Turing Machines cannot simulate the human mind (2207.05700v1)

Abstract: Can a Turing Machine simulate the human mind? If the Church-Turing thesis is assumed to be true, then a Turing Machine should be able to simulate the human mind. In this paper, I challenge that assumption by providing strong mathematical arguments against the Church-Turing thesis. First, I show that there are decision problems that are computable for humans, but uncomputable for Turing Machines. Next, using a thought experiment I show that a humanoid robot equipped with a Turing Machine as the control unit cannot perform all humanly doable physical tasks. Finally, I show that a quantum mechanical computing device involving sequential quantum wave function collapse can compute sequences that are uncomputable for Turing Machines. These results invalidate the Church-Turing thesis and lead to the conclusion that the human mind cannot be simulated by a Turing Machine. Connecting these results, I argue that quantum effects in the human brain are fundamental to the computing abilities of the human mind.