Shadows

Alexander the Great cast a giant shadow over History, conquering most of the known world in his short lifetime (356-323 B.C.). On his way eastward, he visited the city of Sinope (on the north coast of modern Turkey), and there encountered its most notorious inhabitant, a crusty old philosopher named Diogenes. Knowing this man’s reputed wisdom, Alexander offered to give him anything he desired. Diogenes is said to have responded “just stand out of my light,” thereby showing how little respect he had even for Alexander’s shadow.

It was of course this Alexander who founded the city of Alexandria, which is still Egypt’s third largest city. And it was there, a century after his death, that another member of the Greek cultural world, a man named Eratosthenes, made an even more important contribution to our intellectual heritage, as the hero of an entirely different shadow story.

In case you’ve been under the impression that it was Columbus who proved that the Earth is round, not flat, I have news for you – and the news is about 2,500 years old. 

Columbus was not only very late, but he didn’t prove anything. After three voyages to the so-called “New World,” he still falsely believed, to the end of his life, that he’d found a new route to India – (which is why many Native Americans are still called “Indians”).

The fact is that, as long ago as 500 B.C., most educated Greeks believed the Earth to be round – and they had good evidence for this belief, such as the way a ship sailing away from an observer, disappears, little by little, over the horizon. The trouble was that, despite the advances which had already been made in Geometry (which in fact means, ‘the Science of Measuring the Earth’), and, although they believed it to be round, they didn’t have any way of actually measuring its circumference.

Here is where Eratosthenes comes in. He lived in that great city of Alexandria, and he was already important as Chief Librarian of the famous Library there. It was in the same year as his appointment to that position by King Ptolemy III – 240 B.C. – that he set about measuring the Earth. How did he do it? We have to start in the city of Syene (now Aswan). Travelers brought the remarkable information that, in that city, at noon on the day of the summer solstice, i.e. on June 21, there were no shadows! By contrast, in Alexandria (which was farther north from the Equator), there definitely were shadows at noon on that same day (as there were on any day when the sun shone), and any upright object, such as a stick in the ground, cast a shadow. Well, if you, just then, drew a line from the tip of that stick to the tip of its shadow, you got, between the flat ground and that line, a measurable angle. In Alexandria, that angle turned out to be about 7.2 degrees, which happened to be about 1/50 of the 360 degrees into which any circle had, centuries earlier, already been divided. So, if the distance around the Earth really was circular, and you already had a “base-point” of Syene (where the angle was zero), all you had to do was multiply the Syene-to-Alexandria distance by 50 to get a figure for the entire circumference of the planet.

There was only one problem. At that time, nobody knew exactly how far it was between those two cities. Eratosthenes therefore had to hire surveyors to do the measuring. Once he had that figure, however, he immediately knew, by simple multiplication, the distance all the way around the Earth. And, although there is still some uncertainty about his final figures, because of the units he used (not miles or kilometers, but stadia), it’s generally agreed that Eratosthenes came remarkably close to today’s accepted measurement (which is 24,901 miles).

Our other big shadow story brings us back to Columbus. He was the first of several subsequent explorers who were able, with the aid of an almanac, to gain the respect, and practically the worship, of ignorant natives, by correctly predicting that there would be darkness on a certain day at a certain time. It was, of course, a solar eclipse, with the moon casting its shadow by coming between Sun and Earth.

I can only hope that, about the interest and value of all the above information, there is, in your mind, no shadow of a doubt.