How did the Greeks learn that the Earth is round?

When the Greek mathematician Eratosthenes estimated the circumference of the Earth around 240 BC, it was common knowledge that the planet was spherical. But prior to the sixth century BC, belief in a flat earth was common. Early Egyptian, Mesopotamian, Hebrew, and Homeric Greek cosmologies all viewed the Earth as flat. The Hebrew cosmology viewed the Earth as a disk supported by pillars and surrounded by a primal Ocean. Below it is an underworld known as She’ol and above it, again supported by pillars, is the Firmament of Heaven, a solid dome separating the Sun, Moon, stars, and planets from the Ocean of Heaven. It is not clear how or when the shift to the modern view of a spherical Earth came about. The earliest references to a spherical Earth come from ancient Greek sources, but there is no account of how the discovery was made.

Is it possible that under suitable conditions, the Earth’s curvature could be seen with the naked eye? Strictly speaking, what we mean here is a curved horizon rather than the curvature of the Earth. It is, nonetheless, an artefact of a spherical Earth. If Bronze Age people were able to see a curved horizon, it might have given them a strong hint that they were living on a sphere, not a plate.

Almost half a century ago, I watched in wonder as live TV pictures showed Neil Armstrong take his ‘giant leap for mankind’. The blurry pictures appeared to show the curvature of the Moon’s surface clearly visible in the background. It is also apparent in the colour picture Armstrong took as Buzz Aldrin exited the lunar module to join him on the lunar surface.

The Moon is of course much smaller than the Earth at just over a quarter of the diameter. Consequently, the lunar curvature is almost four times as pronounced as that of earth; moreover, it appears so prominent in the photographs as to suggest that curvature should at least be perceptible at ground level.

But first, let’s take a closer look at the picture of Aldrin climbing down the ladder of the lunar module (you’ll have to google it; it is NASA copyright and I can’t post it here). Does it really show the lunar curvature? The answer is ‘no’. The horizon is tilted due to the camera angle; it’s not actually curved. But the horizon is very close – as one would expect on a small planet, and this combines with the camera angle to give an illusion of a curved horizon. For our observer of average height, the distance to the horizon is 2.4 km (1.5 miles) as opposed to 4.7 km (2.9 miles). This is of course an effect of the curvature, but it’s not the same as seeing a curved horizon.

It is often claimed that the curvature of the Earth can be seen from an aircraft, a mountain, or even a tall building. The idea is that if you sight the horizon looking out to sea over a level straight edge such a ruler from approximately a metre, you should be able to see a convex meniscus. Unfortunately, you need to be very high up for this method to work. Standing on a clifftop looking out to sea you will see nothing (I’ve tried). In fact, even from an airliner at 35,000 feet it is hard to see (although it is clearly visible at 60,000 feet from high-altitude aircraft such as Concorde). There are many photographs purporting to show a clear curvature from ordinary airliners, but the ‘curvature’ in these cases will almost certainly be due to barrel distortion of the lens used to take the picture. We can thus rule out any possibility that Bronze Age people could have seen the Earth’s curvature for themselves.

The classic example of a proof that the Earth must be round is the appearance or disappearance of ships over the horizon. As a ship sails away from the land, it will gradually disappear; first the hull, then the superstructure, and finally (for a sailing ship), the masts and sails. Similarly, the upper parts of an incoming vessel will be seen before the hull comes into view. The effect can clearly be seen with a telescope or a pair of binoculars and the internet abounds with photographs and videos taken with high-zoom cameras.

Bronze Age traders were voyaging across the Mediterranean two millennia before the fifth century BC. While ships often kept close to land, prevailing winds meant that it was far easier for Ancient Minoan ships to sail directly from Crete to Egypt, only coasting on the return voyage. The question, then is, why didn’t the Minoans notice the gradual disappearance of their ships below the horizon?

The problem is, there were no telescopes, binoculars, or high-zoom cameras in the Bronze Age. Also, Bronze Age ships were far smaller than modern freighters or liners. If the evidence of the fourteenth century BC Uluburun shipwreck is anything to go by, a typical merchant vessel of that time was only around 15 – 16 m (50 ft) in length, about the size of a present-day Moody 54 sailing yacht. Even the triremes that came into use as warships in the late sixth century BC were much smaller than a present-day coastal freighter.

