Re: Exploiting limitations of Turing machines in Turing tests?

Tero Hakala <tero.hakala@xxxxxx> wrote on Tue, 02 Oct 2007:
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.

I was not aware of any proof that humans can't exceed computational power
of TM's.

There isn't even a real proof of the Church-Turing Thesis, which is that no
formal machine can out-compute a Turing Machine. (In fact, people have
invented bizarre hypercomputers which can exceed the computational power of a
Turing Machine, but none of them are close to physically realizable in this
universe.)

Add that complexity on to the fact that there is no formal model of a human
being, and of course no such proof exists.

But, at the same time, there is no evidence that _anything_ in the physical
universe (much less mere humans) can exceed the computational power of Turing
Machines. Or, to put it another way, can compute some result which is not
computable by a Turing Machine.

While I see now that a given halting problem for some TM/input can indeed
be decided by some TM (thanks for pointing out this error, I should have
known better..)

It's not even that any single TM/input can be decided. It's just that some
TM/inputs are simple enough, that it is possible to decide (by human or
machine) whether THAT PARTICULAR TM/input will halt. But this is not true
for every TM/input. And in fact, for any given potential "decider", it is
possible to construct a particular TM/input that the given decider will be
UNABLE to conclude whether it halts or not.

But is it also possible to argue that for every possible halting problem
that a human can imagine/decide, there exists one single TM that could
solve all of them?

No. Because there are some undecidable halting problems which are specific
to the given TM that attempts to decide them. So THAT TM will be unable to
decide for the particular constructed example. But other TMs could figure
out whether the example halts, as could some humans.

But this is all true for humans too. Each human has (at least) one example
that they can't determine whether it halts, and there are likely plenty of
TM-decider programs that could deal with the example that the human is
failing on.

Furthermore, I see this comparison a bit unfair. As we now consider humans
limited by their known limitations (attention span, memory capabibilities,
life span etc) and on the other side we have a mathematical model of TM
with arbitrary complexity and unlimited memory & operational speed.

Unfair for what purpose? What question are you trying to answer?

What's amazing is that, despite this arbitrary complexity and unlimited
memory and speed, there are STILL some computational problems that Turing
Machines are UNABLE to solve.

Which leads you to the conclusion that the very much weaker computational
devices known as humans, with all their many limitations, can't even do THAT
well. They're even worse.

Do you see how silly it is for people to claim that computers are limited
(by Godel's Incompleteness Theorem, or by TM undecidability problems) -- which
is true -- but then claim (without any proof) that humans are no so limited?
In truth, humans are even WORSE off on these topics than computers.

Would it be usefull to consider similarly limited TM's?

Useful for what purpose? What are you trying to accomplish?

Of course these limitations would also be rather arbitrary, but as far as
any digital computer/symbolic manipulation mechanism would have to be
implemented in the physical world, they are subjected to the laws of
physics that would inevitably pose at least somekind of restrictions.

Aren't you talking about computers? If you're interested in this topic, why
don't you start learning some computer science? That would seem to be the
field that investigates the property of physical devices that perform
symbolic manipulations and computations. Algorithms, complexity classes,
etc. etc.

-- Don
_______________________________________________________________________________
Don Geddis http://don.geddis.org/ don@xxxxxxxxxx
If you saw two guys named Hambone and Flippy, which one would you think liked
dolphins the most? I'd say Flippy, wouldn't you? You'd be wrong though. It's
Hambone. -- Deep Thoughts, by Jack Handey
.

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