With the ATC cuts, this is the only plane many will be getting on this week.
A second plane has hit the topology
Ain’t no way I would pass my driver’s license with parallel universe parking.
Driving instructor: Ok park in that parking spot.
Me: I can’t a car is already in it.
Driving instructor: judgmentally writing it down.
cannabis finally helped me grok the Kline bottle, took a lot of visualizing and mental exploration but I got there
edit: I wanted to pass along the insight I had that helped me, basically to not hold the whole Kline bottle in your mind at once, but to instead look at it from a subjective and temporalized perspective, for example imagine being an ant walking along the surface of the Kline bottle (or if you are an American, driving along the surface). Parsing individual moments on the surface is what helped me inch along and traverse the whole thing, and that spatial intuition helped me finally understand the whole much better … 4-dimensional objects can be really hard to reason about.
The problem most people have is the move that is impossible in a 3d Kline bottle - after you emerge from the orifice in the bottom you move onto the funnel, then into the bottle. You can only do that in 4d - or in experiential snapshots as you did. I’m sure there are animations that do it justice, but they would need to be 3d to do it well - it’s hard to accurately represent 4d in 2d
When I let Google Maps pick the route.
Any fans of 3Blue1Brown? This open problem taught me what topology is
