The Science of Discworld IV Judgement Da

EIGHT



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BEMUSING GLOBE





Roundworld is called Roundworld because, er, it’s round.

From outside. As the wizards perceive it.

From inside … well, that’s a good question.

In the Science of Discworld series, the name does double duty for our planet and our universe. The planet is indeed round – ish – though at various times in history and in various cultures this was not appreciated and other shapes were favoured. The universe … well, we don’t really know what shape that is. Round is an obvious possibility, perhaps too obvious. If you not only have a point of view, but are one, and you can see equally far in every direction, the entire visible world automatically looks round. With you at the centre! Amazing.

In the absence of narrativium, Roundworld does not know what shape it ought to be. Somehow the actual shape, of planet, universe, and everything else for that matter, has to be a consequence of those mysterious rules. But there isn’t a rule that says ‘make planets round’. There isn’t even a rule that says ‘make planets’. The rules as we currently conceive of them say obscure things like iħ∂Ψ/∂t = ĤΨ.fn1 This perverse lack of human focus in the rules drives the wizards mad. Though they do like the fancy symbols, which are obviously magical.

Even worse: the rules are not written down. They are not even implicit in narrativium, since there is none, not until human beings invent it for themselves. The rules operate (we think) behind the scenes; an occasional truly sapient human can draw back the veil and glimpse nature’s cogwheels spinning. So the creatures that live in or on Roundworld (that’s us) play a lengthy guessing game in which they make up rules that seem to work, and then argue about whether they really do. This game has gone by many names: religion, philosophy, natural philosophy, science, or just The Truth. We are still playing it.

In this chapter, we’ll deal with the shape of our planet. The answer is common knowledge, so we’ll focus on the imaginative alternatives that have at times been proposed, the processes that led to the current answer, and the lengths to which some people have gone to deny it. We’ll leave the shape of the universe to chapter 16. That’s a much harder problem, in part because we can’t stand outside the universe and look at it. However, until the 1960s we had the same problem concerning our planet, and that did not stop scientists pinning down its shape and size. Also how old it is, although the accepted scientific figure for the age of the Earth remains contentious in some quarters because some people don’t like the answer, and of course that is all you need to prove it must be wrong.

The ancient Greeks started out thinking the world was flat, but they revised their opinion when they began to appreciate indirect evidence to the contrary. Like several earlier cultures, they were aware that the Moon is a sphere. Superficially, it may look like a flat disc viewed sideways on, but because of its phases, simple geometry reveals that it must be roughly spherical. The Sun, which is difficult to look at without blinding yourself, is a disc that seems to be almost exactly the same shape and size as the Moon, so presumably that, too, is a sphere. Eventually the Greeks concluded that the Earth is a sphere as well – a bit of a surprise because it doesn’t look like one. If you live in mountainous regions the world looks bumpy; if in a desert, away from big sand dunes, it looks flat. But if you look really carefully, you will see ships slowly disappearing below the horizon as they leave harbour, so the sea is curved. Other clues, such as the Earth’s shadow on the Moon during an eclipse, also indicate that the Earth is round. To the Greek worldview, a mix of human-centred and universe-centred thinking, that made narrative sense: a sphere is a perfect geometric form, so of course the gods would have used it to make the world.

After 250,000 years or more of the evolution and cultural development of modern humans, preceded by millions of years of our hominin ancestors, we have developed our own kind of narrativium, in which things happen because we tell each other stories about them, and then become inspired to make them happen. Having told ourselves innumerable stories about the shape of the Earth, most of them wrong, we have finally managed to gain a pretty accurate picture of the shape of our home planet. It is, as previously mentioned, a potato. The potato is very close to a spheroid of rotation, like a beach ball that someone has sat on. A spheroid is not too far away from a sphere. The Greeks did an amazing job for their time.

A spherical shape makes even more sense once you realise that we live on a planet that is similar to the other planets of the solar system, and once you have telescopes revealing that Mercury, Venus, Mars, Jupiter, Saturn, Uranus and Neptune (not to mention Pluto, Ceres, Titan, and many other bodies that are not classed as planets) are round. As above, so below. However, all this relies on logical inference, and it is only relatively recently that we have possessed the technology to look at the Earth from outside. The famous ‘Earthrise’ photo taken from lunar orbit in 1968 by astronaut William Anders of Apollo 8 shows a gibbous Earth, predominantly blue and white but with shades of green and brown, rising above a sterile, grey, mountainous lunar landscape. (The first manned lunar landing, Apollo 11, happened a year later.) This image dramatised our world’s fragility as it sailed through space, forever changing the associations of the word ‘Earth’. Ironically, the astronauts weren’t supposed to have taken it. NASA transcripts include an exchange between Anders and mission commander Frank Borman, who had previously taken a black and white photo of the Earth rising:

Borman: Oh my God! Look at that picture over there! Here’s the Earth coming up. Wow, is that pretty!

