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
Yeah but he's just gonna stab em with a fork anyway?
Think about what that would do to your gut flora.
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
