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

On Mon, 19 May 2008 17:06:44 -0400, mixed nuts wrote:

> mimus wrote:
>
>> On Mon, 19 May 2008 16:05:50 -0400, mixed nuts wrote:
>> 
>>> mimus wrote:
>>>
>>>> On Mon, 19 May 2008 09:54:14 +0100, Frederick Williams 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.
>>>>>
>>>>> Not infinite, five pieces suffice.  At least it's five in three
>>>>> dimensional space, in one or two dimensions one needs aleph_0 many
>>>>> pieces.
>>>>
>>>> I haven't seen or even heard of any-a these five-piece multiplicative
>>>> reassemblies in 3-space, so I'm getting whiffs of weasel from
>>>> somewhere.
>>>
>>> Think square ball.
>> 
>> Square or parallelipipedal?
> 
> Square/regular in the 1-norm or euclidean sense with all angles being
> precisely right or left. But arbitrarily octahedral in a more general
> sense.

"What the Hell game are we playing, anyway? do I dribble this thing or
what?"

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

mp 10

mhm 29x13

Given a manifold M with a submanifold N, N can be knotted in M
if there exists an embedding of N in M which is not isotopic to N.
Traditional knots form the case where N = S1 and M = S3.

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