**From:** Christian Szegedy (*szegedy@or.uni-bonn.de*)

**Date:** Fri Oct 08 2004 - 03:39:30 MDT

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Hi Bill,

Now I have read your writing thorougly and my opinion is

that neither your nor Penrose's arguments are conclusive.

------------------------------------------------------------------------------

First, why do I think that your refutation attempt is flawed:

Your wrote that the construction of Penrose can not

be performed since the human mind is not a Turing machine,

but a finite state machine.

However, every finite state-machine can be modelled by

a Turing machine, so I think that the the construction

of Penrose can be still performed.

More concretely, you wrote:

*> Here is where the argument breaks down. With Turing machines,
*

*> we said there must be some integer k such that the Turing machine
*

*> TM_k will give the same answer to the question encoded by n that
*

*> TM_b gives to question Q2. The integer k exists because we can
*

*> construct a Turing machine TM_x that converts any positive integer
*

*> n into the index of question Q2, and we can combine TM_x and
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*> TM_b to get TM_k. But there is no finite state machine that can
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*> convert an arbitrary integer n into the index of question Q2'.
*

In fact, for Penrose's argument to work, it is irrelevant whether TM_k

is a finite state-machine. The only important point is whether the

reader can be modelled by a Turing machine TM_b or not. Everything

else is irrelevant.

You don't solve anything by answering that his argument is flawed

because the human brain is an even more restricted type of Turing

machine. Then, he could ask: "How comes that an even more

restricted type of Turing machine can solve such a hard problem?"

Does not it really show that the human brain in fact is *not* a finite

state machine?

Still, I don't think that Penrose is right on this point.

But my opinion is that it does not have anything to do with

the question whether we are FSMs or not.

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Now, let me come to my refutation of the argument of Penrose:

Assume that we have a Turing Machine AFRM (average formal

reasoning machine) which is capable of formal reasoning about

as well as an average theorem prover today

(it can even be a finite state machine, but it does not matter).

Furthermore, we formalize the situation described by Penrose

informally in his book. Then ask AFROM the same question

formally we were asked informally by Penrose.

I would bet that AFRM would find the correct answer quite

quickly. (This is an experiment that could be

performed in reality and would be a very impressive

demonstration why his argument fails)

How does it come? Simply, because the correct answer can be

easily formally deduced from the premises that are the

*real input*.

I think that the error in the argument of Penrose is that the

problem was posed to the reader in a different format than he

pretended to pose it.

This format is easily interpreted and solved. In its real format:

when k is explicitely written down (assuming of course that

we are Turing machines, since k depends on the index of the

TM modelling the reader) it can not be answered (and this is a

mathematical fact).

So, the reason why his argument fails is that he does not

actually ask the reader the question

"Will TM_k stop on input k?"

,but:

"Take an extremely complicated true statement S the answering

of which exceeds your mental capabilities. Is S true or not?"

**Next message:**Timothy Jennings: "You might all be aware of this, but just in case ..."**Previous message:**Ben Goertzel: "RE: Human mind not Turing computable according to Eliezer?"**In reply to:**Bill Hibbard: "Re: Human mind not Turing computable according to Eliezer?"**Next in thread:**Bill Hibbard: "Re: Human mind not Turing computable according to Eliezer?"**Reply:**Bill Hibbard: "Re: Human mind not Turing computable according to Eliezer?"**Reply:**Robin Lee Powell: "Re: Human mind not Turing computable according to Eliezer?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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