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.
"This rule implies that 2, 17, and the number of possible human life experiences are all equally distant from infinity." [0]
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?
Had to look that up again to be sure - no, instead what I'm suggesting is the number of possible states of neurons is infinite, and not countably infinite (implied by a cardinality of aleph-null).
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).