The Round Earth

Copyright © Karl Dahlke, 2022

for half a million years, we survived on the plains of Africa, while our human brain grew in size and complexity. Generation after generation eked out a living and raised children to adulthood, as new neural connections formed in side our heads. Our developing brain helped us survive, else we wouldn't have it today. It's an expensive organ, burning a quarter of our oxygen and a quarter of our food. In return, it accurately models the world around us. We understand which animals are food and which animals might consider us to be food. We remember “red next to black is a friend of jack, and red next to yellow will kill a fellow”, to distinguish the venomous snake from the harmless snake. We build stone tools to help us hunt and defend ourselves. Eventually we learned to control fire, a real game changer. However, the brain only has to be accurate on the African savanna. It can be supremely wrong on matters smaller than an ant, or larger than a mountain, shorter than a jiffy, or longer than a human lifetime, faster than lightning, or slower than a glacier. Mistakes in these areas do not affect survival, and are not corrected by evolution. Thus we have no intuitive understanding of quantum mechanics at the atomic level, or general relativity near a black hole, or even the distance to the nearest star - nor should we.

With this in mind, there is no reason we should have an accurate view of the earth. We understand the part we can see, and other than a few hills and valleys, the land appears flat. Thus the earth is flat. That's wrong, but it doesn't cause any trouble, because the earth is indeed flat for hundreds of miles, which is all a hunter gatherer experiences in his lifetime. Even today, some people still believe the earth is flat, and they live their lives unimpeded.

Anyone who has flown across three times zones knows that the earth is round. The sun and your watch are out of sync. Furthermore, the sun and your body are out of sync, also known as jet lag. However, most people have never flown across 3 time zones, and never will. Can we provide evidence that is accessible to almost everyone?

The Greeks were curious about the shape of the earth, and by the fifth century B.C., they all believe the earth was a giant ball, although they had no evidence to support this claim. Our friend Pythagoras may have been the first to propose the round earth, though we don't really know for sure. By 350 B.C., Aristotle, Plato's prize student, had provided three separate lines of evidence supporting the round earth. Each is compelling on its own, and together they are unassailable. The shape of the earth was finally established by science, and yet, people were not convinced. Intuition dies hard, especially if you have held those beliefs all your life.

  1. There are stars that can be seen in Egypt, that cannot be seen in Northern Europe. As you travel north, they fall below the horizon, so to speak. This would not happen if the earth was flat.

  2. Like everything else under the sun, the earth casts a shadow, and once every couple of years the earth's shadow falls across the face of the full moon. Whenever if covers part of the moon, the shadow is always round. We have to pause here, because a flat object, like a dinner plate, can still cast a round shadow, but not all the time. If it is tilted in any way relative to the sun and the moon, the shadow becomes an ellipse. Aristotle watched these shadows all his life, and they were always circular. Therefore the earth is a ball.

  3. When ships sailed off into the distance,they disappeared from the bottom up. At the edge of vision, on a clear day, only the sails are visible. This can only happen if water forms a curved surface, following the curve of the earth.


Go into a dark room with a flashlight and a dinner plate. Place the flashlight on a table, shining towards the opposite wall. Hold the plate in the path of the flashlight, and note the round shadow on the wall. Tilt the plate just a bit, and the shadow becomes an ellipse. Only a perfect alignment casts a circular shadow. In contrast, a ball casts a circular shadow every time.

Days and Nights

Suppose you grew up in a little house on the prairie, and never ventured more than 200 miles from home. Furthermore, you aren't in the habit of documenting lunar eclipses. How can I convince you the earth is round?

There is another line of reasoning that you can perform at home, and I'm surprised Aristotle didn't think of it. If you live in North America, Europe, or Asia, then you have experienced the long days of summer and the short days of winter. Each day is not exactly 12 hours long. And yet, that is exactly what would happen on the flat earth. If summer days are 14 hours long, and winter days are 10 hours long, then the earth is indeed round.


Go back into the dark room with the flashlight and the plate. Hold the plate about 4 feet from the light and notice the bright side and the dark side of the plate. These are day and night on the flat earth. Slowly turn the plate about any axis you like. At some point, the plate is edge on to the light. This is sunrise and sunset on the flat earth. In an instant, the dark side of the plate becomes light, and the light side becomes dark. This holds for another 12 hours, until the plate is edge on to the light again, and then the sides switch back. Day is 12 hours long, and night is 12 hours long, everywhere on the flat earth, all the time.

The same thing happens if you hold the plate still, at any angle, and your friend walks around it with the flashlight. (Remember that the Greeks still thought the sun revolved around the earth.) When the light sweeps across the edge of the plate, day becomes night, and night becomes day, everywhere on earth. The effect is the same.

If you have experienced longer days in summer, and shorter days in winter, and most of us have, then this experiment confirms the earth cannot be a flat disk. It is a ball, with its axis tilted relative to the sun, and that creates longer and shorter days for people who live a fair distance from the equator.

The Size of the Earth

A century after Aristotle demonstrated sphericity, Eratosthenes determined the size of the earth, i.e. the distance around, and he was surprisingly accurate. He enlisted the aid of a friend, paying him to walk some 700 miles. They measured the shadows cast by perfectly vertical sticks at the same time, but 700 miles apart. Those shadows will not be the same, because the earth is curved. They got back together and compared notes, and performed some trigonometry. Carl Sagan describes this bold experiment here.