Round the World

The Earth is roughly spherical in shape, as everyone reading this knows. What's often more of a surprise is that this part of core science has been known to humans for some millennia, and has remained generally accepted and largely uncontroversial. We see mountaintops in the distance before we see the plains below, and we see that masthead of an approaching ship before we see the hull. We see the shadow of the Earth upon the face of the moon during a lunar eclipse, and it is always circular. At different latitudes, we see different stars at night, and the sun casts shadows of different lengths during the day. These pieces of evidence are all documented in ancient times, and were gathered together in Aristotle's treatise On the Heavens (Book II, Ch 14), which means they were all known by around 350BC at the latest. This led to the prediction that you could travel in a particular direction and eventually return to the place from which you started, a hypothesis that was confirmed by the Magellan expedition nearly 2000 years later.

The practical importance of this discovery appears in many engineering situations. It's often necessary for planning and executing journeys of more than a few hundred miles. It's vital for understanding weather patterns. It's vital for long-distance communication: once the railway and the telegraph were standard, it became apparent quite quickly that some system of coordinated time and corresponding time zones was necessary to synchronize watches around the planet. Software engineers dealing with any kind of geographic application learn very quickly that trying to treat latitudes and longitudes as Cartesian coordinates is asking for trouble: and if we go back into the history of mathematics, we find that this is just what sines and cosines were invented for.

In about 180 BC, Eratosthenes of Alexandria used the difference in lengths of shadows at midday at different latitudes to estimate the circumference of the Earth, and this gave a much more accurate figure than the estimate used by Christopher Columbus to convince Queen Isabella that the east coast of China was within reach of a well-provisioned sea voyage. Like many children in school, I read that Columbus was one of the first people to believe that the Earth was round. Not true: instead, he was the first to place enough faith in an optimistically small estimate of the Earth's circumference that he was willing to risk a westward voyage from Europe to China. In the event, his ignorance of geography was turned into good fortune thanks only to the intervention of an unexpected continent in between.

In between the mathematicians of the ancient world and the European renaissance lies the period of the Middle Ages. Readers of many standard histories may be left with the impression that in this period at least, Europeans in particular believed that the Earth was flat. This is generally false: the overwhelming majority of writers who touched on the subject assumed that the reader knows that the Earth is round. These include Augustine, Bede, Aquinas, over 70 other medieval churchmen, and of course a whole range of Arab, Indian and Chinese scholars and sailors. From around 1000AD, the knowledge assumed increasing practical importance as the mariner's compass and sailing into the wind made regular longer voyages possible, particularly over the Indian Ocean. The European renaissance and voyages of discovery did not come from nowhere, but from centuries of gradual technological advances during which common knowledge of the shape of the Earth played a central part. By the time Copernicus was able to write his pivotal work On the Revolutions of the Heavenly Spheres, he could state firmly in his second paragraph that the Earth is spherical, give a short list of demonstrations similar to those above, and know that every educated reader would agree with his book thus far.

Given the importance of the Earth's shape in the day to day life of many professions, why is the story of this knowledge relatively obscure compared to that of the Earth's movement in the solar system? Most educated people today can give a reasonable estimate of when it became known that the Earth goes round the sun: many will say Copernicus; others will guess at Galileo which is roughly accurate to within a century. By contrast, if asked "At around what date did we know that the Earth was round?" many educated people will admit to not knowing at all, or will guess at a similar time in the early modern period.

In the rest of this brief essay, I will propose three reasons for this absence: one scientific, one literary, and one religious.

The scientific reason is that the Earth's daily rotation is intimately linked to its shape, but was demonstrated much later. Ptolemy of Alexandria (who knew of course that the Earth was round) considered but dismissed the idea that the sunrise and sunset were due to the Earth itself rotating, because the surface of the Earth would have to be moving so fast that there would be enormous windstorms everywhere. This is the claim that Copernicus challenges first, before going on to discuss the movement of planets and the Earth around the Sun. Copernicus argues a kind of least-action principle – if the Earth rotating once a day is "too fast to believe", then how much harder is it to believe instead that the sphere of the immeasurably distant stars rotates once a day? To explain the lack of permanent hurricanes, Copernicus suggests that even though gases are attracted to the Earth's surface less strongly than liquids and solids, still they are attracted and pulled round as the Earth itself spins. He even goes so far as to suggest that the moon and sun may similarly attract the things near to them: to explain the lack of perpetual hurricanes, Copernicus even anticipates the law of universal gravitation! So Copernicus did contribute crucially to our knowledge of the Earth's circular motion, and the history of this discovery can understandably be confused with the history of our knowledge of the Earth's circular shape.

