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From: cam@edai.ed.ac.uk (Chris Malcolm    cam@uk.ac.ed.edai   031 667 1011 x2550)
Newsgroups: comp.ai
Subject: Re: IQ is not static, genetic differences inconsequential.
Message-ID: <490@edai.ed.ac.uk>
Date: 3 Aug 89 19:49:11 GMT
References: <485@edai.ed.ac.uk> <4481@uhccux.uhcc.hawaii.edu>
Reply-To: cam@edai (Chris Malcolm)
Organization: University of Edinburgh, Edinburgh
Lines: 80

In article <4481@uhccux.uhcc.hawaii.edu> lee@uhccux.uhcc.hawaii.edu (Greg Lee) writes:
>From article <485@edai.ed.ac.uk>, by cam@edai.ed.ac.uk (Chris Malcolm    cam@uk.ac.ed.edai   031 667 1011 x2550):

>>Studies of human ability to understand and generate complex sentence
>>structures show strict limitations on our ability to handle levels of
>>abstraction.

>Bull.

>>There are many linguistic constructions capable of abitrary
>>levels of recursion, and the level at which we "lose the thread" varies

>What does recursion have to do with abstraction?  Relative clause
>constructions are arguably recursive, but the more restrictive
>relative clauses you stick onto a noun, the more specific the
>reference.  So, if anything, the more recursion is exploited, the
>less the abstraction involved.

>For constructions that make us "lose the thread", maybe you're
>thinking of center-embedding, as in:
>
>	*That that the pig squealed surprised John annoyed Mary.
>
>But the unacceptability of such examples just shows that this sort
>of subject embedding is not, after all, "capable of arbitrary
>levels of recursion".  Anyhow, it has nothing to do with a failure
>to grasp abstractions.
>				Greg, lee@uhccux.uhcc.hawaii.edu

Greg is quite right, abstraction hasn't much to do with linguistic
nesting; but I didn't mean to be taken quite so literally. Our parsing
engine is a cognitively impenetrable black-box, with a number of
well-known limitations, which some computational linguists see as
suggestive evidence of hardware mechanisms, e.g., registers and stacks
of certain sizes, speed of operation, and so on.  What kind of
mechanisms underlie our human conscious abstract thinking is a much
more subtle and open question, but I wished to suggest, by pointing to
the parsing engine as an example, that there were probably hardware
limitations here too.

There is an important distinction here between limitations of principle
and practice. For example, any general purpose (Turing-equivalent)
computer can compute anything computable (within limits of memory etc.).
In that sense all general purpose computers, and all general purpose
programming languages, are equivalent. In practice, however, one
computer may be orders of magnitude faster than another; and this can be
crucial.

In principle my mind is capable of arithmetic of arbitrary complexity.
In practice I'm not much better at handling numbers intuitively than the
smarter birds, and once the arithmetic gets beyond small integers, the
limitations of my mind force me to rely on mental arithmetic - imagining
pencil-and-paper processes, remembering multiplication tables. A further
step in complexity outruns the capacity of my imagination, and I have to
resort to real pencil-and-paper. While my arithmetic processing power,
equipped with pencil-and-paper, is large, it is still, in the end,
significantly limited by my lifespan, and is negligible compared to
computers.

I am not suggesting that, for example, large prime numbers are more
abstract than small integers; simply that since abstraction is
difficult, our in-principle-unlimited powers of abstraction must in
practice acknowledge the qualitatively superior powers of those who can
do the same thing, but so much more quickly and reliably as to seem to
be using wizardry rather than merely improved skills. It is in this
sense that I suggest that there are strict limitations on human powers
of abstraction, although I am sure that better languages and education
could stretch our minds far beyond current levels of performance.

Dijkstra has described computer programming as the art of describing
processes which are too complicated for our feeble minds to understand,
but by careful discipline and method we can nevertheless struggle to an
approximation of a correct description.

As masters of the English language, we are all in principle capable of
writing of Shakespearean quality, but ...
-- 
Chris Malcolm    cam@uk.ac.ed.edai   031 667 1011 x2550
Department of Artificial Intelligence, Edinburgh University
5 Forrest Hill, Edinburgh, EH1 2QL, UK