Thursday, April 03, 2008

The Aztec Number Field

"So, Quitzocatal, how many times do 3 arrows go into 2 hearts? "

"Oh, that is easy, Teacher Moctezan, 12 bones and a remainder of 1 hand.
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9 comments:

Mr roT said...

Cool. Aztlan will give the gringos the bone.

4/03/2008 10:21 PM
Tecumseh said...

"They used the four mathematical operations of addition, subtraction, multiplication and division. But in almost all of the early societies, they could do everything they needed to do, with just those four. They didn't need square roots. They didn't need trigonometry"

Quick, let's write an Aztec precalculus book. All numbers will be rational, no stoopid sines and cosines, and forgeddabout exponentials and logs. Students will love it, we'll all get rich. Who wants to start writing the book?

4/03/2008 11:33 PM
My Frontier Thesis said...

This comes to mind when thinking of those nifty Aztec pyramids.

4/04/2008 1:33 AM
My Frontier Thesis said...

More seriously, there's already a field called indigenous mathematics throughout academia (which this article touches on). I attended a talk about it delivered by a mathematician. It wasn't much more than basic counting patterns worked into shaman fatalistic predictions. Individuals from some tribe (the name escapes me) on the southeast coast, for example, would have a shaman tie knots in long leaves. Depending how many knots were in the leaf determined the individual's future. The shaman had stored in his brain how many knots would decide a future, and so on. There was a bit of complexity to it, and it was interesting in that mathematicians today help shamans articulate certain traditions. But it didn't seem too crucial, say, to colonizing Mars. A couple doctors of engineering made it a point to sneer at the math, and directly and indirectly insult about every native in the lecture hall. That was interesting to watch. I opined more anthropological, on how some tribal elders are a bit jaded by all the deciphering going on with this, as it tends to take away from the "mystery" of their predictions. I was curious if the lecturer (an Anglo-American) ran into any such resistance during his data collection. He said he hadn't. I told him he hadn't conducted enough data collection then.

4/04/2008 1:42 AM
Mr roT said...

It's a fun puzzle and ignorance of our forebears is satisfying. Feynman did some work on the Inca calendar I think.

4/04/2008 2:57 AM
Tecumseh said...

Whatever. Note though that the Babylonians already knew about square roots, and the quadratic formula. I don't think you can even start doing any kind of serious computations with areas and such if you rule out square roots...

4/04/2008 9:12 AM
My Frontier Thesis said...

AI, it's still interesting to look at these respective cultures and civilizations though, right?

As for serious computations with areas, I don't know much about the mathematical prowess of the ancient Central American tribes, but the city of Teotihuacan is said to have been around 30 kilometers square at its peak. Hopefully the religion that embraces, encourages, and applauds Holy suicide (hence, human sacrifice) will die out around Babylon the same way it did in Central America.

4/04/2008 4:50 PM
Tecumseh said...

No offense meant about the Aztecs (though I must say their head-hacking rituals were rather frightening). Sure, study their culture, including their math. But face it -- compared to the math developed by the Greeks (or even the Babylonians and the Egyptians) eons previously, the Aztec math was simply not in the same league.

4/04/2008 11:33 PM
My Frontier Thesis said...

Yes, the Aztecs were too busy painting people blue and chopping heads off to concentrate on such frivolous things as math.

4/05/2008 12:19 AM

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