The following is based on part five of Jacob Bronowski’s BBC series on the history of science and invention, “The Ascent of Man” (1973). It is about the rise of mathematics.
Mathematics is not the mere use of numbers, it is to reason about them.
With the Greeks, that begins with Pythagoras, born about -580. He said that numbers are the language of nature. He showed that in two ways:
- He showed how music that sounds good is music that is played on strings that come in particular lengths – those that are whole numbers.
- In about -550 he took the mathematical discoveries of the Egyptians and Babylonians, which to them were just discoveries, and showed how they followed from the nature of simpler elements – the first known mathematical proofs. It showed how number is bound up with the nature of the world, how it is the secret language of nature.
Proofs in geometry reached their height 300 years later in Alexandria when Euclid wrote down all the main ones in a book, The Elements. It is one of the most copied and translated books in all history.
Greeks applied geometry to the stars, to the motion of the sun and the planets. In 150, Ptolemy wrote down that beautiful model of the heavens, of circles within circles, in a book, which stood for over a thousand years. It came to the West from the Greeks not through the Romans, who cared little for mathematics and science, but through the Arabs.
The Arabs also brought to the West the astrolabe (pictured at the top of the post). It is an instrument that measures the height of a star or the sun that is laid over a star map. With it you can work out your latitude, sunrise, sunset, time for prayer and the direction of Mecca. It was a Greek invention that the Arabs made much more usable.
But more important than Ptolemy or the astrolabe were Arabic numbers, which by adding the number zero (an Arab word), made numbers far simpler to use than the old Roman (or even Greek) sort would allow. The Arabs brought the zero from India in 750, but it took another 500 years to catch on in the West.
Muhammad did not alow his followers to paint the human form, so Arab art becomes a wonderful play of forms. It was math as art. Bronowski shows us the beautiful palace of Alhambra as an example.
One thing the Greeks got completely wrong was how objects are seen in space: perspective. It was Alhazen, one of the great Arab minds, who got it right. That was in the 1000s. In the West Italian painters took to it first in the 1400s. It is what makes the Renaissance paintings so different than what came before.
But even with Alhazen something was still missing from the Greek and Arab picture of the world: time. That was added by the West in the 1600s with the work of Kepler, Newton and Leibniz.
See also:
Abagond 