> -----Original Message-----
> From: Ben Tilly [mailto:ben_tilly / hotmail.com]
> Sent: Sunday, January 21, 2001 08:34 AM
> To: ruby-talk ML
> Subject: [ruby-talk:9662] Re: 101 Misconceptions About Dynamic Languages
>
>
> "Christoph Rippel" <crippel / primenet.com> wrote:
> >
> >"Ben Tilly" <ben_tilly / hotmail.com> wrote in message
> >news:LAW2-F228erOc0Ne0Pa000010ca / hotmail.com...
> >...
> >
> >  Since Till mentions categories it is probably worthwhile to point out
> >that
> >they far form useless in CS.  They are very important for the theoretical
> >foundations of FP and modern FP languages like Haskel use categorical
> >concepts like monads (invented by mathematicians decades earlier) even for
> >their IO-system.  By the way there is a striking similarity between  C++
> >meta template programming and FP programming IMO.
>
> I never said that they were useless. :-)
>
> I suspect that there is a meta-issue here.  Algebraists
> by personality like to investigate ways of manipulating
> things.  Computer languges need to provide a set of
> useful ways to manipulate the world.  It is therefore
> little surprise that algebraists have useful insights
> for language design.
> >...
> > > I find it amazingly characteristic that Christian was
> > > asking what _concepts_ Ruby had to offer the world.
> > > Concepts are ways of applying meaning to problems,
> > > which is what analysts rely on for gaining intuition.
> > > But by and large algebraists do not produce concepts.
> > > They produce useful _formalisms_.
> >
> >The amusing thing is that algebra is often much more down to earth than
> >analysis - that is to say algebraist often come up with constructive
> >algorithms you can (in principle) implement (for example the whole
> >encryption business).  If you want  to be polemic you might say that the
> >only thing an analysist ever does is proving  some (non)existence result
> >about a PDE living in some weird infinite dimensional space.;-)
> >
> You are an algebraist, aren't you?  Admit it.  I even bet
> you eat corn on the cob in a spiral! (*)  You are one of
Not sure - I am probably too chaotic to eat like this.;-)
> THOSE people!!! :-P

Ben (sorry about the Till) I was kidding you - I forgot to mention that these funny
objects for whatever reason seem to model the real world but this real world meaning
is IMO attached to them by physicist not mathematicians.
> Now you named encryption as a contribution of algebra.
> Well to name but one relatively recent advance from
> analysis, consider the theory of wavelets.  This provides
> entire classes of ways to break data in way that tends to
> extract and segment overall smooth data and interesting
> boundaries.  Much real-world data shows this pattern.  As
> a result this is applicable in compression, speech
> recognition, etc.
Sure wavelets are important and the same goes for the more mundane FFTs but they are
useful in large part because of their formal properties (which translates into easy
computations) not because of their inherent meaning - which is properly why they
where not invented by signal processing engineers.

Going off on a tangent the reason why analysis is often spectacularly more
successfully is IMO that its two most powerful abstractions - limits and averaging -
are much more natural in its realm. The same ideas (formalisms?) have been applied
to algebra but to use them successfully tends to be much harder (abstract) and this
expalins IMO why you won't find them applied too often to the bred and butter
discreet world most software engineers encounter every day.

...

Christoph