How have I forgotten this number system?

That’s easy. I couldn’t have forgotten it, as I had never known about it in the first place!

We’re talking about the Cistercian number system. Sounds monkish, doesn’t it?

Yes, that’s what it is; it was developed by Cistercian monks in the Middle Ages. You will recall, I’m sure, that Roman numerals had been used in Europe for an incredibly long time — over a millennium —until our friend Fibonacci convinced the Europeans in 1202 that the Hindu-Arabic system was vastly superior. He was right, of course. But it turns out that there was a third system. Here is an example of the number 4173 in the Cistercian system:

Wait! That represents a 4-digit number? That’s 14 bits of information packed into a single rectilinear symbol?! See if you can figure out how it works. I will wait…

All right, I couldn’t figure it out either. Perhaps the number 5750 would help, as it contains the same digit twice (ah, I’m giving away that this is still in some way a decimal system, as are even Roman numerals in their own way):

And here are two more numbers, 1410 and 1368, respectively:


For the full story, watch the ten-minute video by Alex Bellos; I have his new book on order, and will read it and report back later.


Categories: Math