The Echoes of Ancient Numbers

In the modern world the dominance of a counting system based on the number 10 is so complete that it is hard to imagine using a number system with a different base number.

The number 10 has probably risen to dominance because people have always used their fingers to count and so many ancient people around the world naturally grouped things in tens. But it wasn’t universal. The ancient Celts, for example, seemed to have used their toes as well and so based their number system on 20. And there are still remnants of this system in the modern world. This is why the French get to 60 and suddenly start counting in batches of 20. There is no specific French word for the number 70 (instead they use soixante-dix which translates directly as sixty-ten) and for the number 80 they say ‘quatre-vingts’ (four-twenties) after which they count in another batch of 20 up to 100. Similarly, in English, Abraham Lincoln famously talked of ‘four score and seven years’ instead of 87 years.

What about counting with a numbering system based on the number 60 (a sexagesimal system)? This is what the ancient Babyonians and Sumerians did and, at first glance, it looks completely alien. However, we do in fact continue to use their system all the time - this is the reason there are 60 minutes in an hour, 60 seconds in a minute and also why the day is divided into two lots of twelve.

But why 60?

It turns out that 60 is a fairly sensible number. It is the lowest number that can be divided evenly by 6, 5, 4, 3 and 2 which makes it very useful for trade. So perhaps that is why they decided to use it. Or perhaps, slightly unconvincingly, it is to do with the roughly 360 days in a year which can be divided into 12 groups of 30. But the answer that seems most likely is that there is an alternative way to use your fingers to count.

If you look at your four fingers you will see that they are each divided into three segments (or phalanges). Using your thumb as a pointer you can count along each segment which takes you to 12. Each time you get to twelve, you hold up a finger on the other hand to help you keep track. By the time you are holding up all 5 fingers on the other hand then you have counted five lots of twelve which equals 60. Click on the button below for a video demonstration.

So we are not just a decimal society. We are, at least to an extent, also a vigesimal and a sexagesimal society. Like so much of our language, culture and behaviour, our counting systems retain the echoes of ancient practices.