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Ancient Babylonians Figured Out Forerunner of Calculus (sciencemag.org)
sciencehabit writes: Tracking and recording the motion of the sun, the moon, and the planets as they paraded across the desert sky, ancient Babylonian astronomers used simple arithmetic to predict the positions of celestial bodies. Now, new evidence reveals that these astronomers, working several centuries B.C.E., also employed sophisticated geometric methods that foreshadow the development of calculus. Historians had thought such techniques did not emerge until more than 1400 years later, in 14th century Europe.
Since today is Friday, the most important issue regarding this story will be whether or not the ancient Babylonians were white men.
For the record, Stormfront says, "Bet your ass they were". When asked for comment, Donald Trump said that if elected president, he'll make sure the US has "the classiest calculus of any country."
You are welcome on my lawn.
Archimeded in the first century AD may have built upon Babylonian and Egyptian mathto create true calculus.
"Every time I see an adult on a bicycle, I no longer despair for the future of the human race." - H. G. Wells
How does "several centuries BCE" plus 1400 years = 14th century??
Pain is merely failure leaving the body
Because the youngest end of their date range is less than 100 years BCE, and off-by-one is close-enough. Likely it 200 years older, but that isn't certain. 350 to 50 BCE is the range given.
ancient Babylonians were just poor students of calculus, which their ancient astronaut alien overlords kept trying to teach them unsuccessfully.
While the geometric methods in question were not known to have been applied to such astronomical calculations until the 14th century, they were known to Babylonian mathematicians and the techniques themselves in isolation are not really big news - at least that was the impression I got from a more informative summary elsewhere. This is just "OMG babylonians invented calculus!" clickbait.
Good spot, I didn't notice that.
Neither, of course, did the editors. [snigger] Perhaps shitandpiss and dimmothy are working out their notice periods.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Western European Historians had thought such techniques did not emerge until more than 1400 years later, in 14th century Europe.
FTFY
And their VCR's didn't flash "12:00" all day
Table-ized A.I.
I see Timothy survived the takeover... :-)
On a more serious note, please can we have the "Read more" link back now ? Thanks.
TFA is generally accurate, but it has a name that has no direct translation to english:
оÐÐ Ðо (sorry, slashdot still doesn't do characters well)
And it is pronounce "gha ZEEN toes"
Good article otherwise.
The 14th century started in 1301, so it is not off-by-one.
NB: The message above might reflect my opinion right now, but not necessarily tomorrow or next year.
Whenever I try to picture Timothy, I keep coming up with this:
http://fairlyoddparents.wikia....
Is that wrong?
APK likes to ask for responses to the same things over and over. Maybe he just likes the responses?
That significantly extends the research before granting algorithm patents!
Please, everybody knows that Glorious Nation of North Korea invented calculus long time before that.
This post was brought to you by People's Hacking Army.
Using it analytically to derive the familiar differential and integral calculus is not.
So if calculus is derived from this Babylonian knowledge, should we rename it threerunner?
love is just extroverted narcissism
Blah, blah, blah. I don't pay any attention to them. As far as I am concerned, all religions Babylon.
Civilizations tend to "discover" philosophy, mathematics, literature, drama and great works of music in the centuries after they invent ways of writing those things down.
What's probably going on is that these things have been cropping up intermittently for thousands of years (or tens of thousands of years), but the ideas would usually not survive for very long because it would take unreasonable amounts of human effort to remember and transmit them.
By the way, video finally made it possible to commit dancing to permanent media in the early 1900's, so future historians will probably think of the 1900's and 2000's as the centuries when great dancing was first invented.
From what I've seen of sculptures and stuff they look awfully like murzlums.
Are you saying the sculptures have poor eyesight, like muslims, or that the sculptures look awful (in appearance), like muslims, or that the sculptures look [an] awful [lot] like muslims?
If it is the latter, do the sculptures look like muslims before they exploded, or after?
Mod parent up.
Ancient people were smart. It's today's computer shit weenies who are good at nothing.
... our last best hope for peace.
1401 is "more than" 1400.
Overall a very big deal, as far as I'm concerned. However, I have a copy of Ossendrijver's book, and a few passages in it lead me to have a view otherwise different from what I would've had had I only read the recent media reportings. While I don't see any inaccuracy in the article, it seems somewhat misleading by omission.
I'm not really the bookworm, academic type. This text, reading like a research resource, is pretty dense and has a lot to follow by my standards; I haven't actually sat down and tried to really follow it. Pardon the still yet pedestrian coverage.
Ossendrijver had already reported in his 2012 book that their archaic calculus had been used during computations of the moon's distance from the ecliptic.
Additionally, it's interesting that, in the book, he's pretty emphatic about the ancients' lack of concept of negative numbers in our modern sense every time he mentions their calculus, although they did have a notion of "subtractive numbers," which simply entails the subtraction operation of a smaller "positive" value from a bigger one. Subtraction of bigger numbers from smaller ones seems to have been avoided!
I bet you don't believe in the year 0 BCE either.
I think we've pushed this "anyone can grow up to be president" thing too far.
Whenever I try to picture Timothy, I keep coming up with this:
http://fairlyoddparents.wikia....
Is that wrong?
