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Ancient Tablet Reveals Babylonians Discovered Trigonometry (sciencemag.org)
An anonymous reader quotes a report from Science Magazine: Trigonometry, the study of the lengths and angles of triangles, sends most modern high schoolers scurrying to their cellphones to look up angles, sines, and cosines. Now, a fresh look at a 3700-year-old clay tablet suggests that Babylonian mathematicians not only developed the first trig table, beating the Greeks to the punch by more than 1000 years, but that they also figured out an entirely new way to look at the subject. However, other experts on the clay tablet, known as Plimpton 322 (P322), say the new work is speculative at best. Consisting of four columns and 15 rows of numbers inscribed in cuneiform, the famous P322 tablet was discovered in the early 1900s in what is now southern Iraq by archaeologist, antiquities dealer, and diplomat Edgar Banks, the inspiration for the fictional character Indiana Jones.
Now stored at Columbia University, the tablet first garnered attention in the 1940s, when historians recognized that its cuneiform inscriptions contain a series of numbers echoing the Pythagorean theorem, which explains the relationship of the lengths of the sides of a right triangle. (The theorem: The square of the hypotenuse equals the sum of the square of the other two sides.) But why ancient scribes generated and sorted these numbers in the first place has been debated for decades. Mathematician Daniel Mansfield of the University of New South Wales (UNSW) realized that the information he needed was in missing pieces of P322 that had been reconstructed by other researchers. He and UNSW mathematician Norman Wildberger concluded that the Babylonians expressed trigonometry in terms of exact ratios of the lengths of the sides of right triangles, rather than by angles, using their base 60 form of mathematics, they report today in Historia Mathematica.
Now stored at Columbia University, the tablet first garnered attention in the 1940s, when historians recognized that its cuneiform inscriptions contain a series of numbers echoing the Pythagorean theorem, which explains the relationship of the lengths of the sides of a right triangle. (The theorem: The square of the hypotenuse equals the sum of the square of the other two sides.) But why ancient scribes generated and sorted these numbers in the first place has been debated for decades. Mathematician Daniel Mansfield of the University of New South Wales (UNSW) realized that the information he needed was in missing pieces of P322 that had been reconstructed by other researchers. He and UNSW mathematician Norman Wildberger concluded that the Babylonians expressed trigonometry in terms of exact ratios of the lengths of the sides of right triangles, rather than by angles, using their base 60 form of mathematics, they report today in Historia Mathematica.
As the bible says they all started to speak in different tongues.
but who beat the Babylonians?
What kind of tablet was it? iPad or Android?
#DeleteFacebook
My penis. However, I wrote the formulas in the snow with my piss, and the snow melted :(
Equating a table of pythagorean triples to Euclid is like equating the wheel that Oog invented in 50,000 BC to a Ferrari.
Babylonians don't get credit for trigonometry for being the first to use the concept of similar triangles.
Persians don't get credit for all of algebra because they were the first to write down the quadratic formula.
Aristotle doesn't get credit for absolutely all of math and logic because he invented modus ponens.
Eudoxus and/or Archimedes don't get credit (though arguably they should) for inventing calculus for discovering the method of exhaustion.
On the other hand, Euclid *does* get credit for inventing synthetic geometry and (basic) number theory, because Elements actually contains fleshed-out theories that still form a major part of what would be taught in a beginning course today.
a hurricane! OH MY FUCKING GOD we're all going to die
Live now on the L0de Radio Hour!
http://www.enmtw.com/lrh.html
Guess being masochists really is in the blood of the human race, infringing self harm since ancient Babylonia.
You know, I have discovered a lot of things I don't want the world to know about...
He and UNSW mathematician Norman Wildberger concluded that the Babylonians expressed trigonometry in terms of exact ratios of the lengths of the sides of right triangles, rather than by angles, using their base 60 form of mathematics, they report today in Historia Mathematica.
So what's new about that, beyond the base 60 thing?
The Babylonians didn't invent trigonometry, they invented time travel. They went into the future and stole trigonometry from us.
There's a lot to be said, but Slashdot has been infested with such hilarious Redditors. I never thought I'd miss the days when Digg commenters infested slashdot. Says something when the likes of Digg is far preferred to the likes of Reddit.
moving on...
the famous P322 tablet was discovered in the early 1900s in what is now southern Iraq by archaeologist, antiquities dealer, and diplomat Edgar Banks
From Plimpton 322 wiki,
So my comment isn't earth shattering, but at least you're smarter than you were a moment ago, unlike after reading any of the comments above mine. Go home Redditors, you're drunk.
The tablet doesn't really contain trigonometry as we understand it today. There is no concept of angle, for instance. Some have convincingly suggested alternate interpretations. That paper, by the way, dates from 2002, so this isn't really news.
If I can be modded down for being a troll, can I be modded up for being an orc, or a balrog?
(1) A table of Pythagorean triples does not Trigonometry make;
(2) A table of Pythagorean triples, however ancient, is not going to change trigonometry today;
(3) Credit for discoveries requires that you make your discoveries known. It's terribly fascinating that those people apparently figured this stuff out; but history will remember others as the founders of Trigonometry, and rightly so.
The tablet is missing the entire left section. It would be like finding part of a tablet that says "mc2" and decide that the person must have stumbled upon mass-energy equivalence long before Einstein. It's missing half the equation, and doesn't even define what "mc" is.
They were first or the invented an "they also figured out an entirely new way to look at the subject."
If it was not peer-reviewed, it is ancient crackpottery. Literally. Just saying.
In addition discovering trigonometry, the tablet shows Babylonia showed up hung over to their trigonometry mid-term exam and barely got a passing grade. Lucky for Babylonia, grading on a curve was millennia away from being invented.
