(This concerns a general principle about computer hardware/software, not a specific application. I hope this is the correct subforum.) One of the arguments that some people (e.g., Roger Penrose) use to posit the superiority of humans to algorithmic computers is to claim (without any solid basis) that the human is a non-algorithmic computer. But suppose the human were a non-algorithmic computer. The only advantage that this would confer, as far as I am aware, is that of speed, so that there would still be no advantage in principle, only in practice in that a non-algorithmic computer could complete calculations more quickly. Is there any other advantage? For example, Penrose misuses Gödel's First Incompleteness Theorem, as did Lucas before him; although Fefferman tore Penrose's arguments to pieces, Fefferman did note that the whole argument concerned (the equivalent of) algorithmic processes. So Penrose claimed that the addition of non-algorithmic elements would vindicate his arguments based on Gödel's theorem. But that theorem does not mention time, I do not see that Penrose's claim could have any merit. Is there any substance to the hope that a non-algorithmic (but not mystical) process could add anything of substance besides speed?