The Universal Computer

"Martin Davis is a brilliant mathematical logician who was working with von Neumann at the beginning of the 1950s and came up with some of our best interpretations of Turing’s work. This is a brilliant, accessible and not overlong book looking at the whole evolution of the idea of computing, going back to Gottfried Leibniz – whom I would credit as the grandfather of it all. Davis explains how Leibniz’s ideas became real and important, and he’s fair about the genealogy of whose ideas led to other ideas. Yes, it’s a very good explanation of what computation really is. Because Martin Davis is a mathematician, it’s exactly correct – whereas with a lot of other books, including my own, there are sacrifices to technical accuracy for the sake of a story. Davis is rigorous about what Turing did and didn’t prove, and why it’s important today. Computation is essentially a mapping between sequences of code and memory. It’s a back-and-forth between memory and code, so a profoundly simple thing yet it has powerful consequences. Everything we do, from talking on Skype to watching digital movies, is at heart this extremely simple process. And computers are the engines of that logic. Leibniz envisaged that the entire universe could be represented as digital code. That sounded absolutely crazy in the 17th century, but it’s the world we live in today. There’s almost nothing left that isn’t being digitised. Leibniz also built computers. He even designed – in a 1679 unpublished manuscript – a digital computer using black and white marbles running down tracks that behaved in exactly the same way that our computers work today, running electrons through wires. So there’s no doubt in my mind that Leibniz was the original prophet, Turing was the later prophet, and then you can argue over who actually built what. Yes, the philosophical implications of all this are very interesting."