[Axiom-math] Re: [Axiom-developer] musings on notation

[C Y]

--- root <address@hidden> wrote:

> Notation is a way to encapsulate thought. I think Axiom needs to 
> pioneer a notation to encapsulate the ideas it presents (functors,
> for instance) cleanly so we use mathematics (operators, proofs, 
> state spaces, mappings) to think, compute, and communicate the ideas 
> clearly.

I don't have any profound insights as far as notation, but I would
suggest a particular documentation approach to this type of work.

Mathematical notation is implimented (or at least based on) standard
mathematical ideas because they are intuitive to the normal mathematics
user.  Unique notation, however useful or powerful it might be, will be
rejected by all but a few unless two things happen:

1)  The notation becomes a standard way of doing something useful in a
computer algebra system
2)  End users are compelled to learn the notation because they can't
live without the extra expressiveness/features/etc. it provides.

1) is wrapped up in 2), in my opinion.  And the only way to get a foot
in the door with 2) is to a) document the new notation comprehensively,
clearly, and usably and b) provide non-trivial useful examples where
the new notation solves a problem where old notation would have had
great difficulties.  We have to sell the new notation, not just develop
it.  We have to make people want it.

The tool that comes to mind as an effectively marketed tool is Sun's
new system tool dtrace.  Their strategy was simple but very effective -
they showed useful examples where subtle system problems were
identified by dtrace quickly where no other system tools could have
done it nearly as well.  I think any new notation Axiom is going to
introduce will have to do the same - not just propose it and show it is
elegant, but have cases of it effectively addressing real world (or at
least math world) problems.  Show people that it is worth the time and
pain to learn new concepts and tools.  Then, if people like the new
abilities well enough, perhaps a standard can be created.

I would also suggest this be the figure of merit for proposed new
notation - not only that it be powerful in theory, but shown to be
powerful in interesting examples.  Just my 2c.

CY


                
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