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Cake day: June 12th, 2023

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  • Kogasa@programming.devtoScience Memes@mander.xyznyet
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    22 days ago

    You can imagine tracing a path along a Klein bottle to see that it only has one side. To get more precise than that requires some topological context. If you slice it down the middle it turns into two Möbius strips and an orientation of the Klein bottle would induce an orientation of the strips, which are non-orientable. Alternately it has zero top integer homology, which you can get from looking at a triangulation. The orientable double cover of a Klein bottle is a torus, which is connected (if it were orientable, the double cover would be two disconnected Klein bottles).







  • The standard .NET C# compiler and CLI run on and build for Windows, MacOS, and Linux. You can run your ASP.NET webapps in a Linux docker container, or write console apps and run them on Linux, it doesn’t matter anymore. As a .NET dev I have literally no reason to ever touch Windows, unless I’m touching legacy code from before .NET Core or building a Windows-exclusive app using a Windows app framework.






  • Yeah, specifically for something like coreutils I can’t see the malicious endgame that is suggested by others here. Is the fear that a proprietary version of cat or pwd or printf takes over the ecosystem and then traps users into a nonfree agreement? Or a proprietary coreutils superset that offers some new tool and does the same thing? Or a proprietary coreutils that generates profit for businesses without attribution to the developers? What would stop anyone from just writing their own proprietary set of tools to do the same thing now, even if uutils didn’t exist? Clearly not much, since uutils did exactly that (minus the proprietary bit).

    I personally don’t see a compelling reason to change to MIT, but I also don’t see the problem.






  • Kogasa@programming.devtoScience Memes@mander.xyzManifolds
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    4 months ago

    Manifolds and differential forms are foundational concepts of differential topology, and connections are a foundational concept of differential geometry. They are mathematical building blocks used in modern physics, essentially enabling the transfer of multivariable calculus to arbitrary curved surfaces (without relying on an explicit embedding into Euclidean space). I think the joke is that physics students don’t typically learn the details of these building blocks, rather just the relevant results, and get confused when they’re emphasized.

    For a tl;dr about the concepts mentioned:

    • A manifold is a curve, surface, or higher-dimensional object which locally resembles Euclidean space around each point (e.g. the surface of a sphere is a 2D manifold; tiny person standing on a big sphere perceives the area around them to resemble a flat 2D plane).

    • Differential forms are “things that can be integrated over a manifold of the corresponding dimension.” In ordinary calculus of 1 variable, that’s a suitably regular function (e.g. a continuous function), and we view such a function f(x) as a differential form by writing it as “f(x) dx.”

    • A connection is a way of translating local tangent vectors from one point on a manifold to another in a parallel manner, i.e. literally connecting the local geometries of different points on the manifold. The existence of a connection on a manifold enables one to reason consistently about geometric concepts on the whole manifold.