This is orientable:
this post was submitted on 24 Nov 2024
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That's from that video about flipping a sphere inside out that I'm sure someone thinks is an important and useful concept.
It's interesting because it's highly counter-intuitive that such a thing is possible. It's not supposed to be useful except as an example of a false intuition, which can remind us to be careful in our reasoning.
"Such a thing is possible" It kind of isn't though? It's a sphere that can pass through itself but not be sharply creased...how are these rules not just made up?
Specifically, the thing that exists is a regular homotopy of immersions from the standard embedding to its opposite. The "rules" aren't supposed to be self evident, they're part of a broader context in topology
Hmm, standard embedding to which dimension?
R^(3) specifically
Welp, my head cannot comprehend how that is possible. How is it deforming the shape around?
Maybe I am confusing homotopy and isotopy again.
indeed. how would the world work without this knowledge,
Does it still fit in the square hole?
Moebius is where I draw the line
OK, but what if I just add a 2nd moebius, and twisted them a little, and.... oops, Klein bottle!
Man I loved the part of the movie where he just Moebed on those guys
It's moebing time
Think about what that would do to your gut flora.
Yeah but he's just gonna stab em with a fork anyway?
if Clifford Stoll gave me one of his Klein Bottles i would be quite happy
Also my favourite YouTuber
And yet it still goes in the Square Hole
