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as the Moon. To get to the nearest star, you must multiply that figure by a further 270,000. The diameter of our home galaxy is 25,000 times as great again. The nearest galaxy of comparable size, the Andromeda galaxy, is 25 times as far away. The distance from Earth to the edge of the observable visible universe is more than 18,000 times as great as that. In round figures, 400,000,000,000,000,000,000,000 kilometres.
    Four hundred sextillion. That’s some village.
    We have no intuitive feel for anything that large. In fact, we have little intuitive feel for distances of more than a few thousand miles, and those only because many of us now travel such distances by air – which shrinks the world to a size we can comprehend. From London, New York is just a meal away.
    We know that the universe is that big, and that old, because we have developed a technique that consciously and deliberately sets aside the human-centred view of the world. It does so by searching not just for evidence to confirm our ideas, which human beings have done since the dawn of time, but for evidence that could disprove them, anew and rather disturbing thought. This technique is called science. It replaces blind faith by carefully targeted doubt. It has existed in its current form for no more than a few centuries, although precursors go back a few thousand years. There is a sense in which ‘know’ is too strong a word, for scientists consider all knowledge to be provisional. But what we ‘know’ through science rests on much more secure foundations than anything else that we claim to know, because those foundations have survived being tested to destruction.
    Through science, we know how big and how old the Earth is. We know how big and how old our solar system is. We know how big and how old the observable part of the universe is. We know that the temperature at the centre of the Sun is about 15 million degrees Celsius. We know that the Earth has a roughly spherical core of molten iron. We know that the Earth is roughly, though not exactly, spherical, and that (with suitable caveats about moving frames of reference) our planet goes round the Sun rather than being fixed in space while the Sun goes round
it
. We know that many features of an animal’s form are determined, to a significant degree, by a long, complicated molecule that lives inside the nucleus of its cells. We know that bacteria and viruses cause most of the world’s diseases. We know that everything is made from seventeen fundamental particles.
    ‘Know’ is one of those simple yet difficult words. How can we know, to take a typical example, what the temperature is at the Sun’s centre? Has anyone been there to find out?
    Well, hardly. If scientists are right about the temperature at the centre of the Sun, nobody who was suddenly transported there would survive for a nanosecond. In fact, they’d burn up long before they even reached the Sun. We haven’t sent measuring instruments to the centre of the Sun, for the same reason. So how can we possibly know how hot it is at the centre, when no person or instrument can be sent there to find out?
    We know such things because science is not limited to just
observing
the world. If it were, it would be firmly back in the human-centredrealm. Its power derives from the possibility of thinking about the world, as well as experiencing it. The main tool of science is logical inference:
deducing
features of the world from a combination of observation, experiment and theory. Mathematics has long played a key role here, being the best tool we currently have for making quantitative inferences.
    Most of us understand in broad terms what an observation is: you take a look at things, you measure some numbers. Theories are trickier. Confusingly, the word ‘theory’ has two distinct meanings. One is ‘an idea about the world that has been proposed, but has not yet been tested sufficiently for us to have much confidence that it is valid’. A lot of