On Mon, 12 May 2008 11:08:08 -0500, Tim Weaver wrote:
> 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
I love his _The Cuckoo's Egg_, as agonizing as that epic was, not least
for his new tennis-shoes at the time (nuked); someone on rasfw recently
recommended _Silicon S****-Oil_ as well.
--
tinmimus99@[EMAIL PROTECTED]
11 or maybe 12
mp 10
mhm 29x13
Here is the World.
< _Gravity's Rainbow_
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