Kogasa

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.

Ok, there’s no such thing as native Windows apps for Linux, but there are cross platform GUI frameworks like Avalonia and Uno that can produce apps with a polished identical experience across all platforms, no electron needed

It’s fully cross platform with .NET Core and later.

Thanks

Some of it looks like topology. The curvy horizontal lines turning into curvy vertical lines are symbols relating to the Kauffman bracket, which belongs to knot theory.

https://encyclopediaofmath.org/wiki/Kauffman_bracket_polynomial

I’m with you until the lockin. How does that happen?

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.

It depends on if you use the “relay” feature. If your server is accessible from the outside it shouldn’t be using this though.

Not really, you need to have a basic understanding at least

You might be thinking of a [connection of an affine bundle](https://en.wikipedia.org/wiki/Connection_(affine_bundle). You could learn it through classes (math grad programs usually have a sequence including general topology, differential topology/smooth manifolds, and differential geometry) or just read some books to get the parts you need to know.

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.

It means they admit they were wrong and you were correct. As in, “I have been corrected.”

The argument describes an algorithm that can be translated into code.

1/(1-x)^(2) at 0 is 1

(1/(1-x)^(2) - 1)/x = (1 - 1 + 2x - x^(2))/x = 2 - x at 0 is 2

(1/(1-x)^(2) - 1 - 2x)/x^(2) = ((1 - 1 + 2x - x^(2) - 2x + 4x^(2) - 2x^(3))/x(2) = 3 - 2x at 0 is 3

and so on

Let f(x) = 1/((x-1)^(2)). Given an integer n, compute the nth derivative of f as f^((n))(x) = (-1)^{(n)(n+1)!/((x-1)}(n+2)), which lets us write f as the Taylor series about x=0 whose nth coefficient is f^((n))(0)/n! = (-1)^(-2)(n+1)!/n! = n+1. We now compute the nth coefficient with a simple recursion. To show this process works, we make an inductive argument: the 0th coefficient is f(0) = 1, and the nth coefficient is (f(x) - (1 + 2x + 3x^(2) + … + nx^(n-1)))/x(n) evaluated at x=0. Note that each coefficient appearing in the previous expression is an integer between 0 and n, so by inductive hypothesis we can represent it by incrementing 0 repeatedly. Unfortunately, the expression we’ve written isn’t well-defined at x=0 since we can’t divide by 0, but as we’d expect, the limit as x->0 is defined and equal to n+1 (exercise: prove this). To compute the limit, we can evaluate at a sufficiently small value of x and argue by monotonicity or squeezing that n+1 is the nearest integer. (exercise: determine an upper bound for |x| that makes this argument work and fill in the details). Finally, evaluate our expression at the appropriate value of x for each k from 1 to n, using each result to compute the next, until we are able to write each coefficient. Evaluate one more time and conclude by rounding to the value of n+1. This increments n.

I don’t think you need permission to send someone an email directly addressed to and written for them. I don’t have context for the claims about Kagi being disputed, but I’d be frustrated if someone posted a misinformed rant about my work and then refused to talk to me about it. I might even write an email. Doesn’t sound crazy. If there’s more to the “harassment” that I don’t know about, obviously I’m not in favor.

This has gotta be responsible for some awful mistreatment of alien gut fauna

You’re talking about a metric tensor on a pseudo-Riemannian manifold, I’m talking about a metric space. A metric in the sense of a metric space takes nonnegative real values. If you relax the condition that distinct points have nonzero distance, it’s a pseudometric.

The distance between two complex numbers is the modulus or their difference, a real number

Metric, not measure. Metrics are real by definition.

That’s not a metric. In any metric, distances are positive between distinct points and 0 between equal points