Re: why did the babylonians use a sexagesimal(base 60)numeration system

Question:
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Why did the Babylonians use a sexagesimal(base 60) numeration system?

References:
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The bulk of the answer comes from the great text on the history of 
mathematics:  "Mathematical Thought from Ancient to Modern Times" by 
Morris Kline, published in 1972.  Other texts I enjoy reading are Struik's 
book "A Concise History of Mathematics" and Dauben's book "The History of 
Mathematics from Antiquity to the Present: a Selective Bibliography".

Answer:
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Let me first set a little background into what was going in mathematics at 
the time of the Babylonians.  Until about 3000 BC we really don't find 
many advanced steps in mathematics.  The Babylonians and Egyptians were 
the first to really make strides in advancing mathematics.  However, of 
the two the Babylonians were the first.

Most of our information about the civilization and mathematics of 
Babylon comes from texts which were written on clay tablets.  The texts 
were written in soft clay and baked into stone tablets.  Some of these 
tablets are as old as 2000 BC, however the majority of the ones 
recovered so far are in the period from 600 BC to 300 AD  The texts 
were written in Akkadian with a stick which had a wedge shape called a 
cuneus (the Latin word for wedge).  The script is known as cuneiform 
derived from cuneus.  Kline's book gives an excellent example of this type 
of writing.

The most striking feature of Babylonian mathematics is the base-60 
counting.  However, at first the Babylonians didn't have a symbol to 
indicate the absence of a number in any one position which made their 
numbers ambiguous. A modern day example would be 1001, we use zeros to 
indicate the absence of number in a given position but the Babylonians 
would just write 11, so you would have to use the context of the usage to 
figure out just what number is being referred.  However, much later a 
symbol was developed to indicate the absence of a number.

One misconception is that the Babylonians used base-60 exclusively.  
Sometimes numbers were written with special symbols representing one 
hundred and one thousand.  This gets more confusing since they were used 
together with the base-60 numbers, and again the context of the usage 
determined the actual number.

The Babylonian system of counting, like present day, was composed of many 
historical and regional customs.  In several thousand years people are 
going to wonder why we used 12 inches in a foot instead of some other 
number.  There are several very reasonable theories why the Babylonians 
used a base-60 numbering system.  The first is their system of weights and 
measures.  They used a system which had values in it having the ratios 
1/2, 1/3, 2/3, 1, and 10.  If there is another system with a different 
unit but the same ratios, and political or social forces compel the fusing 
of the two systems.  And if the larger unit were 60 times the smaller, 
then  1/2, 1/3, and 2/3 of the larger unit would be integral multiples of 
the smaller one.  Thus the larger unit might have been adopted because it 
was so convenient.

Another possible explanation comes from the coinage system.  One talent 
and 10 manna could be written as 60 manna.  We do the same thing when we 
write $1.20 and mean 100 cents by the 1.  The scheme for writing amounts 
of money may then have been taken over to arithmetic generally.

The most widely accepted explanation comes from their texts on the motions 
of the sun and moon.  They used the base-60 numeration system exclusively 
in these texts.  These texts are surprisingly accurate.  They represented 
the length of the year to within 4.5 minutes.  Also, the division of the 
circle into 360 units originated in Babylonian astronomy.  This was used 
to divide each of the 360 parts (degrees) into 60 more parts and so on.  
Even the astronomer Ptolemy followed the Babylonian practice.