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Joined 1 year ago
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Cake day: August 3rd, 2023

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  • For me it’s probably the way I self-host overleaf, a online LaTeX editor. The community version has a docker image that’s horribly maintained (because they want to sell enterprise, I reckon), and instead relies on a horrendous amalgamation of setup scripts that wrap docker compose.

    What I have is a Dockerfile that pulls the image, manually installs a second version of TeX with the right dependencies, unlinks the old one and links the second one. Then for the database, it uses Mongo replsets, which be to be manually initialized. So I wrote a health check for the container that checks if the repl set is initialized, and if that fails the health check initializes it.

    It’s horrendous, it’s disgusting, and it’s an all-in-one compose file to get overleaf running. Good enough.




  • You just discovered the field of calculus! If you look closely enough at any smooth function it looks locally linear, and the slope of that linear function is it’s derivative

    Not quite what’s happening here, here the problem is if you consider geodesics on a sphere to be straight. In special geometry they are, for all intents and purposes, but in higher euclidian geometry they form large circles


  • You are absolutely correct, but to add on to that even more:

    When we talk about space, we usually think about 3D euclidean space. That means that straight lines are the shortest way between two points, parallel lines stay the same distance forever, and a whole bunch of other nice features.

    Another way of thinking about objects like the earth is to think of them as 2D spherical manifolds. That means we concern ourself only to the surface of the earth, with no concept of going below the surface or flying up into the sky. In S2 (that’s what you call a 2D spherical manifold), and in spherical geometry in general, parallel straight lines will eventually cross, and further on loop back and form a closed loop. Sounds weird, right? Well, we do it all the time. Look at lines of Longitude, for example.

    We call the shortest line connecting two points in curved manifolds geodesics, as you said, and for all intents and purposes, they are straight. Remember, there is no concept of leaving the sphere, these two coordinates is all there is.

    What one can do, if one wants to, is embed any manifold into a higher-dimensional euclidean one. Geodesics in the embedded manifold are usually not straight in higher-dimensional euclidean space. Geodesics on a sphere, for example, look like great circles in 3D.