"The concept of a "logic diagram" doesn't even apply, no matter how complex. Computers are by definition digital, usually binary at the base, while living nervous systems operate on enormous numbers of connections that express "preferences" along an enormous range"

Yes, the concept of a 'logic diagram' does indeed apply and (computational) complexity has everything to do with it!!!! Every function computed by a parallel (loosely: Non-deterministic) finite state machine (of which a Neural Network is an example) can be computed by some Serial (loosely: deterministic) finite state machine.

The proof is simple and can be exhibited in plain English: In a neural network, 'Signal' propagates from one node to a number of nodes. Map each combination of node activation to 1 single state in a Deterministic Finite. There are not infinite nodes in the neural network, so each combination of states can be completely mapped by some (albeit much larger) Deterministic Finite State Machine.

Lets do demonstration by example, to tone it down a bit. We have millions of implementations of Neural Network Architectures, both out in the 'real world' making nice sums of money for certain industries and also in academia. All but a few of these architectures are written in classical Programming Languages like Java, C, C++, LISP etc. Classical Programming Languages like these are just software articulations fo Finite State Machines (well, maybe not LISP, but whatever). Even more so, they are being run on good-old-fashioned digital computers running good old-fashined Single core computers.

We have simulations of the neurological architectures of Insect visual systems. Running nicely on pentium computers.

Now, parallelism isn't magic, nor is probabilistic function (again, such a probabilistic Non Deterministic Finite Automata is provably not capable of computing any larger class of functions than some equivalent Deterministic Finite Automata much the same as the informal proof above). But, a serial computer simulating a massively parallel network isgoing to be MUUUUUUUUCH Slower. In fact, when I was engaged in writing Neural Networks just 10-15 years ago, simulations of simple architectures with more than a few thousand nodes was out of the question! So, in this case, ROACHES were far better computers than the best desktop money could buy. Now, imagine how many synaptic connections a lab rat has!?

this is a large reason that AI gets its ass handed to it by even pathetically simple real world analogues. Life is a nanoscale self-replicating massively parallel phenomena! It makes our best microcomputers look pathetic!

Now. you MIGHT have a point if the underlying 'physics' of intelligence is not computational- IE, if computing is not really what is 'going on' in brains. If it is not, though, its really hard to see what it might be, and why 'computing things' can't simulate or approximate whatever it is. And believe me, there are many people out there knocking on the doors of these very hard question.

And we may be able to do all of this with serial computation, if 'mind' is a 'computing thing'. Our next generation or two of processors will be able to execute a floating point operation on the stack, and cue up another one before a ray of light has enough time to travel the length of a mans hand- and that would be just one of several thousand cores! So probabilistic or non-deterministic or parallel networks of incredible complexity may be on the table for replication and simulation. Perhaps even whole cortical systems for some small mammals might be possible to simulate!

Yeti