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Astronomical motions provide us with three great "natural" time units: the day, month and year. The day is based on the Earth's spin, the month on the moon's orbital motion about the earth, the year on the earth's orbital motion about the sun. Why do we have ratios of 60:1 and 24:1 connecting the day, hour, minute and second? These relationships were born abouty 6,000 years ago in Mesopotamia (now Iraq) where civilization and city-states first appeared on earth. The Mesopotamiam number system was based on 60, not 10 like ours. It seems likely that the early Mesopotamians were more influenced by the 360 days in a year, the 30 days i a month, and 12 months in the year than by the number of fingers on their hand.
Footnote: The decimal system was promoted during the French Revolution, including decimal time and a decimal week (with 10 days): http://en.wikipedia.org/wiki/French_Revolutionary_Calendar#Ten_days_of_the_week