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Lecture 2 - The Transmission of A Number System

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

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 evolved 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, travelling 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, censors’ records, things of that sort. As a consequence, this system started with the number One.

Student: With One? Not with Zero?

Professor: Right. See in Roman Numerals, Zero isn’t really a value in and out itself.

It wasn’t used independently as a number on its own. If your primary concerns just basic types of record-keeping……

Student: Oh, yeah. I guess you wouldn’t need a Zero to count livestock.

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 text sub mathematics, that has Zero, negative numbers, even some sort of basic algebra, is written in South Asia in the early 7th century. This text makes its way into the Middle East, to Baghdad. And it’s eventually translated into Arabic by a Persian astronomer and mathematician. Once he began his translation, he quickly realizes the advantage 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 10th 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 12th century, an Italian Mathematician named Fibonacci was travelling in North Africa along with his father, a merchant. And while he’s there, Fibonacci discovers this Arabic text. He translates 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 interests, things of that nature.

Within the next century and the half, that becomes the accepted dominant number system in Western Europe.

Any questions? Robert?

Robert: Um, this Fibonacci, is he the same guy who invented that……um…….that series of numbers?

Professor: Ah……yes. The famous Fibonacci sequence. Although he didn’t actually invent it, it was just an example that had been used in your 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?

Carol: So, do we see like an actual change in everyday life in Europe after the Zero comes in? Or they really just……

Professor: Well, well, the change takes place is in the development of sciences.

Carol: Oh.

Professor: Even in basic engineering. It isn’t a radical change. Um, but as you start to get into, again, the theoretical sciences, ah, 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……