r0uv3n
Joined 8 years ago
Joined 8 years ago
There was a guy in his 60s regularly doing very nice circular hiking routes of 40 to 60 km in our nearby forests, and apart from that just being kind of awesome and impressive to see when you look at local routes, actually walking his routes was often a very nice experience with diverse landscapes often along nice small, less used paths. It was great seeing nice weather in the morning, and then oftentimes without any pre-planning just walk or bike to the forest and just start along one of this guy's routes within a few minutes, all in an incredibly hassle free manner and with a result which pretty much always beat out just following the official hiking trails shown on signs etc. I don't know if there's another app right now where you can so easily profit from the experience and knowledge of your local community.
Also the question remains, what do you navigate the planned routes / gpx traces? What happens if you notice you want to improvise and replan to hit some target on the way you saw in the distance while on the trail? This was (and currently still is) absolutely trivial and intuitive to do on Komoot. The best alternative I can think of is maybe brouter+ osmand, but that's really quite clunky in comparison with Komoot (similar to the experience you probably mean when talking about pulling your hair out)
The point where our notions of geometry would break down would be near the singularity, not near the horizon, and we don't even know if a volume enclosed by a horizon (i.e. anything you might call a black hole) necessarily has a singularity inside, it's just that our simple mathematical models all assume one.
Though I do somewhat envy the possibility of having read the article close to publication and feel in some sense part of the history when it crops up again like this.
I can only recommend this as a good starting point for anyone without the time for a full scale education, or in preparation for such, especially if you have some experience with math olympiads (as mentioned also in the introduction).
I only wished I had spent some more time with stuff like category theory before starting my studies, and had had the guts to take more advanced courses directly in my first semester.
With just a bit of prep from these notes I'm pretty convinced that it's possible to directly take e.g. Algebraic Topology, Differential Geometry, Category Theory, or Algebra during the first semester (don't know about number or measure theory, or anything requiring lots of functional analysis, have not engaged enough with those topics to know how good these notes would be as prep).