🚀 go-pugleaf

In article <TED.90Feb26144832@kythera.nmsu.edu> ted@nmsu.edu (Ted Dunning) writes:
>
>In article <3750@uceng.UC.EDU> dmocsny@uceng.UC.EDU (daniel mocsny) writes:
>
>   Can any phenomenon be so truly uncomputable that no logical process
>   could behave equivalently (if not exactly)?
>
>yes.

I should expand on my use of "equivalently." While I agree that some
chaotic systems are probably hopeless to simulate with arbitrary
precision, certainly that does not prevent an artificial system from
being equivalently "interesting." I.e., the artificial system may not
exactly reproduce all the behavior of the chaotic system, but it may
satisfy some of the same performance measures, it may exhibit behavior
that appears to be similarly complex, or it may spend roughly the same
amount of time in the same attractor basins.

What has this to do with AI? Perhaps much. Billions of intelligent
individuals exist today, and NOT ONE of them can exactly duplicate the
behavior of ANY other one. For that matter, none of us can exactly
duplicate our recent behavior. 

I interpret this to mean that intelligence is not a point, but a
space, and arbitrarily many intelligences may exist. Thus a simulated
brain could perhaps deviate substantially from the behavior of the
real brain, and still appear to behave quite intelligently. There is
no one answer to the problem of intelligence, and we probably haven't
exhausted the possibilities yet.

>virtually all chaotic dynamical systems have the characteristic of a
>computational horizon beyond which any particular computer cannot keep
>up with the physical system in doing the simulation.  
>
>the reason for this is that sensitive dependence on initial conditions
>requires that the arithmetic that needs to be done gets harder and
>harder to do fast enough to keep up with real time.  before too long,
>you have a system which requires a computer larger than the entire
>universe to predict.

If we regard the system of (chaotic system + sensor readout) as a
computer giving the state of the system at time t, the question is:
"From where does the chaotic system derive its great computing power?"
For the chaotic system fits quite nicely into the universe, and yet it
performs the equivalent of a seemingly uncountable number of elementary
operations.

>all of this assumes that real numbers have some relevance to the real
>world, which would be pretty hard to verify.

Yes, particularly since no computer I know of always performs real
arithmetic (they usually have to stop the party at some finite
precision). :-) Since I don't know of any tight way to associate real
numbers with the real world, I'm happy enough when a system that uses
"numbers" to make decisions gets an answer I can't distinguish from
another system that uses "atoms."

Dan Mocsny
dmocsny@uceng.uc.edu