In Zeno's famous paradox a tortoise challenged Achilles, the fastest runner in the world, to a foot race.
'Because you are the fastest runner in the world,' said the tortoise, 'you must give me a handicap.'
'That's fair enough,' said Achilles, and allowed the tortoise a 100-metre head start.
At the starting gun, Achilles leapt off the blocks and covered the 100 metres in just 10 seconds. In that time, however, the tortoise had advanced one metre, and so remained ahead. Achilles covered that extra metre in just 0.1 second. But in that 0.1 second, the tortoise had gained another millimetre, and so stayed in the lead.
It took Achilles only one ten-thousandth of a second to cover that millimetre, but in the same time the tortoise had gained another 10 micrometres, keeping just ahead. And so on ad infinitum; Achilles never overtook the tortoise, and the tortoise won the race.
Intuitively, we know this to be nonsense. But the old paradox may still hold a lesson for us when we ask how long it will be before China overtakes the United States to become the biggest economy in the world.
Most economists expect China to pass the US at some point in the next few decades, and the forecast date seems to be getting earlier all the time. In 2003 analysts at Goldman Sachs made waves when they predicted China would overtake the US in 2041. Yesterday John Hawksworth, head of macroeconomics at PricewaterhouseCoopers, published a report arguing it could be as early as 2025, in just 17 years time.
