The science of discworld.., p.12
The Science of Discworld IV, page 12
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.
