Computing was born of necessity. To win the Second World War, the Allies urgently needed to crack the complex codes used by the Axis powers. Fortunately, they had Alan Turing on their side. In a breathtakingly elegant paper, Turing laid out the principles of a machine that could tackle any computable problem. Seven decades later, most of us have Turing machines on our desks; many of us carry them around in our pockets. Computing is transforming society – and perhaps humanity – in ways that we are only beginning to appreciate: from trading bots that roil stock markets to prediction engines that know what we want before we do.