Babylonians Were Using Geometry Centuries Earlier Than Thought

From

http://www.livescience.com/53518-babylonians-tracked-jupiter...

> "It's not an actual trapezoid that describes the shape of a field, or some configuration of the planets in space," Ossendrijver told Live Science. "It's a configuration in a mathematical space. It's a highly abstract application."

> "Actually, this particular tablet has ugly handwriting," Ossendrijver said. "It's slanted. It's like cursive if it were written very rapidly. It's very abbreviated. He left out everything that is not absolutely necessary to follow the computation."

You can read the details here:

http://science.sciencemag.org/content/351/6272/482.full

The supplementary materials give a full transcript of the tablet you linked (one of several):

http://science.sciencemag.org/content/sci/suppl/2016/01/27/3...

> 1 The day when it appears: 0;12, until 1,0 days, 0;9,30.

> 2 0;12 and 0;9,30 is 0;21,30, times 0;30

> 3 is 0;10,45, times 1,0 is 10;45.

> 4 After completing 1,0 days, until 1,0 days 0;1,30.

> 5 0;9,30 and 0;1,30 is 0;11, times 0;30 is 0;5,30.

> 6 0;5,30 times 1,0 days is 5;30. (erasure) 10;45 and 5;30 is

> 7 16;15, the total. From appearance until station the motion is 16;15.

The actual trapezoid is mentioned in another tablet, which is also translated.

To see how the numerals actually work, just look up Babylonian Mathematics. It's a pretty simple base-60 system.

The book "The Riddle of the Labyrinth: The Quest to Crack an Ancient Code" by Margalit Fox is about the deciphering of the Mycenaean Linear B script. One of the striking (to me) things described in the book was how they even figured out how many different characters there were in the script. That image instantly reminded of their description.

Imagine looking at the handwriting of thousands of different people writing a script you don't understand. Some people are sloppy, some precise. Everyone has their own distinctive way of writing and you have to figure out exactly which differences in the characters are actually meaningful. Add in the fact that the writing samples you have span several centuries and changes in writing style and language occurred over that time. Deciphering a script like that is a staggeringly difficult task.

The writing is cuneiform script (https://en.wikipedia.org/wiki/Cuneiform_script), they were created by a wedge on wet clay. I guess our writing would appear as peculiar to ancient eyes :-)

For a general and short introduction to cuneiform I would suggest http://www.amazon.com/Cuneiform-Reading-Past-C-Walker/dp/052... (other books in the Reading The Past series are excellent, too).

Or, if you're interested in other type of ancient writing in general, there's a nice Mayan Hieroglyph workbook online (pdf: http://www.famsi.org/mayawriting/hopkins/MayaGlyphWritingWrk...). It's a great way to waste an afternoon!

The Open University has a beginner's introduction to Babylonian Mathematics

http://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=...

Edit: Here's an audio interview with Mathieu Ossendrijver on this research. The interview starts at the 20:30 mark

http://www.bbc.co.uk/programmes/p03g0d7b

Reminds me a bit of a guy my physics teacher met in the oil fields of alaska. The guy, who had never finished high school (and much less seen Calculus), had figured out a way to calculate the volume of a large, tapering tank using his own shorthand. He had the concept of limits and was essentially doing calculus.

My economics textbook in college was written for students who did not know calculus. I was a bit puzzled by two pages of fairly dense math in it. Examining it more closely, they essentially reinvented calculus using their own weird notation so they could calculate marginal returns, i.e. derivatives.

But hey, the textbook didn't require any scary prerequisites like calculus :-)

I'm guessing that the mentions of fourteenth-century Europe refer to the work of the https://en.wikipedia.org/wiki/Oxford_Calculators , an interesting bunch in their own right.