Anons need not reply. Questions end with a question mark.
So you wrote it in shorthand?
Even today, the high priests, initiates, and also their counterparts are incapable of looking further than their own rear. A parasitic brand that requires symbology and incantation to effectuate an illusion of control. That it would breed this type of thinking is no wonder. Nevertheless, as I AM, so are You.
> Ancient Tablet Reveals Babylonians Discovered Trigonometry
And also invented the Tablet.
Most of the so-called religious myths attributed to ancient Sumer were not myths at all but advanced knowledge recorded in a metaphorical language, as was the practice all over the ancient world.
It would be a mistake to assume that ancient (or even slightly less modern) languages were metaphorical in nature, instead languages tend toward literal interpretations while adding their own metaphors.
You don't need to look beyond modern politics to see this in action: "well regulated" in terms of the second amendment meant "well oiled, calibrated, zeroed, etc" - just as when you take a gun to a range today and have it "regulated" you are having it "tuned up." Modern politicians however would have you believe "well regulated" means "supervised, controlled, registered in a database, etc" because they want to achieve something (no guns or reduced access to guns) which they aren't legally allowed to do, so they take the tack of redefining the words over time ("regulated" never meant "controlled under law" or anything of the sort when it was originally used in the constitution.) Similarly, "free speech" meant precisely that: "you cannot suffer anything for speaking." Modern interpretations however claim that to be a metaphor, that you can suffer for what you say.
Ancient tales of a great civilization being split into many tongues aren't that complex to deduce: they were talking about multiculturalism leading to the decline of the host culture, the same as we see today. When they spoke of a great flood it's because there was a great flood (recorded in geological records worldwide.) Some things certainly got embellished being that mostly theological records are all we have left (incidentally, why anyone destroying any historical landmarks or writings should be tried for treason - being functionally identical to ISIS in destroying history and dooming our progeny to repeat it) but the underlying pieces of the stories are usually based on real things.
Norman Wildberger runs a great Youtube channel. On it you can find a series (which is currently being made and released) about the tablet and ancient math.
Go to the source Luke: Playlist
Nah, I'm just pulling your leg. I'm not really a pseudo-mystical twat.
Shreeve is that you?
Imagine what humans in 3700 years will discover when they found our tablets!
Will $CURRENT_YEAR be the year of the Linux Desktop?
I took an undergraduate degree in History solely for the opportunity to study the Code of Hammruabi, which, along with the Pentateuch of the Bible, is one of the earliest systems of law ever recorded. Only later as a much older man was I able to afford going to Paris to see one of the actual steles on which the Code was inscribed, which was an unforgettable experience (it's a solid piece of obsidian over 7 feet high, with deeply-cut symbols that look like they were made about a year ago. These were people who didn't believe in Agile, not even for a moment!)
I am not terribly strong in mathematics, but I was able to follow the gist of the paper, and I do think their interpretations about the Babylonians preference for exactitude and integer divisions aligns quite well with the precision of their legal work.
From a purely academic perspective, it was an enormously sophisticated and skilled culture for its time.
"We receive as friendly that which agrees with, we resist with dislike that which opposes us" - Faraday
Trigonometry, the study of the lengths and angles of triangles, sends most modern high schoolers scurrying to their cellphones to look up angles, sines, and cosines.
Not like in the old days, when we memorized those trig tables.
Looking something up on your phone isn't any different than looking it up in a printed table. So looking up the sin of some particular angle (other than pi/2, pi/6 etc.) is something everyone has always done. The real challenge is memorizing trigonometric identities. But to be frank, if a student can find the trig identity he needs and use it successfully, who the hell cares? That's a very good result in itself.
Post may contain irony: discontinue use if experiencing mood swings, nausea or elevated blood pressure.
I've got a nit to pick in general here: angles can also be expressed as ratios, and in the general case (general being science and math, but not really applied fields like surveying), it is.
I am talking about angles expressed in RADIANS. A radian isn't even a unit of measure like a degree or grad, both of which are arbitrary units with no fundamental relation to math or science.
Radian angles are the ratio of arc length of the circle swept out by the angle divided by radius.
and its relation to Stein's binary GCD. And also binary GCD's relation to generic programming!
Not exactly, since "well regulated" in the second amendment is referring to the milita, not to the arms.
It seems to me the dark ages started earlier than we think and have lasted longer.. So "we" are really more like 2000 year BEHIND times. Imagine if the questions of Lucretious about the property of atoms and the use of this trig had been continuous... That old saw about the ones unable to learn from history destined to always repeat it.
Right but this isn't like the Tower of Babel story at all.
There is a structure, which may or may not be a tower. Languages and a dispersion of a group of people are mentioned.
But that's it. The Tower of Babel was an already built and well known tower. There was no tribute involved, no threat of destruction.
I guess I'm hung up on your phrase, "Another version of..."
The test for "versionality" can't be this broad. I don't see this story a actually related to the Tower of Babel story at all. They share elements, maybe from the same source in some sense, but if this is all it takes to be "another version of..." then so many texts meet that test it's absurd.
Thank you Dave Raggett
Not exactly, since "well regulated" in the second amendment is referring to the milita, not to the arms.
The meaning of the word didn't change when it was used. It has a direct meaning in the context of a militia: well trained and well equipped.
This is interesting stuff, but my question is, did they use this alternate trigonometry for anything. One alternative is some old crackpot in a Babylonian prison came up with this in his cell. Stamped it out on some old mud. The quest would be if they can find examples of these integer triangles used in construction. That would add a lot to the story. (Hmm, where do I find dimension drawings of some of their buildings accurate enough to test this?)