🚀 go-pugleaf

Larks <Larks@worldnet.att.net> wrote in article
<32F1965C.382A@worldnet.att.net>...
> Xcott Craver wrote:
> > 
> > In article <5cmpbo$nds@agate.berkeley.edu>,
> > Louis Hom <lhom@nature.berkeley.edu> wrote:
> > >So, I'm trying to collect posters' favorite Things in Math & Science.
> > >       For example, one of my favorite things is the solid that you
get
> > >when you rotate y=1/(log x) about the x-axis -- it has finite volume
but an
> > >infinite surface.  So if you had a container that shape, you could
fill it
> > >up with some finite quantity of paint, but it would never be enough to
> > >actually paint the surface of the thing.
> > 
> >         Or, a cylindrical can whose base is the Koch snowflake would
> > do the trick, and would actually fit on a shelf.
> > 
> >         I think it would be more mind-boggling to point out that
> > the can holds a finite amount of paint, but it takes an infinite amount
> > of paint to paint THE INSIDE.  Aren't you technically painting the
> > inside when you fill it up with that finite amount of paint???
> > 
> >         Of course, this problem stems from the abstraction that the
> > layer of paint you lay down on a surface is infinitely thin, which
> > isn't true in reality, and serves as an amusing reminder that areas
> > and volumes are not comparable mathematically the way they are in
> > the real world.

Areas and volumes are comparable in the real world only because of the
notion of thickness.  Mathematical painting presumably assumes zero
thickness, but even mathematicians have to compare units of volume with
units of volume (and not with units of surface area.  And since 0*infinity
can be just about any number from 0 to infinity (in absolute value), things
get interesting.

	Eric Lucas