When was the last time you paused to appreciate the beauty and simplicity of our number system? Compare it, for example, to the Roman numerals, that we all become intimately familiar with in elementary school. Why is it better? To answer that question, try writing a very large number with Roman numerals, or try multiplying with them.
Now there is another ancient number system (in fact there are many) that never gets mentioned in school, even though in some ways it is much more sophisticated and closer to our system than Roman Numerals. I am referring to the cuneiform numerals. These were the subject of our lesson a few weeks ago. Many of the ideas for our class were taken from this video lesson by Jane Kats (in Russian).
We started off the lesson with a discussion of how people communicated quantities a long long time ago. Did people always have numbers? The kids weren’t sure, but they correctly guessed that the answer is no. But then how did someone tell his wife to set three extra cups for tea because guests were coming over? He had to draw three cups or say “Please set up an extra cup, cup, cup.” And what if the wife wanted to tell her husband that three sheep were eaten by wolves that day? She had to draw three sheep or say, “The wolves ate sheep, sheep, sheep.” All because there was no universal symbol for 3, or even 1.
Here is my attempt at representing the situation pictorially. The three cloud-like looking shapes on the bottom are (believe it or not) supposed to be sheep. I certainly would have had trouble communicating with my husband!
As time went on, things slowly improved. First, people came up with a generic symbol that represented one of something. Luckily, it was a symbol that was easy to draw so that those of us who are not artists had a chance. Also, because there was only one symbol, it wasn’t likely to be confused with anything, so any reasonable approximation would do. Here is mine:
But it was still a pain to communicate about large numbers of things. However, tedious tasks often lead to great inventions!
People in ancient Sumaria decided, “We have ten fingers; why not come up with a symbol that means 10?” And they did. It looked just like the symbol for one, only on it’s side. And so writing numbers became just a little less tedious.
At this point in the class, we interrupted our story and let kids play around a bit with the new (but really old) number system. We had them convert some small-ish numbers from decimal to cunieform and the other way around. Even though it was a great step forward for humanity, the kids noticed that writing numbers in cuneiform was much more cumbersome than in decimal.
Based on what I’ve said so far, the cuneiform numerals seem less sophisticated than, say, the Roman numerals. However, the interesting part is how the Babylonians (who inherited and improved upon the Sumarian system) wrote slightly bigger numbers. We told the kids, that after ten there was another special number. Naturally, the kids guessed that this number was 100. Instead of actually telling them the answer, we wrote the following on the board:
After a bit of guesswork and leading questions, the kids were able to figure out that the special number was sixty. A fun joke to tell your kids is that there are sixty minutes in an hour because the ancient Sumarians had sixty fingers.
Of course the kids immediately noticed that the symbol for sixty is identical to the symbol for one (we did not get to other powers of sixty, but they are also the same). We pointed out to them that we have something similar in our number system – the one in the tens position looks just like a one in the ones position, but means something different. But there is one big distinction; our 10 looks different from our 1 because of the 0. In cuneiform, the sixty looks identical to the one, it’s just “technically” in a different column.
The most exciting part of the lesson for the kids came at the end, when they got to write in cuneiform on clay tablets! (Ok, so they were made with modeling clay, but it was close enough).
This gave the lesson a feel of authenticity. The kids were also excited by the fact that you could erase something just by smoothing the clay over with your finger.
They also did some actual calculations:
So the next time someone complains about the difficulty of an arithmetic calculation, suggest to them they try do it in cuneiform. Better yet, tell them to draw an appropriate number of sheep for every quantity involved!