yes. And yet here, for the first time, is evidence he might have been right. This is where we all look at our shoes and mutter something about burdens of proof.
Note that it is still possible to describe consciousness as a computer -- it just has to be a quantum one. I find a lot of us techies relax around strong materialist positions (Penrose, Churchland, Searle) once you have coerced your interlocutor into admitting that there is no way of proving that there isn't an abstract(able) substrate. We can probably all agree that my Core i7 is not a mind. The disagreement amounts to whether or not a computing substrate of which all the relevant components have tidy classical explanations can be a mind, and after reading this, my fence-sitting on that issue is done. Without a single example of a functioning classical-mechanical mind, and strong evidence that quantum effects are nurtured within the brain, it would appear the magical-thinking quantum-worshipping nonsense-spouting materialist weirdos have it this time. Dammit.
that's nonsene, you can use "classical" computation to simulate quantum effects to arbitrary precision (it's how we can do things like simulate NMR spectra with the born-oppenheimer approximation).
The descriptor "quantum" to describe a computer is also actually kind of nonsense, because fundamentally a transistor works because of "quantum effects".
However: While I disagree that penrose's overarching idea that "brains are magic" is nonsense, his specific mechanism invoking microtubules may be correct (and I personally lean towards that mechanism and have for a while)... But I also don't think that has any bearing on "the computability of strong AI". It does however, have a bearing on "trying to develop strong AI by biomimicry", e.g. neural nets, deep learning nets, etc.
No. Only for one-dimensional systems can classical systems approximate quantum ones to arbitrary accuracy. The resulting technique is known as DMRG. (Although there is some crazy 12-dimensional corner case with adiabatic quantum computation I recall hearing about [1], it's totally irrelevant to most simulation in general and especially the sort you are talking about, unless you know of a classical way to find the ground state of all 1-D spin glasses, in which case there are a lot of people at UCSB who would be very excited to talk to you.)
I am aware of Krysta Svore's work at MSR [1][2] (http://www.youtube.com/watch?v=fhW3Sen9TVY) that might be what you are describing, but those "classical" methods certainly do not work on all systems and with arbitrary accuracy. And the iterative approximations do not converge for more complex systems in the lifetime of the universe, nor do we have enough computing power to do so. She is predicting ground state structure, certainly not say excited states where geometry and Berry phase effects and non-adiabaticity come into play.
> And the iterative approximations do not converge for more complex systems in the lifetime of the universe
I'm not arguing computational efficiency, here. Just "possibility". For the most part, say, a chemist like me (if I even resorted to a computational package) would do one or a handful of rounds, take a look, and say, 'that's good enough for me'. In the end, on the scale of things like microtubules, a first order approximation of whatever 'quantum effect' needs to be accounted for will probably suffice because randomness from just about everything else (e.g. brownian motion) will drown things in the noise.
Simulating a quantum system in a classical mechanical system may be possible in a limited sense, for trivial problems, but certainly not at speed. It's straight up P v NP. You will boil an ocean to watch any nontrivial simulation crawl frame by frame.
But you wander off that point and return to the 'wet-and-noisy' argument he addresses explicitly in the abstract. Let's call it the Argument from Noise, or AfM.
Again, if you read the abstract, you'll see K explains how this new discovery makes moot the AfM (but not rebut it, as a rebuttal or refutation requires an argument; making moot merely requires a contradicting observation. E.g. if the cops have a watertight argument for how, why when and where X murdered Y, it's moot if 100 reliable witnesses report X was playing acoustic folk-rock at a nearby cafe at the time.)
Quantum origin of conscience might actually make teleporting not a horrible deal. Perhaps if you make a perfect duplicate of someone consciousness it gets entangled (or other technobable) and causes the person to briefly enter a coma like state until one of the duplicates is destroyed. In that case teleporting a la Star Trek wouldn't be as horrible as it is depicted - i.e. clone someone and then kill one original.
Note that it is still possible to describe consciousness as a computer -- it just has to be a quantum one. I find a lot of us techies relax around strong materialist positions (Penrose, Churchland, Searle) once you have coerced your interlocutor into admitting that there is no way of proving that there isn't an abstract(able) substrate. We can probably all agree that my Core i7 is not a mind. The disagreement amounts to whether or not a computing substrate of which all the relevant components have tidy classical explanations can be a mind, and after reading this, my fence-sitting on that issue is done. Without a single example of a functioning classical-mechanical mind, and strong evidence that quantum effects are nurtured within the brain, it would appear the magical-thinking quantum-worshipping nonsense-spouting materialist weirdos have it this time. Dammit.