'I am thinking about something much more important than bombs. I am thinking about computers' John von Neumann How did computers take over the world? In late 1945, a small group of brilliant engineers and mathematicians gathered at the newly created Institute for Advanced Study in Princeton, New Jersey. Their ostensible goal was to build a computer that would be instrumental in the US government's race to create a hydrogen bomb. The mathematicians themselves, however, saw their project as the realization of Alan Turing's theoretical 'universal machine'. By breaking the distinction between numbers that mean things and numbers that do things, they unleashed the powers of coded sequences, and the world would never be the same. In Turing's Cathedral, George Dyson describes how the most constructive and the most destructive of human inventions were brought into existence at exactly the same time Dyson's account, both historic and prophetic, vividly re-creates the dawn of the digital universe, uncovering a wealth of new material to bring a story of extraordinary men and women and their ideas to life. From the lowliest smartphone app to Google's sprawling metazoan codes, we now live in a world of self-replicating numbers and self-reproducing machines whose origins go back to a 5-kilobyte matrix that still holds clues as to what may lie ahead.