Day19 Play-by-Play

In class we focused on how to represent Babylonian and Mayan numbers. There were still mysteries of the Mayans to clear up, and there was an important comment about the Babylonians that needs to be shared -- because I'd forgotten to mention it earlier, but it seems interesting and important!
- Babylonians:
  1. Here's that important thing: one thing that came up on Friday, when last we met, was that the Babylonians blocked things into threes. This makes perfect sense, and gives their writing some unity. Since you can have at most nine martini glasses, it makes sense that you think about how best to represent nine of anything. And back to "fish fish fish", three-blocking in this case makes a lot of sense.
  2. Another thing is that you'll never see more than 5 boomerangs in a place. Three-blocking does not seem as useful in this case, but if you're already doing it for the ones, you may as well do it for the tens.
    On the other hand, two-blocking would also make sense, since you'll need at most three rows of martinis, and with two-blocking you'll also need at most three rows of boomerangs. Can't you see the Babylonian priests sitting around arguing about this stuff? Maybe there were wars fought over it...:(
- Mayans:
  1. They had a zero, which was really cool, but they also had a strange place value of 360 (when we might have expected a 400 place -- that is, 20². As Tadgh mentioned in class, the Mayans essentially had a "high-Mayan" and a "low-Mayan" number system. This was the priestly variant.
  2. One student noted that 360 will be highly divisible, since it is divisible by 60, which is itself highly divisible (it has proper divisors of 2, 3, 4, 5, 6, 10, 12, 15, 20, 30). We also noted that 360 is close to the number of days in a year. So there are several reasons for why 360 may have been chosen for special treatment.
I've done some example problems on the following two videos, one for each of the Babylonians and the Mayans. I've also included the "Whiteboard work" that I did on my iPad, which contains just the details of writing numbers in each system. That will probably suffice for most of you. The videos basically recap some of the highlights of both systems.
- Babylonian system video: and the ("Whiteboard work")
- Mayan system video: and the ("Whiteboard work")
Notice that I like to use binary trees again, to good effect -- to help me to figure out which digits to write. While it's not essential, trees are very useful! They can help us to break things down easily, and correctly -- to do the accounting properly.

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