Measuring the circumference of the Earth, over 2000 years ago

One of the things that really annoy me is when some people say that it was Columbus who proved that the world was round. Not only did the peoples of the Mediterranean region know that it was round nearly two thousand years before that, one of them Eratosthenes of Cyrene (c. 276 BCE – c. 195/194 BCE) did a remarkably accurate job of calculating the circumference of the Earth.

I had long been meaning to post a description of how this impressive calculation was done but this video shows it very well.


  1. militantagnostic says

    On an episode of The Ring of Truth: An Inquiry into How We Know What We Know physicist Philip Morrison did this measurement using a Cube Van (The Van of Eratosthenes), some masking tape and stretch of highway in the Dakotas that ran straight North South for a few hundred miles. He used a star (I assume it was Polaris) instead of the sun. I recently heard somewhere that Eratosthenes was known as “Beta” because he was the second best at everything.

  2. cartomancer says

    The Columbus story is something that Americans and only Americans pass on. It stems from Washington Irving’s 1828 fictionalised biography of Christopher Columbus, which pits a heroic, forward-thinking Columbus against the hidebound authorities of the Medieval Church, who insist that the earth is flat.

    Of course, the Medieval church insisted no such thing. The sphericity and size of the earth were well known in antiquity and the Middle Ages. In fact it was Columbus who was wrong, because he thought the earth was actually somewhat wider in one hemisphere than the other, making it a kind of pear shape. Columbus appears to have read widely among the Latin works of his ancient and medieval forebears -- Chiefly Pliny the Elder, Seneca, and Pierre D’Ailly’s Imago Mundi. He was not a scholarly man, however, and seems to have got a lot wrong. He was also a tremendous bastard of the highest order of course, but that’s becoming increasingly well known of late.

    The fact that Irving’s story became so popular and widespread has everything to do with the way 19th and 20th century Americans liked to view themselves and their relationship to world history. Early modern Europe had a strong tradition of demeaning and belittling the achievements of the Middle Ages. From Petrarch to Rabelais to Voltaire, the entire culture of the Renaissance and Enlightenment were committed to making the Middle Ages into a period of ignorance and darkness, as opposed to the brilliance of the Classical world and (most significantly) the modern, scientific, “enlightened” west. Americans took this anti-medieval culture and ran with it. They had no medieval history of their own, so by denigrating all things medieval they cast themselves in greater glory -- a new and modern nation without any of that Old World baggage to hold it back. Columbus was raised to the status of a national founder figure after the American Civil War, when a distinctively Catholic hero was needed to appease the Catholic immigrant populations of the East Coast cities and promote national unity. Columbus, in his role as Mr. America, was cast as a forward-thinking, dynamic, go-getter who struggled against Old World complacency and Medieval ignorance to usher in a new and modern age.

  3. jrkrideau says

    I believe too that the Flat Earth myth was used as a handy club to beat at organized religion in the USA possibly combined with so anti-Catholic sentiment.

    No educated European or inhabitant of say the Roman Empire would have fallen for this Flat Earth story.

    On the other hand, one of the famous stories of science that totally annoys me is that Galileo was condemned by the Catholic Church for advocating a heliocentric solar system.

    In one way he was, but not because the Church really objected to the idea on serious theological grounds but because his theory was wrong. A theory that predicts one tide a day is not likely to gain a lot of acceptance particularly if any of the clerics on the Inquisition grew up near the Atlantic Ocean.

    It also is not a good idea to publish something that the Pope takes as a personal insult. It is not clear that Galileo was a great diplomat and it probably never occurred to him that the Pope would think that he was being lampooned as “Simplissimus”.

  4. grasshopper says

    “A theory that predicts one tide a day ..”. Seems to me it was a hypothesis worthy of more examination, rather than a failed theory, especially since Newton was only born the year that Galileo died and the mathematical edifice of gravity he erected did not exist for Galileo to use. In fact prior to Newton, could there have been any “theory” of tides which a heliocentric model of the solar sytem could destroy? Nor could natural philosophers subsequent to the invention of the telescope be comfortable with an earth-centred hypothesis which could not explain the discovery that the inferior planets had phases like the moon. Such knowledge had to trigger a re-examination of contemporary understanding.

