Mrs Beanbag

Creator of Amiga game Mr Beanbag. Demoscener.

Pronouns: she/her
Soundcloud: https://soundcloud.com/mrs-beanbag
Languages: en-GB(native) nl-NL(100% van de uil) de-DE(beginner) es-ES(beginnerer)

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Last Notes

2025-12-05 16:56:21 GMT

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oh yeah of course it does! obvious now you say it lol. but where you have, for instance, a special holonomy group that is, for instance Einstein or Ricci Flat, that property is a property of the restricted holonomy submanifold, or of the ambient SO(n) manifold, or both? or can the SO(n) manifold be basically anything?

2025-12-05 16:24:01 GMT

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sorry, i haven't really studied this and i've been out of academia for well over 20 years and just trying to grasp some concepts that are to be honest far to advanced for me lol, but that's worked as a learning strategy before so..

2025-12-05 15:56:31 GMT

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i mean, for a given restricted holonomy group of SO(n), Hol0, can that be considered a curved manifold embedded in an SO(n) manifold? and can the SO(n) ambient manifold in this case be flat?

2025-12-05 15:29:22 GMT

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ohh, yeah ok 🤔 but in some special cases, those numbers can be smaller, right? for instance a de-sitter space (1,n) embedded in (1,n+1). in fact what i really want to understand at this point is the relationship between embedding and holonomy. i mean a restricted holonomy group of SO(n), which is a subgroup so can that also be an embedding?

2025-12-05 14:43:00 GMT

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oh you might know the answer to this then, because i was looking for a similar result for pseudo-Riemannian manifolds. if you have a n+m manifold, does it have to embed in 2n+2m or are other signatures possible?

2025-12-05 13:20:21 GMT

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ok i do know that the 3-sphere embeds in R^4 though (or in general, the n-sphere in R^(n+1)), i'm still trying to understand embeddings better.

2025-12-05 13:07:45 GMT

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first time i ever met an ordinary mathematician. hello i see you are also in Edinburgh

2025-12-05 13:00:11 GMT

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the logical basis is group theory. the quaternions are isomorphic to the group SU(2), the group of complex hermitian 2x2 matrices with determinant equal to 1. It turns out that every element of SO(3) can be mapped onto two elements of SU(2), which is how quaternions come to be useful for handling rotations. the "mixing up portions" isn't some arbitrary thing. it's what comes out of the maths. and you can have SU(3), SU(4), SU(anything).
SU(2) is also the same group as Spin(3) which pops directly out of the Clifford algebra. it's one of the "accidental isomorphisms".

2025-12-05 12:52:36 GMT

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well yes, but a lot of maths proceeds without the motivation of working out the actual values of anything. it's all done in the abstract. and a whole lot of stuff goes on in there. anyway quaternions are very good for a lot of things of course even in computer graphics. multiplying two of them is very straightforward, for instance. but aside from any practical use, they are hugely important in abstract algebra, topology and geometry.

2025-12-05 12:48:52 GMT

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precomputation? ehh.. mathematics doesn't exist purely for the sake of computer graphics programmers, believe it or not.

2025-12-05 12:43:52 GMT

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oh quaternions are way less mushy than axis angle. axis angle is mushy. quaternions are solid, and very much more generalisable.

2025-12-05 12:42:29 GMT

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right if you're using euler angles, which we're not. but regardless, any rotation can still be represented with at most 3 independent variables. the 4 variables in angle-axis representation are not independent if the axis is unit length (the axis itself is only 2 independent variables, in that case, up to sign, which can be transferred to the angle).
but if we are dealing with Lie groups, the actual rotations are obtained from infinitesimal generators through the exponential map.

2025-12-05 12:38:00 GMT

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if it can be parametrised on the unit ball, surely it embeds in R^3.

2025-12-05 12:34:48 GMT

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it's three. three axes of rotation. and it can be parametrised on the unit ball in R^3.
a rotation can also be represented by a unit quaternion, this is the lie algebra of SU(2) which is the double cover of SO(3). a quaternion has 4 independent variables in general. but for a unit quaternion only 3 are independent up to a sign flip (hence the double cover).

2025-12-05 11:33:24 GMT

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SO(3) only has 3 free variables. its matrix representation may have 9 elements, but they are not independent. that would be GL(3).

2025-11-27 13:16:16 GMT

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nicht lebe, oder nicht wohne?

2025-11-06 17:05:20 GMT

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gotta side with ISO on this one. you can read the spine when the books are sat on a horizontal surface.

2025-09-24 11:19:19 GMT

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1959, Minnesota: https://www.kyocera-avx.com/docs/techinfo/Connectors/The-History-of-Insulation-Displacement-Technology.pdf

2025-06-06 13:28:13 GMT

product idea: tape loader for PCs so you can load size-coded demos from cassette tape

2025-03-28 20:06:55 GMT

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oh wait it's a door, i spent too long looking at that thinking it was a pool table lmao

2025-03-21 15:18:49 GMT

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talking about bogosort levels of deliberately stupid

2025-03-21 15:18:04 GMT

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oh well there's definitely some of it, but not *enough* of it

2025-03-21 15:16:42 GMT

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it's tempting to just go and write a lot of code that doesn't work, or it works in theory but far too slow to be practical

2024-11-21 12:11:31 GMT

you know what, i don't even care how good AI is at coding. if the literal ghost of Donald fucking Knuth showed up at my desk and started typing my code for me, i'd tell him to fuck off back to his grave. It's *my* code and *I* want to do the coding.
[update] i have been informed that Donald Knuth is, in fact, still alive

2024-10-16 16:30:53 GMT

how is anyone ever able to afford to buy a car new? even a small hatchback seems to cost about a year's median salary