Would even a keen-eyed observer have been able to see that the hull of an outward-bound Bronze Age ship vanished while its sails remained visible? Even if they could, would they have been able to do so with enough consistency to realise that it was a distinct phenomenon and not just an artefact of sea, weather, or lighting conditions?

Let us assume that an individual of average height (eye level 5ft 7 in or 1.7 m) is sited on the shore, watching a ship of comparable size to the Uluburun merchant vessel standing out to sea:

Length of hull = 15 m approx.;
Height of hull above waterline = 2 m approx.;
Hoist of mainsail = 15 m approx.

Using a computer program that takes eye height and target distance, and calculates target hidden height, we find that the hull will have just disappeared as the ship reaches 10 km (6.2 miles) from the shore. At that distance, the sail will subtend 15/10,000 = 1.5 e-3 rad = 5 arcmin. This is about the same apparent size as a five pence coin or a US or Canadian dime viewed from 12 metres (39 ft). For a second observer, sited on a clifftop at a height of 10 m (32 ft), the whole of the ship will still be visible, but the hull will subtend an angle of just 2/10,000 = 2 e-4 rad = 0.7 arcmin above the waterline. This is less than the apparent diameter of Venus, and I think that it would be quite difficult to distinguish the hull from the sea even under favourable conditions. In conclusion, I am by no means convinced that it ever occurred to Bronze Age people that ships were doing anything other than vanishing into the distance.

How, then, might sixth century Greek scholars have deduced that they were living on the surface of a sphere? There are several clues that can be gleaned from the night skies. Long before the sixth century BC, astronomers were aware that the stars at night all appear to revolve in a clockwise direction around a fixed point. That fixed point is the celestial North Pole, which is the point in the sky that would be directly overhead if you were standing at the geographical North Pole. But for observers sited elsewhere in the Northern Hemisphere, the celestial North Pole appears in the sky due north and at an altitude above the horizon corresponding their latitude: thus from London, it is to be found at about 51 ° 30’ above the horizon, but from Athens, only 38 °.

The celestial North Pole is currently marked by the moderately bright star Polaris, but in classical antiquity there was no naked eye star close to the spot. Instead, navigators used the entire constellation of Ursa Minor for navigation purposes. It would nevertheless have been apparent from travellers’ tales that the further south you went, the lower in the sky this constellation would appear. Furthermore, constellations that are circumpolar (never setting, or as Homer put it, “never bathing in Ocean’s stream”) as seen from Greece would at times be out of view. But other, more southerly constellations would rise higher in the night sky, and the Southern Cross, which disappeared from the Mediterranean skies around 1700 BC, would come into view. Such reports could only be explained if the Earth was spherical.

Another clue comes from the Moon, whose phases might have been recorded as long ago as 35,000 years. When the Moon sets just after sunset, it is seen as a crescent with the illuminated side facing the western horizon; a half Moon (either waxing or waning) is always to be found 90 degrees away from the Sun; a full Moon always rises at sunset; finally, when the Moon rises just before sunrise, it is seen as a crescent with the illuminated side facing the eastern horizon. The phases of the Moon can easily be simulated by illuminating a ball with a torch in a darkened room and observing it from different angles. The Ancient Greeks could have carried out the same exercise, substituting the torch for an oil lamp or candle. A spherical Moon doesn’t necessarily imply a spherical Earth, but it is inconsistent with a flat earth.

Lunar eclipses provide a confirmatory clue. It would long have been known that a lunar eclipse can only happen when the Moon is full, and that a full Moon happens when the Moon is on the opposite side of the sky to the Sun and its entire Earth-facing surface is illuminated. A lunar eclipse must therefore be caused by Earth getting in the way of the Sun and casting a shadow across the surface of the Moon.

This shadow – a shadow of Earth – always appears circular. While a flat plate could cast a circular shadow, it would not always do so. The shadow would depend on the angle of the plate with respect to the Sun, and it would typically appear elliptical. But, regardless of the where the Moon is in the sky when an eclipse occurs, the Earth’s shadow is circular. This can only be explained by a spherical Earth, which casts a circular shadow from all angles.

