"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
THOSE people!!! :-P

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.

For a specific instance, when wavelet techniques were
first applied to MRI technology, an 8 hour process dropped
to 1 hour and they got better resolution.  (A figure which
has since improved.)  Why?  Because it allowed people to
choose measurements which carried particularly meaningful
information.  Fewer and more meaningful measurements meant
less time in the machine and a better image!  (What they
did is chose a sequence of measurements that were a
wavelet basis.)

So very typically, analysis contributed a way of thinking
about and analyzing data so that meaning can be more
readily found.  Algebra provides a way to transform
information so that, without the right magic trick, it is
impossible to distinguish from absolute garbage!

Cheers,
Ben

* Actual event.  At some department event everyone was
  eating corn on the cob.  Every last one of the
  algebraists present ate in a spiral.  Every last one
  of the analysts (myself included) ate across in rows,
  like a typewriter head.  Since then when I pull this
  out around mathematicians, it isn't perfect but the
  correlation between eating corn and algebra/analysis
  has been surprisingly good.  Makes no sense to me
  either.
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