UmbralRaptor 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> … one of the other grad students just compared me to nomal O_o | <ferram4> I shall beat my problems to death with an engineer.
<bofh>
SnoopJeDi: same
<bofh>
also I'm sorry, tha name "эта хуйня" makes me giggle every time I see it
<Iskierka>
... I may have got caught by an auto-block script from @1aprildaniels. Ellied, bofh, someone else who follows her, mind asking about that?
<Ellied>
what's your @ again?
<Iskierka>
@Kate_ZJ
<Iskierka>
and thanks for being quick on it
<bofh>
PSA: loctite 495 is *amazing* for the type of cuts you get from kitchenware ceramic shards.
<Iskierka>
gluing yourself back up?
* Iskierka
doesn't think she has any superglue around, just hot glue
<Ellied>
Iskierka: her DMs are closed. Okay if I mention you're trans in a public tweet?
<Ellied>
at least I think they are, I can't find them
<Ellied>
yeah they are
<Iskierka>
... I mean while my twitter has no bio I follow plenty of things to make it obvious and have probably retweeted some thing
<Iskierka>
and not like the tweet needs to stay public after acted upon
<Ellied>
sure, just being sure
<Ellied>
okay, tweet's out, will let you know of developments in case you don't see first
<Iskierka>
almost certainly is a false positive, because it was a reply but within the minute I deleted it to move it to replying to a more appropriate tweet, and it was already blocked. Who acts within the minute except by script?
<Iskierka>
at least it means I find out quickly though
<Ellied>
yeah
<Ellied>
ha, finally got Android to mount / and /system rw on boot
<Ellied>
take that, inward-facing security measures!
<Iskierka>
android will do that at all?
<Ellied>
yep, it's actually weirdly easy to remount them post-boot.
<Ellied>
just mount -o rw,remount /system as root does it
<Iskierka>
also on reflection I was actually mentioning I'm trans in the tweet I made so meh @ public tweet. Though once it's done its purpose may as well remove it anyway to limit detectability
<Ellied>
orrrr you could install that garbage app I screened on twitter lol
<Ellied>
yeah I'll delete it as soon as she replies
<Iskierka>
what app would this be?
<Ellied>
system remounter or something, I didn't follow the google play link
<Ellied>
it remounts /system rw, and has banner ads unless you pay for Pro.
<egg|phone|egg>
!Wpn Iskierka
* Qboid
gives Iskierka a Bolzano-Weierstraß theatre
<egg|phone|egg>
!Wpn Ellied
* Qboid
gives Ellied a graviton morphism
<Iskierka>
tbf an app would be convenient in some ways if it wasn't then going to steal root, given phone keyboards. Buuut on the other hand since I bought the pi0 I have *two* OTG connectors
<bofh>
every play has a convergent sub-act?
<Iskierka>
I should be that weird person using their phone with keyboard and mouse
<Ellied>
I would be that person if my phone actually supported OTG as advertised (it doesn't)
<Iskierka>
That sucks. I've only tested mouse but that does work (and it's weeeeeeird using android with a mouse)
* UmbralRaptor
could see that with a Note form factor.
<Ellied>
the latest update from OnePlus actually includes a switch to turn it on, but it doesn nothing.
<Iskierka>
especially gaming mouse
<Ellied>
does*
<egg|phone|egg>
Bofh, so that abc proof has Grothendieck théâtres
<egg|phone|egg>
Without accents but my phone switched language
<Iskierka>
... why have the lights been flickering these past two nights
<Ellied>
ghosts
<Iskierka>
nothing's gone out but every few minutes blip
<Iskierka>
You think they want brownies?
<Ellied>
quick, build a rotating-coil magnetometer or whatever they use in those ghosthunter tv shows
* UmbralRaptor
hungers.
<bofh>
egg|phone|egg: ROFL I have to find these now.
<bofh>
"Bi-Anabelian" what the hell does that mean
<bofh>
I only see Hodge Theaters
<egg|phone|egg>
Bofh: naming things is fun, see also my conifers in my MSc thesis
<Iskierka>
... wait that was in MSc thesis? I thought this was just a joke name for something in principia
<egg|phone|egg>
Bofh: ah right sorry I got confused
<bofh>
!u
<Qboid>
What code point do you want me to look up?
