Turing Machines cannot simulate the human mind

TL;DR

This paper argues that Turing Machines cannot fully simulate the human mind by presenting mathematical, physical, and quantum arguments that challenge the Church-Turing thesis and suggest quantum effects are essential to human cognition.

Contribution

It provides novel mathematical and physical arguments, including quantum considerations, that challenge the Church-Turing thesis and the idea that Turing Machines can simulate the human mind.

Findings

Decision problems computable by humans but uncomputable by Turing Machines

Humanoid robots with Turing Machine control cannot perform all human physical tasks

Quantum devices involving wave function collapse can compute uncomputable sequences

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.