From: barry@arnold.math.ucla.edu (Barry Merriman)
Newsgroups: sci.philosophy.tech
Subject: The impossible look up table (was Re: Dualism)
Date: 14 Sep 92 22:35:31 GMT
Organization: UCLA, Mathematics Department


As so often happens in philosophical discussions of intelligence
and consciousness, somone has introduced the ol' Look Up Table
Of All Possible Conversations, apparently  to help sharpen our intution 
about these elusive phenomena.

A warning: I wouldn't base any intuition on the ol' 
Look Up Table, because, while it does exist in the mathematical
sense, it is not _constructible_ in any foreseeable way. I.e. there is no  
foreseeable _algorithm_ that could possibly generate the look up table that  
people envision (even ignoring issues of computer speed and memory)

It is usually assumed that the table could hold all reasonable
conversations, certainly enough to fool any interagator. 

It (probably) exists because such a table is a certain subset of all 
possible strings of ASCII text. (To make it well defined, one
would have to work harder on the specification, but this seems doable.)

But it is not constructible because:
(1) such a table has no ability to learn new knowledge,
and so 
(2) must have all its knowledge hardwired in.
(3)  Since it needs a virtually unlimited amount of knowledge in 
     to fake learning during interogation, 
(3)  it seems it can't be constructed by  
     a foreseeable algorithm (what kind of
     algorithm can generate unlimited knowledge to put into the table?)

For example, if I had a conversation in which I tried to teach the table to 
play chess, and then tried to play chess with it, it could never
make reasonable moves unless its creator knew what reasonable chess 
moves were. 

Similarly, If I taught it calculus, it could never do it right unless the
creator of the table knew how to do calculus.

While the table doesn't have to appear infinitely smart (maybe
it can't find a proof of the Riemann Hypothesis), since we aren't,
I can't see an algorithm that could generate a table that could
fake the learning ability of a typical human.

The problem with not being able to say how the table could be constructed
is that it is essentially then an entity of unknown complexity, being used
to draw conclusions about real world phenomena (intelligence, consciousness)
that in fact may (probably are) less complex (after all, they evolved
in polynomial time).

While the table usually does throw a monkey wrench into peoples
intuitions, since we can't see how to actually build the table, 
I'd say the table is just as mysterious as these other phenomena, and
thereby should not be used to mold intuition. I bet that most people
just don't think to much about what such a table would entail. Once
you do, the table becomes a bigger mystery than the phenomena its 
meant to probe.

(brains have it easy: they can do computations and learning; its easy
for them to keep up with ever changing conversations. The table neither does  
computations nor learning---its construction would have to be via an incredible 
algorithm! 

Some may say that the table should be constructed simply by interogating
a bunch of brains and recording their answers---seems like an odd way
to develop understanding of the properties of minds. The table is
then just as mysterious as the minds that created it. An odd thing
to take as transparent in the argument.)
--
Barry Merriman
UCLA Dept. of Math
UCLA Inst. for Fusion and Plasma Research
barry@math.ucla.edu (Internet; NeXTMail is welcome)
Newsgroups: sci.philosophy.tech