## Monday, January 04, 2010

### Circular reasoning

Eratosthenes is best known for measuring the size of the Earth. I suggested yesterday that his greatest achievement might have been his ability to imagine a cosmos of a size that would have boggled the minds of his contemporaries.

There is another aspect of his Earth measurement that deserves comment: That circle in yesterday's diagram that represents the Earth.

We have seen the Earth from space, perfectly round and smooth to the eye. For us, the circle in the diagram is no big deal.

But put yourself in the shoes of a typical Alexandrian in the 3rd century B.C.E. Eratosthenes draws a circle and says, "The Earth". Just that: "The Earth."

Plants, animals, hills, valleys, rivers, seas, cities, temples, waves, clouds: All of this -- all of the intricate diversity of the Earth, everything that is of interest and important to the lives of women and men -- Eratosthenes dismisses in his diagram. He draws a circle with a compass and says, “This is the Earth.” Then, having reduced our multifarious globe to a pure geometrical figure, he calculates its size. This, I maintain, was a pivotal moment in human history, an act of stupendous intellectual abstraction that stands as the beginning of mathematical science.

Abstraction! Stealing from the cluttered complexity of things an underlying simplicity. Stealing from the infinite diversity of the Earth its essential circularity. Putting all else out of mind and focusing upon a single geometrical quality that exists only in the mind's eye.

Here, in Eratosthenes's demonstration, for the first time we know about, we see the three pillars of the scientific method working together: 1) an idealized conceptual model of the world (the Earth as a geometrical sphere); 2) quantitative observation (measuring the angle of the shadow and the distance from Alexandria to Syene); and 3) mathematical computation (in this case, the rules of Euclidian geometry). It was Eratosthenes's genius to put them all together.

The Greeks gave us many wonderful things; try to imagine Western civilization without the underpinnings of Greek politics, art, architecture, drama, history. But Eratosthenes’ drawing of the Earth as a geometrical circle represents something as formidable as the plays of Sophocles, the history of Herodotus, or Athenian democracy: a way of abstract thinking that would eventually carry human imagination to the far-off galaxies.

(I have made these observations before in Walking Zero. You will find them explored there in a much richer context, and forgive me for replaying them here.)