Anders: Hey, don’t take that, it’s not scheduled.

Borman: You got a colour film, Jim?fn2

Anders: Hand me that roll of colour quick, will you!

The rest was a triumph of astronautical narrativium over managerial mission schedules.

Even though we now know the world is round, some diehards still refuse to accept the evidence. They ‘know’ that the Moon landings never happened; they were all faked in Hollywood studios. There is no question that this is possible now; movie-makers routinely use computer-generated imagery to create far more complicated things – among them the movie Apollo 13, made 25 years later, with highly realistic special effects. It’s doubtful that the imagery existed then, but of course secret guv’mint projects were concealing technological advances that they only made public much later … Though not, apparently, the relatively straightforward engineering technologies needed to put a man on the Moon. The theory that the Moon landings never happened makes perfect sense provided you think it is possible to sustain a global conspiracy ultimately involving millions of people, prominent among whom were the Russians, who were trying to beat the Americans to their lunar prize.

We don’t want to dissect conspiracy theories, or make any further attempt to convince you that Neil Armstrong and Buzz Aldrin really did land on the Moon in 1969, or, for that matter, that they didn’t. Instead, we want to examine one of the reasons why many people used to believe, and a fair number still believe, that the Earth is flat. Or some other shape that is not the nice round globe of the Earth we encounter in geography lessons.

This reason is the role of inference, as opposed to direct observation. Inferences are always open to interpretation, and there is often enough wiggle-room to permit apparently logical escape routes. Devotees of a flat Earth have used this wiggle-room to devise more-or-less plausible explanations for most of the usual arguments that it is round. Explaining away one piece of evidence for a round Earth often conflicts with explaining away some other piece of evidence, but in a point-scoring debate, few in the audience notice. We, your humble authors, actually have a totally convincing proof that the Earth is round, which does not depend on photos from space, but we’ll save it until the end of this chapter.

Before the 1960s, even the most technologically developed nations could not observe our planet from any vantage point higher than a plane could fly or a balloon could rise. In earlier times, the available evidence was limited to what a groundhog could observe with its own senses, and Pan narrans’s insatiable need to tell explanatory stories led to some imaginative proposals.

One of the earliest cosmologies that we know something about is that of ancient Egypt in the early dynastic period, around 3000 BC. It remained surprisingly unchanged for much of the next three millennia, although new elements came in from time to time and fashions changed. The basis for Egyptian cosmology seems to have been informal observations of natural phenomena, laced with imagination and thickly coated in religious imagery.

Egyptian thinking was strongly influenced by their natural coordinate system, which provided four very clear cardinal directions, each having a deep meaning. Egypt was the ‘black land’ sandwiched between two regions of ‘red land’: a thin fertile strip between wide deserts – though early on the desert areas were more like savannah than the arid expanses they are today. The Nile ran roughly from south to north, and the prevailing wind went the other way. The extent to which this axis was embedded in Egyptian thinking can be gauged from the hieroglyphs for south (a boat with its sails raised) and north (a boat with sails furled). The Sun – considered a god from predynastic times – rose in the east and set in the west.

In Egyptian mythology, the Earth was flat, with a sort-of square aspect because of the importance of the cardinal directions. It was associated with the god Geb. The goddess Nut formed a gigantic arch above the Earth, corresponding to the sky and the heavens. In between was the air god Shu. Various features of the night sky echoed those on the ground; in particular, the Milky Way, a bright, dramatic band of light in the night-time desert sky, corresponded to the Nile. Since the Sun disappeared from the sky in the west and reappeared in the east, it obviously passed under the Earth, through the solid body of the ground. During the night, the Sun god Ra battled with the demons and gods of the underworld, emerging victorious – or at least, as a survivor – each morning. Thanks, you appreciate, to the strenuous efforts and rituals of the priesthood.

Cosmology, you will recall, is the theory of the form of the universe, and it goes hand in hand with cosmogony, its origins. The Egyptians had several creation myths, originating in different regions of the country, and different myths were often combined in a mix-and-match way. A common element in most versions was mentioned earlier: the emergence of the Earth when the primal mound rose from the sea of chaos. The triangular shape of the pyramids is thought to represent, among other things, this primal mound. It has long been known that the Temple of Karnak in present-day Luxor had a ritual function as a representation of this primal mound, but there may be more to it than that. Recently archaeologist Angus Graham has been making geophysical surveys; using electrical resistivity tomography to detect the former course of the Nile through the silt it deposited, he has shown that in ancient times Karnak was located on an island in the middle of the Nile. As the annual floods receded, it would have re-enacted the emergence of the primal mound literally, not just symbolically.