During the sixth century BC, it is likely that Greek scholars pulled these three strands of evidence together and concluded that the Earth is spherical. It is not clear who made the breakthrough, even assuming it was just one person. It is commonly suggested that Pythagoras (c. 570 – c. 495 BC) or at any rate the Pythagorean school first put forward the idea of a spherical Earth.

The pre-requisites for discovering that the Earth is spherical would have been:
1. A literate society with writing technology capable of keeping records of astronomical phenomena.
2. A society in which trade and other long-distance interactions occur, where travellers have opportunities to observe night skies in distant lands.
3. An intellectual climate in which rational investigations of astronomical phenomena are likely to occur.

These conditions were certainly met in the Archaic and Classical periods of Ancient Greece, but what about the earlier civilisations that flourished during the Late Bronze Age in the Mediterranean and Ancient Near East? These civilisations interacted in a ‘Club of Great Powers’ from around 1500 to 1100 BC. Their combined realms spanned 20 degrees of longitude from the Hittite capital of Hattusa at 40° N to Nubia at 20° N; there would have been significant differences between the night skies of Anatolia and the southern reaches of the Nile. The keeping of astronomical records goes back to around 1600 BC in Mesopotamia, and astronomy was also important to the Ancient Egyptians for calendrical and astrological purposes. The first two conditions were certainly met. The Ancient Egyptians and Mesopotamians could surely have deduced that the Earth is spherical. Yet apparently they did not. As noted above, the cosmology of these societies was based upon a flat Earth.

One possibility is that belief in a flat Earth might be an intrinsic feature of the neural architecture of the human brain. South African cognitive archaeologist David Lewis-Williams has noted that a central tenet of many religions is the existence of a three-tiered cosmos with realms located ‘above’ and ‘below’ that of our every-day experience. The Abrahamic tradition of Heaven and Hell are only one example of such a cosmology. Lewis-Williams suggests that the widespread belief in the existence of these other realms arises from visions and hallucinations experienced in altered states of consciousness as may be induced by meditation, psychotropic substances, and various ritual practices. All human brains are wired up the same way, and so all will experience broadly the same visions and hallucinations. The specifics of how they are interpreted varies from culture to culture, but they share the same basic aspects of a Heaven, Earth, and Underworld.

Could this have hampered attempts to interpret celestial phenomena that could not be explained by the standard flat Earth model? Possibly it took the rationalism of the sixth century BC pre-Socratic philosophers to break an ancient, hard-wired mindset, and to allow a truer (albeit still far from complete) view of the cosmos to emerge.

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The Bedford Level experiment

In 1838, an eccentric British inventor named Samuel Birley Rowbotham attempted to demonstrate that the Earth is flat, using a long stretch of water known as the Bedford Level. Rowbotham’s views were based on the Hebrew cosmology of the Old Testament, which depicts a three-tiered cosmos with the heavens above, the earth in the middle, and the underworld below.

In support of his Flat Earth model, Rowbotham recruited the Bedford Level, a 9.7 km (6 mile) section of the Old Bedford River. The latter is an artificial river formed by a partial diversion of the River Great Ouse in the Fens, Cambridgeshire, intended to reduce flooding of the fenlands. It is named after Francis Russell, Fourth Earl of Bedford, who began the project in 1630 although it was not completed in his lifetime. The Bedford Level is an uninterrupted stretch which runs in a straight line to the north-east of the village of Welney.


Rowbotham’s idea was to set up a telescope 20 cm (8 inches) above the surface of the water at one end of the Bedford Level and use this to watch while a boat was rowed towards Welney Bridge at the other end, six miles away. The boat had a flag on three-foot (0.91 m) mast. If the Earth really was curved, the top of the mast would disappear long before the boat reached Welney Bridge. Rowbotham relied on an approximation used by surveyors: the drop expressed in inches is 8 times the square of the distance in miles. After one mile the drop is eight inches; after two it is 32 inches; and after three it is 72 inches or six feet.

