The Transmission Of A Number System

NARRATOR:Listen to part of a lecture in a world history class.

FEMALE PROFESSOR:So, one of the more common topics that comes up in world history, because it’s had a pretty dramatic effect on how different societies evolve over long periods of time, is cultural diffusion.

Now…cultural diffusion is generally defined as the transmission of culture from one society to another. And by culture, we mean anything from artistic styles to, um… you know, technology, science. So, we use “culture” very broadly.A common means of this process taking place is trade, traveling merchants, or trading hubs, places where people from various areas all come together and ideas get exchanged.

Let’s start with the example of the transmission of a number system, a system that used the number zero, from South Asia into Western Europe.

OK, so before this cultural diffusion happened, the dominant number system in Western Europe was the Roman numeral system.The Roman numeral system developed primarily as a means of record keeping, as a way to keep track of commercial transactions, um, taxes, census records, things of that sort. As a consequence, this system started with the number one.

FEMALE STUDENT:With one? Not with zero?FEMALE PROFESSOR: Right. See, in Roman numerals, zero isn’t really a value in and of itself.It wasn’t used independently as a number on its own. If your primary concern’s just basic types of record keeping…FEMALE STUDENT:Oh, yeah, I guess you wouldn’t need a zero to count livestock.

FEMALE PROFESSOR: Or to keep track of grain production, or do a census.And it wasn’t an impediment as far as sort of basic engineering was concerned, either, um, to their ability to construct buildings, roads, stuff like that.But other number systems developed in Asia, systems that do incorporate zero.The mathematics these societies developed included things like negative numbers, so you start to get more sophisticated levels of mathematics.

So… one of the earliest written texts sub-mathematics that has zero, negative numbers, even some sort of basic algebra, is written in South Asia in the early seventh century.This text makes its way into the Middle East, to Baghdad, and is eventually translated into Arabic by a Persian astronomer and mathematician.Once he begins his translation, he quickly realizes the advantages of this system, the types of math that can be done.Soon, the text begins to be more widely circulated through the Middle East, and other mathematicians start to advocate using this number system.So, by the tenth century, it’s the dominant system in the Middle East and as a consequence, algebra and other more sophisticated forms of mathematics start to flourish.

Meanwhile, in Western Europe, the Roman numeral system, a system without zero, was still in place.In the late twelfth century, an Italian mathematician named Fibonacci was traveling in North Africa along with his father, a merchant.

And while he’s there, Fibonacci discovers this Arabic text. He translates the… uh, the text into Latin and returns to Europe.And he promotes the adoption of this number system because of the advantages in recording commercial transactions, calculating interest, things of that nature.Within the next century and a half, that becomes the accepted, dominant number system in Western Europe.

Any questions? Robert?MALE STUDENT:Um, this Fibonacci, is he the same guy who invented that… uh, that series of numbers?<-FEMALE PROFESSOR:-> Ah...yes, the famous Fibonacci sequence. Although he didn’t actually invent it, it was just an example that had been used in the original text…I mean, can you imagine? Introducing the concept of zero to Western Europe? And this is what you go down in history for? Carol?

FEMALE STUDENT:So… do we see, like, an actual change in everyday life in Europe after the zero comes in, or is it really just…FEMALE PROFESSOR: Well, where the change takes place is in the development of sciences.FEMALE STUDENT:Oh.

FEMALE PROFESSOR: Even in basic engineering, it isn’t a radical change. Um, but as you start to get into, again, the theoretical sciences, uh, higher forms of mathematics… calculus… zero had a much bigger influence in their development.OK, now note that, as cultural diffusion goes, this was a relatively slow instance.Some things tend to spread much quicker, um, for example, artistic or architectural styles, such as domes used in architecture.We see evidence of that being diffused relatively quickly, from Rome to the Middle East to South Asia…