Re: I Think I Just Broke a Glass into an Infinite Number of Pieces

On Mon, 19 May 2008 09:59:46 +0100, Frederick Williams wrote:

> Jim Langston wrote:
> 
>> Tim Weaver wrote:
>>
>> > mimus wrote:
>> >
>> >> On Sat, 03 May 2008 21:33:59 -0500, Tim Weaver wrote:
>> >>
>> >>> mimus wrote:
>> >>>
>> >>>> At least, I swept up at least twice as much glass as could
>> >>>> possibly have been in the original.
>> >>>>
>> >>>> And that's only possible if you do an infinite decomposition of
the
>> >>>> object, as exemplified by the Tarski-Banach ball.
>> >>>>
>> >>>> Maybe this is a sign I should mop my kitchen-floor.
>> >>>>
>> >>>> Will I need an infinite mop?
>> >>>
>> >>> Yes, if you have a mobius shaped floor.
>> >>
>> >> Mobius strips are usually finite.
>> >>
>> >> Just unbounded.
>> >>
>> >> Neener.
>> >
>> > By the time you get back to where you started, it's dirty again.
>> > Infinite mopping.  Of course, you could try to find a mop that mops
>> > an infinite area in one go.
>> 
>> Yes, but then you'd need an infinite amount of water to mop the
infinite
>> amount of floor, and since an infinite amount of water would take up an
>> infinite amount of space there'd be no room for the floor to begin
with.
> 
> Consider a cylindrical (in a broad sense) bucket the boundary of the
> base of which is a Koch (snowflake) curve.  Since the curve has infinite
> length but encloses a finite area, the bucket has an infinite surface
> area but encloses a finite area.  So, roll up your infinite area kitchen
> floor to form such a bucket and you can cover it with a finite amount of
> water simply by filling the bucket.

I have it on excellent authority that Cantor was in and out of the
_Nervenklinik_.

And I'd like to see a mechanical or chemical engineer's face when someone
brings this technique up.

-- 
tinmimus99@[EMAIL PROTECTED]
 11 or maybe 12

mp 10

mhm 29x13

We'd be better off in a mental home than we are here:
a quiet garden, little white cells, nurses, supervised walks.

< _Solaris_