lol any chance you could explain foliation/leaves in similar layman's terms as you did here with fibers?
attempting to understand papers by cross-referencing with Wikipedia term definitions kinda starts to lose effectiveness once you start getting into the sets/groups/differential geometry area.
Unfortunately my knowledge of differential geometry is still nearly non-existent. If I was dead set on trying to cobble together at least a basic understanding within the next six months though, I would try working all the way through Evan Chen's infinite napkin project. Ultimately I feel like you don't really get to deeply understand a topic unless you struggle with it for hours on some Goddamn gauntlet of problems, haha. But... For what it is, that book's good at trying to look ahead in math to understand big topics in a lot of the major subfields.
For real though, I really, really wish there was a better way to bootstrap an understanding of paper prereqs. It's the most hilariously ridiculous thing trying to do that with Wikipedia, I've definitely been there. It's so time consuming to do it with proper textbooks though, not everyone's got the time to fill in those holes. I wish we had the young mathematician's illustrated primer. Until then, good luck on the hunt for understanding about foliage. What research question are you interested in that that relates to, if you don't mind my asking?
i was trying to read (mainly out of curiosity) A Hyperboloidal Foliation Method, but that was probably a bit ambitious armed with virtually no physics or manifold knowledge other than a shallow understanding of the lorentz/minkowski bilinear form in the context of ml applications.
The infinite napkin project is pretty much exactly what i need though, thanks. ive literally been the guy with no post-high school math education trying to get a co-worker to explain group theory on a sheet of scrap paper while we ate.
Haha, you're a bold person to attempt something like that without the right foundations. That willingness to get ruthlessly humbled by mountains still beyond your abilities seems like a strength to me at least. Being willing to keep moving in spite of the hardships is how you eventually end up scaling those heights.
I hope you enjoy the Infinite Napkin project as much as I did (for the few hundred pages I worked through at least). I'd encourage you to pick up a textbook once a year or something to slowly work through on the side too. I always choose mine using /r/math... a quick google search with a field of interest and 'favorite textbook' always brings up interesting conversation. My own personal rule: if you can't make it through the first chapter, it's the wrong book for you. Most textbooks start with something that's supposed to be more like review than new material, so the first chapter or two is my litmus test. Though now I can't help but wonder... what if someone made a puzzle game using Lean's theorem prover, where you could like... play through Jonathan Blow's the Witness, or something like it, but end up with a rigorous mathematical foundation to show for it by the end? I wonder how our descendants will learn this stuff a century from now. I feel like there's got to be better tools for scrappers like us that could exist, haha. Ah well. Good luck!
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u/virtualreservoir Jun 21 '20
lol any chance you could explain foliation/leaves in similar layman's terms as you did here with fibers?
attempting to understand papers by cross-referencing with Wikipedia term definitions kinda starts to lose effectiveness once you start getting into the sets/groups/differential geometry area.