Chapter 10: Limits of Computation and Physical Reality
The physical laws of the universe dictate what can and what cannot be computed. The Church-Turing Thesis (CTT) is based on the assumption that the Turing machine is the ultimate computing device and according to the CTT something is computable only if it can be computed by a Turing machine. However, the CTT has not been proved and it can be definitely proved in a universe with specific properties. Whether our universe is such a universe is an open problem as it is an open problem whether the universe behaves like a machine. A broader approach that rejects the CTT and shows that the mechanistic universe and the CTT are incompatible is proposed and discussed thoroughly.