Despite their religious interest in the night sky, the Egyptians seem not to have made a systematic study of astronomy for its own sake. For that, we must turn to another ancient culture: Babylon.

Babylon was one of a variety of civilisations in the Mesopotamian region, the fertile lands between the Tigris and Euphrates rivers. Today this area comprises Iraq, plus parts of Iran, Syria and Turkey. The city of Babylon was in central Mesopotamia, about 80 km south of present-day Baghdad.

During the Bronze Age, Mesopotamia included the empires of the Old Babylonians, Sumerians, Assyrians and Old Akkadians. The New Babylonian and New Akkadian empires followed in the Iron Age. The Sumerians invented cuneiform writing, triangular marks in clay made by a stick, around 3500 BC. They studied the heavens, were aware of the ‘wandering stars’ that we now call planets, and worshipped them as gods. An ancient Sumerian tablet refers to seven heavens and seven Earths.

Babylonian history is usually divided into two periods. The city-state of Babylon became a regional power when the sixth king, Hammurabi, took charge in 1792 BC, and the Old Babylonian period dates from then until about 625 BC. The New Babylonian period followed when Nabopolassar took control following a civil war triggered by the death of the Assyrian king Ashurbanipal. Many more cuneiform astronomical texts survive from the New period than from the Old, but there are enough Old Babylonian texts to demonstrate that their study of the heavens was systematic and organised. The Old Babylonian astronomers produced the first known star catalogue around 1200 BC, but many of the star names are Sumerian, so Sumerian astronomers must have made systematic studies of the heavens even earlier.

The Babylonians paved the way for modern astronomy, and possibly science as well. They observed the motions of celestial bodies, especially the planets, carefully and accurately. Then they looked for patterns, using mathematics to analyse the data. They discovered that many astronomical phenomena are periodic: they repeat at fairly regular intervals. There is a tablet that records how the amount of daylight changes over the year, and a series of tablets called the Enûma Anu Enlil contains the Venus Table of Ammisaduqa, a 21-year record of the motions of Venus and the earliest known discovery of periodic events in planetary motion. This tablet, made around 700 BC, is a copy of an older one, possibly from the early part of the Old Babylonian era.

The Babylonians were assiduous observers, but they had no great interest in theoretical explanations, and we know little about their cosmology. Tablets contain phrases such as ‘the circumference of heaven and earth’, suggesting that they imagined the Earth and the cosmos united in a single round object. The two components were of equal importance, and both revolved in circles. The Babylonians did not link their scientific studies of the planets to their religious views of the cosmos, and they seem not to have thought that the planets themselves move in circles.

After 400 BC, the centre of natural philosophy in the ancient world shifted to Greece. Philolaus, a member of the cult founded by Pythagoras, viewed the cosmos as a central fire, around which the Sun, Moon, Earth and planets all revolve in circles. We don’t notice the fire because it is hidden by the bulk of the Earth. Around 300 BC, Aristarchus of Samos came up with perhaps the first heliocentric cosmology, by the simple expedient of replacing the central fire by the Sun.

The novel idea that the Earth revolves around the Sun received a general thumbs-down from almost everyone else, including virtually all early Greek philosophers. Thales thought that a flat Earth floated on water. Anaximander thought it was a thick disc with a flat top. Anaximenes held that a flat Earth rode on air like the other celestial bodies. Xenophanes maintained that we lived on the flat top of a semi-infinite cylinder, extending downwards for ever (shades of ‘turtles all the way down’). Anaxagoras accepted that the Earth was flat, but Archelaus insisted it was saucer-shaped, which is why we don’t all see the Sun rising and setting at the same time.

Most ancient natural philosophers preferred the theories of Aristotle and Ptolemy, who placed the Earth where any sensible person naturally would: at the centre of things. Plutarch, in a work about the Man in the Moon – the apparent face formed by the darker regions – wrote that the head of the Stoics, Cleanthes, urged that Aristarchus should be called to account for lack of piety towards the gods. Why? Because he had dared to set ‘the hearth of the universe’ (Earth) in motion, and suggested that the heavens are static whereas the Earth rotates in ‘an oblique circle’ and – even worse – spins on its axis.

The heliocentric theory found favour with just one of Aristarchus’s successors, Seleucus of Seleucia, a hundred years later. By then, the Greeks were aware that the Earth is round, and Eratosthenes obtained a fairly accurate estimate of its size by observing the altitude of the midday Sun at Alexandria and Syene, present-day Aswan.

One variant Egyptian creation myth, the Ogdoad, replaces the primal mound by a cosmic egg. The Milky Way emerged from the ocean of chaos as a mound, associated with the goddess Hathor. A heavenly goose laid an egg on the mound, and inside it was Ra. Later, when the cult of the god Thoth rose to prominence, the goose mutated into an Ibis, an aspect of Thoth.

