Leandro wrote...

> Performance is only an issue in some branches of Mathematics, like
> algorithmic, complexity or numerical analysis.

Mainly I was alluding to extremely high-end applications, such as
fluid dynamics, where one is going to have lots of other problems
in dealing with arcane supercomputer architectures and massive
storage requirements, etc... But day to day engineering stuff, things
you would actually use during initial design work ( and not advanced analysis )
are often well within the computational abilities of something like
Smalltalk.  My recollection is that most of my undergraduate FORTRAN
programs ran in just a few minutes... I'm sure that Smalltalk could
handle that with todays computers ( I was an undergraduate a long time
ago...).  In fact, I gambled my Master's thesis on that and was
rewarded with the insight that the ability to interact with a problem
was as valuable as the ability to implement it's solution.  I found
Smalltalk ( V/286, actually, on a 486/DX33 ) to be a very good match
to my problem, developing an algorithm for 2D unstructured mesh generation.
( I needed the mesh for the flow solver, one thing led to another, etc ... ).

> We are not  interested in doing long
> calculations, we are using Squeak to think and understand mathematical
> concepts.

In much of my undergraduate engineering work, we were primarily doing
one-off programs meant to hone our skills in developing numerical software
to meet our own needs.  These were the end products of having first learned
the mathematical, physical, and engineering principles ( probably in separate
coursework ) rather than an integrated learning experience in which one
literally builds upon previous work.  I'm very glad to hear of your
work in this area- I know there are a lot of Statics and Dynamics
engineering students out there who would benefit enormously from having
a highly interactive "textbook", rather than those pages of cut-and-dried
vectors calculus formulas that I had ( too much abstraction is not a
good thing early in the learning process - pages of equations quickly
become nothing but pages of equations, with all physical meaning lost
somewhere in the dazed confusion of too many courses ).

> The important point is that Squeak and Morphic fit exactly in our work.
> (BTW, I'm just beginning to write my manuscripts and classroom notes in
> BookMorphs, and I am discovering the beauty and power of having mathematical
> objects living around the same pages where the definitions and theorems
> they illustrate are written. It's exciting.)

I should think so!  I'd love to see these!

les