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
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.
“Our society has enabled people to go to college for too long without actually contributing anything.”
Yeah, basic graduate level math is a lot more useful than whatever you do with your life to warrant such an attitude.
Oh really? Let’s try a thought experiment, shall we?
In Universe A, let’s round up everyone with at least a master’s degree in math and shoot them.
In Universe B, let’s round up all the mechanics and shoot them.
Which one goes to shit faster?
Did they teach you how to formulate thought experiments in the shop?
Yep.
Big “I don’t need you to make me look stupid” vibes right here