>
> From: The thrill of minimalism <[EMAIL PROTECTED]>
> Date: Fri, 12 Mar 1999 22:35:53 +0000
> Subject: Mersenne: free sphere is half deflated
>
> "Ernst W. Mayer" wrote:
> >
> > Joth Tupper writes:
> >
> > >the Bolzano-Tarski theorem proved (what, back in the 1920's?)
> > >that you could cut a solid 3D sphere into finitely many chunks,
> > >then rearrange the chunks to make another solid (no holes or gaps)
> > >3D sphere with _twice_ the volume. Pretty spooky, I always felt.
> >
> > I don't know about spooky, but 'twould seem to violate conservation
> > of mass (or mass/energy, if you're a postmodern relativist :),
> > 'twouldn't it?
Well... no one said how easy it was to actually take hold of the pieces
and rearrange them. We mathematicians tend to think of our objects as
continuous, infinitely divisible, lumps, but that doesn't work so well
with matter. Quarks, for instance, come in pairs and triplets, never
alone. And if you try to tear a quark pair apart --- you put so much
energy into the system pulling on them that you create two new quarks in
the process. I wonder if anyone has tried to reconcile Banach-Tarski with
physical reality by saying "yes, you can do that, but the amount of energy
it takes to pull the pieces apart and reassemble them turns out to be
enough energy to create the additional mater needed"...
>
> You can map a line segment of "length" 1 onto two line segments of
> length 1 with a simple mapping function f(x)=2x+1 for instance.
Banach-Tarski doesn't do any stretching, just rotating, translating,
cutting.
---
Gordon Bower
PS: Those were SPHERICAL fishes and loaves of bread that Jesus broke to
feed the thousands of people on the shores of the Sea of Galilee. :)
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
