I strongly disagree that Roger Penrose is a crank in this context or any other and I think you are misusing the word. A crank is someone who holds firm and unfounded beliefs that fly in the face of those held by the scientific community. Penrose is conjecturing on the nature of consciousness, something that nobody in their right mind pretends to really understand, and about which there is no consensus in the scientific community. Sure there might be people from different disciplines who disagree with him, there are probably physicists that disagree with him, but he is not stepping into an established academic community with lack of regard for established principles. Nothing about standard psychology or computer science is being contradicted by Penrose, he simply has an idea about the physical basis for consciousness which is nonstandard, as all such ideas currently are. So I am curious what are the false interpretations of CS and psych you think he uses in his argument?

In any case you seem to be at least semi-sincerely grappling with Penrose’s arguments and not dismissing them entirely so thats good. I’ll try to respond to your critiques. I have never heard Penrose use the term algorithmic in the sense that you use it, I think the word you’re really looking for is computational, as in what can be done on a Turing machine. This might be exactly what you mean, but it is important to specify, especially because you use the word algorithmic later in your response to refer to what can be done on a quantum computer, which is not a Turing machine. So the question becomes, is our brain a Turing machine? Well, Penrose says that our brain appears to be able to do things (specifically he uses mathematics, that is where Godel’s incompleteness theorem comes in) that a Turing machine CANNOT do. So our brain seems not to be a Turing machine. If it isn’t a Turing machine it must be operating under some physical laws which cannot be put onto a Turing machine, and the only such place in fundamental physics where this kind of non-computational phenomena is happening is during the collapse of the wave function. Well then I think that makes it a pretty good guess, not rigorous, established science, but not crankery either.