games

Maybe! No but actually the antagonists of both games have the exact same motivations. They're emo losers who are depressed and want to die, but instead of killing themselves, they decide to kill the entire rest of the world with them.

and these are the only two pieces of media that have ever had that villain motive

obviously not, I just thought it was funny to compare a game people like to a game people don't like

unless people don't like Xenoblade 2, idk

I missed this tweet https://x.com/notch/status/2066305707977183687

He is learning things that will never see use for games he will never finish

what does computing determinants from first principles even mean?

isn't it just a recursive definition?

Yeah idk

I assume he means cofactor expansions?

Unless he just means 3x3's which you can solve trivially

find the eigenvalues and multiply

Damn maybe its time to unprivate

I didn't realize I was privated

oh i'm friends only so this service can't scrape me

I don't know why, when solving a determinant, you alternate the signs across matrix value.

That is apart of the cofactor expansion, yes

This is a consequence of the fact that swapping any two rows or columns in a determinant swaps the sign

Yeah, but why do you do it that way? Where does it come from? Where does it go? Cotton eyed joe

Or why does swapping rows or columns swap the sign?

If you want a more concreate explanation, there are geometric interpretations of the determenant I do not know because I do not do geometric algebra

lol

Determanat represents the physical properties of how a matrix is a mapping that transforms an input into an output

so the sign change is kind of a symmetry thing

your geometric explanations are going to be in very high dimensional spaces

its group theory stuff

You get some geometric stuff in 3D

3d matrices are boring

such as the absolute value of the det being the volume of a parallelpiped

I oughta dedicate some time to learn this all fundamentally some time. I got annoyed in intro to lin alg where they say "just do this" but then when I did real lin alg, fuck me, proving these things was tough.

if you are doing 3d, the sign swap is because its impossible to swap just two of the orthogonal basis vectors with a rotation

so a reflection is required

I don't really care about the geometric interpretations of determinant tbh

If you just abstractly view it as an operation with properties (which is what I do) then it is perfectly fine

if its not +-1 or zero then its whatever

unit scalar, not 1

Honestly, all these words mean so little to me anymore. I've never used any of this, but then I'll stumble upon some nasty mathematics that I just brush aside as "eh, he gave matlab code at the end of the paper"

I use this stuff all the time these days

I don't in particular do much determinant stuff other than when doing TA work for lin alg courses, but I am used to it because of how important it is in physics

determinants themselves don't really matter, but there's some interesting things in approximation theory that use the sign swapping to make proofs

like there is no guarantee that an arbitrary sampling on a 2-sphere (and other manifolds in additionally higher dimensions) can have an invertible map to a harmonic decomposition, because smoothly swapping two points on the manifold flips the sign of the map's determinant, and at some point in the swap the determinant has to go to 0

I don't have my the textbook with the name of that property so i had to reconstruct it

Mina the Hollower is already sub hour in the no Out of Bounds category

I'm sorry why exactly does Mina the Hollower have a jumpscare?

I really was not expecting that

shouldn't have stayed in the dark that long

I wanted to know what was in there!

This is the most pretentious trailer I think I've ever seen