MARTIN WOLF Convergent incomes and divergent growth - that is the economic story of our times. We are witnessing the reversal of the 19th and early 20th century era of divergent incomes. In that epoch, the peoples of western Europe and their most successful former colonies achieved a huge economic advantage over the rest of humanity. Now it is being reversed more quickly than it emerged. This is inevitable and desirable. But it also creates huge global challenges. In an influential book, Kenneth Pomeranz of the University of California, Irvine, wrote of the great divergence between China and the west. He located that divergence in the late 18th and 19th centuries. This is controversial: the late Angus Maddison, doyen of statistical researchers, argued that by 1820 UK output per head was already three times and US output per head twice Chinese levels. Yet of the subsequent far greater divergence there is no doubt whatsoever. By the middle of the 20th century, real incomes per head (measured at purchasing power parity) in China and India had fallen to 5 and 7pc of US levels, respectively. Moreover, little had changed by 1980. What had once been the centres of global technology had fallen vastly behind. This divergence is now reversing. That is far and away the biggest single fact about our world. On Maddisons data, between 1980 and 2008 the ratio of Chinese output per head to that of the US rose from 6 to 22pc, while Indias rose from 5 to 10pc. Data from the Conference Boards total economy database, computed on a slightly different basis, indicate that the ratio rose from 3 to 19pc in China and from 3 to 7pc in India between the late 1970s and 2009. The comparisons are uncertain, but the direction of relative change is not. Rapid convergence on the productivity of advanced western economies is not unprecedented in the era following the World War II. Japan was the forerunner, followed by South Korea and a few small East Asian dragon economies - Hong Kong, Singapore and Taiwan. Japan had already begun to industrialise in the 19th century, with remarkable success. After its defeat in the World War II, it restarted at about a fifth of US output per head, roughly where China is today, to reach 70pc in the early 1970s. It attained a peak of close to 90pc of US levels in 1990, when its bubble economy burst, before declining again. South Korea started at 10pc of US levels in the mid-1960s to reach close to 50pc in 1997, just before the Asian crisis, and 64pc in 2009. In the past few centuries, what was once the European and then American periphery became the core of the world economy. Now, the economies that became the periphery are re-emerging as the core. This is transforming the entire world. What this means for us all will be the subject of next weeks column. -Financial Times