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.
<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
<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
<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?
<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
<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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