Unfortunately official recordings don't start until next month, but my wife managed decent capture herself:
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An earlier article version of this talk can be found at:
http://www.livescience.com/44964-why-60-minutes-in-an-hour.html
The talk is based on a passing mention in the following book:
Page 4:Several centuries of continuous [Mesopotamian] observations provided an invaluable body of data for the computation of planetary periods… As it would have been an overwhelming task to convert all these data into the decimal system… the Greeks maintained the sexagesimal system for astronomical measurements… This was also adopted by the Indians as early as antiquity… Then… it reached the Muslims who in turn transmitted this notation to medieval Christian Europe. The sexagesimal division… still used today is thus a living witness to the sexagesimal base once used by the Sumerians… in prehistoric times.
Here's some books that helped me stitch the narrative together:
And more generally about the history of mathematics:
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