Counting to 60 by finger joints...
Q: Why did the Babylonians base their number system on 60? I can understand 10 or 20 but 60????
A: Yes, 10 is easy to see: using the fingers. Twenty, also, is understandable: fingers and toes the way Mayans
may have started their number system. However, sixty does seem strange.
[U of St. Andrews, Scotland] Babylonian numbers
The Babylonians got their base-60 number system from the Sumerians-a folk whose origins we know little
about. The Sumerian culture started about 4000 BC in Mesopotamia (what is now southern Iraq).
The most commonly accepted theory holds that two earlier peoples merged and formed the Sumerians.
Supposedly, one group based their number system on 5 and the other on 12. When the two groups traded
together, they evolved a system based on 60 so both could understand it.
No doubt, a base-5 system came from counting the fingers of one hand. But how does one count by 12s?
Maybe using the finger parts of four fingers? Read on for an idea from J.J. O'Connor and E.F. Robertson of the
University of St. Andrew's in Scotland.
Their theory says: the Sumerians counted to 60 using both hands like we do but with a difference. They used
finger parts instead of whole fingers.
Consider the four fingers of your left hand: ignoring the thumb. The joints divide each finger into three parts. So, we can count finger
parts to reach 12. Here's the trick: I use the fingers and thumb on my right hand to point. Using my right thumb, I point at each finger
part on my left index finger. That gets me to 3. I continue pointing with my right thumb at all the other finger parts on my left hand.
That's how I can count to 12.
Next, I point at each left-hand finger part with my right index finger to raise the count to 24. I've got 5 digits on my right hand and five
12s are 60. That's how I count to 60.
The neat thing about archeological sites is we may unearth a tablet verifying this theory. (Or one totally different.) Someday we may dig
up a clay tablet showing both systems: base 5 and base 12. Wouldn't that be something?
(Answered Jun. 28, 2002)
USATODAY.com, WonderQuest: Babylon's 360 degree circle
Crystal Link: Babylonia
McTutor School of Mathematics and Statistics: Babylonian numerals