This is orientable:
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
“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?
Yeah but he’s just gonna stab em with a fork anyway?
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!
