Shadowy Logic

Title:

Shadows of the Mind

Subtitle:

A Search for the Missing Science of Consciousness

Author:

Roger Penrose

Publisher:

Oxford University Press, 1994

ISBN

0-19-853978-9

I've been enamored of computers since I was twelve. At that time personal computers were barely entering their hobbyist stages. The ACS newsletter was only four years old, and most hobbyist computers consisted of room-size assemblies of cannibalized circuitry and salvaged equipment, usually years away from ever becoming a working machine. The first commercial computer kit was still four years from coming to fruition. And back in Germany, where I lived at the time, all this was but a distant echo, found mostly in the pages of Batman magazines, which I read voraciously.

For Christmas in 1970 I got my first computer, which consisted of a breadboard that held ten toggle switches and ten lightbulbs. Each toggle switch could be used to toggle a gang of ten connections, and by running wires between these connections I could simulate AND, OR, XOR, and NOT gates. Then I could hook the output of these gates to the lightbulbs, to discover that, for example "barometer is falling" AND "humidity is rising" will light up "it's going to rain." This sounds too elementary to mention, but for a twelve-year old boy it opened endless possibilities.

I'd daydream of computers that could play chess, or speak to me, or drive a car. The small problem of programming was hurdled by imagining neural networks that could be trained to act in the desired manner. As a twelve-year old I had no concept of the practical difficulties, and my daydreams never did advance into even rudimentary experimentation, but I had this idea of a jar filled with salt water algae, and connected to an array of electrical inputs and outputs that would allow me to train the amorphous mass.

Once the intricacies of actual programming became available to me, I was even more entranced. In highschool I played for hours with a programmable calculator, built by some Japanese firm, which could be coaxed to start printing in Japanese characters when presented with "random" instructions on its punch cards. Once I got to college I immediately started signing up for programming classes as they became available, learning Fortran, Basic, Pascal, Lisp, and other bizarre languages on the college's ponderous DEC 10.

Anyway, most computer geeks my age have had similar experiences. Today we mostly peck away on IBM compatibles running Microsoft Windows, and code in C++. The dizzying diversity is still there, but has been replaced by HTML and XML and XSL and CSS..., an ever lengthening array of seemingly gratuitous three-letter acronyms. The other thing that hasn't changed is the dream. Feats like IBM's Deep Thought are almost disappointing to us, since we see through the media hype. Where are the computers of Star Trek, capable of talking to us, the cars and planes that drive themselves, or the houses that keep themselves clean and picked up?

Roger Penrose, who is a tiny bit older than I am, must have listened to kids like me talk about their dreams. I ended up wondering if something about a computer that can think like a human being bothers him, because in Shadows of the Mind, and its fore-runner The Emperor's New Mind, the renowned mathematician argues that, unless we discover some new thing, some new law of nature, we'll never be able to build such a machine.

Sure, a physicist who argues that we'll never be able to break the speed of light and make day-trips to Betelgeuse isn't necessarily bothered by space-flight since that particular speed limit has been verified by a hundred years of experimentation, and so a mathematician should reasonably be allowed to take the position that thinking machines cannot be built, supposing that there are mathematical reasons for believing that. However, Penrose's arguments are so horribly tenuous, and his approach to them so filled with vehemence, that it aroused my suspicions from the very beginning that I started reading Shadows of the Mind.

The book itself is a fairly dry read. Folks who are unacquainted with the arcana of mathematical argument may find it impenetrable, or at least too convoluted to follow easily. It is essentially a response to the critics of The Emperor's New Mind, and Penrose found it necessary to lard it heavily with mathematical notation which might be more convincing to his critics than the more readable prose of the earlier book. I had to track my way through with dozens of small yellow sticky notes, so that I could flip back and forth through the book to follow Penrose's arguments and his abstruse use of symbols.

The argument is a simple one at root. Both Kurt Goedel, a German mathematician of no small importance, and Alan Turing, a British mathematician whose work inspired modern computers, had discovered a startling notion. Suppose that you have a system of logic or a universal computing machine (a Turing machine) that is complex enough to check the truth of any logic statement you care to feed into it. It turns out that there is always at least one logic statement that it won't be able to figure out: itself. No matter how you extend the logic system or the Turing machine, it will never be able to decide if it, itself, is correct. These notions are known as Gödel's Incompleteness Theorem, and Turing's Halting Problem.

Penrose argues that, in order to build a thinking Turing machine, we'd have to be able to create a Turing machine that can figure out everything that human beings can figure out. On top of that, we'd have to be able to figure out the Turing machine itself, since we did create it, ourselves. This is the kicker: if we can do that last bit, then we're clearly more than just a Turing machine, since Goedel and Turing proved that a mere Turing machine cannot do that.

Penrose isn't arguing for souls or spirits, nor any other supernatural mechanics. He just doesn't believe that the human mind is computable, that the mind isn't reducible to a set of algorithms or rules. What is required, he writes, is some mechanism that is not computable. As a mathematician he has plenty of examples at hand of non-computable systems. From the outset he suggests that such a system must be available to the world of matter and natural laws to make the human mind possible.

After completing his arguments against the computability of the human mind, Penrose sets to work examining the world of matter and natural laws for spots where non-computable things might be happening. He points out that Newton's universe, as modified by Einstein, is perfectly deterministic and quite computable. There seems to be nothing there to help us out. Next he takes on the realm of quantum mechanics, which is even more mysterious and bizarre than Special Relativity, but whatever is there that isn't deterministic is still computable as a mere matter of chance and probability. Earlier Penrose has gone to great pains to show that randomness doesn't help us get around the limit of mere logic systems.

