Massimo Pigliucci issued a spirited counterblast to computationalism recently, which I picked up on MLU. He says that people too often read the Turing-Church hypothesis as if it said that a Universal Turing Machine could do anything that any machine could do. They then take that as a basis on which to help themselves to computationalism. He quotes Jack Copeland as saying that a myth has arisen on the matter, and citing examples where he feels that Dennett and the Copelands have mis-stated the position. Actually, says Pigliucci, Turing merely tells us that a Universal Turing Machine can do anything a specific Turing machine can do, and that does not tell us what real-world machines can or can’t do.
It’s possible some nits are being picked here. Copeland’s reported view seems a trifle too puritanical in its refusal to look at wider implications; I think Turing himself would have been surprised to hear that his work told us nothing about the potential capacities of real world digital computers. But of course Pigliucci is quite right that it doesn’t establish that the brain is computational. Indeed, Turing’s main point was arguably about the limits of computation, showing that there are problems that cannot be handled computationally. It’s sort of part of our bedrock understanding of computation that there are many non-computable problems; apart from the original halting problem the tiling problem may be the most familiar. Tiling problems are associated with the ingenious work of Roger Penrose, and he, of course, published many years ago now what he claims is a proof that when mathematicians are thinking original mathematical thoughts they are not computing.
So really Pigliucci’s moderate conclusion that computationalism remains an open issue ought to be uncontroversial? Surely no-one really supposes that the debate is over? Strangely enough there does seem to have been a bit of a revival in hard-line computationalism. Pigliucci goes on to look at pancomputationalism, the view that every natural process is instantiating a computation (or even all possible computations. This is rather like the view John Searle once proposed, that a window can be seen as a computer because it has two states, open and closed, which are enough to express a stream of binary digits. I don’t propose to go into that in any detail, except to say I think I broadly agree with Pigliucci that it requires an excessively liberal use of interpretation. In particular, I think in order to interpret everything as a computation, we generally have to allow ourselves to interpret the same physical state of the object as different computational states at different times, and that’s not really legitimate. If I can do that I can interpret myself into being a wizard, because I’m free to interpret my physical self as human at one time, a dragon at another, and a fluffy pink bunny at a third.
But without being pancomputationalists we might wonder why the limits of computation don’t hit us in the face more often. The world is full of non-computable problems, but they rarely seem to give us much difficulty. Why is that? One answer might be in the amusing argument put by Ray Kurzweil in his book How to Create a mind. Kurzweil espouses a doctrine called the “Universality of Computation” which he glosses as ‘the concept that a general-purpose computer can implement any algorithm”. I wonder whether that would attract a look of magisterial disapproval from Jack Copeland? Anyway, Kurzweil describes a non-computable problem known as the ‘busy beaver’ problem. The task here is to work out for a given value of n what the maximum number of ones written by any Turing machine with n states will be. The problem is uncomputable in general because as the computer (a Universal Turing Machine) works through the simulation of all the machines with n states, it runs into some that get stuck in a loop and don’t halt.
So, says Kurzweil, an example of the terrible weakness of computers when set against the human mind? Yet for many values of n it happens that the problem is solvable, and as a matter of fact computers have solved many such particular cases – many more than have actually been solved by unaided human thought! I think Turing would have liked that; it resembles points he made in his famous 1950 essay on Computing Machinery and Intelligence.
Standing aside from the fray a little, the thing that really strikes me is that the argument seems such a blast from the past. This kind of thing was chewed over with great energy twenty or even thirty years ago, and in some respects it doesn’t seem as important as it used to. I doubt whether consciousness is purely computational, but it may well be subserved, or be capable of being subserved, by computational processes in important ways. When we finally get an artificial consciousness, it wouldn’t surprise me if the heavy lifting is done by computational modules which either relate in a non-computational way or rely on non-computational processing, perhaps in pattern recognition, though Kurzweil would surely hate the idea that that key process might not be computed. I doubt whether the proud inventor on that happy day will be very concerned with the question of whether his machine is computational or not.