[00:00.00]Listen to part of a lecture in a world history class.
[00:05.00]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. [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……um……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, travelling 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, um, taxes, censors’ records, things of that sort. [01:20.15]As a consequence, this system started with the number One.
[01:25.00]Student:With One? Not with Zero?
[01:27.55]Professor:Right. See in Roman Numerals, Zero isn’t really a value in and out itself. [01:33.50]It wasn’t used independently as a number on its own.[01:37.10] If your primary concerns just basic types of record-keeping……
[01:41.28]Student:Oh, yeah. I guess you wouldn’t need a Zero to count livestock.
[01:45.28]Professor:Or to keep track of green 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 text sub mathematics, that has Zero, negative numbers, even some sort of basic algebra, is written in South Asia in the early 7th century. [02:27.00]This text makes its way into the Middle East, to Baghdad.[02:31.00] And it’s eventually translated into Arabic by a Persian astronomer and mathematician. [02:36.50]Once he began his translation, he quickly realizes the advantage 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 10th 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 12th century, an Italian Mathematician named Fibonacci was travelling 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 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 interests, things of that nature. [03:43.70]Within the next century and the half, that becomes the accepted dominant number system in Western Europe.
[03:51.00]Any questions? Robert?
[03:55.00]Robert:Um, this Fibonacci, is he the same guy who invented that……um…….that series of numbers?
[04:01.10]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 your original text. [04:11.55]I mean, can you imagine? [04:13.40]Introducing the concept of Zero to Western Europe? [04:17.33]And this is what you go down in history for?
[04:22.00]Carol:So, do we see like an actual change in everyday life in Europe after the Zero comes in? [04:29.50]Or they really just……
[04:31.00]Professor:Well, well, the change takes place is in the development of sciences.
[04:36.00]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, ah, 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……