifies the number times by the nth power of the base, which is usually ten. So the numeral ‘2’ in 20 represents the number 20 but not number 2, and so on.
For Nagarjuna, emptiness gives rise to all things because for anything to be a ‘thing’ at all, it has to be delineated and outlined in such a way that its boundary is clearly marked from all other things. Without emptiness, such boundary construction would not be possible. There is a saying quoted in Joseph’s paper that emptiness must be there so that the architect could work on defining an area with walls — otherwise this defining an area would not be possible. Furthermore, one can also see that emptiness is also everywhere in anything. Since all things change their forms, their characters and so on, their “empty” feature needs to be present as a condition which makes the changes possible.
We can talk quite a lot about these things, but I’ll keep this for the later posts.