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The Zig-Zagging History Of The Number Zero


So think of all the numbers you've encountered today - the clock in your smartphone, maybe the date on your calendar, the numbers on that highway sign. And those are just the ones you can see. It's easy to take numbers for granted. They're the scaffolding that our economy, our technology, huge parts of our daily life, are built on. But there was a time when a zigzagging line didn't mean two and a vertical line didn't mean one and a circle didn't mean zero. Just how that system developed is a question that's fascinated Amir Aczel since his childhood. He's a math and science writer, and his new book is "Finding Zero: A Mathematician's Odyssey To Uncover The Origins Of Numbers."

AMIR ACZEL: To me, the invention or discovery of numbers is the greatest intellectual invention of the human mind. I have say invention or discovery because that's a huge problem in the philosophy of mathematics. Did we invent numbers, or do they exist regardless of us? But writing numbers is certainly an invention, and that invention is what has obsessed me all of my life.

WESTERVELT: You also explore some of the faults, starts and dead-ends along the way to our current system of numbers, which are known as Hindu- Arabic numerals. Could you talk about some of the number systems that, I guess you could say, have gone extinct?

ACZEL: Right. The Maya had a very interesting number which they used in calendars. And there was a zero there, actually. That number system didn't go anywhere. And then of course, there's the Babylonian number, (unintelligible) numbers, and they did not really have a zero. Sometimes they'd leave a space. And the best example - and my favorite - is the Roman numerals. And if you want to try something interesting with the Roman numerals, try to create the multiplication table and you can see it's very complicated. So and, the reason is that the numbers don't cycle. They have to use, say, L for 50 and C for 100. So it's unique, while we can use the same sign, like two, in different places. Two with a zero after it is 20. Two alone is just two. You can create numbers using the cyclicity of the numerals. And that's something that no other number system that I know of has.

WESTERVELT: Why is zero, specifically, so important?

ACZEL: Without a zero, you couldn't allow the numerals to cycle. You couldn't do this example that I gave, the two followed by zero stands for 20, creating that great economy where just nine signs plus a zero allow us to write any number that we want.

WESTERVELT: What sparked your interest in finding the origin of zero? You take us on this quest around the world.

ACZEL: I first became interested in numbers - my father was a ship's captain for cruise ship in the Mediterranean, and one of the favorite ports was Monte Carlo. And what I saw there were these numerals, and they're very beautiful, on a roulette table in the fanciest casino in the world. These numerals just captured me, my attention and my fascination. And it sort of - that really led me to pursue a career in mathematics and statistics. And then I became very interested in where these numerals came from. Everybody says, oh, numbers come from India. And I wanted to know how they came from India, and then I became aware of the big controversy with British scholar G. R. Kaye.

WESTERVELT: Who was convinced that the zero came from the West.

ACZEL: Exactly, and he was actually an expert on India, but he was biased. He writes in one of his papers, like, Indians think that their history started several million years ago and of course this is nonsense and the numerals don't come from India.

And the person I follow in the book, Georges Coedes, a French scholar, tried to prove the opposite. And this particular style that I'm after throughout this book that I'm trying to find is that zero that he used to defeat Kaye and his followers.

WESTERVELT: Your book is called "Finding Zero," so this isn't really a spoiler. I mean, you traced the earliest-known written representation of zero to this crumbling 7th century tablet that you find in Cambodia, and its stacked amid ruins of other ancient artifacts. What was going through your mind?

ACZEL: It's the greatest euphoria in my life. And I have a feeling I'll never have a moment like that ever again. And I just looked at it. I couldn't dare touch it, as if it were fragile - which it wasn't, it's a piece of stone weighing several tons. Greatest moment in my life.

WESTERVELT: Tell us its significance, what it said. Where was the zero, and what did the zero mean there in that writing?

ACZEL: Well, it says Chaka 605 began in the fifth day of the waning moon. So it's really an astronomical description of the beginning of a year and a calendar called Chaka. So luckily, they had the date there. So because the date has a zero, we have the first zero. And they had to write a zero. And what the rest of the tablet talks about is about slaves to be given to a king and sacks of white rice and several other things. So it's a list of gifts to a local king.

WESTERVELT: Amir, we knew this tablet existed. I mean, why was it so important to find the physical object?

ACZEL: Well, often times you read when you do research about something that disappeared. And when something is gone, it's really far from being the same anymore. To me, it was important to recover this artifact with the earliest zero because I feel it's important to see it and continue to study it. And there's a monument to this great invention of the human mind, the ability to write something down that represents complete nothingness.

WESTERVELT: Amir Aczel speaking with us from WGBH in Boston. His new book is called "Finding Zero." Thanks so much for speaking with us.

ACZEL: Thank you very much. It was my pleasure. Transcript provided by NPR, Copyright NPR.