Foundations of Modern Science

Science 1650-1750

Pierre de Fermat (1601-1665) was a French jurist who did mathematics in his spare time contributing to probability and number theory

Blaise Pascal (1623 – 1662) was a French mathematician who designed and built the first mechanical calculator and also set the foundations of probability theory and projective geometry (used in modern computer graphics)

The English genius Isaac Newton (1642-1726) set the foundations of modern science by providing the laws of motion and universal gravitation that not only explained the Kepler's laws but also several other astronomical observations. His theory stayed unchallenged until Einstein's theory of relativity, 300 years later. For objects moving well below the speed of light, Einstein's theory reduces to Newton's. Therefore all engineering design is based on Newton's theory.

Newton built the first reflecting telescope and made several contributions to optics.

Newton also invented calculus, independently of the German mathematician Gottfried Leibniz (1646 –1716). Leibniz improved Pascal's calculator and he designed the first mass produced mechanical calculator. He also refined the binary number system that eventually because the foundation of digital computers.

.In short the analytical tools for the Western technological developments were all in place by 1750.

Why was China left behind?

Instead of trying to answer that question I want to take a look of mathematics and science in the west going back 2000 years. 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.

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.

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.

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 and were picked by Copernicus 1700 years later.

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.

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