Klein bottle in front o’ me…

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Klein bottle in front o’ me…

24th March 2004

Klein bottle in front o’ me…

posted in Math and Science |

Reading Stu Savory today I was reminded of the three dimensional topological phenomenon of Klein bottles. There’s something unsatisfying about the three dimensional representation since manifestly there is an inside and an outside to these puppies. You could pour water in the mouth and store it in the bell. The topological wonderment of a mobius strip is far more powerful for me because I can see that any portion has two sides but the whole thing has only one. Abstracting from that experience with the mobius strip, I expect to be unable to contain things within a Klein bottle and so I am oddly disappointed by the three-space representation.

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There are currently 2 responses to “Klein bottle in front o’ me…”

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1 On March 24th, 2024, Stu Savory said:
Frank,
you wrote: “since manifestly there is an inside and an outside to these puppies.”

Try the following thought experiment.

Pour a liquid INTO the “neck”. It’s INSIDE, right? Now put your thumb over the hole and shake the Klein Bottle. See? The liquid has wet BOTH sides of the glass of the neck.
So the inside IS the OUTSIDE, OK?

Stu
2 On March 25th, 2024, fp said:
I like the experiment, I just have trouble with the lack of a fourth dimension to fold that bottleneck through so it doesn’t confuse matters with a 3D intersection with planar boundary of the container.