2026-06-05T03:08:54Z https://yabu.me Mrs Beanbag https://yabu.me/npub19khyrrjtmw8u7n5dhtx2z0fr4l82dga074d82xm6qmvv45cxktqsfsvmq6 https://ftp.ieji.de/accounts/avatars/110/672/687/777/409/561/original/9b52dbb5f65ccab7.png https://ftp.ieji.de/accounts/avatars/110/672/687/777/409/561/original/9b52dbb5f65ccab7.png https://yabu.me/nevent1qqstxyr88qd0zw5grlnp5ut4w3fpg0sqw82xp39eja9kg4d6czvxp2gzyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzwz6edf In reply to <a href='/nevent1qqstq8kyrk7kxutwmpu6srpze0q0tyadf5n28j4tmnra830tv97p2ygdzk85v'>nevent1q…k85v</a><br/>_________________________<br/><br/>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? 2025-12-05T16:56:21Z https://yabu.me/nevent1qqsgmvwgh6rapcxcy6akch4a8vkkhg0lpekkdqly8jq3k7lqff8ekmqzyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzq2a3j7 In reply to <a href='/nevent1qqswxsa7q9jjmyv4j0zwfuw8kaf0xfek5xa54lad5ngs9ww5kvvqj5stfwuqn'>nevent1q…wuqn</a><br/>_________________________<br/><br/>sorry, i haven&#39;t really studied this and i&#39;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&#39;s worked as a learning strategy before so.. 2025-12-05T16:24:01Z https://yabu.me/nevent1qqswxsa7q9jjmyv4j0zwfuw8kaf0xfek5xa54lad5ngs9ww5kvvqj5szyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzguexlw In reply to <a href='/nevent1qqsdz3264nas5w845ar55x669zrl2pdc3rzrkpxmedfkh0en8e2ehxskpza4u'>nevent1q…za4u</a><br/>_________________________<br/><br/>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? 2025-12-05T15:56:31Z https://yabu.me/nevent1qqsp2dqg54jg5rcyhuxuwltgj86jpu9m8n2mgapzprs757c0qqel0hqzyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzclcttd In reply to <a href='/nevent1qqsq6eype6sdny9kfwv5djp3q0uqu7g84kxhzgat0c27d449mtwf5yqarjwv3'>nevent1q…jwv3</a><br/>_________________________<br/><br/>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? 2025-12-05T15:29:22Z https://yabu.me/nevent1qqsg4ak8gw36jjuml6ymkvca79kule60p38006pe6sjx093su637k0szyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzs2q2a6 In reply to <a href='/nevent1qqs2hctklmwjwasdfjjp2ehcwum9432a5t0h6xkq6zqqvg9dcgdhw7sac03yt'>nevent1q…03yt</a><br/>_________________________<br/><br/>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? 2025-12-05T14:43:00Z https://yabu.me/nevent1qqsr9mwdmyspxhjvxerz4rexs92l85rjfgqltxjcdju5hrmeh06z9gqzyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzmevjq0 In reply to <a href='/nevent1qqs83hstwjlc0let28plcaal9702ydlv65se5l9zhk3dvjgh5kpmd8cmgu67f'>nevent1q…u67f</a><br/>_________________________<br/><br/>ok i do know that the 3-sphere embeds in R^4 though (or in general, the n-sphere in R^(n+1)), i&#39;m still trying to understand embeddings better. 2025-12-05T13:20:21Z https://yabu.me/nevent1qqs0yqv5d0a4d9t9pprhq3jsas4sactqd7mpjqxjkpe47crhzqv5ylqzyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzwfwkes In reply to <a href='/nevent1qqs87qd70w4d3sejcslx0wcfcmz5vrtculcl5rvm6zz8cmgw2t74mwq2vawfq'>nevent1q…awfq</a><br/>_________________________<br/><br/>first time i ever met an ordinary mathematician. hello i see you are also in Edinburgh 2025-12-05T13:07:45Z https://yabu.me/nevent1qqs8w3cmj8fcuyht6z589guck4wyn7q39jaqnyz2yqwus7eg4myzupszyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evz09qh6u In reply to <a href='/nevent1qqsf99pte4dwea4da2pnn728fdncu52ukq9l0smwj7zjxueu7rdmhkcualue0'>nevent1q…lue0</a><br/>_________________________<br/><br/>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 &#34;mixing up portions&#34; isn&#39;t some arbitrary thing. it&#39;s what comes out of the maths. and you can have SU(3), SU(4), SU(anything).