We live in strange times. A machine plays the strategy game Go better than any human; upstarts like Apple and Google destroy industry stalwarts such as Nokia; ideas from the crowd are repeatedly more innovative than those from corporate research laboratories. Andrew McAfee and Erik Brynjolfsson know what it takes to master this digital-powered shift: we must rethink the integration of minds and machines, of products and platforms, and of the core and the crowd.

The balance now favours the sec...