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 so astonished and impressed with this kind of work. When I look at that tablet all I see are a bunch of triangle impressions like scales. I wonder how it is read.
> "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."
Clay tablets texts were written in soft clay mass, just pressing the clay with the wooden stylus produces the marks. Only once it's baked it is durable.
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 :-)
Oresme in Paris did it graphically. The calculators apparently produced the "mean speed theorem". It's written in the full text of the paper:
"The “Oxford calculators” of the 14th century CE, who were centered at Merton College, Oxford, are credited with formulating the “Mertonian mean speed theorem” for the distance traveled by a uniformly accelerating body, corresponding to the modern formula s = t•(v0 + v1)/2, where v0 and v1 are the initial and final velocities (12, 13). In the same century Nicole Oresme, in Paris, devised graphical methods that enabled him to prove this relation"
History of math class... one of the assignments was to find the error in a Babylonian secant table and also reason out how the computing error happened. Fun.
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[ 3.7 ms ] story [ 48.7 ms ] threadBut hey, the textbook didn't require any scary prerequisites like calculus :-)
http://thumbs.media.smithsonianmag.com//filer/67/a8/67a8aa02...
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.
Apparently mathematicians haven't changed much in millennia :)
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.
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!
(It's pronounced cune-iform, apparently, rather than cune-ay-ee-form with a diphthong)
/kjuːˈniːᵻfɔːrm/ kew-NEE-i-form or /ˈkjuːnᵻfɔːrm/ KEW-ni-form
Even a little web browsing wasted a lot of time. It lead me to read about word dividers:
https://en.wikipedia.org/wiki/Word_divider
IMAGINEIFWEDIDNOTUSESPACESATALL! OR·WRITING·WITH·INTERPUNCTS
https://en.wikipedia.org/wiki/Interpunct
Also Zlango was going to be the new writing system: https://en.wikipedia.org/wiki/Lango_%28app%29
I seems smartphones have killed it.
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
http://science.sciencemag.org/content/351/6272/482
"Ancient Babylonian astronomers calculated Jupiter’s position from the area under a time-velocity graph"
As gene-h noted, it's interesting because it's something close to calculus but done so early in history.
"The “Oxford calculators” of the 14th century CE, who were centered at Merton College, Oxford, are credited with formulating the “Mertonian mean speed theorem” for the distance traveled by a uniformly accelerating body, corresponding to the modern formula s = t•(v0 + v1)/2, where v0 and v1 are the initial and final velocities (12, 13). In the same century Nicole Oresme, in Paris, devised graphical methods that enabled him to prove this relation"
http://care.diabetesjournals.org/content/17/2/152.abstract