Ancient Babylonians Used Geometry That Anticipated Calculus

[n2doc]

By Erik Gregersen

In an article published in the January 29, 2016, issue of Science, Mathieu Ossendrijver, a historian of science at Humboldt University in Berlin, describes how Babylonian astronomers between 350 and 50 BCE used geometric methods thought to have been invented 1,400 years later to calculate the motion of Jupiter.

The Babylonians in effect constructed a graph with velocity across the sky as the vertical axis and time as the horizontal axis. By calculating the area under a curve on such a graph, one can obtain the total distance an object has traveled across the sky. In the case of Jupiter, the Babylonians described its motion as what looks like a trapezoid on the graph. They then calculated the trapezoid’s area. Their geometric methods were very similar to the Merton theorem, which was discovered by mathematicians at Oxford’s Merton College in the early 14th century and proved graphically by French bishop Nicholas Oresme around 1361. Such methods are a precursor to calculus.

http://www.britannica.com/story/ancient-babylonians-used-advanced-geometry-

the paper

http://science.sciencemag.org/content/sci/351/6272/482.full.pdf

[Gregorian]

1. Very cool We stand on the shoulders of giants.

But really we stand on the shoulders of everyone who came before us. Incremental concepts that lead to the next. Pretty amazing. I've always said that no one has invented anything. It is all presented to us, we just have to see it. The wheel was a small piece of log rolling down a hill, or a rock. Our brains are the mystery.

[longship]

2. Take that Gottfried von Leibniz and Isaac Newton!

You both lose!


BTW, I love the calculus. It made undergrad physics easy-peasy!

As Newton said, "I have stood on the shoulders of giants." Von Leibniz would have said the same, if only to battle with Newton.


(Newton and von Leibniz both independently invented calculus at the same time. They fought for the rest of their lives over it. Today's calculus uses von Leibniz's notation.)

[bvf]

7. Newton had better connections, IIRC.

That's great about Leibniz, though.

[phantom power]

3. Numeric integration!

[MisterP]

4. and Egypt's like, "oh, that ol' thing?"

[Jim__]

5. Galileo was also credited with a version of this theorem.

From How original is Galileo’s work on kinematics?:

...

Galileo stated a theorem similar to the mean speed theorem in his book Two New Sciences published in 1638.

The time in which any space is traversed by a uniformly accelerated body starting from rest is equal to the time in which that same space would be traversed by the same body moving at a uniform speed whose value is the mean of the highest and last speed of the prior uniformly accelerated motion.

There is a small difference between this formula and the Merton rule. The Merton school and Oresme used the speed at the middle moment, while Galileo used half of the highest and last speed of the constant acceleration motion to apply the mean speed theorem. To explain Galileo’s rule by reference to the Fig.MR, the area of the triangle OAB is equal to that of the square OACD whose height is half of OA. Galileo’s rule is true of a special case when the initial velocity is zero and the acceleration is positive, while the Merton rule holds true even when the initial velocity is not zero and the acceleration is negative. Galileo’s rule, however, has its own merit of being easy to verify experimentally. Measuring the meantime speed of constant acceleration motion was difficult at that time, but the last speed was easily measured by converting the constant acceleration motion into constant velocity motion.

...

Did Galileo discover the mean speed theorem or the double distance rule independent of the Oxford Calculators or Oresme? This is a point in dispute among historians of science. Takahashi Kenichi, a Japanese historian of science, denies the influence, taking up a letter from Galileo to Paolo Sarpi dated 16 October 1604 as a counterevidence. ...

[Moostache]

6. It is things like this that make me loathe religion...

If not for the Dark Ages, we would be living in a society 1,500 years more advanced than we are now.

Hundreds of generations have lived a life that was unnecessarily harsh, deprived of advances that are tantalizingly close in concept and frustratingly distant in grasp...all for the power grab of the Catholic Church and the destruction of society in those lost 1,500 years.