Sunday, October 15, 2006

Before posting some much belated responses to Dennett's paper on "True Believers" I want to address some issues about Turing's paper.

One of the objections Turing anticipates is what he calls the "continuity from the nervous system." The idea is that the human nervous is not a discrete state machine, and therefore it is not possible to mimic the behavior of the nervous system with a discrete state machine.

Turing's response to this surprised me. He says that "...if we adhere to the conditions of the imitation game, the interregator will not be able to take advantage of this difference."

Now, keep in mind that the purpose of Turing's paper is to support the claim that the imitation game is a valid substitution for the question "can machines think?" So his response that the imitation game won't distinguish an important difference between humans and discrete state machines suggests a lacking in the imitation game. The question is, which of the following are true:

a) the imitation game cannot make an important distinction and therefore is not a sufficient test, or
b) the differences between a continuous state machine and a discrete state machine are irrelevant when trying to determine if a machine can pass the imitation game, or
c) the difference between a continuous state machine and a discrete state machine are irrelevant when trying to determine if a machine can think
We can take for granted that (b) is true for the moment, after all Turing admits this, but I think what Turing was trying to refute is (a) and (b). If not, it's what he should be attempting to refute. See, the objection about the human nervous system was made by people who didn't even consider the imitation game - so that the fact that the differences between discrete and continuous machines doesn't do anything to effect the outcome of the imitation game does nothing to refute the original argument. It's up to Turing to convince us that even though the imitation game is not affected by the differences between a continuous state machine and a discrete state machine, the imitation game is still a good substition for the question about intelligent machines.

All of this about discrete state machines vs continuous state systems led me to consider some questions Turing did not address.

There is evidence from quantum machanics that the universe is discrete. So that, on some level, the nervous system is itself discrete. Assuming this is true, the discreteness of the universe would only be true "at the atomic or subatomic" level, but the fact remains that we can give a discription of the universe in terms of a discrete state machine. Which, as we know, means that any other discrete state machine is able to simulate it (run it) - given a enough time and memory. So, if it were proven that that the universe is discrete, we would know, with certainty, that a computer could simulate intelligent systems, because intelligent systems exist in the universe.

Of course this would only be interesting from a theoretical level, since the amount of memory and speed needed would make the problem of actually simulating the universe (or any physical description at such an atmic level) intractable. Also, we would have a situation in which the intelligent systems exist on the machine - but the machine itself (taken as a whole) is not an intelligent system any more than the universe itself is. The machine would be simulating the entire universe, in which intelligent systems are only a fraction of what it's simulating; the intelligent systems might be thought of as virtual machines that our real machine is simulating.

Once we know that it would be theorectically possible for intelligence systems to exist on discrete state machines in this way (which is up to quantum machanics to prove) we'd know that it *can* be done, perhaps without the need of simulating everything in the universe.

My other question is related: can a discrete state machine simulate any continuous system? I'm not sure if it theoretically true that one can, but it seems that given enough precision a discrete state machine can become accurate enough for the fractional differences between it and the continuous system it is simulating to be irrelevant.

In fact, the extent to which the discrete state machine is sucessful in its simulation is probably determined by the degree of accuracy being demanded. It can always be better, since it can always be more precise - infinitely more precise, since we're attempting to simulate a continuous system. (Are discrete state machines by definition finite? I don't think so, since the theoretical Universal Turing Machine is infinitely large, and certainly discrete. But, on the other hand, we can never build an actual Universal Turing Machine).

If it is true that the universe is actually discrete, not continuous, but that we think of the human nervous system as a continuous system, then it follows that a discrete system (the quantum universe) is simulating a continuous system (the human nervous system). Simulation probably isn't the right word here...but it's meant to suggest that if the universe can go from discrete to seemingly continuous, then we can do it too.


Blogger Jonathan said...

I obviously don't know enough about quantum mechanics (although the cover of Elegant Universe is staring me down right now) to maintain a strict belief in either a discrete or a continuous universe. But I tend towards continuous, as my conception of a particle moving through space includes it moving freely without any sort of stepwise motion.

However, as far as humans (nay, all life on Earth) go, I think it's clear that we are composed of universal Turing machines: DNA.

12:40 AM  

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