Popular Science Feature - Aristotle's Imagination

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Feature - Inside the Imagination of Aristotle - Brian Clegg

Infinity has been baffling people since the ancient Greeks - take a look at Aristotle's ingenious way of thinking about it.

Infinity is one of those subjects that in part is fascinating just because it’s so difficult to get your mind around. In principle it’s okay. One philosopher commented ‘if you know what “finite” means and you know what “not” means you should have a basic idea of what infinity is about’. But when you come to pin it down it’s infuriatingly slippery. We know – and the ancient Greeks knew – that you can’t have a biggest number. If there was one (let’s call it something suitably Greek like Homer), what’s wrong with Homer+1? So the numbers go on for ever… but that doesn’t turn infinity into a manageable concept.

In fact, the Greeks were so uncomfortable with infinity that the word used for it, apeiron, had the same connotations that chaos has today – something uncontrolled, unmanageable and dangerous.

Aristotle was to do a fix on infinity that, with the exception of Galileo, would last pretty well unchallenged all the way up to the nineteenth century. Aristotle tends to get a lot of bad press these days. I have lost count of the popular science books I have read that lay into him for being an armchair natural philosopher (did the ancient Greeks have armchairs?), sitting in splendid isolation and thinking of bizarre explanations for the natural world that could not be put to any scientific test. But we can hardly blame Aristotle for that – and it’s impossible to find fault with the superb analogy he was to use when it came to dealing with infinity.

The secret, he reckoned, to dealing with this concept is to treat it as a potential. Something that could in principle be, giving us its indirect implications, but in practice isn’t there. Just described like this, his idea doesn’t seem great shakes, but remember it’s the analogy that made it. Infinity, Aristotle said, is like the Olympic Games.

At first sight this is another of those bizarre comparisons that don’t do a lot for the understanding. Infinity is like the Olympic Games. Surely this is about as useful as the way we describe almost anything that restarts after a disaster as like a phoenix (rising from the ashes). For that matter, an ogre (according to the movie Shrek) is like an onion. But the Olympic Games analogy is much more than descriptive waffle.

The Olympic Games exist, says Aristotle. You can’t argue with that. If a passing little green man were to step out of his flying saucer (this is my addition to the story – Aristotle didn’t mention little green men) and asked you ‘is there such a thing as the Olympic Games?’ you would have to answer ‘Yes.’ But imagine the little green man was then to ask, in the bizarre syntax of its kind, ‘Show me this Olympic Games of which you speak,’ you would be stumped. There is nothing to produce – because the Olympic Games aren’t on right now. So the Olympic Games both exists and doesn’t – it has a potential existence – and that, said Aristotle, is just how it is with infinity.

Aristotle’s brilliant fudge would be joined by a much more concrete concept of infinity, but not for over 2,000 years…

Brian Clegg is a popular science writer whose books include A Brief History of Infinity and Light Years.

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