Ancient Greece: Democracy and Eratosthenes’ Earth

City-states and the first vote

Greece was never one country. It was hundreds of small city-states, each called a polis, with its own laws and army. In Athens, in 508 or 507 BC, a reformer named Cleisthenes gave power to the assembly of citizens. The word democracy means “rule of the people”. Citizens raised their hands in the assembly, and jurors used pebbles or bronze discs to vote in court. This was still a limited democracy: only free adult men born in Athens could take part. Women, enslaved people and foreigners could not. Even so, the idea that ordinary citizens decide has travelled to our time.

Asking for natural causes

Around 600 BC, Thales of Miletus tried to explain the world without gods hurling thunderbolts. He thought that everything came from water, which is probably wrong, but his method was new: look for causes in nature itself and argue about them. Tradition says he even predicted an eclipse, though this is disputed. Others followed, and the Greeks gave us the word philosophy, “love of wisdom”. They did not agree on the answers. They agreed that every claim must be defended with reasons, and that is the seed of science.

A round Earth

By 350 BC educated Greeks knew that the Earth is round. Aristotle gave arguments in his book On the Heavens. During a lunar eclipse the Earth’s shadow on the Moon is always curved and round, and only a sphere casts a round shadow from every direction. Travellers who go south also see new stars rise above the horizon, which would not happen on a flat plate. So the question was no longer the shape of the Earth. It was its size. Nobody had a way to measure it yet.

The well at Syene

Eratosthenes of Cyrene lived from about 276 to 194 BC and led the great library in Alexandria. He heard of a curiosity in the southern town of Syene, today Aswan. At noon on the summer solstice, the Sun lit the whole bottom of a deep well, and upright objects cast no shadow. The Sun stood exactly overhead. Eratosthenes realised that this could be turned into a measurement. All he needed was the same moment in another town, and the distance between them.

The shadow at Alexandria

At the same moment in Alexandria, which lies to the north, a vertical stick did cast a shadow. Eratosthenes measured its angle: 7.2 degrees, or one fiftieth of a full circle. He knew that the Sun is so far away that its rays arrive almost parallel. So the angle of the shadow must equal the angle at the centre of the Earth between the two cities. The distance from Alexandria to Syene, he said, was therefore one fiftieth of the Earth’s circumference. A stick and some geometry had measured a planet.

The result

The distance between the cities was given as 5,000 stadia. Multiplying by 50 gives 250,000 stadia. How long is that? The Greek stadion was not one fixed unit. With a 157.5-metre stadion the answer is about 39,400 kilometres, and with 185 metres it is about 46,000. The true circumference at the equator is 40,075 kilometres. Some luck helped, as the cities are not exactly on one line north-south. Still, the method was sound. Eratosthenes’ own book is lost, and we know his method from a later writer, Cleomedes.

The Library and what remained

The Library of Alexandria was founded by the Ptolemies in the early third century BC. Scholars from around the Mediterranean came to read, copy and argue. Its decline was gradual, not the work of one fire, as the story often says. The Greek heritage was huge: Euclid’s geometry, Archimedes’ levers and buoyancy, Hipparchus’s star catalogue, and Aristarchus’s idea that the Earth moves around the Sun. Much of it travelled through Arabic books and back into Europe, where it lit the way for the Renaissance.

Greece: Thinking About the World