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Article 3398 of comp.ai.philosophy:
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>From: c89ponga@odalix.ida.liu.se (Pontus Gagge)
Newsgroups: comp.ai.philosophy
Subject: Re: Humongous table-lookup misapprehensions
Keywords: algorithmic complexity
Message-ID: <1992Feb1.221715.8179@ida.liu.se>
Date: 1 Feb 92 22:17:15 GMT
References: <1992Jan28.164711.8184@husc3.harvard.edu> <1992Jan31.134529.11147@cs.ucf.edu>
Sender: news@ida.liu.se
Organization: CIS Dept, Univ of Linkoping, Sweden
Lines: 53

clarke@acme.ucf.edu (Thomas Clarke) writes:

>I don't recall any mention of algorithmic information theory (a la Chaitin).

>The look up table AI trivially passes the Turing test, but the table cannot
>fit within our universe by the usual sort of argument:  there are only 10^80
>atoms etc. etc.

>In order to exhibit a device that passes the Turing test, we therefore have to
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>be clever.  We must find an algorithm that compresses the table enormously
>so that a manageable Turing machine program can produce behavior that passes  
>the test.  [The digits of pi over-fill the universe, but can be generated by a  
>very small program.]

Well, personally, I think that even if there is *one* DFA, the table-cheater, that could
pass (if uninterestingly), not all DFA:s that do must be algorithmical transformation
of the table-cheater. In particular, an *interesting* AI would have quite a different 
structure.

I certainly agree that we have to be clever to make any AI!

>However, even given such an algorithmic compression, there is still the  
>question of logical depth.  It might be the case that the computation of  
>appropriate test responses requires computation time which is an exponential  
>(or worse) function of the length of the test conversation.  Without a Penrose  
>oracle (to coin a term) algorithmic AIs would then all eventually fail the  
                         ^^^^^^^^^^^^^^^
>test. [Can satisfiability be solved in polynomial time?]

Non sequitur. *If* this is the case, it merely makes the transformed DFA:s
fail the test.

>The usual argument about ultimate computational speed applies here: Planck's  
>law sets the minimum switching energy of the machine elements and the speed of  
>light sets the maximum size of the machine. Einstein's law gives the equivalent  
>mass of the switching energy so that if the machine is fast enough, too much  
>mass is concentrated into too small a space and the machine collapses into a  
>black hole taking any computational results with it.  

Well, this is an interesting aspect of practical computability, at least.

>At any rate, the question of whether a hypothetical device can pass the Turing  
>test should consider physical as well as logical limitations. 

Perhaps. I wonder, though, whether it helps.
--
/-------------------------+-------- DISCLAIMER ---------\
| Pontus Gagge            | The views expressed herein  |
| University of Link|ping | are compromises between my  |
|                         | mental subpersonae, and may |
| c89ponga@und.ida.liu.se | be held by none of them.    |
\-------------------------+-----------------------------/


