When Steve Jobs returned to Apple as chief executive in September 1997, the computer maker was valued at $3bn — less than one-tenth the value of German conglomerate Siemens, Europe’s largest industrial group both then and now.

Fast forward two and a half decades, and Apple’s market capitalisation exceeds not only Siemens — at $1.42tn the iPhone maker is worth more than the entire Dax index of Germany’s 30 leading companies.

Valuations of companies have often been used to make misleading comparisons: there is a cottage industry of pundits who have tried to compare the value of large multinationals to the GDP of entire countries. But sometimes, such contrasts can illuminate powerful trends about the state of nations.