The image of the cosmos as an egg is common to many cultures. Typically either the universe or important deities come into existence when the egg hatches. The egg may be all that initially exists, or it may rest on a primal ocean. In Hindu mythology the Brahmanda Purana, a Sanskrit religious text, describes the cosmic egg at length. Here brahm means either ‘cosmos’ or ‘expanding’ and anda means ‘egg’. The Rig Veda refers to hiranyagarbha, ‘golden womb’. This floated in nothing until it fragmented into two parts, heaven and Earth. In Chinese Buddhism, Taoist monks told of a god called Pangu, born inside the cosmic egg, who broke it into heaven and Earth when he emerged. In Japanese mythology, a cosmic egg floats in a vast sea.

The Finnish epic Kalevala has a novel slant on creation, which it attributes to a duck that laid fragments of an egg on the knee of the air goddess Ilmatar:

One egg’s lower half transformed

And became the Earth below,

And its upper half transmuted

And became the sky above.

From the yolk the Sun was made,

Light of day to shine upon us;

From the white the Moon was made,

Light of night to gleam above us.

This extract exemplifies a common feature of many myths: they are human-centred. They explain the vast, enigmatic cosmos in terms of a familiar everyday object. An egg is round, like the Sun and the Moon. A living creature emerges from it, so the egg functions as a symbol for the source of all life. Crack one open, and you see two main colours: yellow yolk, and white. These just happen to be the colours of the Sun and the Moon. It is no wonder that images of this kind became so widespread. It just takes a certain combination of logic and mysticism, akin to the Egyptian association between the Sun god and a dung-beetle because both pushed a ball around.

The same combination is characteristic of Discworld narrativium; it is why so much on Discworld ‘makes sense’ even though it is about wizards, witches, trolls, vampires, elves and magic. All you need is a small amount of ‘suspension of disbelief’, as they say in science fiction circles. After that, everything is perfectly sensible. The main difference in ancient times was that there was very little disbelief to suspend. The universe-centred way of thinking was confined to a few deep thinkers in a few cultures.

As Greek civilisation became subsumed under the Romans, the main centres for the study of the natural world moved to Arabia, India, and China. Europe entered a lengthy period often referred to as the Dark Ages, a name that suggests (correctly) that we know very little about them, and also (incorrectly) that this is because nothing much happened on an intellectual level. There was a lot of scholarly effort, but most of it went into theology and rhetoric. What we now consider to be fledgling science struggled.

It is often claimed that in medieval times the Earth was thought to be a flat disc, but the evidence is ambiguous, except very early on. Around AD 350 St John Chrysostom deduced from the Bible that the Earth floated on the waters below the firmament of heaven, a view shared by St Athanasius at much the same time. In about AD 400 Bishop Severian of Gabala considered the Earth to be flat. Unusually, he also believed that the Sun did not travel beneath it during the hours of darkness, but instead nipped back round to the north, hidden from view. By 550 Cosmas Indicopleustes, an Egyptian monk, was doggedly following Egyptian tradition and offered theological arguments for a flat Earth, but with a new twist: the shape was that of a parallelogram surrounded by four oceans.

Many medieval writers definitely knew the world was round, although many believed that no humans lived on its underside, the antipodes. The important regions of the world formed a hemisphere, and in drawings and text it was easy to confuse this with a flat disc. A famous case is the seventh century AD Bishop Isidore of Seville, who wrote in his Etymologiae: ‘The mass of solid land is called round after the roundness of a circle, because it is like a wheel. Because of this, the Ocean flowing round it is contained in a circular limit, and it is divided into three parts, one part being called Asia, the second Europe, and the third Africa.’

At first sight, ‘round’ here seems to mean a flat disc, not a sphere. Maps of the period, known as T and O, T-O, O-T, or orbis terrarum maps, draw a round O outside a capital T. This divides the O into three parts: Asia above the horizontal stroke, Europe and Africa to the left and right of the vertical stroke. Rotate it through a right angle and it looks much like a modern map, though distorted. The oceans all join up and there is a complete ring of water surrounding the land. However, the map could be a projection into the plane of a hemisphere, and that seems to be the prevailing opinion among scholars today. On the other hand, the statement that the oceans are ‘contained in a circular limit’ is difficult to reconcile with a round Earth, especially since the reason is stated to be ‘it is like a wheel’. Do the scholars protest too much?

