
Möbius Strips Defy a Link with Infinity - Pharmakon
https://www.quantamagazine.org/mobius-strips-defy-a-link-with-infinity-20190220/
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ericpauley
The subtitle is in clear contradiction with the paper, the first sentence of
which claims that this was proven for 3 dimensions in 1962.

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mc32
It doesn't seem to contradict it in my reading it. (Basically it refuses to be
packed infinitely in tame [1962] and now wild embeddings])

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macawfish
Totally different thing, but reminds me of the Hopf Fibration, which you
should really look up if you never have before.

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alanbernstein
I'm not sure I'm grasping the significance of this, is there an article or
video you'd recommend?

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macawfish
Definitely this one!
[https://youtu.be/10sDqSUjXHc](https://youtu.be/10sDqSUjXHc)

Think about how you could fill a 2D plane with infinite parallel lines, one
for every single point on a real line. Imagine, for example, running vertical
lines through every point on the x-axis, how this would fill the entire plane.

The Hopf Fibration is similar. It's a way of filling all of the space on the
surface of a 3-sphere (which locally feels like 3D Euclidean space) with
interlocking circles. Each of these circles can be mapped a point on an
ordinary sphere.

Thinking of it in the other direction: for every point on the surface of an
ordinary (2-)sphere, you can assign a circle on the surface of a 3-sphere. By
taking into consideration all of the points on the 2-sphere, and all of the
circles they represent, you can fill the entire surface of the 3-sphere with
these interlocking circles!

