egg|nomz|egg changed the topic of #kspacademia to: https://gist.github.com/pdn4kd/164b9b85435d87afbec0c3a7e69d3e6d | Dogs are cats. Spiders are cat interferometers. | Космизм сегодня! | Document well, for tomorrow you may get mauled by a ネコバス. | <UmbralRaptor> egg|nomz|egg: generally if your eyes are dewing over, that's not the weather. | <ferram4> I shall beat my problems to death with an engineer.
<egg> bofh: let's assume we have two oriented inner product spaces U and V
<egg> bofh: and consider the homomorphisms between the two
<egg> bofh: afaict this forms a Lie groupoid on the two-point manifold, but let's not go to Lie groupoids, they're silly
<egg> bofh: however: what happens to the Lie algebra?
<egg> bofh: the matrix Lie group thing of exp tX in G falls apart, because how can exp tX not be an endomorphism
<egg> bofh: meooow
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<bofh> egg: uuuuuuh
<bofh> okay this is not a matrix lie group, definetly not compact either?
<bofh> yuck
<bofh> let me poke Faraut
<egg> bofh: well, it's not a group, obviously
<egg> it's a groupoid
<egg> afaict it's a Lie groupoid where the object manifold is the 2-point manifold, but Lie groupoids having a manifold structure on the objects is a bit overkill
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<egg> bofh: faraut?
<egg> bofh: the groupoid is going to have a manifold structure, so you could look at left-invariant vector fields there I guess
<egg> the manifold is just two copies of SO(n), and the groupoid structure makes one act on the other
<egg> bofh: but what happens to e.g. V wedge V = so(V), if there are two vector spaces involved
<bofh> 01:37:25 <@egg> bofh: the groupoid is going to have a manifold structure, so you could look at left-invariant vector fields there I guess
<bofh> okay I see what you're attempting to do now.
<bofh> but now conversely I'm not sure if you're still dealing with a wedge product if you have two separate vector spaces involved.
<egg> bofh: well that structure has to eggsist somehow but yeah
<bofh> I'm still a bit at a loss why it has to and can't be simplified or turned into something separable at least, but I feel like I'm missing some motivating stuff here.
<egg> bofh: motivation is stronkly-typed reference systems
<egg> bofh: if they move wrt each other, what kind of animal their mutual angular velocity? if you identify the spaces, sure, you get so(3), but that's awkward
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<bofh> whitequark: okay not sure how so(3) is awkward, it's about as nice of a space as I could envision getting in a wedge product context.
<whitequark> wh
<whitequark> im confuse
<egg> whitequark: I think bofh meant egg
<egg> whitequark: but feel free to join the Lie talk
<egg> we're all clueless anyway
<egg> bofh: no i mean it's awkward to identify the two spaces
<egg> bofh: R3 from one reference system and R3 from a different reference system
<egg> bofh: which is how you get the change of reference system to be in SO(3) rather than Hom(U, V) for oriented inner product spaces U, V
<bofh> Yes but I'm not seeing how SO(3) is much worse than Hom(U,V) here.
<SnoopJeDi> not until today have I seen a SUSY talk that began discussing supersymmetry as "okay, augment these particles with scalar partners, that's a chiral multiplet, and augment these with vector partners, that's vector multiplets."
<SnoopJeDi> I'm very annoyed that the field gives such remarkably technical talks about such cool math to a general audience of nonexperts
<egg> bofh: because then you get into absurd things like taking the square of your change of reference system
<egg> bofh: they're different reference systems, identifying them allows weird unnatural things
<egg> <egg> bofh: motivation is stronkly-typed reference systems
<bofh> Okay, I can see the motivation for this now. But I'm still uncertain on what mess of a structure you get here.