<br/><br/>SU(2) is also the same group as Spin(3) which pops directly out of the Clifford algebra. it&#39;s one of the &#34;accidental isomorphisms&#34;. 2025-12-05T13:00:11Z https://yabu.me/nevent1qqsxc5jf0w9fay6c3edq0h0nsrg6z8tjah4ce0vqmtjgu4s5tav55vqzyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzu44hu0 In reply to <a href='/nevent1qqsvam6uyuzzdjvy4u9dhawqjm0cdq4ss6euy09gy7ta7376a0urtnqd8vu0u'>nevent1q…vu0u</a><br/>_________________________<br/><br/>well yes, but a lot of maths proceeds without the motivation of working out the actual values of anything. it&#39;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. 2025-12-05T12:52:36Z https://yabu.me/nevent1qqsqxx4udfeyg3cclpvumcgfs3aekvvxrhddwny5vkjyz2xknn6xl3qzyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzmr0cqc In reply to <a href='/nevent1qqsq97479d3zm97xyxgz6sad0tq2ela9jm0sy7krcfnsctccexlufrc3whhkd'>nevent1q…hhkd</a><br/>_________________________<br/><br/>precomputation? ehh.. mathematics doesn&#39;t exist purely for the sake of computer graphics programmers, believe it or not. 2025-12-05T12:48:52Z https://yabu.me/nevent1qqsx874s3d0cenhn0fszzklf6vys26txf98hx6xurppwql7z7rxvr0gzyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evz4jrp7x In reply to <a href='/nevent1qqsrltxzj6m0jnkw78xc5czwusghsqyfmkws6zz7567zmsjl8pyrrhsre7pw3'>nevent1q…7pw3</a><br/>_________________________<br/><br/>oh quaternions are way less mushy than axis angle. axis angle is mushy. quaternions are solid, and very much more generalisable. 2025-12-05T12:43:52Z https://yabu.me/nevent1qqsrltxzj6m0jnkw78xc5czwusghsqyfmkws6zz7567zmsjl8pyrrhszyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzk4mumd In reply to <a href='/nevent1qqszuz66zvcpgfpjvdeu55leg8k7nql83w2xfh463s9mpmv4393qkxc3aal9h'>nevent1q…al9h</a><br/>_________________________<br/><br/>right if you&#39;re using euler angles, which we&#39;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).<br/><br/>but if we are dealing with Lie groups, the actual rotations are obtained from infinitesimal generators through the exponential map. 2025-12-05T12:42:29Z https://yabu.me/nevent1qqs0qvr8lrkzezkahcg6jax3wu4rvrwsx3cqu7xslr8uy4enxhhaxrqzyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evz7l9fkw In reply to <a href='/nevent1qqszk0z3k2uhhtd3hxzc9hxr6dznsdnphszr46qn0x3q59avcvrgrfgdgr34q'>nevent1q…r34q</a><br/>_________________________<br/><br/>if it can be parametrised on the unit ball, surely it embeds in R^3. 2025-12-05T12:38:00Z https://yabu.me/nevent1qqsfrvmhkhcyd9v7r0y9ezgen7ptwne756tn4anau8egjf8484af5nszyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzuwxc8j In reply to <a href='/nevent1qqsvydx0940q336t8ydngglggqlnk3p0yjtd8020djeecktmct4dmss68nmrd'>nevent1q…nmrd</a><br/>_________________________<br/><br/>it&#39;s three. three axes of rotation. and it can be parametrised on the unit ball in R^3.<br/><br/>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). 2025-12-05T12:34:48Z https://yabu.me/nevent1qqsgja2te3kkpk6cwslwyqlg55jy3m5gyxak0uj5ejfks0qezyq4slqzyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evz4qjlna In reply to <a href='/nevent1qqs8j43mkjr6r38nlllzndw80q4drgmncz5lh38rtknf8jgvhl3xh2qle6xv9'>nevent1q…6xv9</a><br/>_________________________<br/><br/>SO(3) only has 3 free variables. its matrix representation may have 9 elements, but they are not independent. that would be GL(3). 2025-12-05T11:33:24Z https://yabu.me/nevent1qqsxq0weq4g6x4k2me29x8h57jaqqtffdkr42793q0t2q9p6ulj8vtszyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evznf2gwq In reply to <a href='/nevent1qqsws3gwlcreutj0chz0zlr8s73axmz3nxhenylk028wzfyhej4x3qg4pawaq'>nevent1q…awaq</a><br/>_________________________<br/><br/>nicht lebe, oder nicht wohne? 