Turing had suggested that a Turing machine could be used to simulate the activity of a neuron. Combining several Turing machines just produces a new Turing machine, so the brain, by Turing's way of thinking, had to be a Turing machine, too. But if Penrose is right, then the brain isn't a Turing machine. So what could it be that's going on in the brain that makes it different from ordinary matter? In Shadows Penrose has zeroed in on microtubules, which are structural elements in most cells, from many single celled organisms to the neurons in human brains, and which have certain intriguing properties. Could it be, Penrose muses, that these microtubules somehow manage to do something non-computable for us, something that a Turing machine cannot do?

The secret, suggests Penrose, may not be in either General Relativity, nor Quantum Mechanics, but in the eventual combination of the two, a kind of Quantum Gravity. Penrose spends some time examining a few intriguing proposals that have been made in the direction of unifying the two theories, which include one that suggests a form of time travel. Some experiments with human perception of consciousness, he writes, may indicate that there is a quantum component, a fuzziness, to the moment when we think.

Consciousness, Penrose argues, may be smeared out in time. We think of it as happening now, but, in fact, it might not have a fixed position in time. Some of it comes from the future, from actions we might take, but haven't - maybe never will. This sounds like science fiction, but is really no more bizarre than Einstein musing what the world might look like while riding on a beam of light, or Kekule dreaming of chains of atoms dancing in space and forming rings as if they were snakes biting their tails.

Though Penrose suggests that consciousness may have something to do with Quantum Mechanics, or even Quantum Gravity, he admits that he really has no way of knowing what, in the end, will be the non-computable mechanism by which the human mind overcomes the Turing machine. All that he knows is that there has to be something, something that no one is currently aware of.

Penrose would seem to have made an ironclad argument for his case. However, there are a few curious features of his reasoning that need closer examination. From the outset, he is reluctant to be specific about what he means by consciousness. He characterizes it as a quality that human beings have, and that allows human beings to do the sort of stuff that a Turing machine cannot do. It would seem to be a perfectly reasonable thing to do, since letting a variable sit on the side-lines while you're working on the rest of the problem is something mathematicians do routinely. However, in this case Penrose's approach hides some other assumption.

Penrose assumes that human beings could, in fact, prove that a thinking Turing machine is correct. Could it be that our minds cannot be proven to be correct? How would we go about building a Turing machine that may not be correct? Well, Microsoft - and most other software manufacturers, to be fair - seems to manage pretty regularly to build programs that crash or hang at random moments. Further, proving correctness assumes that the set of inputs and outputs is finite and consistent from one run to the next. At this time there's nothing to suggest that we'll ever be able to prove correctness except for the most trivial of cases.

In other words, we don't know how to even start proving that a program is correct, not to mention a program that is as complex as one that can think like a human being. Penrose tries to make a case for proving correctness "in principle," as opposed to "in practice," but it isn't even clear that it is possible "in principle." If the human mind is actually a Turing machine, and we somehow managed to write a program that exactly duplicates its operation, then, according to Turing, we'd not be able to prove that it was correct. Turing never proved that a Turing machine wouldn't be able to make a copy of itself.

At times Penrose's argument takes a strange turn, where he seems to be suggesting that merely knowing about the Turing Halting Problem, or Gödel's Incompleteness Theorem, is evidence that human beings surpass the limits of a Turing machine. I have to assume that the professor from Oxford, who received international honors for his work, knows that that's not so and didn't mean to make that suggestion.

Penrose seems to hang his hat on the fact that humans can prove mathematical propositions. He generalizes that to say that, evidently, human beings can prove all mathematical propositions. But there are literally dozens of mathematical propositions that no one has proved. Maybe their proofs are beyond the capacity of the Turing machine that runs the human mind? Penrose doesn't try to justify his optimism.

Penrose isn't above emotional arguments. At the very beginning of the book he conjures up the specter of ethical issues associated with thinking computers. He then invites the reader to agree with him that thinking computers cannot be built with current technology, since then these ethical issues go away. Incredible!

Initially Penrose refuses to commit to specifics regarding what consciousness might be. But when he returns to consider consciousness near the end of Shadows, he is clearly talking about personal awareness of one's own actions and perceptions. So why the coyness in the beginning?

Well, because he makes a point earlier to show that, no matter how one extends a Turing machine, it is still just a Turing machine, with a Turing machine's unavoidable limitation. Whenever he talks about what makes consciousness non-computable, it's a nebulous thing that he does not want to look at too closely. If it were something well defined, like a Turing machine's ability to examine it's own internal states, then it would be clearly computable. By inviting the reader (and no doubt himself) to take his eye off of this particular ball, Penrose manages to make it look like a magic bullet, when in fact it's just a red herring.

But it's not like the book is a waste of time and effort - a considerable amount of effort even for me. (I majored in math twenty years ago, but at least I did major in math.) Penrose's arguments need to be considered carefully. They have far reaching implications, even if he is wrong. For example, if the human mind is in fact a Turing machine, there must be things that we may never be able to know. In fact, Steven Pinker thinks so, as he writes in How the Mind Works. How do we ever know that we are right, besides direct empirical evidence? In the end I thought the book had been worth my time.