I was reading the book "Emperor's New Mind" by Roger Penrose which deals with understanding the nature of mind in the sense that it is algorithmic or not. In one of the chapters he explains that the deterministic world of the Newtonian Theory can still be non-computable. He explains this as follows: Assuming that the state of universe can be described by a pair of natural numbers (m,n) then, if the universe is computable there would be a turing machine which would compute the state at the next instant. Let the universal turing machine U be imitating this machine. Then, if the machine acting on m i.e., U(m) stops the next state would be (m+1,n) and if U(m) does not stop, the next state would be (n+1,m). Since we cannot determine if the machine U will stop or not algorithmically, we conclude that the universe is non-computable though it is deterministic. Can anyone explain me how do we conclude the next state using the above argument. In particular, why is next state (m+1,n) if U(m) stops?