<bofh> mlbaker: ^
* egg bakes mlbaker
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<mlbaker> egg: so basically I don't think "oriented inner product space" is the correct notion of "vector space equipped with a reference frame"
<egg> mlbaker: well, conceptually you have an oriented inner product space and then a bunch of bases witch which you equip it; but since the baseless space isn't something you can nicely represent it's convenient to ignore the baseless space and just look at the spaces-with-reference-system (while forbidding things that wouldn't be coordinate-free)
<mlbaker> well okay, an oriented IPS has a canonical choice of "class of positively oriented ON bases"
<mlbaker> also what's your definition of homomorphism of IPS? does that mean isometry?
<mlbaker> orientation-preserving isometry*
<egg> yeah
<egg> mlbaker: basically the whole question is "what if SO(V) but between two spaces"
<egg> (and then what happens to so(V) and its good friend V wedge V)
<mlbaker> there is no group structure
<mlbaker> on the set of orientation-preserving isometries from one object to a different one
<egg> mlbaker: sure but there's a groupoid structure if you take the inverses
<mlbaker> it carries an action of SO(V) on one side and SO(W) on the other
<egg> what do you mean
<mlbaker> SO(V) acts by pullbacks, SO(W) by pushforwards
<mlbaker> so then i guess you could talk about fundamental vector fields associated to those actions?
<egg> you mean on the orientation-preserving isometries?
<mlbaker> yeah
<egg> I don't think you need to bring in those actions
<egg> hmm
<egg> hm, the groupoid ends up having SO(V) and SO(W) anyway
<egg> I think
<whitequark> equation groupie
* egg scratches head
<mlbaker> yeah
* egg scritches head
<mlbaker> SO is just the automorphism group of the object in your two-object category
<egg> yeah
<egg> it's this but the object is the two point manifold https://en.wikipedia.org/wiki/Lie_groupoid
<egg> (there are lie algebroids in the theory of lie groupoids, but since they use smooth object manifolds it quickly gets very overkill for this)
<egg> s/smooth/indiscrete/ rather
<mlbaker> I mean, it seems like that's exactly what you're after?
<mlbaker> your object manifold is a 0-manifold, things will simplify considerably
<egg> yeah
<egg> mlbaker: the question then is whether this particular Lie algebroid can be related to wedges in some way
<egg> algebroid is a weird word https://en.wikipedia.org/wiki/Lie_algebroid
<mlbaker> trying to parse the defn
<mlbaker> uhh so this thing they're calling the t-fiber tangent space
<mlbaker> is literally just like... two tangent bundles
<mlbaker> it's the tangent bundle of V, disjoint unioned (as sets) with the tangent bundle of SO(W) disjoint union Hom(V,W)?
<egg> mlbaker: well I suppose it's SO(V) disjoint union SO(W) disjoint union SO(V, W) disjoint union SO(W, V) (let's just call them all SO)
<mlbaker> okay and then he pulls it back through e, getting a bundle over the two-point manifold..
<mlbaker> ah good point, forgot the other direction
<mlbaker> well
<mlbaker> one of those disjoint unions though is a set-theoretic one
<mlbaker> the other two are actually of manifolds
<egg> there's a smooth structure on all four of those though
<mlbaker> ugh i'm just trying to picture this thing
<mlbaker> so the fiber of T^t G above an element of G (a morphism) is what?
<mlbaker> say the fiber above id : V->V
<mlbaker> t^{-1}(V) is a disjoint union of SO(V) and SO(W,V)
<mlbaker> so the tangent bundle to that thing also has 2 connected components
<egg> what monstrosity have i created
<mlbaker> okay, but the fiber (T^t G)_{id} only contains stuff from one of those components
<egg> is it 2 or 4 connected components
<egg> the groupoid has 4 connected components as a manifold, right?
<mlbaker> yeah
<mlbaker> G has 4
<mlbaker> but t^{-1}(V) is just the set of morphisms with target V, so that has two components
<egg> ah, right.
<mlbaker> uhh
<mlbaker> why do i feel like this construction simplifies a lot in our case
<egg> it's just so(V) and so(W)? Ꙩ_ꙩ
<mlbaker> the fibers t^{-1}(p) are all *connected components* of G
<mlbaker> so like
<mlbaker> you might as well just write this thing as TG?