2025-11-27T13:16:16Z https://yabu.me/nevent1qqsq3u6kpksqk9eryeu8grs2azkkef4u8e0djwl2f245s7uhzgr28wqzyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzn3anep In reply to <a href='/nevent1qqstmqr7enyeatzjsjxjslt9feh3x3e4wr35w6eek26yfgclecxs70sulgmwg'>nevent1q…gmwg</a><br/>_________________________<br/><br/>gotta side with ISO on this one. you can read the spine when the books are sat on a horizontal surface. 2025-11-06T17:05:20Z https://yabu.me/nevent1qqstkwntz3fxvghu59vd97dyus3hvhhktsfxlmhw3g0xmg0j0lk8c6czyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzcmxfer In reply to <a href='/nevent1qqswkq3cja76mce97g5hyg4fs9jkvvqv4krcu63hcp59twfv73ashuss664m6'>nevent1q…64m6</a><br/>_________________________<br/><br/>1959, Minnesota: <a href="https://www.kyocera-avx.com/docs/techinfo/Connectors/The-History-of-Insulation-Displacement-Technology.pdf">https://www.kyocera-avx.com/docs/techinfo/Connectors/The-History-of-Insulation-Displacement-Technology.pdf</a> 2025-09-24T11:19:19Z https://yabu.me/nevent1qqs0jkux7tvp4h2nru9sxxkkhmpqafs5pef6dqpynzjsp0txlf5yssszyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evz2wqt6a product idea: tape loader for PCs so you can load size-coded demos from cassette tape 2025-06-06T13:28:13Z https://yabu.me/nevent1qqspy5vny68dcsauf6ps5y3j8gj6c30h3vkqgvlq0hzu50mwyz2qafqzyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evztuwqqg In reply to <a href='/nevent1qqs9y4tjfekzxqfu6zx9tfq5x97kc0av9gs99upj5v9frhrznpuaptqac4ltl'>nevent1q…4ltl</a><br/>_________________________<br/><br/>oh wait it&#39;s a door, i spent too long looking at that thinking it was a pool table lmao 2025-03-28T20:06:55Z https://yabu.me/nevent1qqs0920ya577p072agqqt9ytrvng7u4pg9rl2s2c5hydjcr7kl07pxczyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzc3yxyf In reply to <a href='/nevent1qqsxuz6yvxh3hea74nvu7ym4yw9n7jtgs8dcp7n9dqgxx7a3ddenhtcx8u5w3'>nevent1q…u5w3</a><br/>_________________________<br/><br/>talking about bogosort levels of deliberately stupid 2025-03-21T15:18:49Z https://yabu.me/nevent1qqsxuz6yvxh3hea74nvu7ym4yw9n7jtgs8dcp7n9dqgxx7a3ddenhtczyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzhlj35p In reply to <a href='/nevent1qqsfqwwcjafl7rkhazvkkv6ryjrhrkzlmnxr2lsay5y9k8654r4pejgpt95d3'>nevent1q…95d3</a><br/>_________________________<br/><br/>oh well there&#39;s definitely some of it, but not *enough* of it 2025-03-21T15:18:04Z https://yabu.me/nevent1qqs22xlsn2ld7mh4flnnvtqt4uezzpl98eplc894y8sst2ftvu9wzrszyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evz46q30a In reply to <a href='/nevent1qqsday4fh36hg3y8jdjunng995uzecs4wexwd90zfxerue5ewa3papsxvz3dv'>nevent1q…z3dv</a><br/>_________________________<br/><br/>it&#39;s tempting to just go and write a lot of code that doesn&#39;t work, or it works in theory but far too slow to be practical 2025-03-21T15:16:42Z https://yabu.me/nevent1qqsrcsa0u8ugqng3nsxg959w4msrd3gvrq3vf8wx6gggntafrkrfn0qzyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzzgwvkz you know what, i don&#39;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&#39;d tell him to fuck off back to his grave. It&#39;s *my* code and *I* want to do the coding.<br/><br/>[update] i have been informed that Donald Knuth is, in fact, still alive 2024-11-21T12:11:31Z https://yabu.me/nevent1qqsrcqdkv9hzxv4u9kusqvmvjzghgedrpnre2q2pmyszcs0qdwezgeszyqk6usvwf0dcln6w3kavegfaywhuaf4r4l645agm0grd3jknq6evzmsj972 how is anyone ever able to afford to buy a car new? even a small hatchback seems to cost about a year&#39;s median salary 2024-10-16T16:30:53Z