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
I’m not actually sure if it isn’t actual bullshit. Like, start at Matt Parker/Numberphile “And if you keep doing this sequence you’ll notice it comes up with every other prime number.” sort of stuff, head off the deep end and then keep going.
captain_aggravated@sh.itjust.works 5 months ago
That’s from that video about flipping a sphere inside out that I’m sure someone thinks is an important and useful concept.
kogasa@programming.dev 5 months ago
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.
captain_aggravated@sh.itjust.works 5 months ago
“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?
kogasa@programming.dev 5 months ago
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
idegenszavak@sh.itjust.works 5 months ago
indeed. how would the world work without this knowledge,
captain_aggravated@sh.itjust.works 5 months ago
I’m not actually sure if it isn’t actual bullshit. Like, start at Matt Parker/Numberphile “And if you keep doing this sequence you’ll notice it comes up with every other prime number.” sort of stuff, head off the deep end and then keep going.