"take the most modest of all symbols, namely, 0, which stands for the number zero. The Roman notation for numbers had no symbol for zero, and probably most mathematicians of the ancient world would have been horribly puzzled by the idea of the number zero". *
"When we speak of no-mind or ‘don’t know’ mind I believe that many Zen practitioners have a problem completely attaining this state of mind. The history of Zero or ‘nothing’ has had a tenuous past in the evolution of Western Philosphy. Christianity, as well as Judaism, did not accept the idea of ‘nothing’ until the 17th Century. In the Catholic Church, to even speak of ‘nothing’ was considerd a heresy and a giving rise to the Devil. After all, if God was the creator of all things, then the negation or lack of existence must be the work of the devil. No wonder we have such a difficult time with this concept.
In our Zen Practice no meaning is great meaning, and great meaning is no meaning. It is sometimes called zero mind. So what is zero mind? If you go around and ask, “Is zero a number?” You will get very interesting responses.
If someone says zero is a number, then you can do anything with zero. To examine this we can look at the following calculations. 9 x 0 = 0. Then, 9 = 0/0. O.K.? Then, if you say it’s a number, then 0/0 = 1. So 9 = 0/0 = 1, and 9 = 1. As a computer programmer I so often come across the ‘divide by zero’ error in one of my queries. So if we can’t divide by zero, is it a real number?
This state of mind exists outside of logic, it exists in a realm of universal consciousness. Our ‘don’t know mind’ isn’t held by the law of mathematics, yet math wouldn’t function without zero. The rules governing the use of zero appeared for the first time in Brahmagupta's book Brahmasputha Siddhanta (The Opening of the Universe), written in 628. Here Brahmagupta considers not only zero, but negative numbers, and the algebraic rules for the elementary operations of arithmetic with such numbers. In some instances, his rules differ from the modern standard. Here are the rules of Brahmagupta:
The sum of zero and a negative number is negative.
The sum of zero and a positive number is positive.
The sum of zero and zero is zero.
The sum of a positive and a negative is their difference; or, if their absolute values are equal, zero.
A positive or negative number when divided by zero is a fraction with the zero as denominator.
Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator.
Zero divided by zero is zero.
It took another thousand years for Western Mathematics to catch up to this ancient Indian concept to sunyata. Zero mind can do anything. If you say zero is a number, then zero is a number. If you say zero is not a number, then zero is not a number; this simply doesn’t matter. Zero contains everything; and everything returns to zero. This is Zen mathematics, so zero mind is very interesting. If you keep zero mind, then you can do anything **
* in Alfred North Whitehead
"The Importance of Good Notation"
from Whitehead's An Introduction to Mathematics
Henry Holt & Co, 1911
from Chapter V “The Symbolism of Mathematics”