When Athens went to war with Sparta some 2,500 years ago, the Greek historian Thucydides identified one simple cause: a rising power threatened to displace a ruling one, leading inexorably to conflict.

As Graham Allison explains, in the past 500 years, great powers have found themselves in 'Thucydides's Trap' 16 times. In 12 of the 16 - from war between the French and the Hapsburgs in the 16th century to the two world wars of the 20th - the results have been catastrophic.

Today, the same structural forces propel China and the US toward a cataclysm of unseen proportions, even as both sides insist that such a war could never occur.