People have grown more literate over time but I don’t know if they’ve really gotten any smarter. The New York Times reports that “people who question whether the Earth is round [are] running local Republican parties in Georgia and Minnesota and seeking public office in Alabama.”

By the fifth century B.C.E, the Greeks were confident enough that the Earth is an orb that they were making predictions about its circumference. For the math-challenged among you, that was two and a half millennia ago. Plato estimated the circumference as 64,412 kilometers (40,000 miles). The actual number is 40,096 kilometers (24,901 miles), so Plato was off by 60 percent.

One hundred and fifty years later, Archimedes gave an estimate of 48,309 kilometers (30,000 miles), which was only off by only 20 percent. In the third century B.C.E, Eratosthenes came very close to the correct answer with an estimate of 40,250 to 45,900 kilometers (25,000 to 28,500 miles). It’s fascinating to know how he arrived at this range.

He observed that the Sun was not casting a shadow down a well in the town of Syene, Egypt, which is now known as Aswan. From this he concluded that the Sun was directly overhead, which wasn’t quite true. He observed that on the same day of the year, a rod perpendicular to the ground in Alexandria, Egypt cast a shadow that was 7° 12′ from perpendicular.

He only needed a couple more inputs to make his calculation. First he figured out that 7° 12′  was one-fiftieth the size of a 360° circle. Then he needed to know how far Syene was from Alexandria. It’s unknown how he determined this but he found the result of 805 kilometers or 500 miles. This, too, was a little off. The correct distance would have yielded an angular measurement of 7° 30′ rather than 7° 12′.  Another problem was that Alexandria is not due north of Syrene.

Despite these errors in his numbers and assumptions, his method was sound. He took the distance between the two cities (805 km) and multiplied by fifty. That gave him a circumference of 40,250. That’s astonishingly close to the modern estimate of 40,096.

What I find astonishing is that Eratosthenes understood that the problem actually could be solved in such a way. It’s not something that would occur to 99.99999 percent of all the human beings who lived before him, and nearly the same percentage of people who have lived after him. Yet, it’s surprisingly simple to solve once you accept and understand the principles involved. You need to know how to measure the angle off perpendicular for sunlight, and you need to know how to multiply. There’s no advance calculus or trigonometry involved.

I guess the first thing that needed to be understood is that there are 360° in a circle. The problem is really more a conceptual difficulty than anything else. And if begins with the theory that the Earth is round.

Of course, we know the Earth is round now because we’ve gone to outer space and taken pictures of it. That really ought to have settled all dispute, but apparently it hasn’t for the people running the Republican Party in Georgia, Minnesota and perhaps soon in Alabama.

Personally, I think the idea that the Earth is flat was ever widely believed, at least among the educated, is highly overrated. There was a big dispute over whether the Earth or the Sun is at the center of the Solar System which famously pitted the Catholic Church against Galileo, but that’s different from a belief that the Earth is round.

I guess the world appears flat unless you do a little investigating. Certainly, sitting at the beach and looking out at the sea, you can detect the curvature of the horizon. But most folks don’t live at the beach. Another clue is that everything else we can see in the sky, from the moon and the Sun to the planets and stars is clearly spherical. Why should the Earth be different?

In any case, I don’t believe most Ancient Greeks thought about or understood these things any better than most contemporary Americans. People have always been pretty simple on average and those who can think scientifically have always been a tiny percentage of the whole.

But the modern world we live in was made possible by that tiny percentage and the rest of us ought to be humble enough to defer to them on scientific questions like the shape and circumference of the Earth and whether and why it is warming. And we definitely shouldn’t vote for a party led by people who think the Earth is flat more than 2,000 years after Eratosthenes correctly guessed its actual size.