Id love to get TIMMY from south park out of my head, but he'd not care
These orbits are all elliptic curves, second order curves basically. With enough observations one could construct some kind of regression, extrapolation based predictions. So what the clay tablets contain could be simple prediction tables. Can one tell the difference between extrapolation or regression prediction and trapezoidal quadrature?
sed -e 's/Chuck Norris/Rajnikant/g' joke > fact
On a related note how does 1st and 2nd century BC count as "Ancient Babylon". That was toward the end of the Hellenistic period of what was barely left of Babylon. Ancient Babylon by archaeological standards (to avoid conflating it with any number of other empires that just happened to share the same geographical area) had ended some 1000 years before. In fact the article suggests that the 2nd century BC tablets were actually copies handed down from as far back as actual ancient Babylonian mathematical texts in or around 1700 BC. Which is quite a bit more interesting.
So what they really mean is Persian mathematicians during the Hellenistic period in the area that was known as ancient Babylon and now modern Iraq, but I guess that doesn't have the same ring.
How do you think they figured out the formula for the volume of a sphere? Or proved that the area of a circle was proportional to the square of its radius when it's impossible to construct a square of the same area in a finite number of steps with ruler-and-compass methods? The same techniques were rediscovered in China around the 3rd century CE, again as a result of trying to calculate the area of a circle.
I think the basic ideas behind integral calculus are pretty much inevitable when you have mathematicians messing with geometry problems that can only be solved with successive approximations -- although inevitable only because eventually someone really smart will get bored with doing things the long way.
What's distinctive about modern calculus is it's connections to analytic geometry and algebra (algebra with good notation, I might add). This allows us to generalize problems in a way that transcends geometric resemblance, e.g., the area under the curve of any polynomial.
Post may contain irony: discontinue use if experiencing mood swings, nausea or elevated blood pressure.
Why are we always so surprised to hear that ancient civilizations had smart people too? Our brains haven't really evolved in any significant way since then. They probably knew stuff that would blow our minds. But, all it takes is a few apocalyptic, natural disasters and/or catastrophic wars to erase a civilization and all it had achieved. There are probably many civilizations we don't even know about that disappeared entirely.
In our brief few hundred years of modern history we've discovered some pretty cool stuff. I can only imagine what a civilization that enjoyed relative stability for hundreds more might have learned.
The article mentions trapezoids. Did the Babylonians approximate curved regions with trapezoids, or did they just use trapezoids? Finding the area of a trapezoid doesn't require calculus.
What bothers me really is after thousands of years and reading tons of history, we failed to understand the simple thing the biggest culprit was/is the Religion. Why don't we just try to get rid of it.
It is not only and merely Western civilization that had discovered things and then gone on to make claims that that.
Muslims play exactly the same sort of game when they claim that Islam had a "Golden Scientific Age". This game gets played continually, yet people don't actually scrutinize these claims.
http://wikiislam.net/wiki/Setting_the_Record_Straight_-_The_Non-Miracle_of_Islamic_Science
I'm wondering how much ancient knowledge had been destroyed when Islam swept through the Middle East and beyond in the 7th and 8th centuries.
The Babylonians understood that the area under a graph of velocity of something is its position. They estimated that area using polygons. And that's it; none of this would have been news to Greek mathematicians, so why drag 14th century Europe into the story? Of course, the Babylonians didn't find ways to integrate or differentiate functions, nor did they invent a clear notation. (By the way, have you ever tried reading old Greek mathematical treatises? It's hell.)
Environmentalism is a religion Are you going to stop the environmentalists?
When we picture you Coren22 we keep coming up with this from your post history showing apk smacked you down http://slashdot.org/comments.p... on your huge technical mistakes. It's not wrong of him to spank your incompetent ass making you publicly eat your words.
Sorry for nitpicking, but it actually started in 1300.
https://en.wikipedia.org/wiki/...
NB: The message above might reflect my opinion right now, but not necessarily tomorrow or next year.
1. You have to actually get a technical point right before you can claim a victory, you can't just claim victory before you actually win, or you look like Buch with "Mission Accomplished" over his head when Saddam fell.
2. You couldn't make anyone eat their words, your arguments are repetitive and easily debunked. You have never actually won an argument, you just fall back on repeating the same argument over and over in hopes of getting the other person to shut up, which I refuse to do.
3. One person looking at your code is not a code review. Code reviews happen out in the open among a group of security researchers. It isn't like you have anything special in your script, it would take a few lines of shell script in Linux and Windows Powershell. Download all the other people's work, combine them, sort them and unique them. Simple shit man, stop being afraid someone will steal it from you, as there is nothing there to steal, and copyright covers you from stealing. If people steal your software from the source code, YOU CAN SUE THEM!
4. You really need to stop losing to the wet paper bag of your own arguments, it just makes you look incompetent when you keep making the same arguments, and keep supporting yourself.
5. Stalking people, and trolling everything they post is a sure way of coming off as creepy. I defend people I see you attacking, because I have been attacked by you, that doesn't make the other person my sockpuppet, and it doesn't make you automatically win an argument. If you want to have a civil conversation, have a civil conversation. Stop stalking people and posting the same shit over and over which has been proven to be inaccurate or silly.
APK likes to ask for responses to the same things over and over. Maybe he just likes the responses?