Re: A question of semantics

Thanks for the responses.  Yes, one of the examples I was thinking of
was the same one as Estel Telcontar described, and I started to think
of what classes of uncertainty I could describe in English.  I found
that I could handle most of them, but only in restricted contexts.
There are several where a description turns into a discussion, just
to explain a simple, basic concept.

As I said, more drastic ones occur in mathematics.  The following
are all fundamental, simple (indeed, almost trivial) concepts - but
ONLY when described in the right way.  Teaching them is done by
explaining them badly, giving examples and consequences, and getting
the student to work with them until the concept gels.  I.e. the
student has to learn the language of mathematics and its concepts.

    1) The concept of a variable.  Either as standing for an unknown
variable (as in 10th year algebra) or as standing for an element of
a set (as in axiomatic algebra).  NOWADAYS, the first is a concept
in most languages of technological communities, but think of it in
the 16th century.  Newton et al. had major difficulties, both in
grasping it and then in communicating it.  The second is still not
easily communicable outside mathematics.

    2) The concept of "with probability one", as in statistics.  I
have had to try to get this across to people with science degrees
and little knowledge of mathematical probability and have had major
difficulty.  They often just CAN'T break out of the mindset of
discrete mathematics.

    3) Wavefunction collapse in quantum mechanics, in such a way
as to make the two-slit experiment a natural consequence.  Einstein
had trouble with this one :-)

Yes, mathematics is a family of constructed languages that is a far
cry from the ones that (I think) people here are interested in, but
it has some examples of very basic, REALLY simple, concepts that
cannot practically be expressed in any natural language.  The fact
that mathematics uses the same words shouldn't confuse us into
thinking that they have the same semantics.

I don't think that such issues are unique to it.


Regards,
Nick Maclaren,
University of Cambridge Computing Service,
New Museums Site, Pembroke Street, Cambridge CB2 3QH, England.
Email:  nmm1@cam.ac.uk
Tel.:  +44 1223 334761    Fax:  +44 1223 334679

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