Re: Exploiting limitations of Turing machines in Turing tests?

On 18 Ott, 12:17, Tero Hakala <tero.hak...@xxxxxxxxxxxxxxx> wrote:
Don Geddis <d...@xxxxxxxxxx> wrote:
Humans do a lot of different things. But yes, one important thing they do is
process information. So it can be useful to abstract them as computing
machines of some kind, and see just what kind of computing machine they
correspond to.

...

Ie. in some sense we are approaching brains as if they were somekind of
TM.

Not that they "are" a Turing Machine. But that their computations (of course!)
are limited by (at least!) the same things that limit TMs. (Plus a lot more,
due to resource constraints.)

And now I'm not sure if this is the right way to proceed.

Again, for what purpose? What are you trying to accomplish?
Modelling humans as Turing Machines is useful for some purposes, and not for
others.

Well, let's consider just the information processing aspect.. I'm trying to
figure out if TM is indeed a good model of humans or does it pose
some limitations that can leave out some important properties of thinking
process.

For example, we have a concept of irrational numbers e.g. Pi or Sqrt(2)
that can't be presented in terms of rational numbers, and use
them as we play around with mathematics.. How can TM
handle such things? Of course, it can present Pi as Pi-symbol but
there are uncountable infinite number of irrational numbers, so
TM is incabable of presenting them all by just assigning different
symbols to each one.

We don't reason with uncountably many irrational numbers at the same
time.

We have a concept of the set of irrational numbers plus a few concepts
about a few irrational numbers we cared to give a name to, like pi and
e, plus the concepts about a few subsets of irrational numbers (like
the set of irrational square roots of integers).
It doesn't seem to me that you need infinitely many symbols to hold
those concepts.

In fact, while the concepts of the sets represent infinitely many
objects, they can be described by only finitely many symbols.
Otherwise, math textbooks would have infinitely many characters.

Is the number of possible concepts that one can imagine (and do
somekind of "computation" with them) uncountable infinite so that
TM can't capture them all, and hence is insufficient model for
human cognition?

Can you imagine uncountably many concepts at the same time?

<snip>

.

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