  5. Pierce R. Butler says

    jrkrideau @ # 4: … it probably never occurred to him that the Pope would think that he was being lampooned as “Simplissimus”.

    Especially since Galileo apparently intended his parody to skewer a relatively obscure academic in the first place.

  6. wsierichs says

    The Pythagoreans reputedly believed in a spherical Earth as far back as the 6th century BCE. However, there’s an argument that they based this on the idea that a sphere was a perfect form and therefore its perfection would be modeled by the Earth.

    The Ptolemaic geocentric system that the Catholic Church endorsed included planetary orbits that were perfect circles. That’s what tripped up Copernicus. While he postulated a heliocentric system as a way to explain astronomical observations that did not match predictions by the Ptolemaic system, he kept the perfect-circle concept of planetary orbits. So the observations did not match his system’s predictions either. It was Kepler who recognized that the orbits were elliptical, not circular, thereby allowing accurate predictions of planetary movements.

    I have copies of sermons by several prominent 4th century CE bishops who preached that the Earth was flat, because of statements in the Bible. So it’s not entirely fictional that the Church accepted a spherical Earth. Like some other issues in the Middle Ages, educated people likely understood the reasons why the Earth was spherical, but many less- or uneducated people followed the flat Earth idea.

    So Columbus was talking to people who understood the Earth was a sphere. His argument that Asia was much closer to Europe than educated people thought might have been a mistake, but it’s possible he was manipulating things to make his westward journey sound practical and get him the money he needed. He probably would not have gotten any friendly ears if he knew and had stated the likely distance between the two continents. And an interesting suggestion I read once was that some fishermen in southern France/northern Spain might have known about and fished on the Grand Banks and knew that there was land nearby. If Columbus had picked up on that fact from fishermen he knew (they probably rarely talked about it so no one else knew about the fertile fishing grounds), that might have given Columbus the idea that Asia really was not all that far to the west. This sort of puzzle is one of the things that makes history so fascinating.

    A final historical tidbit: Even if Columbus had never sailed west, Europeans would have learned of the Americas only a few years later because of Portuguese ships that were blown west by a storm while traveling down the west side of Africa. The ships ended up on the coast of Brazil.

  7. jrkrideau says

    # 5 grasshopper

    Seems to me it was a hypothesis worthy of more examination…

    Err no. Anyone who lived on the coast of a major ocean such as the Atlantic would fall over laughing at the hypothesis. It was not a matter of theory, just simple observation.

    I live in Canada and it’s a bit like someone from Jamaica or Australia telling me it is impossible to walk across a lake. I have walked, cycled, skated and driven cars on a lake.

    I suspect, with no evidence at all, that Galileo was able to come up with this theory because he lived his entire life in central Italy mostly a long way from the sea coast so he had no real experience with tides.

    @7 wsierichs

    I have copies of sermons by several prominent 4th century CE bishops who preached that the Earth was flat, because of statements in the Bible

    I had not heard of these but I am not terribly surprised. Given the level of total ignorance shown by some US preachers I imagine we can expect something similar in the early church. And IIRC even some clerics who accepted a heliocentric solar system had a lot of difficulty with the southern hemisphere and how it would work.

    On the Galileo issue though, he was in Rome where some of the best astronomers in Europe were Jesuits. They were not likely to believe in a flat earth. They were also not likely to buy the one tide a day theory plus, IIRC, he had managed to alienate the Jesuit leadership so they were not going to function as an amicus curiae at the inquisition.

    Err, can you give me a reference on the Portuguese ships to Brazil? This sounds interesting and I have recently become interested in Brazil.

  8. grasshopper says

    Jrkrudeau, it seems to me that whether or not Galileo could explain the tides with his embryonic theory misses the point. The fact that the earth circled the sun was finally undeniable. The telescope gave him the capacity ability to observe the phases of Venus, and also those of the Jovian moons. I read you as saying that because a heliocentric view of the solar system couldn’t explain tides, it explained nothing.

    A less well known fact about Galileo was that he is the earliest known proponent of string theory. He believed that if you had a piece of string long enough, you could very easily measure the circumference of the earth, in much the same spirit as Archimedes’ belief that he could move the earth if he had a long enough lever.

