I sort of agree with Scott Aaronson on why he thinks consciousness is finite[0].
The problem, IMO, that Penrose has is that his theories border closely on mysticism - there's some quantum "magical" process whereby consciousness arises. Both pictures are incomplete, but Aaronson's is the most plausible.
Thanks for the link. I do have trouble with the above statement, and what follows it, as I would think that the number of states of the human body (or even just the brain & nervous system) would be infinite (that is, in the sense of the infinite cardinality of real numbers) and not countably infinite (as in the set of whole numbers). This would follow from the entire system operating as a biochemical process, and neuronal stimulus being an analog signal between a finite number of neuron cells. Thoughts?
I suggest the number of possible states is infinite since the signals between neurons are analog (though I acknowledge this one-word categorization is a major simplification of the actual process of neuronal stimulation).