This approximation holds good for the distances involved, but it fails to take account of the height above the ground of the observer. A more accurate calculation shows that the portion of the boat hidden from Rowbotham’s view would be zero after a mile, 8 inches (0.2 m) after two miles, and 2 ft 8 inches (0.81 m) after three miles. Nevertheless, only the top of the mast would be visible at three miles, and long before it reached Welney Bridge the whole of the boat would have disappeared. Instead, it remained completely visible throughout its journey, which Rowbotham took as proof that the Earth is flat.

Based on his observations, Rowbotham published a pamphlet entitled Zetetic Astronomy, which he expanded into the book Earth Not a Globe in 1865. He suggested that the Earth is a flat disc with its centre at the North Pole, and that it is surrounded by a wall of ice. The Sun and Moon were located 3,000 miles (4,800 km) above Earth, and the stars and planets were a further 100 miles (160 km) away.

But Rowbotham had made an elementary mistake. He had failed to realise that the effects atmospheric refraction close to the water can cancel out the effect of curvature, making the Earth’s surface appear flat or even concave. The same effect can make the Sun appear above the horizon shortly before it actually rises, or after it has set. The phenomenon was well known in Rowbotham’s day, and it was routinely allowed for by sailors navigating at sea, and by surveyors.

Rowbotham’s views understandably attracted very little attention until 1870, when a supporter by the name of John Hampden (unrelated to the Civil War-era politician) wagered £500 that that nobody could repeat the experiment and show that the Earth was other than flat. The challenge was taken up by none other than Alfred Russel Wallace, co-proposer of the theory of evolution by natural selection. Wallace’s day job was a surveyor, and he would have known how to avoid the pitfalls that had affected the original experiment albeit he was apparently unaware of Rowbotham’s efforts. £500 was a considerable sum of money at the time (over £50,000 at today’s rates) and Wallace doubtless saw it as an opportunity to make some easy money. With the benefit of hindsight, perhaps he shouldn’t have.

Wallace noted that the parapet of Welney Bridge was 4 m (13 ft. 3 in.) above the water but that the Old Bedford Bridge, at the other end of the Bedford Level, was somewhat higher. To this bridge he affixed a calico sheet with a black stripe, which he positioned so that the lower edge of the stripe was also 4 m (13 ft. 3 in.) above the water. The centre of the stripe would be as high as the line of site as a telescope he set up Welney Bridge. Midway between the two bridges he set up a long pole with two red discs attached, the upper one having its centre the same height above the water as the centre of the black band and of the telescope, while the lower disc was four feet below it. The telescope, upper disc, and black band were thus all the same height above the water; the greater height than that of the earlier experiment would reduce the effects of atmospheric refraction. If the Earth was flat, the upper disc as viewed through the telescope would appear level with the black band. If on the other hand the Earth was round the upper disk would appear above the black band.

To ensure fair play, John Henry Walsh, editor of The Field magazine, was appointed as an independent referee. Walsh was a good choice, as he was not personally acquainted with either Hampden or Wallace. He also had prior experience deciding wagers. But shortly after funds were lodged with Walsh to guarantee the wager, Hampden demanded a referee of his own. Wallace was agreeable, but Hampden chose fellow flat earth enthusiast William Carpenter. Furthermore, Walsh was unable to remain at the Bedford Level for the whole duration of the experiments and a surgeon named Martin Wales Bedell Coulcher stood in for him as Wallace’s referee.

As might be expected, the experiments showed the upper disk apparently raised above the Old Bedford Bridge marker. Coulcher sketched the view through the telescope, and Carpenter signed it to affirm that this was what both men had seen.

Then things started to go awry. Carpenter declared that the result did not prove that the Earth was round because the telescope had not been levelled and did not have cross-hairs. Wallace obtained a spirit level and a smaller telescope equipped with cross-hairs, and then performed the experiment again. The outcome, of course, was exactly the same as before. Both referees then sketched what was seen in the second telescope, and Coulcher signed the sketches. But now Carpenter refused to accept the result because the distant marker appeared below the middle one as far as the middle one did below the cross-hair, which he claimed proved that the three were in a straight line, and that consequently the earth was flat.

