A question the internet answers badly

The Shadow That Measured the World

Columbus did not prove the Earth was round. Educated people had known it for nearly two thousand years — and a librarian in Alexandria had already measured its size to within a few percent, using nothing but a shadow, a distance, and the angle between them. Do his measurement yourself, then meet the rest of the story.

The schoolbook scene — Columbus sailing west against a world that feared the edge — is one of the most durable false things in popular history. The Earth's roundness was settled Greek science by Aristotle (c. 350 BC), and around 240 BC Eratosthenes of Cyrene did something more: he worked out how big it is, without leaving Egypt. Here is the whole of his method, live. Move the controls and watch the circumference of the planet fall out of two numbers.

The trick is that the sun is so far away its rays arrive essentially parallel. So the angle a vertical stick's shadow opens at the northern city is exactly the angle between the two cities seen from the Earth's centre. That angle is a known fraction of a full turn; the distance is that same fraction of the way around the planet. One ratio gives you the whole sphere.

Eratosthenes got 250,000 stadia (he rounded to 252,000 so it divided neatly into 360°). Whether that is breathtakingly accurate or merely good depends on a length we no longer know for certain — try the three candidate stadion lengths above. With the short Egyptian unit he is within about 1%. That is the honest shape of the achievement: the method is exact; the conversion is where the uncertainty lives.

So what was Columbus actually arguing about?

Not the shape of the Earth. The experts who doubted him — the Salamanca commission — doubted his arithmetic. Columbus had talked himself into a too-small Earth (leaning on al-Farghani's miles read shorter than intended, and on Marinus of Tyre), which let him believe Asia lay only ~77° of longitude west, an easy sail. The true figure is about 180°. His critics were right: no ship of 1492 could carry provisions across that much open ocean. He survived only by colliding with a continent nobody in Europe knew was there. The "visionary against the flat-Earthers" is precisely backwards — he was the one with the bad map.

Where the flat Earth came from

The belief that medieval people thought the world was flat is itself a modern invention. Its most famous source is a novelist's embellishment:

1. c. 350 BCAristotle, On the Heavens — argues the Earth is a sphere: ships' hulls vanish before their masts, the shadow on the Moon in an eclipse is always curved, and the stars shift as you travel north or south.
2. c. 240 BCEratosthenes measures the circumference — the instrument above.
3. c. 1230 ADSacrobosco's De sphaera mundi — a textbook teaching a spherical Earth, standard in European universities for some 400 years.
4. c. 1320 ADDante's Commedia takes a round Earth for granted, with gravity pulling toward its centre.
5. 1492Columbus sails — believing, like every educated contemporary, in a round Earth; he is simply wrong about its size.
6. 1828Washington Irving publishes a part-fictional Life and Voyages of Christopher Columbus and invents the dramatic scene of clergy at Salamanca objecting to a round Earth on scriptural grounds. It never happened.
7. 1991Jeffrey Burton Russell, Inventing the Flat Earth, traces the myth's spread to 1870–1920 and to Irving, Draper, and A. D. White: "with extraordinary few exceptions no educated person … from the third century B.C. onward believed that the Earth was flat."

So the next time the story comes around — the lone genius, the fearful flat-Earthers, the proof at the horizon — remember the librarian with the stick. The Earth's roundness wasn't proved in 1492. It was measured seventeen centuries earlier, and the answer was a shadow long.