Re: Dangerous knowledge

[Ronnie Brown <ronnie.profbrown@btinternet.com>]

It is easy to criticise others but I think there is a general problem 
with mathematics teaching (in my limited experience in the UK)
of mathematicians not explaining what the subject is about, or even 
thinking that this is necessary, or useful. I would like to direct 
attention to our
`Knot exhibition'
http://www.popmath.org.uk/exhib/knotexhib.html
and the discussion of what we were trying to achieve in
http://www.bangor.ac.uk/~mas010/icmi89.html  :
in broad terms, this was to show through the medium of knots some of the 
methodology of mathematics. The advantages of knots for this aim are many.

In some ways the spirit of this exhibit is expressed by the slogan
`advanced mathematics from an elementary viewpoint'.
So how much of the baggage can you throw away and still get to, say, a 
real calculation?
I once did a sample Todd-Coxeter enumeration of a presentation of a 
finite group of order 8  to a class of unprepared 14 year olds, 
(fortunately
I was prepared to do this!) and had them helping me  fill in the table 
(just as well , too) and draw the Cayley graph.

I feel there is a real hunger in the public and in other sciences to 
find out what is going on in mathematics which has some kind of excitement,
preferably in terms of new ideas, rather than solving say the Goldbach 
Conjecture. Higher dimensional algebra is quite useful in this respect.
One can discuss what is or should be a higher dimensional formula, and 
why the idea  might, or might not, be relevant to brain function! (I've 
done this too for an audience of neuroscientists.)

Also discussed  in
http://www.bangor.ac.uk/~mas010/promotingmaths.html
is the heretical idea of `promoting mathematics' to students of 
mathematics!

The point I am getting at is that there may be  something we can do about
`But generally, science documentaries are disappointing, and maths ones
even more so.' as suggested by Robert, and the start may be conveying 
certain attitudes to the many
students studying mathematics seriously. Is this done enough?

Perhaps those interested in category theory are in a better position to 
deal with these problems than those with no such interest!!???


Ronnie Brown



Robert Seely wrote:
> Actually, I think Dana understates the problem with this program.  It
> suffers from what I call the "PBS documentary syndrome" (equally
> afflicting the BBC, however, so the name is not universal enough!):
> it repeatedly tells you what's cool about its topic, without ever
> actually telling you what the topic really is.  Afraid to scare
> viewers away with the actual details of the topic, it just talks about
> it in terms so general (and often over-inflated or sensationalized,
> which was Dana's point) they are really quite meaningless.
>
> Though not perfect by any means, I think a recent 4-part series "The
> Story of Maths" narrated by Marcus du Sautoy does better - he even
> tries to sketch some proofs.  (The episode closest to "Dangerous
> Knowledge" would be the fourth.)  Even better is an old series (but
> still to be found on Youtube!) called Mathematical Mystery Tour.
>
> But generally, science documentaries are disappointing, and maths ones
> even more so.  It's a pity, because you actually can get an audience
> of non-specialists to understand (at least a little) what mathematical
> results etc are about.  I teach an honours Liberal Arts maths & logic
> class, and a surprisingly large percentage can actually appreciate the
> beauty of (eg) natural deduction proofs in predicate logic, basic
> theory of natural numbers (infinitude of primes, irrationality of
> primes, the fundamental theorem of arithmetic, ... ), simple
> axiomatics (we do Boolean algebras as an example), and even Godel's
> theorems, and the "Lambek calculus" for linguistics (even a bit of
> category theory there!).  This isn't a mickey mouse course (sample
> class tests available on request!), and it's a challenge to many of
> the students.  The point is: they are willing to make the effort if
> they know you're not being condescending, and that you are giving them
> "the real thing", not some pablum that only looks good in the box.
>
> I wish more TV documentary producers took that attitude - they might
> get a slightly smaller audience, but their audience will appreciate
> their efforts more.
>
> -= rags =-
>

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