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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.
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.
The concept of limit is not only not simple, I believe it to be false. It's a very useful theoretical concept, as is the real number line, but I do not believe that it has any actual existence in the world outside of mathematics. Just because you can't look at something close enough to see where it dissolves into pieces doesn't mean that it's actually continuous. This is why Xeno's paradoxes were so annoying. Most of them rely simplicity on the assumption of continuity, which is intuitive, but false. (Some of them have more complex failing, however. Achilles and the Tortoise also relies on the sums of infinite series being not being finite.) But Cantor's solution was not the way the universe solves the problems.
I think we've pushed this "anyone can grow up to be president" thing too far.
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.
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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.
At the least, it's a new perspective about how history progresses and attempts to describe the development of the arts and mathematics based on the sole defining purpose of the culture that brings it about. The later stages are when cultures develop into civilizations at which point the defining purpose has run its course and dies. I guess at the most, it's an eerily accurate prediction and description of the world today (written 100 years ago). According to him, the defining purpose western civ is based on Norse culture's search for the infinite which it can never reach. Calculus is an example as are shared cultural myths (Arthurian legend and search for the Holy Grail).