[00:00.00]NARRATOR: Listen to part of a lecture in a world history class.[00:05.00]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.[00:18.25]Now…cultural diffusion is generally defined as the transmission of culture from one society to another,[00:25.40]and by culture, we mean anything from artistic styles to, uh… you know… technology, science…[00:33.82]so, we use “culture” very broadly. [00:36.38] 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.
[00:49.34]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.[01:00.00]OK, so before this cultural diffusion happened, the dominant number system in Western Europe was the Roman numeral system. [01:09.00]The Roman numeral system developed primarily as a means of record keeping, as a way to keep track of commercial transactions, uh, taxes, census records, things of that sort. [01:20.15]As a consequence, this system started with the number one.[01:25.00]FEMALE STUDENT: With one? Not with zero?[01:27.55]FEMALE PROFESSOR: Right. See, in Roman numerals, zero isn't really a value in and of itself. [01:33.50]It wasn’t used independently as a number on its own. [01:37.10] If your primary concern's just basic types of record keeping… [01:41.28]FEMALE STUDENT: Oh, yeah, I guess you wouldn't need a zero to count livestock.[01:45.28]FEMALE PROFESSOR: Or to keep track of grain production, or do a census. [01:48.90]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.
[02:00.00]But other number systems developed in Asia, systems that do incorporate zero. [02:06.40]The mathematics these societies developed included things like negative numbers, [02:11.52]so you start to get more sophisticated levels of mathematics.[02:15.35]So… one of the earliest written texts of mathematics that has zero, negative numbers, even some sort of basic algebra, is written in South Asia in the early seventh century. [02:27.00]This text makes its way into the Middle East, to Baghdad, [02:31.00]and is eventually translated into Arabic by a Persian astronomer and mathematician. [02:36.50]Once he begins his translation, he quickly realizes the advantages of this system, the types of math that can be done. [02:45.00]Soon the text begins to be more widely circulated through the Middle East, [02:49.77]and other mathematicians start to advocate using this number system.
[02:54.00] So, by the tenth century, it's the dominant system in the Middle East [02:59.00] and as a consequence, algebra and other more sophisticated forms of mathematics start to flourish.[03:05.77]Meanwhile, in Western Europe, the Roman numeral system, a system without zero, was still in place.
[03:13.66]In the late twelfth century, an Italian mathematician named Fibonacci was traveling in North Africa along with his father, a merchant.[03:24.00] And while he's there, Fibonacci discovers this Arabic text. [03:28.30]He translates the… uh, the text into Latin and returns to Europe. [03:33.77]And he promotes the adoption of this number system because of the advantages in recording commercial transactions, calculating interest, things of that nature. [03:43.70]Within the next century and a half, that becomes the accepted, dominant number system in Western Europe.
[03:51.00]Any questions? Robert?
[03:55.00]MALE STUDENT: Um, this Fibonacci—is he the same guy who invented that… uh, that series of numbers? [04:01.10]FEMALE PROFESSOR: Ah, yes, the famous Fibonacci sequence. [04:04.70]Although he didn't actually invent it—it was just an example that had been used in the original text… [04:11.55] I mean, can you imagine—[04:13.40]introducing the concept of zero to Western Europe, [04:17.33]this is what you go down in history for?
[04:20.33] Carol?
[04:22.00]FEMALE STUDENT: So… do we see, like, an actual change in everyday life in Europe after the zero comes in, [04:29.50]or is it really just…[04:31.00]FEMALE PROFESSOR: Well, where the change takes place is in the development of sciences.[04:35.45]FEMALE STUDENT: Oh.
[04:36.00]FEMALE PROFESSOR: Even in basic engineering, [04:38.10]it isn't a radical change. [04:40.30]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.[04:53.55]OK, now note that, as cultural diffusion goes, this was a relatively slow instance. [05:01.00] Some things tend to spread much quicker, um, for example, artistic or architectural styles, such as domes used in architecture. [05:10.30]We see evidence of that being diffused relatively quickly, from Rome to the Middle East to South Asia…
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