The Pursuit of "Useless Knowledge"

It seems that starting with the Egyptians and Babylonians people of around the eastern Mediterranean were curious about nature. Greek speaking scholars made a lot of progress until circa 400 when the heavy hand of the church put a brake. When for a few centuries Islam was liberal, Arab speaking scholars resumed the progress. When the grip of the church was loosened in the 12th century progress resumed from where it had stopped, hence the rush to the old Greek and Latin manuscripts and the Arabic translations.

Max Weber (Ferguson, p. 27) states that Confucians sought rational adjustment to the world while westerners sought rational mastery of the world. Ferguson disputes that view but I think Weber did not go far enough. Chinese thinkers focused on human well being without being bothered by useless knowledge. The westerners pursued useless knowledge.

The Earth is not flat

Aristotle (384–322 BCE) gave detailed arguments why the earth is a sphere, including the shape of its shadow during a lunar eclipse and that travelers going south see southern constellations rise higher above the horizon. It is claimed that Pythagoras (6th century BCE) was the first one to make the claim but he had provided no arguments.

Eratosthenes of Alexandria (276–194 BCE) used trigonometry to estimate the circumference of the earth. His result was roughly 10% accurate.

The idea of a spherical earth spread to India (circa 500 CE) and from there to China. However, it was disputed by early Christian writers before it gained acceptance in Europe.

The Earth goes around the sun

Aristarchus of Samos (circa 310-230 BCE, a bit later than Epicurus) proposed the heliocentric system and placed the planets in their proper order from the sun. Eventually his ideas lost to the geocentric system of Ptolemy (90-168 CE) that used a very complex model (epicycloids) to reconcile astronomical data with the idea that the sun and planets rotate around the earth. However mentions of Aristarchus ideas survived in manuscripts.

Another important mathematician/astronomer was Hipparchus of NIcaea (190-120 BCE) who invented trigonometry and discovered that the axis of the earth rotates with a period of about 28,000 years (procession of the equinoxes).

The ideas of Aristarchus were revived 1700 years later by the Polish mathematician Copernicus (1473 –1543) who lived in the region of Royal Prussia that belonged to the kingdom of Poland. He knew Greek and read Greek authors and even translated some of them into Latin.

There are few classic Chinese writings dealing with these topics. A poem by Qu Yuan (343-278 BCE) asks cosmic questions but it does not deal with answers. Chinese astronomy “took off” during the Tang dynasty (618-907 CE) and relied on Indian astronomers who moved to China.

Archimedes (circa 250 BCE) proved using rigorous mathematics that
223/71 < pi <22/7 or 3.1408 < pi < 3.1429 (true value 3.14159).

In China, the scholar Zhang Heng (78-139 CE) stated that pi was the square root of 10 or 3.16. He also wrote "The sky is like a hen's egg and is as round as a crossbow pellet. The Earth is like the yolk of the egg, lying alone at the center. The sky is large and the Earth is small." Source:
That is the closest we have of Chinese knowledge that earth is a sphere. Clearly it is a geocentric, not a heliocentric system.


Western Mathematics was not the sole province of classical Greece. During the Arab Golden Age there was a flurishing of Mathematics. The most famous mathematician is al-Khwarizmi] (c. 780 - c. 850) who was Persian but wrote in Arabic. “Algorithm” is derived from his name. The word “Algebra” is also Arabic.

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