Re: [sl4] Alan Turing's results are profound

From: Charles Hixson (
Date: Thu Oct 15 2009 - 10:15:24 MDT

As far as we can tell the brain operates on a finite set of inputs.
Consciousness ignores most of the incoming signals, but they exist at
the interface. So for the purpose of this discussion Turing machines
are relevant.

I rather agree that Turing machines don't have much to do with actual
implementation of an AI, but they're easy to prove theorems about, and
they can be proven equivalent (within certain constraints) to any other
computer, so they're useful for setting a framework.

Just to be clear I am denying the assertion "A brain doesn't work on a
fixed set of inputs, nor even on a predictable set of inputs." on the
grounds that the sensory nerves are finite in number, and each one is
finite in the number of states that it can occupy. If either of these
assertions is challenged, then I see reason to disagree with my
conclusions, but both seem (to me) rather certain. You may not be able
to predict which inputs will be used, but you can create a set of all
possible input signals for any situation, and then create a family of
Turing machines that cover those signals. (Yeah, it's an unreasonably
large set. This kind of explosion happens when you are trying to prove
things with vague boundaries. The fact that it's unreasonably large
doesn't keep you from determining characteristics that are true for all
members of the set.)

Larry wrote:
> I've been too busy for much of anything lately but have to
> jump in.
> While turing machines are mathmatically interesting, they
> have little relevance to AI. A brain doesn't work on a
> fixed set of inputs, nor even on a predictable set of
> inputs. As such the halting problem is irrelevant to
> it, it doesn't work in isolation like a turing machine.
> Of course on a universal level, a brain being just one
> more piece of the cosmos. We could easily see either see
> the halting problem in an infinite universe, or state
> machine wrap around in a finite one. But even then
> its facing much bigger challenges like running out energy,
> or the "big crunch", these two possible fates will be of
> only intellectual curiousity.
> On Thu, 15 Oct 2009, Stathis Papaioannou wrote:
>> 2009/10/15 Mu In Taiwan <>:
>>> 1 - Turing proved things about Turing Machines in 1936; not computers.
>>> Turing Machines are not the same as physical computers; they are
>>> mathematical abstractions that cannot and do not exist in the real
>>> world.
>>> This is a fact of physics. There's just no room for the tape.
>> Physical computers are finite state machines and a Turing machine can
>> emulate any finite state machine. Most likely, brains are finite state
>> machines and therefore Turing emulable. Brains seem to work following
>> the laws of physics and as far as we are aware the laws of physics are
>> computable. There have been some attempts to argue otherwise; for
>> example, Roger Penrose thinks that brains harness exotic physics and
>> are therefore hypercomputers, not finite state machines. But almost
>> no-one agrees with Penrose.
>> --
>> Stathis Papaioannou

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