mimus wrote:
> On Mon, 12 May 2008 23:25:47 +1000, Peter Webb wrote:
>
>> "mimus" <tinmimus99@[EMAIL PROTECTED]
> wrote in message
>> news:WZGdnYk6ysIsorXVnZ2dnUVZ_qHinZ2d@[EMAIL PROTECTED]
>>
>>> On Mon, 12 May 2008 18:36:20 +1000, Peter Webb wrote:
>>>
>>>> "mimus" <tinmimus99@[EMAIL PROTECTED]
> wrote in message
>>>> news:8uCdnZuH0sBCzIDVnZ2dnUVZ_hKdnZ2d@[EMAIL PROTECTED]
>>>>
>>>>> 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.
>>>>
>>>> Technical note: Mobius strips have a single boundary.
>>>
>>> ok fine.
>>>
>>> (As soon as I read that, my head tried to encompass an unbounded
>>> Moebius strip and couldn't do it.)
>>
>> Well ...
>>
>> Imagine the width of the Mobius strip was infinite. You would then have
>> a surface that was unbounded in both directions, finite in one
>> direction and infinite in the other - sort of like a cylinder, but its
>> not. Nor is it a Klein bottle or cross-cap. It can't be embedded in R^3
>> as it self intersects. But it is a reasonable interpretation of an
>> "unbounded Mobius strip", whatever its real name is (if it has one).
>
> <squint>
>
> A single-sided infinite plane or saddle or a single-sided sphere, is
> what it looks to me like what we're lookin' at, yes it does. Yes.
>
> I think Klein bottles cheat with that penetration business-- tearing is
> a no-no in algebraic topology, even though that's how you make a Moebius
> strip, and also in a sense how they work up the matricial representation
> of one, swapping connection-points or vertices in the matrix
> representing an ordinary strip or tube.
>
> http://www.kleinbottle.com
Speaking of Klein bottles, Cliff Stoll gave an interesting talk last year
at
TED. He did eventually break out a Klein wine bottle.
http://www.youtube.com/watch?v=Gj8IA6xOpSk
--
Tim Weaver
"Usenet is like a herd of performing elephants with diarrhea - massive,
difficult to redirect, awe-inspiring, entertaining, and a source of mind-
boggling amounts of excrement when you least expect it."
- Gene Spafford, 1992
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