Dr Toby Ord, Balliol College, University of Oxford
In computer science, there are many theoretical machines in a hierarchy of increasing power. The most powerful is the Turing machine, which is roughly like a desktop PC with unlimited time and memory. No matter how you try to extend the power of a Turing machine, you never get anything more powerful - well, at least that is what people are usually taught. In fact, there are definitely theoretical machines more powerful than Turing machines, it is possible that some of these may be physically realisable, they have serious implications for the philosophy of mathematics, and they are really interesting. It doesn’t matter if you haven’t studied computer science before - I’ll get you quickly up to speed, then push on into the relatively unknown.