The true meaning of the tablet has eluded experts until now but new research by the University of New South Wales, Australia, has shown it is the world’s oldest and most accurate trigonometric table, which was probably used by ancient architects to construct temples, palaces and canals.The ancients in general were better at math than we understand them to have been. We have forms of math they didn't have, but they had forms we have lost or abandoned, and sometimes they end up enabling pretty sophisticated mental work. In this case, it looks like the ancient Babylonians invented a form that was actually better than anything that has replaced it.
However unlike today’s trigonometry, Babylonian mathematics used a base 60, or sexagesimal system, rather than the 10 which is used today. Because 60 is far easier to divide by three, experts studying the tablet, found that the calculations are far more accurate.
“Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles,” said Dr Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science.
“It is a fascinating mathematical work that demonstrates undoubted genius. The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.
Of course, invention in Iraq did not end with ancient Babylon.
14 comments:
"Because 60 is far easier to divide by three, experts studying the tablet, found that the calculations are far more accurate"
This, sort of, is why I'm a fan of the Imperial system over the metric for dimensions in design. Twelve inches can be divided into thirds or fourths equally easily, decimal systems not so much.
That was one of the more staggeringly dumb lines in the puff piece.
Well, it's technically correct, but practically speaking, irrelevant. Rounding to the nearest few decimal places in a base ten system is good enough, especially for calculations for dimensions for building a building, where in reality, within an inch is about as accurate as you're going to get in the construction, no matter what.
The base doesn't matter, except perhaps for teaching elementary division. Whatever you pick as a base, there'll be an infinite number of integers incommensurate with it, so real-world division "decimals" are going to be truncated anyway. Unless every bridge and building you make uses only ratios of 3 to 4 cubits, so the only angles you ever deal with are from the triangles of the 3/4/5 flavor. Maybe that's why they picked 60 as a base?
That's not a bad opening theory. I was curious about the choice of 60 as a base.
Sixty is divisible by ALL THE THINGS (2,3,4,5—and also of course 6,8,10,12,15,20, 30). It's a handy base to use if you want to subdivide it. Much better than 10, which is only divisible by two and five.
(However, "novel kind of trigonometry", oh please.)
That sounds very plausible as well. It's the kind of thing we would be unlikely to do -- changing off of base 10 would be anti-democratic! -- but clearly it made sense to them. And, also, clearly it worked very well given the technology they had to hand.
I suspect they may have used base 12 for everyday, as less unwieldy, and then perhaps base 60 came out of that (12 * 5) for more advanced or ceremonial calculation. Twelve is also a "natural" base for humans (10 fingers plus 2 hands/palms), and I wish we used it. ;-)
What's wrong with base 16?
You could argue that our Imperial liquid measurements are more advanced than the metric ones. They are based on powers of 2--our ancestors must have anticipated the use of computers :-)
I am a big fan of an Imperial pint.
What's wrong with base 16?
Not divisible by three. Primorials FTW! ;-)
As a designer, let me tell you that dividing things by three is a frequent desire, and it's much easier in imperial vs. metric. Odd divisions just look better to the eye, frequently, than even divisions.
http://neoneocon.com/2017/08/24/the-ancient-history-of-math-plimpton-322/
She wrote about the same thing as here.
I had a much grumpier take http://idontknowbut.blogspot.com/2017/08/babylonian-trig.html. By a strange coincidence, Prof Wildberger happens to have just written a book to revolutionize teaching geometry.
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