Are Neural Nets Turing Equivalent?

[Peter Cariani]

Dear Peter "Definitely non-Turing",
When you say "Are neural networks Turing equivalent?" are you talking about
strictly finite neural networks (finite # elements, finite & discrete state
sets for each element) or are you allowing for potentially-infinite
neural networks (indefinitely extendible # elements and/or state sets)?
The first I think are equivalent to finite state automata (or Turing machines
with fixed, finite tapes) while the second would be equivalent to Turing
machines with potentially infinite tapes. I would argue that potentially
infinite tapes are purely Platonic constructions; no physically realized
(not to mention humanly usable) automaton can have an indefinitely-
extendible tape and operate without temporal bounds (i.e. the stability of
the physical computational device, the lifespan of the human observer(s)).
For this reason, it could be argued that potentially-infinite automata
(and the whole realm of computability considerations) really have no
relevance to real-world computational problems, whereas finite automata
and computational complexity (including speed & reliability issues) 
have everything to do with real-world computation.
   Does anyone have an example where computability issues (Godel's Proof,
for example) have any bearing whatsoever on the problems we daily 
encounter with our finite machines? Do computability considerations in
any way constrain what we can (or cannot) do beyond those already
imposed by finite memory, limited processing speed, and imperfectly
reliable elements?
        -Peter "Definitely non-Turing, but possibly for different reasons"


P.S. If we consider neural nets as physical adaptive devices rather than
purely formal constructions (as in the early Perceptrons and Sceptrons,
which actually had real sensors attached to the computational part),
then there are contingent measurement processes, which, strictly speaking
are not formal operations. Turing machines, finite or potentially infinite,
simply don't sense anything beyond what's already on their tapes and/or
in their state-transition tables, while robotically implemented neural
nets operate contingent upon (often unpredictable) external events and 
circumstances.