The literary reason is that the story of the Earth's shape lacks drama. It's like trying to write a love story about a couple who stays happily married for decades – it's dull! There is no hero thrown in jail, no individual of brilliant insight rejected by an ignorant public or a corrupt establishment, no centuries of darkness redeemed by a final enlightenment. Even worse, there's nothing that makes us today feel superior to people at other times and places with whom we feel no intellectual kinship. It doesn't fit with the narrative of modernity: instead of a revolution in thought that throws out everything that went before, it is an example of continuity, in which ancient and medieval science built a platform upon which modern science was built. If it's a dull story that doesn't fit with the standard narrative, much better to ignore it than to dwell on it. Or romanticize it: any sensible movie-maker would probably prefer the popular myth of Columbus as a steadfast and unique believer in a new idea, rather than an opportunist adventurer who got lucky in spite of using some very bad data.

The third and most controversial reason is to do with religion. During the 19th century, books like John William Draper's History of the Conflict between Religion and Science and Andrew Dickson White's History of the Warfare of Science with Theology in Christendom dwelt considerably on a few medieval authors, particularly Cosmas of Alexandria who taught of a flat earth in a 6th century work called Christian Topography. Though we know today that such flat-Earth believers were the exception rather than the rule, this mistake about the middle-ages spread into the 20th century and is still with us (see the Wikipedia article on the Flat Earth Myth). The Flat Earth Myth seems to me like an unfortunate and very human accident – Cosmas' choice of title suggests that he wanted to promote his views as decidedly Christian, and later antitheist critics have been more than happy to agree with him on this score. The story reminds us that we're prone to believe things that fit with our pre-existing biases, and that fact-checking assertions about what most scholars did or not did believe in a time as distant as the middle-ages is difficult.

Science offers two important and readily accessible methods for avoiding such errors. The first is to read primary sources. For example, to find out if Copernicus could assume that the Earth was round, and what other prior knowledge could be safely assumed, who better to read than Copernicus himself? In his first and most revolutionary chapter, parts of which were mentioned above, Copernicus cites the Pythagoreans, Plato, Aristotle, Ptolemy, Plutarch, Averroes, Martianus Capella's medieval encyclopedia, and Psalm 92:4, to name but a few. Even in the cases where he proposes different explanations (for example, Ptolemy on the movement of the Earth and Averroes on that of Mercury), he assumes that their observations were correct. His "prior art" quote for the relativity of motion comes from Virgil's Aeneid, and that for the sun lighting all things comes from Sophocles' Electra. So much for the irrelevance of a liberal arts education! His demonstrations emphasize continuity with the past wherever possible, partly because he wants his theory to have the best possible chance of being accepted by his contemporaries. You might hear a scientist today claim that the scientific revolution threw out everything that came before: this has become standard in the retelling, and deriding distant people is always easier than taking the time to understand them. But for many of the pivotal minds who made that revolution, their debt to the past was gratefully and humbly acknowledged.

The second, and most important method, is to observe the world. Take the time to convince yourself that the Earth is round – don't take someone else's word for it. Take a pair of binoculars to the top of a hill and watch the ships at sea. Note the date of the next lunar eclipse (there's one coming up on April 4th 2015, mainly visible over the Pacific regions) and look at the Earth's shadow (and first, look at the way the full moon is opposite to the sun in the sky and convince yourself that what you're seeing is the Earth's shadow!). If you travel to a distant place at a different latitude, look for a familiar constellation like Orion and see that it is higher or lower in the sky at the same time of night. These are the things that can make us fall in love with the system of the world: these are the things that make us scientists. And if you see them, remember with pride that for thousands of years, people have seen the same things with their own eyes, and in so doing, have seen beyond themselves.

Dominic Widdows, March 2015.