A delegation of American executives flew to Beijing in April for a secret meeting just blocks from Tiananmen Square. They had come to court the new kingmakers in one of the strangest experiments in money the world has seen: the virtual currency known as Bitcoin.

Against long odds, and despite an abstruse structure, in which supercomputers “mine” the currency via mathematical formulas, Bitcoin has become a multibillion-dollar industry. It has attracted major investments from Silicon Valley and a significant following on Wall Street.

Yet Bitcoin, which is both a new kind of digital money and an unusual financial network, is having something of an identity crisis. Like so many technologies before it, the virtual currency is coming up against the inevitable push and pull between commercial growth and the purity of its original ambitions.

In its early conception, Bitcoin was to exist beyond the control of any single government or country. It would be based everywhere and nowhere.