Re: Exploiting limitations of Turing machines in Turing tests?

Tero Hakala <tero.hakala@xxxxxxxxxxxxxxx> writes:

In comp.ai Don Geddis <don@xxxxxxxxxx> wrote:

I was recently contemplating Turing tests and Turing machines
(TM) and was wondering if the fundamental limitations of TM can
be exploited to discover whether the conversation partner in a
Turing test is a digital computer AI or a real person.
No, they can't. Because humans are subject to the same limitations.

Can you elaborate this a little bit? I was not aware of any proof
that humans can't exceed computational power of TM's. While there
are arguments that the human thought process might be understood/
modelled by a computer analogy, there a lot of contrasting views
also.

I am not the person you asked to expand but, hey, this is Usenet...
You are right, there is no such proof. From a mathematical point of
view one could ask either side to prove the case: that an idealised
human brain either is == TM or is != TM, but from a scientific point
of view it makes more sense to expect those that image there is some
way for a wet lump of neurons to escape the limitations of formal
computation to propose how it does this, and to demonstrate the
mechanisms involved.

There is, of course, not even any proof that the restrictions
originally published by Turing apply to all "reasonable" models of
computation. This proposition is called the Church-Turing thesis.
There are models of computation that can exceed these limits, but none
capture our intuitive sense of what it means to compute or to reason
(for example, they usually have a component that "just knows" the
answer).

While I see now that a given halting problem for some TM/input can
indeed be decided by some TM. Is it possible to prove that for
every possible halting problem that a human can imagine/decide,
there exists one single TM that could solve all of them?

Not yet, and probably never. Proving things about humans is not yet
possible!

Furthermore, I see this comparison a bit unfair. As we now consider
humans limited by their known limitations (speed, attention span, memory
capabibilities, life span etc) and on the other side we have
mathematical model of a TM with arbitrary complexity and
unlimited memory. (and we don't have similar mathematical model for
humans)

Of course it is unfair -- that is the trick for proving convincing
upper bounds! If TMs were restricted, one could argue that just a few
more cells of tape, or another tape, or just a few more steps and the
halting problem would terminate. By having computations that can not
be programmed on an idealised, unbounded machine, we get convincing
upper bounds on what is computable.

<snip>

--
Ben.
.

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