Be that as it may, there are many references from early Christian times indicating knowledge of a round Earth, but that raised a more difficult theological issue. A round Earth requires the existence of antipodal regions, diametrically opposite to the geographical regions that were then known to Europeans. The existence of these regions wasn’t a problem, but there was general disbelief that they were, or could be, inhabited. The objection was not that people would fall off, but that no one had been there to see whether there was any land – and if there were, whether there were people. It was a perfectly scientific objection: the problem was lack of evidence. Shortly after the sack of Rome in 410, Saint Augustine of Hippo addressed the issue in his City of God:

… as to the fable that there are Antipodes, that is to say, men on the opposite side of the Earth … that is on no ground credible … Although it be supposed or scientifically demonstrated that the world is of a round and spherical form, yet it does not follow that the other side of the Earth is bare of water; nor even, though it be bare, does it immediately follow that it is peopled … Since these people would have to be descended from Adam, they would have had to travel to the other side of the Earth at some point … It is too absurd to say, that some men might have taken ship and traversed the whole wide ocean, and crossed from this side of the world to the other, and that thus even the inhabitants of that distant region are descended from that one first man.

Full marks for geography, then.

The history of flat versus round Earth is complex, open to many divergent interpretations, and littered with myths. A common one is that Columbus had to overcome a widespread belief that the Earth was flat in order to persuade the Spanish royal family to allow him to try to sail westwards to India. Actually, the main obstacles were twofold: the correct belief that the round Earth was too big for this to work according to Columbus’s schedule, and the cost.

Columbus fudged the figures.

Educated people seriously began to wonder whether the Earth really might be flat, or at least not the conventional spheroid, in the Victorian era, around 1850. Paradoxically, the new spirit of scientific enquiry was encouraging some people to question well-established observations of the shape of our planet. It is worth remembering that this was also a period when belief in the spirit world flourished. It wasn’t just Biblical creation that was coming under fire from science. Although no reputable scientists seem to have reverted to believing in a flat Earth, several prominent figures in society did. What motivated them was often a fundamentalist attitude to the Bible, coupled with naive or idiosyncratic interpretations of its contents.

One of the most celebrated flat-Earth disputes was the Bedford Level experiment. The Bedford Level is a long stretch of the Old Bedford River in Norfolk, remodelled as a straight canal. If the theory that the Earth is round has any merit, it ought to be possible to observe the curvature by sighting along the surface of the river. In 1838 Samuel Birley Rowbotham did just that, wading into the river with a telescope and watching a boat as it rowed the six miles to Welney bridge. He reported that the boat’s mast, five feet tall, remained in view the entire time: clear evidence for a flat Earth.

Rowbotham led a colourful life. He was an organiser of an Owenite commune in the Norfolk Fens, which practised the socialist utopian views of the reformer Robert Owen. After allegations of sexual peccadillos, Rowbotham travelled the country giving lectures about why the Earth is flat and science had got it wrong. At a lecture in Blackburn, a member of the audience asked why ships disappear from the hull up when they sail out to sea, until only the tops of the mast remains visible. Unable to answer, Rowbotham fled the lecture hall, but he learned from the debacle, improved his debating skills and found plausible counters to the usual arguments for a round Earth. He published his views in 1849 in a pamphlet called Zetetic Astronomy. Later he put them in a second pamphlet, The Inconsistency of Modern Astronomy and Its Opposition to the Scripture, whose title hints at a possible motive.

Public scepticism ran high, and he was repeatedly asked to carry out proper experiments, but he always refused. By 1864, however, the pressure had become so intense that he set up an experiment on Plymouth Hoe, an open area of ground where Sir Francis Drake memorably played bowls in 1588 while waiting for the tide to turn so that he could attack the Spanish Armada.fn3 If the Earth were round, then only the top of the Eddystone lighthouse, 14 miles away, would be visible through a telescope; if it were flat, the entire lighthouse would be visible. The result was decisive: only half of the lantern was visible. Rowbotham resorted to a standard pseudoscientific response to contrary evidence: ignore it and claim the opposite. Under the name ‘Dr Samuel Birley’ he allegedly sold cures for all human diseases and claimed the ability to prevent ageing. His patents include one for a life-preserving cylindrical railway carriage. In 1861 he married his laundress’s sixteen-year old daughter, and they had fourteen children.

In 1870 John Hampden wagered that he could show, by repeating Rowbotham’s Bedford Level experiment, that the Earth is flat. He encountered a formidable opponent: Alfred Russel Wallace, who had trained as a surveyor. We met Wallace in The Science of Discworld III: Darwin’s Watch. On 1 July 1858 his paper ‘On the perpetuation of varieties and species by natural means of selection’ was read to the Linnaean Society, along with a very similar work ‘On the tendency of species to form varieties’ by Charles Darwin. In his annual report the President of the Society, Thomas Bell, wrote: ‘The year which has passed has not, indeed, been marked by any of those striking discoveries which at once revolutionize, so to speak, the department of science on which they bear.’ The two papers had announced the theory of evolution by means of natural selection.

At any rate, Wallace accepted Hampden’s wager. His surveyor’s training allowed him to avoid the errors of the preceding experiments and he won the bet. Hampden published a pamphlet alleging that Wallace had cheated, and sued for his money. Several lengthy court cases ensued, and eventually Hampden was jailed for libel.

