SCOTT SIMON, HOST:
How did the decimal point come to be? - the dot that divides whole numbers. Historians are revising its origin story. Glen Van Brummelen studies the history of math and astronomy at Trinity Western University in British Columbia. He was working at a math camp for middle schoolers when one night he and a colleague were translating a Latin manuscript.
GLEN VAN BRUMMELEN: I was working on the manuscript of this astronomer, Giovanni Bianchini. I saw the dots inside of a table - in a numerical table. And when he explained his calculations, it became clear that what he was doing was exactly the same thing as we do with the decimal point. And I'm afraid I got rather excited at that point. I grabbed my computer, ran up and down the dorm hallway looking for colleagues who still hadn't gone to bed, saying, this person's working with the decimal point in the 1440s. I think they probably thought I was crazy.
SIMON: He traced the decimal point back 150 years further than previously thought, to a little-known mathematician in Ferrara, Italy, named Giovanni Bianchini.
VAN BRUMMELEN: He was using the decimal point, actually, in two different contexts. We don't exactly know which was first, but probably he was using it in conjunction with surveying instruments to find distances across fields or altitudes of buildings and so on. But then, what we hadn't been entirely clear on is that he ended up borrowing this for his work in astrology. He was an administrator for the court in the Duchy of Ferrara. And one of his roles at that time would have been to cast horoscopes to be able to see into the future.
SIMON: Should we make clear that when you say astrology, this wasn't what we think of as of, you know, Pisceans are fish and have two faces, but the position of planets.
VAN BRUMMELEN: Yes. That's right. What we read in the newspapers today is what's known as sun horoscopes. And they're very, very simplified compared to the practice of astrology back in the 15th century. The mathematics that's required means you need to be able to know exactly where the planets are at any given time. And this is a very complicated mathematical problem. You might remember the sine from your trigonometry experience in high school.
Obviously, they didn't have a calculator to compute these quantities, so they would have compiled tables for the sine, for instance. And so suppose you're using this table. It tells you what the sine of 43 degrees is. It tells you what the sine of 44 degrees is. But planets don't just hop from one degree number to the next. They travel continuously between them. So they're going to be moments when you're going to have to work out the sign of a number that's between 43 and 44 degrees. And that's where we find the dots in his tables - are in the process of finding a sine that fits between two values in the table.
SIMON: What's the significance of this finding, do you think?
VAN BRUMMELEN: With Bianchini, we can see that this decimal system came from real-life problems, like surveying and measuring. And a real-life problem at the time would have been the astrological needs for the court at Ferrara. And that's actually the power of our decimal fractional number system - the fact that you can use the same number system to balance your checkbook, to measure distances, to transfer it to all sorts of different contexts. It's a universal system. And so I would say the point to remember - forgive the pun - is that it shows that mathematics comes from all sorts of concerns all over human experience.
SIMON: Mathematics historian Glen Van Brummelen. Thanks so much for joining us, Professor.
VAN BRUMMELEN: Thank you.
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