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Article 3354 of comp.ai.philosophy:
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>From: clarke@acme.ucf.edu (Thomas Clarke)
Subject: Re: Humongous table-lookup misapprehensions
Message-ID: <1992Jan31.134529.11147@cs.ucf.edu>
Keywords: algorithmic complexity
Sender: news@cs.ucf.edu (News system)
Organization: University of Central Florida
References: <1992Jan28.164711.8184@husc3.harvard.edu>
Date: Fri, 31 Jan 1992 13:45:29 GMT

In article <1992Jan28.164711.8184@husc3.harvard.edu> zeleny@zariski.harvard.edu  
(Mikhail Zeleny) writes:
| In article <1992Jan25.224700.8656@ida.liu.se> 
| c89ponga@odalix.ida.liu.se (Pontus Gagge) writes:
| 
| >This debate has continued beyond my endurance level as a normally
| >passive reader. Avaunt, ye scurvey bandwidth complainers!
| 
| You won't find me among their scrofulous ranks.  The more, the merrier,
| that's what I say.
 
I take that as an invitation.  Pardon if I reproduce/anticipate things already
said; the news here in Florida is running a couple of days behind.

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.]

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?]

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.  

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