Rowbotham was not to be silenced. In 1883 he set up the Zetetic Society, a forerunner of the Flat Earth Society, with himself as president. It had branches in England and the United States. One of his supporters, William Carpenter, published Theoretical Astronomy Examined and Exposed – Proving the Earth not a Globe using the pseudonym Common Sense. He followed it with A Hundred Proofs the Earth is Not a Globe. One was the observation that many rivers flow for long distances without descending more than a few feet, an example being the Nile, which drops one foot in a thousand miles. ‘A level expanse of this extent is quite incompatible with the idea of the Earth’s convexity. It is, therefore, a reasonable proof that Earth is not a globe.’

It pays to check the facts. The Nile is fed from Lake Victoria, although there are other rivers that run into the lake so it is technically not the source. It flows more than 6,500 km to the Mediterranean Sea. The lake is 1,140 metres above sea level. So the river drops, on average, slightly under one metre for every six kilometres of its length. Over a thousand miles, it drops about 900 feet, not one.

People with extreme religious beliefs, who adopt a human-centred view of the world despite attributing its creation to an all-powerful deity, tend to have problems with universe-centred thinking. Lady Anne Blount was a Biblical literalist, and a rather unimaginative one to boot. Not only did she view the Bible as the sole source of reliable information about nature; she had no doubt that it states that the Earth is flat. Convinced that no true Christian could believe in a round Earth (so much for Augustine), Lady Blount set up a magazine, Earth not a Globe Review. In 1901 she founded another, called simply Earth.

That was the year when the geographer Henry Yule Oldham repeated the Bedford Level Experiment using a better experimental design. He placed three vertical poles in the river, at the same height above the water. When viewed through a theodolite, the middle pole was almost three feet above the other two, a result that is consistent with a round Earth of the correct diameter. Until the Earthrise photo became available, this experiment was widely taught in schools to demonstrate that the world is round. Lady Blount’s response was to hire a photographer, Edgar Clifton. In 1904, using a telephoto lens placed two feet above the river, he took a picture looking back from Welney bridge to where Rowbotham had started it all by wading into the river, six miles distant. The photo showed a large white sheet, touching the surface of the water. Apparently the result surprised him: he knew the sheet should not have been visible. Lady Blount gave the picture a lot of publicity.

How did Clifton get his photo? Was it a fraud? That would be easy to arrange. Take the photo from much closer, then switch plates when performing the actual experiment in the public eye. Or place the sheet or camera higher than claimed. Alternatively, Lady Blount might have got lucky: the result could have been a mirage. Temperature differences in air bend light, in ways that depend on which regions are hotter and which colder. A ‘superior image’ mirage would have led to similar results.

Even in these allegedly enlightened times, belief in a flat Earth survives, remarkably unaffected by a wealth of contrary evidence, though it is definitely a minority view. The International Flat Earth Research Society, usually referred to as the Flat Earth Society, was set up in 1956. The Society’s most recent proposal for the shape of the Earth is a disc centred at the North Pole, surrounded by a 150-foot wall of ice at its rim (Antarctica). As evidence, the Society cites the logo of the United Nations, which depicts exactly this arrangement except for the ice wall. The logo is based on an azimuthal equidistant projection centred on the North Pole, which is one standard mapmaking method for turning a round Earth into a flat map.

Given the attitudes of the religious right and other pressure groups in America to issues like evolution and climate change, and Young Earth Creationism – which believes that the Bible proves the Earth is at most 10,000 years oldfn4 – it wouldn’t be a great surprise to read in tomorrow’s papers that some school board in Boondocks Mississippi is insisting that science lessons should ‘teach the controversy’ about the shape of our world, by giving equal time to the proposition that it’s flat.

We now come to the most curious twist in the story of the Bedford Level Experiment. A few years earlier, in 1896, the American newspaper editor Ulysses Grant Morrow carried out a similar experiment on the Old Illinois Drainage Canal. But he wasn’t trying to emulate Rowbotham and prove that the Earth is flat. Morrow intended to prove that it’s curved. In the experiment, his target, just above water level eight kilometres away, was clearly visible. Morrow concluded that the surface of our planet is curved, but not like a ball. Instead of the world being convex, it is concave, like a saucer. This claim makes more sense once we appreciate who sponsored Morrow’s research: the Koreshan Unity Society, founded by Cyrus Teed in the 1870s.

Teed, a doctor, was fascinated by alchemy. He carried out numerous experiments, often using high voltage electricity, and in 1869 he gave himself a severe electric shock. He claimed that while he was unconscious a spirit had contacted him, telling him he was the Messiah. He changed his name to Koresh, Hebrew for Cyrus, and set out to save the soul of humanity. Teed’s reformulation of our planet’s shape stemmed from this experience. It went much further than merely proposing a hollow interior. According to his Cellular Cosmogony, we are inside the Earth, a hollow ball with the Sun at its centre. Gravity does not exist; instead, we are pinned to the planet’s surface by centrifugal force. The Sun is operated by batteries, and the stars are distorted images of it.

