60 - Numberphile

The ancient Babylonians used a number system with base 60 (sexagesimal). Tablet image courtesy of Bill Casselman and Yale Babylonian Collection - more at http://www.math.ubc.ca/~cass/Euclid/y...

This video features Thomas Woolley - he tweets at https://twitter.com/#!/thomasewoolley

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Videos by Brady Haran

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  Science & Technology

[TheDiggster13]

I actually thought he was going to say 'because the babylonians had 60 fingers' when he was talking about why they used 60.

[elistonium]

64 divides really well with 2 and powers of 2 but little else.

[GaryHurd]

Babylonian, and Hebrew numerology held the number seven signified "completion." This magic number has obvious astronomical associations as it is the number of visible "planets," remembering that the ancients thought that the sun and moon were planets circling the Earth.

[GaryHurd]

A circle divided in half (with a "count" of 360 degrees) gives straight 180 degree lines, and in quarters a right angle of 90 degrees. The application to piling up mud bricks, and laying lines for the first cities are obvious. They also had a 10 day market calendar, and you can imagine the interesting combinations. We owe the mathematics of trigonometry to the Sumerians and their circle obsession.

[GaryHurd]

Actually, the place to start is Sumerian astrology. Their cosmology believed the circle was the "perfect shape," that the earth was a circle (disk), and the planets traveled circles. They observed the ~365 days of a year. Since 365 lacks symmetry it can't be "perfect." 360 has periods of 60, and 90. The Sumerian idea that a temple Holy Day didn't "count" as a day was the answer. The obvious Holy Days (the equinox, and solstice days, + one or two more) made the "real" 360 day year work.

[TheJayman213]

so sexagonesimal would be even more handy than dozenal if it weren't for the drawback of needing 60 different symbols.

[Xolroc Lowell]

One way to say it would be that they used a combination of base 5 and base 10, but the simplest description is that they weren't using a number system that can be considered as having a base.

[Malcolm Pagett]

This channel has such a mad on for brown paper. I don't blame then, it's awesome.

[Honopena]

they have done it already >:p

[Vriska Serket]

That's true. Maybe the Babylonians have a special symbol for 60 so we consider it to be a base 60?

[gregg4]

No, to write 50 they would just write L.

Since the value of the number was based on the letter used rather than position, they were not using any particular base.

[Vriska Serket]

The romans to make 7 would write out 1 set of 5 and 2 sets of 1. Were they using base 5?

...

Actually, I have no idea. I'm going to google that.