🚀 go-pugleaf

Here is the original argument under discussion:

  1. Systems with an appropriate causal structure think.
  2. Programs are a way of formally specifying causal structures.
  3. Physical systems implement programs.
  4. Physical systems which implement the appropriate program think.

I have been arguing that this argument is unsound because (2) is false.
By no means do I dispute the conclusion, though of course others would.

 David Chalmers writes:
>Chaos is only a problem if we need to model the behaviour of a particular
>system over a particular period of time exactly -- i.e., not just capture
>how it might go, but how it *does* go.  This isn't what we're trying to do
>in cognitive science, so it's not a problem.  We can model the system to
>a finite level of precision, and be confident that what we're missing is
>only random "noise."  So while we won't capture the exact behaviour of System X
>at 3 p.m. on 12/22/89, we'll generate equally plausible behaviour -- in other
>words, how the system *might* have gone, if a few unimportant random
>parameters had been different.

 M. B. Brilliant writes:
>I second that.  The goal of AI is not to model a particular mind, but
>to create a mind.

These objections seem to grant at least a part of my point - some of the
characteristics of some causal systems cannot be specified by programs.
I agree that an AI need not model any particular person at a particular
time.  But since the error in a numerical model is cumulative over time
slices, it's not just the behavior of the system at a given time that
won't match, but also the general shape of the trajectories though the
state space of the system.  If a numerical model of the brain is claimed
to be accurate except for "noise", and therefore claimed to be conscious,
then it must be shown that what is called "noise" is irrelevant to
consciousness (or thinking).  Fluctuations that seem to be "noise" may
have significant consequences in a chaotic system.

 David Chalmers continues:
>Incidentally, you can concoct hypothetical analog systems which contain
>an infinite amount of information, even in this sense -- by coding up
>Chaitin's Omega for instance (and thus being able to solve the Halting
>Problem, and be better than any algorithm).  In the real world, quantum
>mechanics makes all of this irrelevant, destroying all information beyond
>N bits or so.

Quantum mechanics can't destroy any information - it just make the
information statistical.  Note that in the wave formulation of QM, the
probability waves are continuous, and propagate and interfere
deterministically. No probability information is ever lost, but retrieving
the probabilistic information can be time consuming.  The physical system
need not "retrieve" the probabilistic information; it can react directly.

John Nagle writes:
>    2.  Recent work has resulted in an effective way to solve N-body
>        problems to an arbitrary level of precision and with high
>        speed.  See "The Rapid Evaluation of Potential Fields in
>        Particle Systems", by L.F. Greengard, MIT Press, 1988.
>        ISBN 0-262-07110-X.
>
>        Systems with over a million bodies are now being solved using
>        these techniques.

It's not enough to do fast and accurate calculations; the calculations
must remain fast no matter how accurate the simulation has to be.  Every
computer must have a finite word size, so when accuracy levels require
multiple words to represent values in a state vector, the model will slow
down in proportion to the number of words used.  This effect is
independent of the efficiency of the basic algorithm.