Hampden eventually agreed to allow Walsh to review the results and make a decision. Both sides submitted reports, and after considering these Walsh ruled in Wallace’s favour and published the reports and his conclusions in The Field. Ignoring Hampden’s protests, he awarded the £500 wager to Wallace.

At this point, things got decidedly ugly. Hampden went to court to get his money back and won because at this stage it was still in the hands of Walsh and had not yet been paid to Wallace. He published a pamphlet alleging that Wallace had cheated and not content with that, he wrote Wallace’s wife Annie threatening to kill her husband. The death threats landed Hampden in jail for three months. Early in 1871, Wallace sued for defamation and was awarded £600. But Hampden transferred all his assets to his son-in-law and claimed he could not pay. Wallace was left having to pay the court costs. The row continued for another twenty years, during which Hampden was twice imprisoned for defamation. It was only brought to and end by Hampden’s death in 1891.

The whole affair left Wallace significantly out of pocket. He had not been a wealthy man before the wager not least of all because his financial acumen fell rather short of his abilities as a scientist. As a result, he struggled financially until 1881, when he was awarded a £200 p.a. pension thanks to the lobbying of Charles Darwin. Wallace was also criticised for becoming involved with a wager to ‘decide’ an issue which had long been an established scientific fact. All in all, it was a thoroughly unpleasant episode in the life of one of the greatest scientists and thinkers of the nineteenth century.

In 1901, Henry Yule Oldham, a lecturer in geography at King’s College, Cambridge, repeated the Bedford Level experiment using three poles fixed at equal height above the water level, which he viewed with a theodolite and a plate camera. Oldham’s version of the Bedford Level experiment was regarded as definitive because of the photographic evidence. He presented his results in a lecture at the British Association for the Advancement of Science, and they were taught in schools for many years until the first photographs taken from space became available in the late 1940s.

As is often the way with what the late Sir Patrick Moore once described as ‘independent thinkers’, the Flat Earthers were not about to give up. In 1904 Lady Elizabeth Anne Blount hired photographer Edgar Clifton to use a camera equipped with telephoto lens to take a picture from Welney Bridge of a large white sheet touching the surface of river six miles (9.7 km) away, at the position Rowbotham had conducted his original experiment. The camera was mounted two feet above the water, and Clifton was able to obtain a picture of the target, which should have not have been visible. The experiment, of course, suffered from the same vulnerability to atmospheric refraction as had the original. Needless to say, this did not stop Lady Blount from publishing the pictures far and wide.

To this day, Flat Earth enthusiasts continue to champion the Bedford Level experiments as having proved that the Earth is flat. A search on Youtube will reveal an attempt in 2016 to recreate the Rowbotham’s original experiment using a laser pointer mounted on the rear deck of a kayak. Problems faced by the researchers included the discovery that the kayak deck sloped upwards and ‘best judgment’ had to be applied to place the laser ‘as level as possible’. The video has received 1,600 ‘likes’ against 805 ‘dislikes’, but many of the 2,404 comments posted are unfavourable.

It would be a worthwhile project – possibly for a science ‘outreach’ group – to repeat the Bedford Level experiment with modern equipment. In the meantime, anybody who seriously believes that the Earth is flat is urged to take a look at this spectacular video of the Turning Torso building in Malmo, viewed from successively greater distances on the Danish side of the Øresund strait between Denmark and Sweden.

Eratosthenes’s experiment

“They all laughed at Christopher Columbus
When he said the world was round”

George and Ira Gershwin were responsible for some of the most memorable songs of the last century, but this particular line highlights a common misconception. In 1492, when Columbus’ small fleet sailed from Palos de la Frontera in Spain, it had been the best part of two millennia since any serious scholar had believed that the world was flat.

The ancient Greeks were not only aware that the Earth was spherical, but around 240 BC they made an estimate of the circumference and obtained a surprisingly accurate result. Eratosthenes of Cyrene (276 – 194 BC) was a Greek polymath who held the post of Chief Librarian at the Library of Alexandria. He had heard that in Syrene (now Aswan), the noontime Sun on the day of the summer solstice lit up a well, casting no shadow on the side and implying that it was directly overhead. At Alexandria, however, the Sun did not quite reach the zenith and therefore did cast a shadow. By measuring the length of the shadow cast by a vertical rod of known height, the angular distance of the Sun from the zenith in Alexandria at noon could be determined. Of course, Eratosthenes couldn’t simply look at his watch to see when it was noon, so he would have relied on the shadow being at its minimum length at noon.

