00:00Oh, sure. Yeah, well, we all use zero and the nine symbols, one through nine, to write all numbers in our daily lives today. But we don't realize how much thought over hundreds, even thousands of years went into developing the numbers that we write today, in which zero is, of course, the most important aspect.
00:21So we were able to write all numbers, however large they are, just using the ten symbols, zero through nine. And that development took thousands of years. It went through various stages and originated in India, which is why we call it the Indian number system or the Hindu number system today. Hindu number system refers, Hindu refers not to the religion, but to the people who developed the system thousands of years ago. And that's what's now used around the world.
00:49So in ancient Indian philosophy, there's this notion of Shunyata. And that's really the philosophical idea behind the zero developing. Shunyata referred to the state of zerowness that you're trying to achieve in meditation, emptying one's mind of sensations and emotions and thoughts.
01:07And that philosophical idea eventually started being notated down in linguistics as an empty sound. And then eventually it came into mathematics as the empty number, a number that signifies nothing.
01:21And that was a revolution in world mathematics, recognizing zero as a number just like any other number. And that's what allows us to write any number now using just ten symbols. This is the system that developed in India over thousands of years and now it's taken over the world.
01:38You mentioned a few references from ancient Indian texts that allowed the popularization of this. Would you like to mention some of them for the audience?
01:46Sure. Yeah, zero, even though it was invented by mathematicians like Ramla Gupta, who really wrote out the rules for the arithmetic operations on zero. Zero plus any number is that number. Zero times any number is zero.
02:01These were rules that were written by Ramla Gupta for the first time, recognizing zero as a number.
02:05But the fact that zero had made its way into the minds of non-mathematicians, that the common people were using zero is evidenced by the fact that many non-mathematical books and literature talked about zero.
02:22So there's this famous novel, Vasavdatta, from the fourth century, written by Subandhu. It's a novel filled with similes and metaphors in beautiful ornate language.
02:34And at one point it describes the stars in the sky as being zero dots on a blue rug in the sky. At that time zero was written as a dot, not as a circle.
02:42And then over time zero started being recognized as a number, just like any other number, that dot started getting bigger and bigger.
02:49And now we write it as a circle, as big as any other number. But the zero dot was used as the symbol for zero already in the fourth century by common people, by everybody, not necessarily mathematicians and scientists, as is evidenced by this appearance in this novel for the fourth century.
03:09You mentioned some references in Yajurveda and others. Would you like to mention them as well?
03:14Yeah, another very important philosophical breakthrough in ancient Indian philosophy was the study of very large numbers.
03:21So in the Yajurveda, there are names for all numbers up to 10 to the 12. In other words, one with 12 zeros after it.
03:28In most other cultures, people didn't talk about numbers more than the hundreds or the thousands.
03:33And here in ancient India, they were thinking about one with 12 zeros after it, numbers that big.
03:39And in fact, in a lot of Buddhist literature, there's a story in the Lalit of Istara where Buddha is described as telling the numbers all the way up to 10 to the 53.
03:54In other words, one with 53 zeros after it. He says that that's equal to a Dalakshana.
03:59And he has names for all the numbers up to one Dalakshana, which is one with 53 zeros.
04:04So this idea, these philosophical ideas of large numbers and of zero being something that is not just nothing,
04:12but is something that should be written and thought about, these two philosophical streams really are what led to developing the way we write numbers in the modern world.
