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|zz|egg>
hm maybe i'm just confused again
* egg|zz|egg
scratches head
<mlbaker>
do you mean for all t, R'(t) R(t)^{-1} should lie in so(W),?
<egg|zz|egg>
yes
<egg|zz|egg>
mlbaker: yeah i think that's the coordinate-free version of "the derivative of a rotation matrix is the product of some antisymmetric matrix with the rotation matrix"
<mlbaker>
the product coming in just because it's (L_g)_* of the element of the lie algebra, basically?
<egg|zz|egg>
(in fact you can use that to prove it, in any coordinates you'll get rotation matrices for R, and ARR^{-1} and R^{-1}AR are both antisymmetric for antisymmetric A)
<egg|zz|egg>
i think so? usually when it's about matrices it's shown by doing boring matrix manipulation and not petting Lie groups
<mlbaker>
bleh
<mlbaker>
i'm so confused
<egg|zz|egg>
mlbaker: if we go back to the motivating example of having V and W be two different reference systems, R is the rotation relating one to the other, and that tells you that you can express their mutual angular velocity as an angular velocity in either reference system
<egg|zz|egg>
this was a message from Cpt Obvious
<mlbaker>
like
<mlbaker>
if V=W=R and <v,w>_1 = vw while <v,w>_2 = 2vw
<mlbaker>
then SO(V,W)=
<mlbaker>
doesn't it consist solely of x|->sqrt(2)x
<mlbaker>
er, plus minus
<egg|zz|egg>
yeah
<mlbaker>
what is the manifold dimension of SO(V,W) when dimV=dimW..
<mlbaker>
does it depend on the choice of bilinear forms
<egg|zz|egg>
dim V has to be dim W, otherwise things cease to be invertible which is sad
<mlbaker>
yeah
<egg|zz|egg>
and the manifold dimension is dim SO(dim V), because it's really SO(n) by any other name
<egg|zz|egg>
mlbaker: s/\|->/↦/
<egg|zz|egg>
ow no qboid
<egg|zz|egg>
we have no bots left :-/
<egg|zz|egg>
well, _whitelogger
<egg|zz|egg>
but it doesn't do much aside from logging
* egg|zz|egg
pets _whitelogger
<mlbaker>
how is it SO(n)?
<egg|zz|egg>
give V and W any ONB, use that to identify them with R^n, SO(V, W) is SO(n)
<egg|zz|egg>
it's SO(n) but affinified, there's no distinguished identity
<egg|zz|egg>
I Can't Believe It's Not SO(n)
* egg|zz|egg
meows at bofh
<mlbaker>
uhh okay i think i see what's going on now
<mlbaker>
so the category of n-dimensional oriented inner product spaces consists of only a single isomorphism class
<UmbralRaptor>
"I’m assuming we are in L2 orbit. All the Ball documentation and Team X stuff seems to assume L2 rather than heleocentric drift away."
<UmbralRaptor>
aaaaaaaAAAAAAA
<UmbralRaptor>
(actually, I don't need to scream much. The undergrad involved in setting up an orbital survey, however…)
* UmbralRaptor
🔪 whoever thought 66% uptime was fine
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<SilverFox>
would 60Hz/s be an acceleration?
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<SnoopJeDi>
SilverFox, the most natural way to read those units is "rate of change in frequency", i.e. df/dt. Definitely not a linear acceleration unless you're using wacky cosmologist units or something?
* UmbralRaptop
blinks
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<UmbralRaptop>
"We are looking for at least 2-6 years’ experience in MicroStation,"
<UmbralRaptop>
… what are you doing with a resume that I must have taken down 6 years ago?
<egg|work|egg>
!u
<SnoopJeDi>
UmbralRaptop, recruiter headhunting you or something?
<UmbralRaptop>
SnoopJeDi: ish
<UmbralRaptop>
Something left over from a previous career, apparently.
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* egg|work|egg
scritches UmbralRaptop
* raptop
chirps happily
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* raptop
glares at radvel. Fit faster!
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<raptop>
Rule of holiday asymmetry: services are down for longer than you get time off.
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<bofh>
raptop: painfully accurate :/
<SnoopJeDi>
Today's entry in "things I accidentally learned": Intel TurboBoost
<raptop>
That sounds vaguely cursed
<oeuf>
raptop: meow
<oeuf>
bofh: meow
<oeuf>
!seen kmath
<oeuf>
;seen Qboid
* raptop
meows at the lack of bots
* oeuf
meows at the lack of quarks
<raptop>
By removing the strong force, we have achieved a chemical free channel!
<SnoopJeDi>
Seems plausible. Considering the amount of coffee I drink and how much more y'all do in a day, I imagine there's more than enough integrated energy in #kspacademia to reach GUT scale.