Re: The border crossing - integers in a ghetto

[Gavin Wraith <gavin@...>]

In message <CABcj=tkN-TG=-+pnOi72ud7=7NOr-mYnGK-MQqkyuwbRKCE7FQ@mail.gmail.com>
          Dirk Laurie <dirk.laurie@gmail.com> wrote:

>Well, now! Before posting, I edited out as too abstruse a section
>which referred to Dedekind cuts, Peano's axioms and Bourbaki
>[1] as examples of the sort of thing we do _not_ need in Lua. But
>since you seem to be fluent in Haskell, isn't that a better space
>for such notions?

>[1] Was it Peter Henrici who referred to Wirth's post-Pascal
>languages as "the Bourbakification of computer science"?

I had not heard that one. The student's maths society at Sussex
University once invited Bourbaki to come and give a lecture.
They got a letter back "Je suis desole' que, 'a cause de ma grande
timidite', c'est impossible d'accepter votre geniale
invitation."

Yes Haskell would be better. Gofer better still, because its
prelude was not designed by committee. But computer science has had a
healthy influence on maths, I think. Not least because geniuses
like Dijkstra and Knuth were practical and not snared
by metaphysical nonsense. Questions like "are the integers
a subset of the reals" betray a lack of understanding IMHO.
A better question is not "what xxx's are?" but "what do you
want to do with xxx's?". There is more to datatypes than
type theory - without knowing the circumstances of a
particular problem you have insufficient criteria to
compare one algorithm with another. On the other hand
the joy of coding can be very bad for learning maths.
The necessity for concentrating on formalism hides the
fact that maths is what goes on in mathematician's heads.
Mathematicians are not generally formalists - unless
they are logicians, of course.
Debugging is salutary, though, because it shows how easy
it is to assume things without realizing it. I like to
tease business users of computers by saying that in the
end the greatest advantage of computers will be recognized
to be not their speed but their stupidity - because they will
reveal by it our own.

I do not use Lua for maths, but for little scripting jobs and
because it has so many qualities to admire.

--
Gavin Wraith (gavin@wra1th.plus.com)
Home page: http://www.wra1th.plus.com/