<mlbaker> -_-
<egg> hm, right
<mlbaker> okay, so T^t G is literally just TG in our case, rofl
<mlbaker> and now you pull it back along e
<egg> mlbaker: yeah see that's why i was reluctant to go down that route, M being a nontrivial manifold makes this very overkill :-p
<mlbaker> okay but now this is strange
<mlbaker> because once you pull back along e
<mlbaker> the thing you end up with is just
<mlbaker> the bundle whose fiber over V is just so(V)
<mlbaker> and whose fiber over W is just so(W)
<mlbaker> so basically nothing more than the disjoint union of the lie algebras
<egg> yeah Ꙩ_ꙩ
<egg> huh
<mlbaker> i.e.
<mlbaker> all the information you were hoping to get about SO(V,W)
<mlbaker> is just gone lmao
<egg> yes, this is weird
<mlbaker> which I guess we shoudl have seen coming
<mlbaker> since if a lie algebroid is the analogue of a lie algebra
<mlbaker> then of course it'll only see behaviour near the 'identity of the lie groupoid'
<egg> yeah
<egg> okay but what happens if we look at SO(V)- and SO(W)-invariant vector fields on T(SO(V,W))
<mlbaker> those are probably equivalently just the fundamental vector fields
<mlbaker> those of the form A_p = d/dt[ p * e^{tA} ] |t=0 for A running through so(V)
<mlbaker> where * denotes the SO(V)-action on SO(V,W)
<egg> right
<egg> right-invariant vector field :-p
<mlbaker> actually is that even right
<mlbaker> so like
<mlbaker> the action of V on SO(V,W) need not even be transitive right
<mlbaker> SO(V)*
<mlbaker> if dim V is much less than dim W
<egg> oh yeah, that case might get tricky
<egg> I was thinking about dim V = dim W
<mlbaker> ah ok
<egg> aka I Can't Believe It's Not so(n)
<mlbaker> then it is definitely transitive :P
<mlbaker> yo btw
<mlbaker> the definition of 'skew-symmetric endomorphism'
<egg> if dim V is not dim W, the "inverse" part of the groupoid seems iffy
<mlbaker> doesn't even really generalize
<mlbaker> i mean, the condition is <Av,w> = <v,-Aw> right
<mlbaker> basically coming from differentiation of the isometry condition
<egg> yeah
<mlbaker> if Av and w live in different spaces then yeah
<mlbaker> what does this even mean
<egg> yeah, same with V wedge W vs. Hom(V, W), the usual map falls on its face
<egg> however, V wedge W is a thing, so we've got that going for us, which is nice
<mlbaker> why is V wedge W a thing?
<egg> oh it's not
<egg> right.
<egg> derp.
<egg> yeah, none of this is likely to make sense.
<egg> but somehow something still has to exist
<egg> if we have R(t) in SO(V, W), what is R'
<egg> how the hell is it 5:50 already
<egg> i should sleep rpobably
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<mlbaker> a v.f. in SO(V,W) along the curve R? :P
* UmbralRaptop is failing to sleep, so have a paper http://sci-hub.tw/downloads/8814/10.1038@s41586-018-0677-y.pdf
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<mlbaker> a redefinition? please no
<UmbralRaptop> mlbaker: the current definition is bad, and should feel bad.
<mlbaker> yeah i read about it more
<mlbaker> i guess for all intents and purposes the redefn would be backward compatible
<UmbralRaptop> yeah
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<egg|cell|egg> Bofh: nice
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<egg> bofh: wait, you RTed something about timescales? are they poking at timescales?
<egg> bofh: also lol: last page (appendix 2) of https://www.bipm.org/utils/en/pdf/CIPM/CIPM2017-EN.pdf?page=23
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<UmbralRaptop> Bah, a weather forecast that gave the temperature in meV would be awesome https://twitter.com/planet4589/status/1063437077776338946
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<UmbralRaptop> "Remember: Classes come first, grad school applications come second, this [research] comes third. Also, sanity should be somewhere in there." My advisor to an undergrad.
