Re: [Phys-l] zero width?

[John Denker <jsd@av8n.com>]

On 10/15/2007 09:11 PM, Michael Porter wrote:

> I guess this is my objection -- if you are going to go for  
> approximations and mathematical descriptions anyway, why do you need  
> the chalk? 

Mathematically, I don't need the chalk.

Pedagogically, the chalk is a convenient way of making
the point, using resources available in the classroom,
making the point in a way that anybody who wants to
understand can understand.

As for those who don't want to understand, they will
always find a way to not understand.  I'm not going to
worry about that.

> Whether Ben drew something with zero width really depends  
> on your tolerance for the above mentioned uncertainty, 

The uncertainty is a red herring.  It is an unhelpful distraction.

At any reasonable level of abstraction, the students can see
the chalked region as _representative_ of some well-behaved
slightly abstract region, and if the representation is imperfect, 
it is easy to ignore the imperfections.  They are part of the
representation, not part of the underlying idea.  The imperfections 
are not a problem in theory, and they are not a problem in practice;  
they are only a problem if you have some misbegotten hybrid with 
not enough practicality AND not enough abstraction.

Geometry exists and is reasonably well-behaved.  The fact that
we cannot use chalk to represent triangles smaller than 1 nm,
and cannot use chalk to represent triangles bigger than 20,000
km is a problem with the /representation/, not a problem with
the geometrical ideas.  You have to look past the chalk to 
see the ideas.

The idea that you can do things with boundaries of regions that
you could not do with the regions themselves is not a trivial
idea.  It is a deep, totally non-smart-alecky answer to the
original question.

  http://en.wikipedia.org/wiki/Dedekind_cut