What excited Europeans was the belief that they had both the right and the means to ‘make’ or remake America in Europe’s image, or even as an improved version of the old continent.

On Europe’s Inner Asian frontier, demographic expansion long seemed as hobbled as it was in mainland North America until the 1750s.

Pre-industrial China had reached a ‘high-level equilibrium’, a plateau of economic success. Its misfortune was that there was no incentive to climb any higher: the high-level equilibrium had become a trap.

Turning their back on a maritime future may have been a concession to their gentry officials (who disliked eunuch influence), but it was also a bow to financial constraints and the supreme priority of dynastic survival.

China grew quantitatively, not qualitatively. Part of the reason, Elvin argued, was the inward turn we have noticed already: the shrinking of China’s external contacts as the Ming abandoned the sea.

Perhaps because of the distinctive ecology of the Near and Middle East, where agrarian society played second fiddle to long-distance trade, Islam was strikingly cosmopolitan. Muslims were first of all members of the umma, the great body of Islamic faithful, and only secondly subjects of their territorial ruler.

Shared faith, and common acknowledgement of the Sharia or Islamic law, helped make Ottoman rule acceptable in the Fertile Crescent, Egypt and North Africa, while the sultan’s role as Islam’s champion against the Christian infidel gave him a strong claim on the loyalty of the faithful.

If every country depended upon foreign suppliers and customers, the web of mutual dependence would be too strong to break.

By one calculation, Russia’s land surface increased from 2.1 million square miles in 1600 to some 5.9 million a century later.