I never knew about this. It turns out that the ancient Babylonians invented a sexagesimal number system, meaning that instead of counting to 10 they counted to 60. This numbering system was more convenient for fractional calculations than a decimal system because the base (60) had more factors (2,3,4,5,6,10,12,15,20,30) than the base (10) in decimal (2,5). This means that there are many more one digit fractions making division easier. Another interesting source shows just how advanced their astronomy, trigonometry, and algebra were at such an early date.

This site makes many of the same points but also illustrates the symbols that the Babylonians used to represent numbers from 1 to 59. The interesting thing about looking their symbols is that it looks like they started with a base 10 numbering system and then expanded it to a base 60 numbering system. Perhaps as they began doing calculations, they realized that they had too many infinite fractions and chose to change the base to reduce this. For the new base they simply took the lowest common multiple of 2, 3, 4, and 5, which is 60. If they wanted to include the next prime number, 7, they would have had to use base 420, which may have been unworkable. So they compromised.

The other interesting fact that I did not know was that the Greeks and Europeans carried on sexagesimal notation on through the fifteenth century for astronomical and mathematical calculations. It seems strange to think that many people doing very advanced calculations just a few centuries ago were using a totally different numbering system than we use today. It is also interesting that the vast majority of the population did not actually use the sexageseimal numbering system for calculations, but only an educated elite who needed to do complex calculations. Nonetheless, sexagesimal notation was used for telling time, as there are sixty minutes in an hour and sixty seconds in a minute. So, our conception of time is directly related to the numbering system invented by the Babylonians.

I am going to try to learn more about this.

## Wednesday, October 05, 2005

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