<egg|work|egg> UmbralRaptop: sanity is highly theoretical research
* egg|work|egg meows at UmbralRaptop, bofh, mlbaker, et al.
* UmbralRaptop scritches egg|work|egg behind the ears
* UmbralRaptop assumes that anyone who meows is a cat.
<egg|work|egg> but i'm an egg
<UmbralRaptop> ¯\_(ツ)_/¯
<UmbralRaptop> you eggsibit macro scale quantum behavior
<egg|work|egg> eggshibit
<egg|work|egg> or eggsbibit? hmm
<egg|work|egg> not the most common unit https://en.wikipedia.org/wiki/Exbibit
<UmbralRaptop> That's a lot of bits
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<UmbralRaptop> egg|work|egg: Yay?
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<egg> bofh: piiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiing
<egg> bofh: 
<bofh> egg: pong
<bofh> I literally *just* glanced on IRC, what is up?
* egg scritches bofh
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<egg> !wpn bofh
* Qboid gives bofh a floating timezone
<egg> whitequark: https://twitter.com/whitequark/status/1063495683292811264 just continuously shift your timezone so you're synchronized with different people in turn
<whitequark> it me
<egg> whitequark: true
<raptop> egg: Mars time?
<egg> eggsactly
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<egg> !wpn regex
* Qboid gives regex a polarized psychiatrist
<regex> Sounds useful
<egg> !wpn mlbaker
* Qboid gives mlbaker an extensional alternator
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<egg> bofh: what timezone is mlbaker in
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<egg> whitequark: seems nobody took notice of the iceland discussion in https://en.wikipedia.org/wiki/Talk:Brown_rat#HOAX_map_removed though
<SnoopJeDi> Alberta's rat thing is bizarre
<SnoopJeDi> great propaganda
<bofh> egg: EST, nominally.
<egg> bofh: ... is it actually bofhtime,
<egg> !meow bofh
<Qboid> (1,2): error CS1660: Cannot convert `lambda expression' to non-delegate type `object'
<Qboid> System.Func`1[System.String]
<Qboid> (1,2): error CS0103: The name `bofhtime' does not exist in the current context
* Qboid meows at bofh
<egg> !bofhtime
<egg> !csharp bofhtime()
<Qboid> 2018-11-16T14:26:56,071
<bofh> (in practise, we met at 4AM while working on a quantum computing assignment. I believe I was introduced to them by a mutual friend who, uh, "let me introduce you to this friend of mine who just slams adderall and regularly stays on campus for like 3 days in a row" was I believe the sentence to describe me)
<bofh> (so make of that what you will,)
<egg> bofh: is everyone you know like that
<egg> !wpn bofh
* Qboid gives bofh a turbulent Metal Gear
<SnoopJeDi> Metal Gear?!
<bofh> egg: mostly just the mathematicians.
<egg> bofh: hmm
<bofh> (while I'd wager to say over half the people I know have clinical ADHD, most don't also have my particular brand of craziness to go with it, or at least anywhere near my extent of it).
<SnoopJeDi> bofh, I think there's something in here about how academic demographics are based on survivorship bias. Something something hyperfocus is an additional buffer against more or less open hostility to earnest curiosity?
<egg> !wpn bofh
* Qboid gives bofh a non-conforming explosive immersion
<iximeow> !wpn egg
* Qboid gives egg a vanadium nova
<egg> !wpn iximeow
* Qboid gives iximeow a ☢
<egg> well, i guess with the nova,
<SnoopJeDi> oh also hooray for CGPM Resolution A?
<iximeow> wow... my very own ☢
<iximeow> what's that?
<SnoopJeDi> the resolution that redefines SI starting next April
<SnoopJeDi> AFAIK there was really no contention expected, they took their time to make sure the (currently experimental) Planck constant could be constrained to the necessary level of precision
<SnoopJeDi> but it's still exciting to retire Le Grand K
<egg> SnoopJeDi: Kazakhstan was absent so didn't vote yes though :-p
<SnoopJeDi> egg, I haven't followed along very closely tbh, were they the only non-yes?
