🚀 go-pugleaf

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.

Exactly.  The problem stems from extending mathematics to the physical
world while retaining multiple assumptions which apply only in 
the abstract mathematical sense.  If I may get philosophical for a 
sentence or two, that's where mathematics and physics part company.  
In physics, a result must make sense; in mathematics, it must follow
from mathematical manipulation and, if it makes no sense, it is 
added to the list of examples of things deserving of a Nobel prize,
if only math had one.

> 
>  ,oooooooo8     o     ooooo@math.niu.edu  --  http://www.math.niu.edu/~caj/
> o888'   `88   ,888.    888
> 888          ,8'`88.   888   "What he can do with numbers would make a
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> ____________________8o888'______________-Hank Jennings, _Twin_Peaks._ _____


Larks  -- Wondering what a night with a $1000/night hooker would
           entail.