We revisit the question (most famously) initiated by Turing:Can human intelligence be completely modelled by a Turing machine? To give away the ending we show here that the answer is \emph{no}. More specifically we show that at least some thought processes of the brain cannot be Turing computable. In particular some physical processes are not Turing computable, which is not entirely expected. The main difference of our argument with the well known Lucas-Penrose argument is that we do not use G\’odel’s incompleteness theorem, (although our argument seems related to G\’odel’s) and we do not need to assume fundamental consistency of human reasoning powers, (which is controversial) we also side-step some meta-logical issues with their argument, which have also been controversial. The argument is via a thought experiment and at least partly physical, but no serious physical assumptions are made. Furthermore the argument can be reformed as an actual (likely future) experiment. Non-computability of human intelligence