🚀 go-pugleaf

Right.  You have to define what you mean by "painting".  As I see it, it's
covering a surface with a uniform layer of paint a certain thickness. 
(Somehow you have to convert surface area to volume, and the only way to do
so is to define how thick the layer of paint is.)  If the paint is
infinitely thin, then the volume of paint used is SA*T (surface area *
thickness).  If SA is infinte, then the thickness must be 1/infinity, where
this infinity is of a greater degree than the infinity of the surface area.
 In other words, if the paint is sufficiently infinitely thin, you *can*
paint the surface.

There is a problem with the argument "if you can fill it, you can paint the
inner surface, and therefore you can paint the outer surface":  As you
approach the asymptote at infinity, the layer of paint becomes thinner and
thinner to an arbitrary degree, since it is being squeezed between to
curves that become arbitrarily close together.  Yes, if you are allowed to
paint the outer surface with an infintely thin layer, you can cover it with
a finite volume.  However, this is contrary to the definition of painting,
which generally refers to coverage with a finitely thin layer.  Therefore,
in the same sense that you can't paint the solid, you also can't really
fill it.

	Eric Lucas

Erik Max Francis <max@alcyone.com> wrote in article
<32F043B4.3CC3DD9D@alcyone.com>...
> Jeffery Young wrote:
> 
> > I know the math, but the physical explanation doesn't sit with me.
> 
> The physical explanation is the distinction between mathematical surface
> area and volume and realistic surface area and volume, when it comes to
> painting a surface or filling a volume with paint.
> 
> -- 
>         Erik Max Francis, &tSftDotIotE / email:  max@alcyone.com
>                       Alcyone Systems /   web: 
http://www.alcyone.com/max/
>  San Jose, California, United States /  icbm:  37 20 07 N  121 53 38 W
>                                     \
>                "I am become death, / destroyer of worlds."
>                                   / J. Robert Oppenheimer (quoting
legend)
>