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Babylonian Numerals

The Babylonian civilisation in Mesopotamia replaced the Sumerian civilisation and the Akkadian civilisation. 

From the number systems of these earlier peoples came the base of 60, that is the sexagesimal system. Yet neither the Sumerian nor the Akkadian system was a positional system and this advance by the Babylonians was undoubtedly their greatest achievement in terms of developing the number system. Some would argue that it was their biggest achievement in mathematics.

Often when told that the Babylonian number system was base 60 people's first reaction is: what a lot of special number symbols they must have had to learn. Now of course this comment is based on knowledge of our own decimal system which is a positional system with nine special symbols and a zero symbol to denote an empty place. However, rather than have to learn 10 symbols as we do to use our decimal numbers, the Babylonians only had to learn two symbols to produce their base 60 positional system.

Now although the Babylonian system was a positional base 60 system, it had some vestiges of a base 10 system within it. This is because the 59 numbers, which go into one of the places of the system, were built from a 'unit' symbol and a 'ten' symbol.

Here are the 59 symbols built from these two symbols.

Now given a positional system one needs a convention concerning which end of the number represents the units. For example the decimal 12345 represents

1 cross 104 + 2 cross 103 + 3 cross 102 + 4 cross 10 + 5.

If one thinks about it this is perhaps illogical for we read from left to right so when we read the first digit we do not know its value until we have read the complete number to find out how many powers of 10 are associated with this first place. The Babylonian sexagesimal positional system places numbers with the same convention, so the right most position is for the units up to 59, the position one to the left is for 60 cross n where 1 lte n lte 59, etc. Now we adopt a notation where we separate the numerals by commas so, for example, 1,57,46,40 represents the sexagesimal number

1 cross 603 + 57 cross 602 + 46 cross 60 + 40

which, in decimal notation is 424000.

"Chance favors the prepared mind." - Louis Pasteur