Scientists always anger those who prefer the Earth to be flat

In 1870 a biologist set out to test a popular myth. A sceptic had bet £500 that nobody could prove the Earth was anything but flat and Alfred Russel Wallace, short of cash, took him up. The experiment involved a long canal with three bridges, a marker lowered to the same height above the water from each one; and a sighting along the line which showed that the central marker appeared to be above those at each end. The Earth was curved.

Wallace gained nothing but the hatred of true believers. A hint of their response comes from a letter to his wife: "Madam – If your infernal thief of a husband is brought home some day on a hurdle, with every bone in his head smashed to pulp, you will know the reason."

Flat Earthism goes back a long way and is alive today, for one English primary-school child in five believes in it. Although all science is conditional, the evidence, most experts agree, is against it (although as recently as the 1970s enthusiasts agreed that pictures of the Earth from space proved it to be a flat disc). A subtle proof of our planet's real shape came from Isaac Newton. He was told by a sailor that his ship's pendulum clock, accurate in London, lost two minutes a day at the equator. Newton realised that – given that the rate at which it ticks turns on its distance from the Earth's centre of gravity – it swung more slowly because the globe bulged at the Equator and must hence be flattened at the poles. Time, he realised, could be transformed into space.

It still is. The Global Positioning System measures the shape of the Earth with astonishing accuracy. A receiver on the ground picks up signals from its many satellites and, by measuring the delay in receiving the signal from each one – and several can be seen at once – works out precisely where it stands. The speed of light is such that, if just a single satellite was used, an error of one millionth of a second in the receiver's clock would lead to an inaccuracy of 300 metres. However, cunning software allows the satellite clocks to check each other so that with the right instruments and with enough heavenly milestones, the position of the surface can be measured within millimetres.

The system shows how uneasy is the ground beneath our feet. The Earth's shape changes as its continental plates move, and the growing bulge as they strain against each other may soon mean that, for the first time, an earthquake can be predicted (but not, alas, a tsunami, for the GPS beam cannot penetrate water). Alarmingly, the patterns of movement suggest that an unexpectedly large seismic shock may soon be due on the eastern side of the Andes, not too far from where Wallace himself made his early collections. The system does the same for volcanic eruptions, for it reveals that volcanoes heave and sag over many centimetres as the molten rock deep below swells and shrinks. Parts of Etna, for example, are slumping at around 20cm a year, which means that it will probably not erupt any time soon. GPS shows also that volcanic islands such as Tahiti are sinking into the Earth's crust, but at no more than 5cm a century.

The technique has also been used to measure the thinning of the ice caps and the rising of the seas as the world warms. In coastal Greenland the land has risen fast over the past decade as its burden of ice has been shed. In Antarctica, too, the same is true, with a loss of ten billion tons of ice in 15 years and a rebound of the rock to match. The newly released water has contributed to the overall rise in sea level of 1.5mm a year in the five years from 2005.

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