Re: Exploiting limitations of Turing machines in Turing tests?
 From: tchow@xxxxxxxxxxxxx
 Date: 02 Oct 2007 14:06:26 GMT
In article <fdt045$k4c$1@xxxxxxxxxxxxx>,
Tero Hakala <tero.hakala@xxxxxx> wrote:
In one thing that TM's and brains seem to be different is that the
number possible of TM's is infinite, but countable (in the sense
that natural numbers are). While in working human brains, the
neurons get their information in analog manner from other neurons
(ie. real numbers come into play here) if we discount
quantization effects. So it seems that brains (or dynamics of brain)
are uncountable infinite and therefore exceed the number
of possible TM's.
This is true only if the "analog manner" you speak about cannot be simulated
by highprecision rational numbers. It is not at all clear that if one
perturbs the inputs to a neuron by, say, 10^(1000000) then its behavior
will change.
And if we take the quantum mechanics into
account, we seem to get into a bottomless swamp. (And TM's, being
deterministic, would have also some difficulty to handle quantum
aspects.. as far as QM is considered valid in the form as it is now)
As far as computation is concerned, it is again not clear whether
quantum mechanics buys you anything. Any *finite* sequence of "truly
random" digits can be handled by the TM model of computation. An infinite
sequence cannot, but again it is not clear that such an infinite amount
of information can be "used" in the operation of the brain.
Can this be considered a valid distinction between brains and TM's?
Possibly, but it's not at all clear. The sticking point is that the
differences you posit rely on infinitely long sequences of numbers, or
an infinite amount of information, and it's not clear how such things
can be relevant physically. It's also not clear how we can test such
a theory in the lab, given that any experiment we can actually carry
out must take a finite amount of time and work with finite precision.

Tim Chow tchowatalumdotmitdotedu
The range of our projectileseven ... the artilleryhowever great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. Galileo, Dialogues Concerning Two New Sciences
.
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 Re: Exploiting limitations of Turing machines in Turing tests?
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 Re: Exploiting limitations of Turing machines in Turing tests?
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