Geometry for the soul
After the crisis of √2, geometry became the core of Greek learning, and around 300 BCE Euclid gathered its best results into the Elements: thirteen books, one unbroken chain of proofs. After the invention of printing it became, by many counts, the most published book in the Western world after the Bible.
Albert Einstein thought this was one of the two foundations of modern science. In a 1953 letter he named them: the formal logical system of Euclid’s geometry, invented by the Greeks, and the Renaissance discovery that causes could be found by systematic experiment. Then he added a line that speaks directly to this course’s question. It’s no surprise, he wrote, that the sages of China didn’t take these steps:
The astonishing thing is that these discoveries were made at all.
Albert Einstein, letter to J. E. Switzer, 1953
Plato valued geometry so highly that, according to later tradition, his Academy warned off anyone ignorant of it. The argument here is that we usually misread this. We assume geometry was a prerequisite, a foundation you finish before moving on to other subjects. There’s some truth in that, but it misses the heart of the matter.
For Plato, geometry was moral and political education. It turns the mind away from shifting appearances toward what never changes, and a mind trained that way is freed from petty interests. Without geometry, Plato thought, you could become neither a philosopher nor a truly free person.
Music is number you can hear
Why was music one of the four mathematical arts? According to a Pythagorean legend, the discovery began with the sound of hammers in a blacksmith’s shop. The version that actually works uses a single stretched string. Stop it at half its length and it sounds the same note an octave higher. Stop it at two-thirds and you get a fifth; at three-quarters, a fourth. The intervals that sound most harmonious come from the simplest ratios of whole numbers.
So music was not a matter of performance or calculation. It was reasoning about proportion: number you can hear.
The one-string instrument
Greek teachers demonstrated harmony on a monochord, a single string with a movable bridge. Choose an interval to move the bridge and listen. Then try the Chinese method below it.
Another view
China discovered the same ratios. The method called 三分损益 sānfēn sǔnyì, “take away a third, add a third,” is recorded in early texts like the Guanzi and the Annals of Lü Buwei. Taking away a third of a string’s length is the Greek 2 : 3, a fifth. Adding a third gives the 3 : 4, a fourth. Repeat the steps and you get China’s five-note scale.
The craft was extraordinary. The 65 bronze bells buried with the Marquis Yi of Zeng in 433 BCE each ring two distinct pitches, depending on where they are struck. What differed was the home this knowledge lived in. In China, tuning belonged to ritual and to the calendar; pitch pipes and calendars were studied together as part of cosmic order. In Greece, the same ratios became a theory of proportion pursued for its own sake. Once again the contrast is not ability, but purpose.
Two ways to read the sky
Both civilizations watched the sky closely, but for very different reasons.
In China, astronomy was statecraft
The emperor ruled as the Son of Heaven, by Heaven’s mandate. Eclipses, comets, and unusual stars could be read as Heaven’s verdict on his rule. So astronomy was state business, a matter of legitimacy. An imperial bureau of astronomers watched and recorded the sky, and under the Ming dynasty private study of astronomy was forbidden.
That official watchfulness produced some of the finest records in the world. In 1054, Song dynasty astronomers recorded a “guest star” bright enough to see in daylight for twenty-three days. Today we can still see what it left behind: the Crab Nebula. Astronomers continue to use Chinese records of comets and eclipses.
In Greece, the sky was a puzzle
Greek astronomy started from two assumptions. The heavens are perfect and unchanging, and the earth is imperfect and full of change. Since the Greeks prized what doesn’t change, the heavens were the natural place to look for it.
But a few lights in the sky misbehave. The planets, the “wanderers,” drift slowly eastward against the stars, then stop, move backward for weeks, stop again, and resume. Plato is said to have set his students a challenge that later writers called “saving the phenomena”: explain the wanderers’ irregular motions using only perfectly regular ones.
The mathematician Eudoxus, a younger contemporary of Plato, answered with nested spheres, each turning at its own steady rate. Later astronomers, from Apollonius and Hipparchus to Ptolemy, refined the idea into circles riding on circles, called epicycles. Each circle turns steadily, yet together they produce the loops we see.
