## History for the fantasy buff: More on number systems

Last week I mentioned that the Romans had a base 12 (“duodecimal”) system for fractions. Crazy! But there was a method to their madness. Multiplication and division are easier in base 12 than in base 10. 12 has a bazillion factors (1, 2, 3, 4, and 6). We still see remnants of the Romans’ duodecimal system in some of our measurement systems and especially in our 12-hour, 60-minute clock.

As it happens, while base 10 is pretty much universal in the modern world, in the ancient world it was anything but.

The Mayans used base 20. So did the ancient Celts and the Maori.

The ancient Egyptians in the Old Kingdom used a binary numeral system. THINK WHAT AMAZING COMPUTER PROGRAMMERS THEY WOULD HAVE BEEN.

And base 5 is found in many ancient cultures, often with the word for “5” being the same as the word for “hand” or “fist.”

It is seldom necessary in a fantasy novel to world-build to the level of how the characters write their numbers but if you do, you have the freedom to get plenty creative. (There is even a tribe in Papua New Guinea with a numeral system that’s base 27.) Where you’re most likely to need something numerical is in dealing with money. Whatever your world’s currency is, how is it split into smaller coins? Fourths, fifths? Tenths? Twelfths? Halves? And what are the smaller coins called?

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### 4 Responses to History for the fantasy buff: More on number systems

1. Jessi Gage says:

Base 27?! That sounds complicated. But then so does base 12. I guess you get used to whatever your number system is.

• Amy Raby says:

Yeah, and I think a lot of the ancient cultures just didn’t do much advanced math in them, so if they were awkward for multiplication or division, maybe it didn’t matter because they weren’t doing those things. It seems that as the math got more advanced, the number systems had to change to become easier to work with. Although it’s hard to know which came first–there’s a chicken and egg problem.

2. I heard an interview with a mathematician around Christmas that talked about some of this. Apparently, there are cultures that don’t even have systems like this. I forgot all the technical terms, but their math works more like a young child’s. Not that it’s simplistic or anything. It actually sounds really complex and fascinating. Anyway, they count in something like multiples. So, if I recall right, when marking how many more from 1 to 10, if their multiple is 3, the answer would be 3. For them 3 and 9 (3,6,9) are equivalent. It was a bit difficult to wrap my brain around, but apparently, this is closer to how very young children see numbers, and it just sounded absolutely fascinating. I hope I explained that so it made even a little sense. 🙂

• Amy Raby says:

That does sound interesting. I don’t understand how it works, but it’s amazing how many different ways of solving these universal problems people have come up with.