May 21 2008
Is Roger Penrose just a simulation of a physicist?
Today’s crazy thought was inspired by Scott Aaronson’s lecture notes/discussion on The Emperor’s New Mind. He notes that, for human thought to be computable then it must be equivalent to a Turing machine. So, the author of The Emperor’s New Mind, Roger Penrose, must be equivalent to a particular machine M.
Does M output the following sentence?
“Roger Penrose will never output this sentence.”
Well, we don’t know what that means — for a person to “output a sentence”. For a classically defined Turing machine we know what it means, but not for humans. I’m sure Roger Penrose could say the above sentence but that’s not what the statement means. I certainly don’t know, though I can talk nonsense as much as anyone.
It did bring to mind a discussion with Nick in a previous comment thread, about believing one’s own opinions. From the accusation that “you always believe your own opinions are right” it seems reasonable there must be people who believe their own opinions are wrong. Why would one hold opinions that you acknowledge to be wrong? Is it even possible?
I suggest that one of the limitations of the Turing machine M, which we call Roger Penrose, is that it cannot believe things it doesn’t believe. Obviously! The fact that I thought it worth writing a blog post about is probably what makes this crazy.
Given that some people think the concept of truth doesn’t make sense because of postmodern theory I don’t find it hard to believe that there are people who would consider their own opinions to be wrong.
The issue isn’t whether Turing Machine M, Roger Penrose, will ever output the sentence, but whether M will ever be able to truthfully state that the sentence is either true or false.
In The Emperor’s New Mind, Penrose infers that human consciousness cannot be represented by a Turing machine M because susceptibility to the halting problem is somehow incompatible with the phenomenon of self-awareness. From here he leaps to the conclusion that computationally-based AI will never achieve the goal of self-awareness, because any given computational process can be represented by a Turing machine.
He then goes on to suggest that consciousness might instead be embodied by a quantum computational process.
I have a number of problems with this. Firstly, a quantum computer is essentially no different from a massively parallel Turing machine, and as I understand it it is always possible to represent a quantum computer with a non-quantum equivalent, albeit one that will take a heck of a lot longer to solve the same problems. And quantum computers are as susceptible to the halting problem as any other. It seems as if what he really wants is for the brain to exhibit hypercomputational faculties - for which no working physical model has yet been determined to my knowledge.
Secondly, if the human consciousness were susceptible to the halting problem - if there were some kind of input you could subject it to that would cause it to go into a non-terminating series of operations - why would this be incompatible with being self-aware? He fails to explain this, presenting it as if it were somehow obvious that the one infers the other. Surely, before you go claiming that a Turing machine can’t experience self-awareness, you need first to define what you mean by self-awareness….which he doesn’t, other than speculating that a computer can have no ability to ‘feel’ the sensation of self-awareness.
Then there’s the problem of a ‘finite input’. The finite input that a human consciousness is subjected to is the entire continuum of neurological and endocrine inputs plus other environmental factors that impinge upon the brain during its existence from the first flicker of awareness until its eventual demise. During that time the consciousness itself evolves continuously. Its inputs (and its outputs) terminate when it does. It isn’t a closed system. But a mind implemented on a semiconductor based platform wouldn’t have to be a closed system either. The instantaneous state of the conscious mind at a given moment in time might be represented by a Turing machine working on a finite chunk of sensory input but it would be a Turing machine built on a shifting substructure that would continuously and subtly alter the way it operates.
Really, the Turing Machine idea is a massive red herring because it represents an idealised machine that is instantaneously handed a single finite input to work on and receives no other inputs while it’s busy chewing away on that ticker tape until it produces its output (or not, as the case may be). It’s a closed system. As such, it’s not unlike a perfect circle - it’s a hypothetical construct. You can’t represent a human mind by one but then you also can’t really represent a computational device (virtual or otherwise) by one - because such a device isn’t a closed system either. You could represent it by a Turing machine but it wouldn’t be a true representation because it doesn’t take into account the fact that you can interrupt it (by pulling the plug if necessary).
Quantum consciousness isn’t necessary, I think, to resolve the artificial problem that Penrose has concocted in order to deny the possibility of self-aware AI running on a computer. This doesn’t mean that it can’t possibly exist, but it’s not a necessary ingredient.
I recall that a while back Roger Penrose and Stuart Hameroff were working on an idea involving ‘microtubules’ - seemingly inert filament-like structures in neurons - as possible components in a quantum computational faculty in the brain. Maybe, just maybe, our ability to intuitively solve problems at great speed needs a quantum ingredient to explain it. As I understand it most neurobiologists disagree at the moment. But this is an entirely separate issue to that of self-awareness.
I can respect Penrose as a mathematician and physicist, and to be fair I did enjoy reading The Emperor’s New Mind - it’s an entertaining stroll through some interesting areas of mathematics - but the conclusions he draws about the human mind seem to be redundant and I don’t really see how they follow from the mathematical ideas he presents. I’ve yet to read his second outing on consciousness - Shadows Of The Mind - but I’m planning to take a look sometime.
I have to say that the dispute he had with Kleenex over their alleged use of Penrose Tilings on their toilet paper was rather silly as well. Especially given that Penrose Tilings are, by definition, aperiodic tilings, thus the pattern on the toilet paper in question can’t possibly have actually been a Penrose tiling. Kleenex chickened out and settled out of court. I’d have seen him.
Big comment, Lurkinggherkin! ;-)
I agree that Penrose’s arguments in The Emperor’s New Mind were very poor, though I’d go further and just state he was clutching at the mysteriousness of quantum mechanics to explain other things he found mysterious. I have never heard of anyone who seemed qualified in discussing quantum stuff to be remotely impressed with his argument. And I don’t think there are many neurologists who feel that grasping to quantum mechanics will ease the explanation much.
Yeah, well you know what I’m like when I get going!
Try this quote from the White Queen in Alice through the Looking Glass to help with holding opinions http://www.davidpbrown.co.uk/nota-bene/believe-the-impossible.html