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Unfolding Nature Shop: Unfolding Nature: Being in the Implicate Order

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I believe I have a stronger argument than Roger Penrose that human mathematical thought is non-compu
    #12893056 -

I believe I have a stronger argument than Roger Penrose that human mathematical thought is non-computable.

The human brain is a machine so suppose we have a machine that proves theorems and is equivalent to human mathematical intuition. When fed a paper into the machine it answers either yes, no or undecidable. Every computer is computably enumerable.  Consider The following two postulates:

A) This machine corresponds to the computer N.
B) When fed a question the machine does not give false results.

Suppose we feed into the machine the following string of symbols replacing the symbol N with the exact number:

ASSUMING THE COMPUTER N DOES NOT GIVE FALSE ANSWERS, IF THE COMPUTER IS FED THE STRING OF SYMBOLS GIVEN NOW, WILL THE COMPUTER SAY NO?

We see now that one of the two postulates must be false.

Edited by illusionsofman (07/13/10 02:04 PM)

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Re: I believe I have a stronger argument than Roger Penrose that human mathematical thought is non-compu [Re: illusionsofman]
    #12893132 -

Huh? 

Reminds me of John Searle's Chinese room

Although I'm not really sure what you are saying.

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Re: I believe I have a stronger argument than Roger Penrose that human mathematical thought is non-compu [Re: Amber_Glow]
    #12893349 -

Searle is a retard, but let's not get into that.

OP, what you're saying is almost identical to an explanation I've heard of Goedel's incompleteness theorem (in the book I Am A Strange Loop).

Basically you're 100% correct -- as far as anyone knows, no matter how your computational symbol-manipulation system is constructed, there will always be meaningful statements which cannot be resolved due to self-reference.


--------------------
Weedmaster P knows the truth.

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Re: I believe I have a stronger argument than Roger Penrose that human mathematical thought is non-compu [Re: laserpig]
    #14317771 -

I been thinking a lot about Roger Penrose’s excellent books and I agree that it would be at least very difficult to build a computer that was more intelligent that a human but I think it would not be impossible. If he is saying that the set of all halting problems the community of human mathematicians can become perfectly certain about is infinite non computable and correct I disagree for the simple reason that if you break a proof down into its most individual basic steps each step would be less that a trillion number of pages long and thus computable. Perhaps we can discover theorem proving machines that are smarter than humans by just taking random Turing machines connected to a main computer running a video game tournament. Consider a five second interval of human conscious existence. This includes thoughts both conscious and subconscious memory retrieval and sensory perceptions. I would argue that for a restricted amount of intelligence the number of distinguishable intervals will be finite although it may be in the trillions. Do you think it would be infinite? Now suppose that in all that exists a machine is built that can produce any one of these intervals. Suppose it produces every one of these intervals- the order does not matter. Thus every possible human life would be produced. The only explaination for why we do not see non-sensical things like monsters coming out of the ground and why we see an order to our world is that in all that exists such a machine is never built perhaps for ethical reasons. This may provide proof that a computer cant posses conciousness. By modeling the brain humans in the future might be able to enumerate all these intervals on a computer and perhaps using biological matter connected to a computer build a machine that can simulate a chosen interval. Now just consider the subset of intervals in which the person is wearing magic rings on their fingers. From this set use a quantum experiment to randomly choose an interval, determine if that interval is aesthetically pleasing and if it it build a machine to simulate it and know that in parallel universes all other aestetically pleasing intervals will be chosen and simulated. Than by placing these magic rings on you would enter heaven.

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Re: I believe I have a stronger argument than Roger Penrose that human mathematical thought is non-compu [Re: illusionsofman]
    #14318000 -

squiggles

nothing but squiggles

ripples, crashing into land

sounds made

noises muttered

ideas, concepts, holding hands ,

speak of reality they do

touch reality, know reality, affect reality, describe reality

they do not.


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

Oh Snapz

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Unfolding Nature Shop: Unfolding Nature: Being in the Implicate Order

General Interest > Philosophy, Sociology & Psychology
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