Koreshanity attracted adherents, and Teed preached celibacy,fn5 reincarnation and communism, as well as weird science. A foray into politics led to an assault by his opponents, and the injuries led to his death in 1908. With its leader gone, the cult faded away.

Now, there is a rather trivial sense in which Teed is right. A solid Earth surrounded by the rest of the universe can be transformed into a hollow Earth, surrounded by an infinite expanse of rock, whose interior contains the rest of the universe. All laws of nature, equations of mathematical physics and so on, can be transferred into the transformed coordinates. They will (usually) look different, but the two realisations match perfectly, are logically equivalent, and are physically indistinguishable. As far as mathematicians are concerned, they are ‘the same’.

To obtain a hollow Earth, use a geometric transformation invented by Ludwig Magnus in 1831: inversion. Choose a point in space as the origin; then transform a point distance d along a radius to the point that is distance 1/d along the same radius. This transformation leaves the sphere of unit radius unchanged, because 1/1 = 1, but it swaps the inside and outside of the sphere, because if d is bigger than 1 then 1/d is less than 1. The centre of the sphere goes to infinity; infinity goes to the centre of the sphere. Do this with the origin at the centre of the Earth and you get a hollow planet with the rest of the universe inside it, surrounded by an infinite expanse of rock.

You can play this game with any description of nature. You can use it to argue that the United Nations logo is the true shape of the Earth. You can rewrite astronomy in an Earth-centred frame of reference. If you transform every law of nature to match, no one can contradict you. There is a sensible way to play the game: some transformations take precedence because they lead to simpler equations. But Hollow Earth theories that use inversion as justification apply meaningless transformations that tell us nothing new about reality.

Some kind of world existing inside our planet, that is, underground, is a common element of many religions. We’ve already encountered the ancient Egyptian belief in the underworld. The Judaeo-Christian vision of Hell, until a few centuries ago, had elements in common. The Hindu Puranas tell of an underground city called Shamballa, and the same story occurs in Tibetan Buddhism. However, none of these myths suggests that the Earth is a hollow ball.

In 1692, the astronomer Edmond Halley, a leading scientist of the period, famous for a comet, was trying to explain why compasses don’t always point towards magnetic north. He suggested that the variations in direction could be explained if the Earth were a series of concentric spherical shells: a surface shell 800 kilometres thick, two smaller shells within it, and a solid ball in the middle. He thought that they were separated by atmospheres, rotated at different speeds, and had their own magnetic poles. Escaping gas at the poles glowed to create the auroras. It was a kind of magnetic version of Ptolemy’s crystal spheres, and like that theory, it explained a great deal and was completely wrong.

Pseudoscience got in on the act in a big way in 1818, when John Symmes advanced a similar model, in which the outer shell was 1300 kilometres thick with huge circular openings at both poles. Inside were four more shells, also with polar apertures. You have to remember that this was seventy-seven years before the Norwegian explorers Fridtjof Nansen and Hjalmar Johansen reached latitude 86˚ north in 1895, and ninety-one years before Robert Peary reached the North Pole in 1909 – or, as now seems plausible, got very close but maybe didn’t quite make it. Symmes agitated for a polar expedition, and his follower James McBride seems to have convinced the US President John Quincy Adams to authorise and fund it. But the incoming President Andrew Jackson put a stop to the idea.

In 1826 McBride published Symmes’ Theory of Concentric Spheres, and a flurry of similar theories and books quickly followed. Among them were the 1906 Phantom of the Poles by William Reed, which abolished the secondary shells inside, and Marshall Gardner’s 1913 A Journey to the Earth’s Interior which sported an interior Sun. As late as 1964 the (probably pseudonymous) Dr Raymond Bernard’s The Hollow Earth proposed that our planet’s open interior is the source of UFOs. It also explained what happened to Atlantis, and indeed was where the Atlanteans fled to when their continent disappeared. Rather desperately, the book referred to the Ring Nebula as proof that hollow worlds exist. This structure, just over one light year across and 2300 light years away, is an expanding shell of gas expelled by a red giant star on its way to becoming a white dwarf.

