X-Message-Number: 8645
Date: Tue, 30 Sep 1997 21:17:35 -0700 (PDT)
From: John K Clark <>
Subject: Digital Shakespeare

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Mon, 29 Sep 1997 "John P. Pietrzak" <> Wrote:
                

        >What I've not brought up here is the question of addressing. The
        
        >real computer on your desk uses only two symbols; but the regions
                >which hold those symbols are all individually addressable.
            

True but just like physical structures, even the most complex data structures 
are built of very simple parts and there is nothing simpler than an on off 
switch.    


        >Sir, I happened to be talking about a system that you brought up,
                >the AIC.  


AIC is not a system, it is a measurement of the shortest algorithm that can 
produce a given string, and it is a measurement we can never know, and 
therefore of very limited usefulness                



        >The encoded length of an algorithm on a 16 bit machine is DIFFERENT
        
        >than the encoded length of an algorithm on an 8 bit machine, which
        
        >in turn is DIFFERENT than the encoded length of an algorithm on a
                >Turing Machine. 
           
So what?
           


        >Wouldn't you think, then, that this means the results you achieve
        
        >from your much more fundamental binary Turing Machine w.r.t. the AIC
                >would NOT apply to other  processors?


NO, and what does the AIC have to do with the price of eggs? In general a  
Turing Machine will never be running the shortest program that can produce a 
given output, or to be more precise, it might be but we can't prove that it 
is.
               
      >1) You say determining Nth digit of Pi is complex.     

      >2) I say determining Nth digit of Pi time-consuming, not complex.
      
      >3) You say time-consumption is complexity, bring up AIC as definition
            >of complexity without time, and refute AIC, thus supporting your claim.
               
OK.

        >4) I also refute AIC, on grounds other than time-based.
      

Yes, but your other grounds seemed to be largely, I just don't like it.


        >5) You question second refutation, eventually describing AIC on TM.
               

I said that every computer, even a massively parallel one, can be reduced to 
the same model, a Universal Turing Machine with a sequential tape of only 2  
symbols. I said that this was a very powerful idea because it allowed us to  
figure out properties that all computers must have in common regardless of  
their superficial differences, like the number of bits their processors can 
handle at one time. I said nothing about AIC in this context, I did not say 
that the program running on the Universal Turing Machine must be the shortest 
one possible that could emulate the real world computer because we can never 
know what that program is.
               


        >6) I use H-U TM definition to show simplest solution to AIC is
                >trivial on TM (encoding C language style "printf" statement in FSA). 
               

But you don't know that just copying a string is the shortest way to 
reproduce it, in fact that would only be true if the string in question was 
random. Yes, most strings are random but you can never prove that any 
particular one is. 
               

         >This forms my refutation of your refutation of my refutation of AIC, 
               

And this forms my refutation of your refutation of my refutation of your 
refutation of ... ah, I'm sorry, what were we talking about? (:>)  
               


        >do you really believe that the category [intelligence ], beyond
                >inclusion or exclusion of members, is meaningless?
               

No, its not meaningless.



        >Is there no other important relationship between the members other
                >than the fact that they are members?
               

That's the only relationship I know of but that's enough. For example, 
putting Newton, Einstein and Turing in the category "intelligent" seems to 
work very well together in the real world, adding a oak tree to that category 
does not.


        >what axioms you choose to believe in are up to you, but the logic
                >will still work


If you pick the wrong axiom, like "poison will not harm me", you'll end up 
dead.          


        >You can't expect people to answer questions truthfully when their
                >own survival is at stake;
               

Yeah, you're right, but you'd think that if your survival was at stake it  
would be extra important solve puzzles correctly, but for reasons I don't 
understand  it just doesn't seem to work that way.

                                         
                                        John K Clark          

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