The Universe 07
The desire to learn drives scientific inquiry
In Alexandria, at that time, there lived a man named Eratosthenes. One of his envious contemporaries called him “beta”—the second letter of the Greek alphabet—because, he said, “Eratosthenes was second-best in the world in everything.” But it seems clear that, in many fields, Eratosthenes was “alpha.” He was an astronomer, historian, geographer, philosopher, poet, theater critic, and mathematician. He was also the chief librarian of the Great Library of Alexandria. And one day, while reading a papyrus book in the library, he came upon a curious account.
Far to the south—he read—at the frontier outpost of Syene, something notable could be seen on the longest day of the year. On June 21st, the shadows of a temple column, or a vertical stick, would grow shorter as noon approached. And as the hours crept towards midday, the sun’s rays would slither down the sides of a deep well which on other days would remain in shadow. And then, precisely at noon, columns would cast no shadows and the sun would shine directly down into the water of the well. At that moment the sun was exactly overhead.
It was an observation that someone else might easily have ignored. Sticks, shadows, reflections in wells, the position of the sun: simple, everyday matters—of what possible importance might they be? But Eratosthenes was a scientist and his contemplation of these homely matters changed the world; in a way, made the world. Because Eratosthenes had the presence of mind to experiment: to actually ask whether, back here, near Alexandria, a stick cast a shadow near noon on June the 21st. And it turns out, sticks do.
An overly skeptical person might have said that the report from Syene was an error. But it’s an absolutely straightforward observation. Why would anyone lie on such a trivial matter? Eratosthenes asked himself how it could be that at the same moment a stick in Syene would cast no shadow and a stick in Alexandria, 800 kilometers to the north, would cast a very definite shadow.
Here is a map of ancient Egypt. I’ve inserted two sticks, or obelisks. One up here in Alexandria and one down here in Syene. Now, if at a certain moment each stick casts no shadow—no shadow at all—that’s perfectly easy to understand, provided the Earth is flat. If the shadow at Syene is at a certain length and the shadow at Alexandria is the same length, that also makes sense on a flat Earth. But how could it be, Eratosthenes asked, that at the same instant there was no shadow at Syene and a very substantial shadow at Alexandria? The only answer was that the surface of the Earth is curved. Not only that, but the greater the curvature, the bigger the difference in the lengths of the shadows. The sun is so far away that its rays are parallel when they reach the Earth. Sticks at different angles to the sun’s rays will cast shadows at different lengths.
For the observed difference in the shadow lengths, the distance between Alexandria and Syene had to be about seven degrees along the surface of the Earth. By that I mean: if you would imagine these sticks extending all the way down to the center of the Earth, they would there intersect at an angle of about seven degrees. Well, seven degrees is something like a 50th of the full circumference of the Earth; 360 degrees. Eratosthenes knew the distance between Alexandria and Syene. He knew it was 800 kilometers. Why? Because he hired a man to pace out the entire distance so that he could perform the calculation I’m talking about. Now, 800 kilometers times 50 is 40,000 kilometers. So that must be the circumference of the Earth. That’s how far it is to go once around the Earth.
That’s the right answer. Eratosthenes’ only tools were sticks, eyes, feet and brains—plus a zest for experiment. With those tools, he correctly deduced the circumference of the Earth to high precision with an error of only a few percent. That’s pretty good figuring for 2,200 years ago.
Then, as now, the Mediterranean was teeming with ships. Merchantmen, fishing vessels, naval flotillas. But there were also courageous voyages into the unknown. 400 years before Eratosthenes, Africa was circumnavigated by a Phoenician fleet in the employ of the Egyptian pharaoh Necho. They set sail—probably in boats as frail and open as these—out from the Red Sea, down the east coast of Africa, up into the Atlantic, and then back through the Mediterranean. That epic journey took three years—about as long as it takes Voyager to journey from Earth to Saturn.
After Eratosthenes, some may have attempted to circumnavigate the Earth. But until the time of Magellan, no one succeeded. What tales of adventure and daring must earlier have been told as sailors and navigators, practical men of the world, gambled their lives on the mathematics of a scientist from ancient Alexandria?
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