turing equivalence

[Noel Sharkey]

I have been pleased with the response to the Turing
equivalence issue both on the net and in my personal
mail. I have not had time to digest all of this yet, but
i have learned a few fundamental things that i didn`t know
and will pass them on by and by. But i still have not seen
a real formal proof.

Jay McClelland does not think that this is a very worthwhile
pursuit because "Turing equivalence is not a guarantee of
capturing the kinds of intelligence that people exhibit but
Turing machines do not, such as: Speech perception, pattern
recognition, retrieval of contextually relevant information
from memory, language understanding and intuitive thinking."

While this may be true, we do not know whether something
like Turing equivalence is a NECESSARY condition for the
performance of such human phenomena.

Jay says, and I agree, that, "We need to start thinking of
ways of going beyond Turing equivalence." But the
question here must be, how do we know when we have
gone beyond Turing equivalence without first having found
out whether or not we have it.

I am working in connectionism because I am interested in
explanations of human cognition and certainly, at present,
connectionism offers a new and exciting approach. I think from this
perspective it is useful the use of external memory aids etc. by humans
is interesting - Turing discusses this himself.
However, computer science has been developing formal analytic tools for
a long time, let us not throw all these insights away because of a lot
of flag waving enthusiasm. If we can find formal equivalences then we
know where our new theory stands in relation to the old and we can
demonstrate its power without descending into waffleware.

Having said this, I wouldn't like to spend too much time
on it myself.

noel

p.s. if this puts people off writing to the net about
turing equivalence, I would still be very happy to have
your replies directed to me personally.