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From: mason@endor.uucp (Richard Mason)
Newsgroups: comp.ai.philosophy
Subject: Re: Turing Test: opinions on an idea
Message-ID: <6813@husc6.harvard.edu>
Date: 19 May 91 03:23:34 GMT
References: <1991May13.133711.102@athena.mit.edu> <2200@seti.inria.fr> <5577@cui.unige.ch>
Sender: news@husc6.harvard.edu
Reply-To: mason@endor.UUCP (Richard Mason)
Organization: Aiken Computation Lab, Harvard University
Lines: 32

In article <5577@cui.unige.ch> afzal@cui.unige.ch (Afzal Ballim) writes:
>
>To which the answer is a definite no.  Given that the number of *sentences*
>alone in English is transfinite, it seems improbable at best to imagine that
>the number of conversations could be finite.
>

Transfinite? You mean uncountably infinite?  Surely not...

There are only so-many-thousand words in an Oxford English Dictionary.
There might be more English words, but surely only a finite number since
only a finite number of people have been making them up for a finite period
of time.  Now it's true that a sentence can THEORETICALLY be of arbitrary
length, but in practice we could put a finite limit on the allowed length
of English sentences.  A thousand-word limit would be adequate, but let's
make it a billion billion to be on the safe side.  Similarly, we can safely
say that conversations are only allowed to last for a billion billion
sentences.  So we have a finite number of combinations of words making a
finite number of sentences, and a finite number of combinations of
sentences (a billion billion factorial is still finite) which means a
finite number of conversations.

You may want to assume that the English language will last forever (i.e. a
countably infinite period of time), in which time we will coin a countably
infinite number of words.  You might also remove the restrictions above, so
that both sentences and conversations can be of *ANY* finite length.
You still have a countable infinity of countable infinities, which adds up
to one countable infinity and not uncountable infinity.

All this is completely idle chatter and should not in any way be
interpreted as support for the "construct a game tree for English
conversations" idea, which I regard as utterly infeasible and ridiculous.