When Carl Sagan Demonstrated the Earth Is Spherical with a Stick

They hold conventions around the world (!), traditional media give them more and more airtime, and they launch homemade rockets risking their lives, but the underlying truth doesn't change: Flat Earthers are wrong, and the Earth is spherical.

In fact, their vision is so absurd that it was already disproven and buried 300 years before Christ by the mathematician Eratosthenes of Cyrene. In another fabulous excerpt from the original Cosmos saga, the eternal Carl Sagan explains how Eratosthenes determined the circumference of the Earth, even with several unknown data points and a significant margin of error.

Eratosthenes of Cyrene and a spherical Earth

The story begins in Alexandria, where Eratosthenes was put in charge of the city's famous Royal Library at the request of Pharaoh Ptolemy III. Possessor of one of the greatest minds of antiquity, Eratosthenes was surprised by a small anecdote he read in a papyrus.

Apparently, during the summer solstice (today defined between June 20 and 22 for the northern hemisphere), at what was the border post of Siena (today the city of Aswan), something fascinating happened: At high noon, all vertical objects, from columns to simple sticks stuck in the ground, stopped casting any shadow, and sunlight reached the bottom of wells.

Anyone could have easily ignored that anecdote, but that was not the case with Eratosthenes...

From Eratosthenes to Carl Sagan

In the words of Carl Sagan, Eratosthenes was a scientist, and he acted like one. He conducted an experiment in Alexandria using a stick, and verified that during the summer solstice, the stick did cast a shadow.

Others would have concluded that the report from Siena was wrong, but lying about something so small (and wasting a papyrus for it) doesn't make much sense. So, how is it possible that on the same day, at the same hour, a stick in Siena casts no shadow but in Alexandria it does?

Assisted by a small map of Ancient Egypt and two obelisks marking the locations of Alexandria and Siena, Sagan arrives at the only valid explanation: The surface of the Earth follows a curve, and the larger the curvature, the greater the difference between the lengths of the shadows.

Now, Eratosthenes had to make some assumptions for the subsequent calculation, but his result yielded a distance between Alexandria and Siena of 7 degrees across the Earth's surface. In a rounding process, Eratosthenes established that the distance between the two cities was 5,000 stades.

If 7.2 degrees is 1/50 of a circle, then multiplying 5,000 stades by 50, Eratosthenes arrived at 250,000 stades for the Earth's circumference. The question is: Did he use the Olympic stade, or the Egyptian stade?

With the former, his margin of error was on the order of 10 percent. With the latter, the calculation gives almost 40,000 kilometers, an error of less than 1 percent.

The point is that even working with very imprecise tools (sticks and shadows, basically), Eratosthenes achieved what 'modern' men with satellite imagery, GPS, and free tools at their disposal don't seem to understand, or rather, don't want to understand.

Source: Official Carl Sagan YouTube channel