"<a href=""https://www.youtube.com/watch?v=Gfr50f6ZBvo&amp;t=34m00s"">34:00</a> here they are conflating cognition with consciousness. There's an important difference. Penrose's work is on the problem of internal qualitative experience", ie. phenomenal consciousness. You can agree that Turing machines can achieve general Intelligence as per reasoning, understanding, problem solving, task competence in the world, without agreeing that such capacities entail phenomenal consciousness. The disagreement is not that you can't explain general Intelligence in terms of Turing machines, but that you can't explain phenomenal consciousness that way. Briefly, the issue is that no chain of changing primary qualities (quantities in terms of physical processes of matter or of shifting around bits of information that symbolically represent quantities) can possibly necessitate a deduction of a quality of experience. There is no point at which the manipulation of quantities suggests that the quantities are a given experience, like greenness. All we have in neuroscience is correlations between brain states and professed experiences. No logical connection has been found, but worse than that, it seems conceptually impossible to ever find such a logical connection, and this is the hard problem of consciousness.