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"Mathematicians Crack Mystery of Babylonian Clay ..." Topic

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214 hits since 4 Sep 2017
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Tango01 Supporting Member of TMP04 Sep 2017 3:50 p.m. PST

…Tablet ‘Plimpton 322'.

"Plimpton 322, the most famous of Old Babylonian tablets (1900-1600 BC), is the world's oldest trigonometric table, possibly used by Babylonian scholars to calculate how to construct stepped pyramids, palaces and temples, according to a duo of researchers from the School of Mathematics and Statistics at the University of New South Wales (UNSW), Sydney, Australia.

Plimpton 322, a 3,700-year-old Babylonian tablet held in the Rare Book and Manuscript Library at Columbia University in New York.
Plimpton 322, one of the most sophisticated scientific artifacts of the ancient world, likely came from the ancient Sumerian city of Larsa, which was located near modern-day Tell as-Senkereh in southern Iraq.

The tablet was most likely written between 1822-1762 BC (around the time of Hammurabi, the sixth king of the First Babylonian Dynasty).

It was discovered in the early 1900s by the archaeologist, academic and adventurer Edgar J. Banks, the person on whom the fictional character Indiana Jones was based.

In the 1920s, Banks sold the tablet to the American publisher and philanthropist George Arthur Plimpton…"
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Personal logo Bowman Supporting Member of TMP05 Sep 2017 5:30 a.m. PST

Fascinating. But is this correct?

We also demonstrate how the ancient scribes, who used a base 60 numerical arithmetic similar to our time clock, rather than the base 10 number system we use, …….

Isn't our time clock based on a combination of duodecimal system (base 12) and our minutes and seconds on sexagesimal (base 60)? Our angles are based on a sexagesimal system of sorts as 6 times 60 degrees equals a full circle. And all triangles have to have 180 (3 X 60) degree internal angles.

I'm very interested in the Maya and they used a vigesimal system (base 20). I must say that doing simple adding and subtracting is easier with the Mayan system than using Roman numerals. They also co-invented the zero.

So base 10 counting probably started with counting our fingers. Base 12 counting probably started with the thumb counting the 12 segments of the four remaining digits. I assume the Mayans got their system counting fingers and toes? But how do you get a base 60 counting system?

Personal logo etotheipi Sponsoring Member of TMP05 Sep 2017 10:18 a.m. PST

But how do you get a base 60 counting system?

You apply a little thought first and drive your system based on the desire to divide evenly by 2, 3, 4, 5, and 6. You get multiples of those for free (10, 12, 15, 20, 30), which also turn out to be convenient units if you have ten fingers. And you realize that throwing a 7, 8 or 9 in there radically increases the overhead for minimal return.

I have a history of math book somewhere that details how one of the sexigesimal system developing societies went through (roughly) that logic in developing their number system, based on several overlapping fragments of their math history. It's a reasonable explanation, and one likely to evolve separately roughly the same way in general (though different in detail) in isolated societies.

It's similar to Euclid didn't invent geometry. He collected, documented, and systematized what people had know for centuries. Again, it seems reasonable that with motivation (efficiency, profit) would standardize a system this way. We still do (and fail to do) this today. And we are often just as clear about the origins of our systems.


IIRC, I believe the four fingers and segments was a second most likely for duodecimal systems after ten fingers and two feet.

Personal logo Bowman Supporting Member of TMP06 Sep 2017 8:34 a.m. PST

You apply a little thought first and drive your system based on the desire to divide evenly by 2, 3, 4, 5, and 6. You get multiples of those for free (10, 12, 15, 20, 30), which also turn out to be convenient units if you have ten fingers.

Sure. But a simple counting system comes first.

The utility of a larger sexagesimal system is also useful for fractions as 1/2, 1/3, 1/4, 1/5, 1/6, 1/10, 1/12, 1/15, 1/20, and 1/30.

So I'm wondering if your typical Babylonian goes to market and buys onions, does she buy 5 onions or a 1/12th of a "X" (where X is their word for 60)?

As Babylonian numerals go, they seem to have a decimal system. They have two symbols, one (a straight line) for single units and one (a bent line) for tens. For example, 1 bent line is 10, 3 bent lines is 30 and 5 bent lines is 50. 4 bent lines and 3 straight lines is 43. Simple.


But no zero.

Personal logo Cacique Caribe Supporting Member of TMP07 Sep 2017 9:12 p.m. PST

Mathematicians crack ancient clay tablet?

Clumsy mathematicians!


goragrad07 Sep 2017 11:13 p.m. PST

Well contrary to the tablets of the Sea Kings, apparently this theory is well baked.

Personal logo Cacique Caribe Supporting Member of TMP08 Sep 2017 6:46 a.m. PST

Lol. Good one!


Personal logo Bowman Supporting Member of TMP10 Sep 2017 5:01 p.m. PST

Yikes! The humour here has me reaching for some tablets……..aspirin.

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