60 Days

The Big Smoke

About 60

Astronomers in early civilizations in Mesopotamia knew that the solar year is not 360 days. 360 days would certainly be a much more convenient length year than is 365.25.... however, according to the article "Calendar" in my Britannica (1963 edition - for things historical I prefer older editions) (v.4, p.622-623)- they used a 12 month, 354 day, "lunar" year, and eventually (ca. 9th c. B.C.) realized that it could be adjusted to the solar year by adding (intercalating) seven extra lunar months every 19 years. Other changes were also made to more closely synchronize the solar and lunar calendars.

So, briefly, the Babylonians (who gave us base 60 for time-keeping) did not have a 360-day year. Neither did the Greeks, and these were the major "mathematical powers" of the ancient western world. The article on "Fractions" (v.9, p.576) really explains it. As I am not sure whether this is still in current editions, I'll quote the significant part: "When they decided to take 120 units as the length of the diameter of their standard circle (probably because its numerous factors, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 40 and 60, made the representation of fractions easy), the circle (using the old value 3 for Pi) became 360 units."
 
Then, as we know, they divided each degree into 60 units (our minutes), and each "minute" into 60 units (our seconds). Yes, the modern divisions of the earth are directly traceable to this. The only real connection between these and the divisions of the day is the penchant of the Babylonians to subdivide units by 60.