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 Terrestrial 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:

Buzz Aldrin

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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Tower of the Winds, Athens

The recently restored Tower of the Winds in the Roman Agora of Athens is an octagonal marble clock tower. It features a combination of sundials, a water clock, and a wind vane and is reputed to have been built by Andronicus of Cyrrhus around 50 BC. However, it might date to as early as the second century BC, predating the rest of the agora.

Erechtheion on the Acropolis of Athens

The Erechtheion on the north side of the Acropolis of Athens,  which was dedicated to Athena and Poseidon. It is best known for its Caryatid porch, although the six figures now on the site are facsimiles. One of the originals was removed by Lord Elgin and forms part of the collection of Elgin Marbles controversially retained by the British Museum. The other five are in the nearby Acropolis Museum.