[Kevin OMalley]

Oops, shouldn't have said all.

I guess I don't follow. Where does the 360 degrees in a circle come from again? How did these cultures attain base 12 counting? I haven't run into any explanations that make sense yet, perhaps you have.

If they could do something as sophisticated as count in base 12, surely they could count how many days in a year there were. Being off by 5 days/year means that within a short time, their seasons go out of whack and their harvest gets affected.

[lepton]

12 is divisible by 2,3,and 4. Halves, quarters and thirds are easy to divide. Likewise, 60 is divisible by all of those, as well as 5. This has great advantages in making math simpler and fractions less common. We see its legacy in the day being two 12 hour periods, circles being 360 degrees (making manual trigonometry far less complicated), hours being 60 minutes, minutes being 60 seconds. The Babylonians used all of these conventions, and influenced all of their neighbors. Until the 1700s, most measuring systems, and many coinage systems, used a mixture of 12s and 3s.

10 is only divisible by 5 and 2.

[lepton]

Oh, and many older calendars had an "extra" period, with 5 or 7 days, to adjust for this known difference.

[null and void]

How did these cultures attain base 12 counting?

Because of the easy math. Unlike 10, 12 is evenly divisible by 1,2,3,4,and 6. Several early societies went for base 60, for easy division by 1,2,3,4,5,6,10,12,20, and 30.

Learning 60 different characters for numbers was more trouble than it was worth, though...