What is a Universal Turing Machine (UTM)?
As physicists have become more and more interested in complex systems, the notion of algorithm has become increasing important, together with the idea that what physical systems actually do is computation. In other words, due to complex systems, physicists have begun to consider the notion of algorithm as physics. And the UTM now begins to emerge as a fundamental physical concept, not just a mathematical concept [Deutsch (1997), Wolfram (2002)]. To a mathematician a UTM is a formal, artificial, unambiguous language for formulating algorithms, a language that can be interpreted mechanically, and which enables you to specify any algorithm, all possible algorithms. That’s why it’s called “universal.” What is a UTM to a physicist? Well, it’s a physical system whose repertoire of potential behavior is extremely rich, in fact maximally rich, universal, because it can carry out any computation and it can simulate the behavior of any other physical system. These are two sides of a single coin.