<egg> yeah
<SnoopJeDi> double hooray
<egg> voting ^
<SnoopJeDi> oh nice, I didn't know from their site if the voting was part of the open session or not
<SnoopJeDi> not that I ended up watching any of the stream anyway >_>
<SnoopJeDi> the metrological talks look great and I intend to revisit them
<SnoopJeDi> the one at IPAC by the head Canadian metrologist was great: he mixed up ppm and ppb on a slide and despite correcting it verbally, a room full of academics couldn't help themselves but pick on it :P
<SnoopJeDi> bofh, egg, today's happy hour link email may be of mild interest: https://www.quantamagazine.org/amateur-mathematician-finds-smallest-universal-cover-20181115/
<egg> ah, a new smallest one, not the smallest
<egg> the omission of articles that is customary in news titles leads to confusion when the definite article can carry such weight :-p
<SnoopJeDi> yea the title is...awful
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<raptop> !u ☢
<Qboid> U+2622 RADIOACTIVE SIGN (☢)
<raptop> iximeow: ^
<raptop> !choose nynorsk|nyanorsk
<Qboid> raptop: Your options are: nynorsk, nyanorsk. My choice: nynorsk
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<egg> raptop: are scallops cats? https://en.wikipedia.org/wiki/Scallop#Eyes
<egg> or are they even reflectors
<egg> since they actually use the reflective bit to focus, they might be even more cats than cats
<raptop> ow
<egg> raptop: (B) a scallop eye in which there is a lens with a low refractive index and an image-forming, concave spherical mirror overlying a pigment layer at the back of the eye.
<egg> scallops are cats!!!!
<raptop> cat interferometers at that o_O
<egg> raptop: the reflective bits of cats or dogs or spiders are just part of the detector really, whereas here it's properly in the opticks!
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<B787_300> regex: velocity map of stars?
<regex> nearby exoplanets.
<regex> legend in left lower corner
<B787_300> what is the length of the bars represent?
<B787_300> ah
<regex> I do believe the distance from the ecliptic judging by Trappist-1
<raptop> B787_300: distance above/below the plane of the projection
<B787_300> yeah it shows in the legend
<SnoopJeDi> what's the number of rings encoding?
<raptop> number of planets
<SnoopJeDi> ahhh
<B787_300> SnoopJeDi: number of planets
<B787_300> also what is the difference between transit and imaging methods? i didnt think we could direct image exoplanets
<B787_300> raptop: ^ that might be a you question
<regex> Direct imaging may be of larger planets that transit.
<regex> whereas a transit can also simply be a dip in light.
<raptop> One moment
<SnoopJeDi> direct imaging afaik means exactly what it sounds like
<raptop> Directly imaged planets are large/bright enough and distant enough to be resolveable with fancy optics
<SnoopJeDi> raptop, which is mostly "block out/subtract" the host, right?
<raptop> SnoopJeDi ninja'd me with the link
<B787_300> so they are fucking huge planets then
<raptop> SnoopJeDi: yeah. Basic coronagraphs would about like you'd think. Vortex and Lyot ones are dark magic
<raptop> B787_300: Yeah, lowest mass is probably around 2 jupiters? Also they skew very young (<20 million years?)
<B787_300> i want the free flying coronagraph mission that nasa did the concept for a while back
<raptop> Like Exo-S?
* raptop gazes hopefully at HabEx
<B787_300> yeah the habex starshade
<egg> !wpn -add:wpn scallop
<Qboid> egg: Weapon added!
<egg> !wpn whitequark
* Qboid gives whitequark a really big һοmοɡاурһ
<egg> !wpn regex
* Qboid gives regex a combining reader-writer khopesh
<egg> !wpn B787_300
* Qboid gives B787_300 a skaarj comma
<raptop> !wpn -add:adj nali
<Qboid> raptop: Adjective already added!
<raptop> !wpn egg
* Qboid gives egg a conical emergency
<raptop> uh
<raptop> We require additional conifers?
<egg> aaaaaa
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