[Haskell-cafe] Re: small boys performance

[Steve Downey]

Many years ago, I got a B- in abstract algebra, and an A+  in
differential geometry.

Now I know why I worry about the blue glow of an unplanned criticality
excursion occuring in my brain.

On 3/14/07, Dan Piponi <dpiponi at gmail.com> wrote:
> On 3/14/07, Andrzej Jaworski <himself at poczta.nom.pl> wrote:
> > I am glad you are interested Dan.
> > ...
> > I do not intend to bore anybody with differential geometry but as I was
> > pushed that far let me add that if Haskell was made to handle Riemannian
> > geometry it could be useful in next generation machine learning research
> > where logic, probability and geometry meet.
>
> I believe that you can probably handle (pseudo-)Riemannian geometry in
> the framework sketched here:
> http://sigfpe.blogspot.com/2006/09/practical-synthetic-differential.html
>
> That only goes as far as playing with vector fields and Lie
> derivatives but I think that forms and tensors should fit just fine
> into that framework.
>
> There's a simple way to use types to represent tensor products, and
> that's sketched here:
> http://sigfpe.blogspot.com/2006/08/geometric-algebra-for-free_30.html
> (Forget that that's about geometric algebra, the thing I'm interested
> in is the tensor products.)
>
> So I'm guessing there's a way of combining these to give a framework
> for (pseudo-)Riemannian geometry. But it'd only be a good framework
> for answering certain types of questions - in particular for things
> like numerical simulation. The important thing is that you'd be able
> to read off accurate numerical values of quantities like curvatures
> without any need for symbolic algebra.
> --
> Dan
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