as another poster mentioned, Aaronson has done a great job of covering this -- waay better than I ever could. But the TL/DR is that Penrose believes there's something quasi-magical about thinking that can't be done with Turing machines, and therefore needs all kinds of special physics to get going. It' just so patently naive and absurd to a working computer scientist that it makes me suspect his ego/judgment ratio is a bit high.
Is your claim that we understand consciousness and thus we are certain that it can be implemented algorithmically or that it can be implemented algorithmically no matter what or something else entirely?
pretty much "it can be implemented algorithmically no matter what". There is just no evidence that the physical brain takes advantage of subtle quantum effects to do what it can do; it's extremely unlikely that any machine could do so at normal body temperature.
Intuitively, I don't see any vital need to introduce special types of computation to explain consciousness. It seems very likely to be a phenomenon that emerges from the right kind of information processing, regardless of the physical nature of the computation.