Mapmaking can’t distinguish the geometry of the interior of a sphere from that of the exterior, although differences arise as soon as the surface extends into the third dimension. The peaks of mountains would be closer together if they were inside the Earth. Not surprisingly, there are some big problems with Teed’s theories. Many can be resolved by special pleading, such as strange refractions of light, but these extra features come very close to reformulating conventional physics in an inverted frame of reference, and have no serious substance. Centrifugal force doesn’t work as a substitute for gravity, because it always acts at right angles to the planet’s axis of rotation. The perceived force would be zero at the poles, and only at the equator would it act in the observed direction, at right angles to the surface. The oceans would migrate to form circular pools at the poles, hundreds of kilometres deep. A central Sun would lead to rapid overheating. A large open interior would block seismic waves from earthquakes, contrary to observations. Smaller caverns would not be a problem in this regard, though. Satellite measurements of gravity wouldn’t work, and neither would satellite orbits.

Fiction is unconstrained by mere facts, and there are many fictional depictions of a hollow Earth. An early example is Niels Klim’s Underground Travels, published by Ludvig Holberg in 1741. The hero falls through a hole in the Earth while caving, and lives on the inside of the outer shell of the planet, and on a separate central ball. In 1788 Giacomo Casanova wrote a five-volume blockbuster Icosaméron about a brother and sister who discover a race of hermaphrodite dwarves inside a hollow Earth. Symmes’s pseudoscience found a fictional outlet in Captain Adam Seaborn’s 1820 Symzonia: a Voyage of Discovery. The most familiar story of this subgenre is Jules Verne’s 1864 Journey to the Centre of the Earth, which has inspired a number of movies, only loosely related to the original. The novels that come closest to a genuine hollow Earth are those in Edgar Rice Burroughs’s Pellucidar series, beginning with At the Earth’s Core in 1914, where the Earth’s surface is an 800 km thick shell illuminated by a central Sun, with numerous species of quasi-intelligent and intelligent beings living on the inside surface. The hero ends up in Pellucidar when his mechanical mole refuses to turn and burrows directly downwards into the Earth.

In recent times, hollow worlds have turned up in the media and in computer games.

We promised an unorthodox but solid proof that the Earth is round. Not satellite photos: those are fakes, you understand – NASA never managed to get satellites in orbit, or if they did, their photos of a planar planet are being suppressed, along with secret transcripts from visiting aliens and the true pictures of the Face on Mars.

No, the proof lies in airline schedules.

We can all get on the internet and book flights. The information on airline websites has to be correct, barring a few accidental errors, because millions of passengers – including conspiracy theorists – would have noticed if it weren’t. Websites list innumerable flights every day, and you can work out the travel times. Commercial jet aircraft, used on the major routes, all travel at much the same speed – let’s say 800 kilometres per hour in round figures. The exact figure doesn’t matter; the point is that it’s fairly uniform. It has to be: commercial pressures would put any airline that flew significantly slower than the rest out of business. Anyway, most long-haul aircraft are made by the same small number of companies.

It is therefore possible to draw up a reliable list of approximate distances (which are proportional to the times) between selected cities: say Cape Town, Honolulu, London, Los Angeles, Rio de Janeiro and Sydney. Simple geometry – you can draw triangles with a ruler – reveals that if the world is a plane, then Honolulu, Rio de Janeiro, Cape Town and Sydney (in that order) must lie along a path that is very close to a straight line. The travel times along that path are 13, 8 and 14 hours respectively, a total of 35 hours. Since the path is almost straight, and distances are proportional to times, that total time must be pretty close to the time it should take to travel directly from Honolulu to Sydney.

However, the actual figure is 14 hours.

Even allowing for minor errors in the approximations, the discrepancy is far too large, so the hypothesis of a flat planet must be rejected. The figures can’t lie: not even the most dedicated conspiracy theorist would suggest that global corporations are conspiring to lose large sums of money.

fn1 This is Schrödinger’s equation, the one that says a cat can be both alive and dead. Do you see why? Isn’t it obvious? Oh, since you insist. Let Ψ = A (alive) to deduce that iħ∂A/∂t = ĤA. Then let Ψ = D (dead) to obtain iħ∂D/∂t = ĤD. Add these two equations and rearrange to get iħ∂(A+D)/∂t = Ĥ(A+D). That’s a cat that’s alive and dead, and it satisfies the same equation. (To preserve unitarity, a few 1/√2’s are also needed … but you know that.)

fn2 Command Module Pilot James Lovell.

fn3 This tale is probably untrue, but it’s a good story, so it survives – much like the story of a flat Earth. Never underestimate the power of narrativium.

fn4 Archbishop James Ussher’s scripture-based calculation that the Creation dates to the night before Sunday, 23 October 4004 BC is a little bit too recent because of archaeological records that are hard to dismiss. A retreat by 4000 years neatly avoids the issue. Ussher’s date is so precise because he figured that Creation happened exactly 4000 years before the birth of Christ. Why the deity is so obsessed with decimal reckoning in multiples of one planetary orbit is not explained.

fn5 A poor choice for any cult. The most effective way of spreading a belief is to tell adherents to teach it to their children.