# 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 high-precision 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 tchow-at-alum-dot-mit-dot-edu

The range of our projectiles---even ... the artillery---however 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

.

**References**:**Re: Exploiting limitations of Turing machines in Turing tests?***From:*Ben Bacarisse

**Re: Exploiting limitations of Turing machines in Turing tests?***From:*Tero Hakala

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