  9. cartomancer says

    grasshopper, #5

    The standard late medieval explanation for the tides was that of Albertus Magnus (de natura locorum), which suggested that the tides were caused by the influence of the moon and, to a lesser extent, the other planets, transmitted through light rays onto various portions of the earth. The process was thought to be similar to how water expands when heated (“tumesces” in contemporary parlance), and different tidal ranges and phenomena were chalked up to different places on the earth receiving different combinations of influences from planets at different angles of incidence.

    This astrological theory was not specific enough to test, of course. It was recognised in the thirteenth century, by Robert Grosseteste and others, that the precision of measurement possible to thirteenth century science was not good enough to predict the precise locations of the planets above the earth and angles of incidence of the rays coming from them such that exactly what rays cause what could be worked out. So a heliocentric model would not have proved an insurmountable barrier to this explanation -- the comparative importance of the other planets apart from the moon was never hammered out, and the influence of the moon was obvious and primary enough to give the theory credibility (it was just that the mode of influence was thought to be light, or light-like emanations, rather than gravity).

    Incidentally, the Middle Ages were not quite as hostile to a heliocentric universe as is often supposed. The notion that Mercury and Venus, at least, were orbiting the sun rather than the earth was known through the works of the late antique compiler Martianus Capella -- whom Copernicus cited in his preface as an influence.

  10. Owlmirror says

    Back in 2014, Ken Ham had his famous debate with Bill Nye. I had the idea of coming up with responses to Ham’s arguments, but never compiled them into anything like a coherent whole.

    One of Ham’s slides was NASA imaging of the Earth from space.

    What Ken Ham said (from the debate transcript) was:

    By the way, I agree. You can show the Earth is not flat.
    There’s a video from the Galileo spacecraft showing the Earth, and speeded up of course, but spinning. You can see it’s a sphere. You can observe that. You can’t observe the age of the Earth. You don’t see that. You see again, I emphasize, there’s a big difference between historical science, talking about the past, and observational science, talking about the present.

    So I had the idea of responding to this as follows:

    Thousands of years ago, even before Christianity arose, philosophers argued that the Earth was round, even though they couldn’t see the Earth from space. It was an inference from available evidence; an inference that became stronger the more evidence they looked at. It was even possible for the ancients to estimate the size of the Earth using the angles of the rays of the sun in two cities, the distance between those two cities, and some geometrical calculations. So I think it’s worth asking: Were they wrong to come to this conclusion, given that they couldn’t actually see the whole Earth from space?

    The disagreement about the age of the Earth is far more fundamental than Ham implies. Just as flat-Earthers disagree about the Earth’s shape, Young Earth Creationists are disagreeing about the Earth’s shape in the fourth dimension of time; its duration. The scientific estimates of the age of the Earth are inferences based on some very basic physical facts, and just as the ancients could make more observations supporting the Earth being round, modern scientists kept finding more and more evidence that supported the confidence levels of the Earth’s age. But if it’s wrong to make inferences based on evidence, that undermines the entire basis of science.

    [This probably needs more work, given that Ham also tossed some chaff about radiocarbon dating million-year-old wood, and dating the Mt. Saint Helens eruption to millions of years ago, and decay rate constancy being an assumption, and so on]

  11. grasshopper says

    Owlmirror, your comment is a nice companion piece to Aron Ra’s recent post about asking a creationist to support his arguments with evidence. I also very much like your observation that Young Earth Creationists are disagreeing about the earth’s shape in the fourth dimension -- it’s duration. I haven’t come across that before.

  12. Eric Riley says

    20 seconds in and he’s already wrong -- Eratosthenes did not use (nor did he need to use) his ‘knowledge of right angle trigonometry’ to perform the calculation.

    He sets up the problem nicely, but glosses over (badly) the argument for a flat Earth and a close sun. He ignores two _assumptions_ made by Eratosthenes -- (1) the Earth is spherical; (2) the rays from the sun arrive as parallel lines.

    How *did* he measure the angle made by the sun’s rays? Probably with a scale drawing and subdividing angles until he gets to his reported figure of 1/50th of a circle. Almost certainly not by calculating the arctangent of a ratio. He also -- again, almost certainly -- did not use degrees as his angle measurement (and not to an accuracy of 1/8th of a degree).

    While about half right -- this video is a mix of right and wrong -- the wrong is grating.

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