Flat Earth Versus Spherical Earth

In the Smoky Drinky Bar on Saturday night, Gráinne was arguing in favour of a Flat Earth with Brigitte and myself (conversations like these only ever happen in the Smoky Drinky Bar).

Never having had to argue against a Flat Earth, I cast around for evidence against it. What about the view from outer space? “Photoshopped,” said Gráinne. And who knows, perhaps it was? After all, I’ve never been to outer space. What about the view of the Earth from an airliner 10 km high? Didn’t the horizon have a visible curve? “An illusion,” Gráinne replied.

Eventually I fell back on my own maritime experience of seeing ships hull down below the horizon (or, same thing, the disc of the setting sun vanishing below the horizon). I even dug up a video of a ship hull down:

But afterwards it occurred to me that Gráinne could have dismissed this as well. She could have said that what we were seeing here was a submerged or sunken ship.

Since Saturday night, I’ve continued to think about ways of proving that the Earth is round. This morning I began thinking about how a little archipelago of islands might easily be visible from each other. How far was it possible to see out across the sea on a spherical Earth?

I used the Theorem of Pythagoras to work this out. If the spherical Earth has a radius R, and an island rises a height H above the surface of the Earth, how far is the distance D to the horizon, as seen from the top of the island? The answer, with a spherical Earth of radius 6371 km was that the distance to the horizon from an island of height H km above sea level is about 113√H km. So from an island 10 metres above sea level you can see 11 km, and from an island 100 metres high you can see 35 km, and from an island 1000 metres high, you can see 113 km.

Since  I was thinking about an archipelago of rocky islands, like those in Greece, I wondered if it might be possible for some Greek islands to be seen from the tops of nearby islands.

Using Google Maps, I soon found that the highest point on the island of Milos was 730 m. So, using my horizon distance formula, this meant that it was possible to see for 95 km in all directions. Plotting that circle on a map, I was astonished to find that from the Prophet Elias on Milos it was possible to see 12 or more other Greek islands. And from the top of a 1000 m high mountain (Mount Hymettus) just a little southeast of Athens, it was possible to see 113 km in all directions:

Furthermore, because the two circles overlapped, it meant that from the top of the mountain near Athens, on a clear day it was possible to see the top of the Prophet Elias on Milos.

And that meant that it was possible to communicate very quickly between Athens and Milos, using fires by night, and mirrors by day. And since in antiquity, unlike now, there were probably plenty of clear days, that would have meant that communication between all the Greek islands would have been very rapid. And this rapid communication would have extended to Crete, in the centre of which stands the 2,456 m high Mount Ida, from which Milos would also have been visible. It may have taken the Ancient Greeks many days of sailing or rowing to actually go from one island to the next, but communication between the islands would have been very fast. A short message like “Persian fleet near Karpathos” could have been flashed to every Greek island in the Aegean Sea within hours of the fleet being spotted. No wonder Greece was made up of a league of lots of tiny states.

It also struck me that, given the unique topography of the Aegean, the Greeks were ideally placed to be able to see that, while some nearby islands were visible to them, and not others, the Earth (or rather the sea) had to be curved. If the Earth and the sea was flat, all the islands should have been visible from each other. It was probably possible for them, using geometry, to work out how how far each island was distant from the others.  And they could also have used geometry to find out how high the highest point on each island stood above sea level. So, going back to my Pythagoras equation, if they knew H and D, they could also find R, the radius of the Earth.

And of course Pythagoras was Greek, and so was Aristarchus of Samos (shown with balloon near the coast of Turkey) who not only knew about the sphericity of the Earth, but also that the Earth went round the Sun, 2000 years before Copernicus. And the Greeks were probably great geometers because of where they lived.  In other countries, with the view obscured by hills and mountains, there was no such natural laboratory as the Greeks had in which to conduct geometrical investigations over long distances.

I then extended my investigations to the rest of the Mediterranean.

Here I found, again to my surprise, that it was possible, using one or two intervening islands (like Pantellaria and the Galite islands), to quickly communicate between Tunisia and Sardinia and Sicily. And also to communicate between Corsica and Italy and France. And this meant that the sea-going Carthaginians in what is now Tunisia also had fast communication channels by which they could control the western Mediterranean.

And all this spun out of a good-natured conversation with Gráinne.

P.S. I could have got the math wrong, of course.