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From: curry@hpl.hp.com (Bo Curry)
Subject: Re: What's innate? (Was Re: Artificial Neural Networks and Cognition
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Date: Fri, 27 Jan 1995 19:32:54 GMT
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: curry@hpl.hp.com (Bo Curry) wrote:
: > Really? The level of sophistication with which a 4-year-old deals
: > with language (counterfactuals, nested intentionals, subordinate
: > clauses) is comparable in complexity to quite high-level
: > algebra.

jerrybro@uclink2.berkeley.edu wrote:
: Perhaps it would clear things up if you explain what you
: mean by this.  The skill of doing algebra *is* the skill of
: manipulationg symbols in a certain way.  If you do a wrong
: manipulation, your work needs to be redone.  I'm not sure that
: the skill of speaking *is* the skill of manipulating words
: taken as meaningless variable names.

Of course it isn't.

: In short, I take issue with the claim of comparability.  This
: also goes for learning, since I suspect it would not be easy 
: for a child to learn a language purely as a game of ordering words
: in sentences, without learning the meanings of the words.
: If a baby genuinely learned a language as if it were a sort of
: algebra, I don't think it would do very well.

: Certainly, algebra has a meaning, but is it at all comparable
: to the meaningfulness of language?

I don't want to spend *too* much time trying to understand
preschool arithmetic. But what I had in mind when I referred
to this was a sort of intuitive understanding of, and
ability to manipulate, numerical and geometric quantities.
Very much like the alleged "special genius" of Gauss, which
someone referred to. Kids learn an intuitive meaning for
small integers, and ways to manipulate them. Algebra is
then somewhat analogous to clause inversion, and in this sense
it need not be more precise than language. The intuitive
grasp of proportionality, inverse proportionality, etc,
which can be expressed entirely qualitatively, seem much harder
to learn than similarly complex linguistic tricks.

But, I don't want to make too much of this, since I haven't
(and am unwilling to) thought about it enough to sustain
a long argument. An analogy is like a mule - it's tough to
get it to carry you very far from the stable.

Bo