Eratosthenes found that the angular distance was a fiftieth of a whole circle (i.e. 50/360 = 7.2 degrees) and that the distance from Alexandria to Syrene was therefore a fiftieth of the circumference of the Earth. He then used a value of 5,000 stadia for the distance between the two cities (clearly a rough estimate) to obtain a value of 250,000 stadia for the Earth’s circumference.

Unfortunately, we don’t know the exact value of the stadion Eratosthenes used. The stadion (from which we get the word ‘stadium’) was defined as 600 Greek feet, but different values of the foot were used in different parts of the Greek world and Eratosthenes’ stadion is thought to have been anywhere between 150 and 158 meters (492 and 519 feet), making the distance from Alexandria to Aswan 750 -790 km (466 – 490 miles). We thus obtain a value of 37,500 – 39,500 km (23,300 – 24,500 miles) for the Earth’s circumference, which is very close to the accepted value of 40,075 km (24,901 miles). The actual distance from Alexandria to Aswan is 843 km (524 miles), giving a value of 42,150 km (26,200 miles).

Eratosthenes made the following assumptions: firstly, the Sun is so distant that rays of light reaching Alexandria and Syrene are effectively parallel; secondly that Syrene is located on the Tropic of Cancer (the latitude where the Sun is directly overhead on the summer solstice); and thirdly that Alexandria lies on the same meridian as Syrene.

Eratosthenes’ first assumption was correct, but the other two were not entirely accurate. The Tropic of Cancer is currently located at latitude 23°26′12.7″ N, but in Eratosthenes’ day, it was lay at approximately latitude 23°43′ N. Syrene lies at 24°05′ N 32°54 E, 22 minutes of an arc north of the Tropic of Cancer as it then was; and three degrees further east than Alexandria, which lies at 31°12′ N 29°55′ E.

Essentially, Eratosthenes’s experiment entailed simultaneous measurements the sun’s altitude at two separate locations on the same meridian. The experiment was simplified by choosing the solstitial sun at noon, and a second location that he either believed or approximated to be due south and at the latitude of the Tropic of Cancer. Had both been the case, he would have obtained an answer of 41,600 km (25,850 miles) based on a second location 7°29′ due south of Alexandria. Today we could easily replicate the experiment with two observers equipped with clinometers at John O’ Groats and Weston Super Mare, which are very close to sharing a common meridian and are 810 km (503 miles) apart. The experiment demonstrates how fundamental data can sometimes be obtained from a subtle but easy to measure phenomenon.

Heel Stone at Stonehenge

DSC03611

The sun famously rises over the Heel Stone at Stonehenge at the Summer Solstice. The alignment was first noticed by the antiquarian William Stukeley in the early eighteenth century, but it is not exact. The summer solstice sunrise, as viewed from the geometrical centre of the monument, actually occurs just to the left of the Heel Stone.  During the third millennium BC, when Stonehenge was constructed, the sun would have risen even further to the left. It is therefore likely that the Heel Stone once had a now-missing twin sited to its left, and the summer solstice sun rose between the pair.

Perigee full moon

The reasonably common phenomenon of full Moon coinciding perigee was completely ignored until the media discovered the term ‘supermoon’ a few years ago, Perigee (minimum distance from Earth) varies between 356400 and 370400 km (average 362600 km) and apogee (maximum distance from Earth) varies between 404000 and 406700 km(average 405400 km), so on average a perigee full Moon will appear 12 percent larger and 25 percent brighter than one occurring at apogee.

However, perigee on 14 November will be the closest one since 1948, and the Moon will appear 14 percent bigger and 30 percent brighter compared with the smallest apogee full Moon. This still isn’t an enormous difference, and prior to the current frenzy over ‘supermoons’ was only of interest to astronomers. Here in Britain, of course, we are in any case set to see absolutely nothing.