Save the phenomena
A planet rides a small circle (the epicycle) whose center moves around a large circle centered on Earth. Both turn at perfectly steady speeds. Watch what the planet appears to do against the stars.
Shrink the epicycle to zero and the backward motion disappears. Two uniform motions, combined, explain an irregular one.
Here is the method in its purest form: explain change through what does not change. In this reading, Greek astronomy is the prototype of all later science. Kepler replaced circles with ellipses, and Newton replaced crystal spheres with laws of motion, but the goal stayed the same: to find the unchanging rules beneath changing appearances.
What did “saving the phenomena” ask astronomers to do?
The course’s answer
So why did science begin in Greece and not in China? Not, this course insists, because the Greeks were smarter. The difference lies in cultural structure: how each civilization understood human nature and how it tried to bring that nature to completion.
China, a society of farmers, acquaintances, and kin, held up ren as its highest ideal and cultivated it through ritual. Whether a scholar studied the classics, Tang poetry, or the four arts of the cultivated person (the zither, the board game weiqi known in English as go, calligraphy, and painting), the aim was a humane heart.
Greece, a society of strangers bound by contract, held up freedom as its highest ideal and cultivated it through a free science: argument, proof, and deduction, knowledge that explains itself and so shapes a free mind. Two civilizations with different ideals took different roads. In this reading, they were different destinies, not a success and a failure.
Another view
This question has a famous history. The British biochemist Joseph Needham spent decades documenting China’s science and technology in Science and Civilisation in China, and he asked why modern science arose in Europe when China had led in so many technologies for centuries. Historians call it the Needham Question.
Many historians now question the question. Nathan Sivin and others point out that modern science didn’t arise in ancient Greece either. Greek science faded after antiquity, and the Scientific Revolution happened in seventeenth-century Europe. It drew on Greek, Islamic, Indian, and other sources, and it depended on experiment, printing, universities, and new institutions. The cultural answer given here is one piece of a larger puzzle, in which institutions, economics, and chance also played a part.
And ideas keep crossing. In 2015 Tu Youyou won the Nobel Prize for the malaria drug artemisinin. A key clue came from a fourth-century Chinese handbook by Ge Hong, which said to soak sweet wormwood in cold water rather than boil it. That hint led her to extract the drug at low temperature.
Closer to home
You have probably met the Greek idea without knowing it. The four mathēmata became the medieval quadrivium. Joined by grammar, logic, and rhetoric, they made up the seven artes liberales, the liberal arts, which literally means the arts suited to free people. That is the root of the American liberal arts college and its general education requirements. When an engineering major has to take philosophy, they are living this course’s argument.
The rest of the case is visible in American science too. In 1956, two Chinese-born physicists in the United States, Tsung-Dao Lee and Chen-Ning Yang, asked whether the laws of nature can tell left from right. Chien-Shiung Wu, at Columbia, designed the experiment that showed they can. Lee and Yang won the 1957 Nobel Prize for a question about as “useless” as physics gets. Ability was never the issue. In this course’s terms, it was always about the ideal and the setting.
What to keep
- Plato valued geometry as training in the unchanging, and so as education for freedom.
- The Greeks treated music as number and the sky as a puzzle: explain change through the unchanging.
- China knew the same musical ratios and kept better records of the sky, but placed that knowledge in the service of ritual and rule.
- The course’s answer: science began in Greece because Greek culture made freedom its ideal and free inquiry its path, not because of intelligence. Other historians add institutions, exchange, and chance.
Think it over
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Sources and further reading
- Plato, Republic, book VII.
- Albert Einstein, letter to J. E. Switzer, April 23, 1953.
- Joseph Needham, Science and Civilisation in China, Cambridge University Press, 1954 onward.
- Nathan Sivin, “Why the Scientific Revolution Did Not Take Place in China — or Didn’t It?”, Chinese Science 5, 1982.
- Lothar von Falkenhausen, Suspended Music: Chime-Bells in the Culture of Bronze Age China, University of California Press, 1993.