<egg|phone|egg>
Bofh: lgbt-anabelian
<bofh>
⊠⊞-Hodge Theater
<bofh>
there we go, had to look up the codepoints
<Iskierka>
I am disappointed that discord markdown doesn't support marquee. I wanted to annoy people with a driving train
<bofh>
hey, that's the nice name
<bofh>
the nastier one is Θ^{\pm\text{ell}} NF-Hodge Theaters
<Iskierka>
why does electronics that you handle get weird gunk in it
<Iskierka>
this old phone has something GREEN under the volume control
<egg|phone|egg>
Ah so it's just standard terminology of modern number theory O_o
<Iskierka>
numbers are silly
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<UmbralRaptor>
Most things are silly.
<bofh>
^
* UmbralRaptor
feels a need to be silly now.
<icefire>
;quote
<kmath>
icefire: <Ellied> just because we just elected an incompetent fascist dictator to the presidency and are about to start dying from mass loss of health insurance doesn't mean our public transit isn't crap
<UmbralRaptor>
Silly, not depressing.
<UmbralRaptor>
;quote
<UmbralRaptor>
;quote
<kmath>
UmbralRaptor: <Ellied> I don't even know. For some reason a gate voltage between 2 and 3 volts appears to cause it to go mad and summon ghosts.
<UmbralRaptor>
better
<Iskierka>
... did you use a greek question mark or something?
<UmbralRaptor>
Phone automatically added a trailing space.
<icefire>
which apparently im not trimming
<icefire>
oh well :effort:
<bofh>
how does one add a quote?
<UmbralRaptor>
;quote add Something silly.
<kmath>
UmbralRaptor: Added 'silly.' [8]
<bofh>
;quote add 01:09 < egg|phone|egg> Bofh: Upon seeing the diagram the student was canonically enlightened
<UmbralRaptor>
Wait, what? I thought wrote had to be in #bottorture.
<bofh>
should prolly remove the timestamp
<Iskierka>
;quote 8
<Iskierka>
not like that?
<UmbralRaptor>
;quote remove Something silly.
<UmbralRaptor>
;quote del Something silly.
<kmath>
UmbralRaptor: Not found.
<UmbralRaptor>
;help
<kmath>
UmbralRaptor: Commands: print_rpn rpn c youtube yt seen tell isup mission mission add mission del mission stats mission list mission search outcome add outcome del outcome search wolfram wa help roll spacedock wikipedia w rose quote quote add quote del quote list apod
<icefire>
;quote add egg|phone|egg Bofh: Upon seeing the diagram the student was canonically enlightened
<icefire>
I hate you kmath
<Iskierka>
what did you even manage to do with this quote script
<icefire>
its the pipes
<Iskierka>
is it clogging them?
<icefire>
sure
<UmbralRaptor>
Note to self: do not let icefire write password management software.
<icefire>
nobody should
<icefire>
use bcrypt and save yourself a lifetime of hassle
<Iskierka>
... now I want to make an IRC bot that claims to securely store your password for you, but will only listen and respond in public channels
<bofh>
yeah, ust use bcrypt
<UmbralRaptor>
Like tweet at her?
<bofh>
um. not *that* bcrypt, lol.
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<Iskierka>
Aaand gonna go to bed. Will see if April has checked twitter tomorrow
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<icefire>
clearly I wasn't in my right mind when I wrote quote functionality
<Ellied>
in that it should have been written better, or that it shouldn't have been written at all?
<UmbralRaptor>
Normal people: get drunk and say something embarassing. icefire: gets drunk and writes IRC bots.
<icefire>
probably wasn't drunk
<icefire>
or maybe I was, don't really remember
<bofh>
rofl
<SnoopJeDi>
programming: not even once
* UmbralRaptor
wonders if anyone has done that meth meme with Erdös.
<bofh>
I think I've seen it done before but not sure, was awhile ago.
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<egg>
!wpn bofh, Fiora, котя, and whitequark
* Qboid
gives bofh, Fiora, котя, and whitequark a descending theory of everything
<egg>
UmbralRaptor: s/ö/ő/
<Qboid>
egg thinks UmbralRaptor meant to say: /me wonders if anyone has done that meth meme with Erdős.
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<Greys>
I wish one of those explainditorial channels would do a big inspection and explaination of why foods in america cost what they do, specifically beef, ham, chicken, and turkey each; given american culture beef should really cost less than ham, and why is turkey about the same cost as chicken at all given the horrible things we do
<Greys>
but then also going into how the price of corn and wheat is artificially reduced by government intervention
<Greys>
and also how government intervention reduces the supply of all these things to maintain stability in the market
<Greys>
also briefly explain how government intervention reducing supply to maintain safety is totally different from maintaining market stability
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<whitequark>
UmbralRaptor: which meth meme
<egg|work|egg>
!wpn whitequark
* Qboid
gives whitequark a Sturm-Liouville modem/railgun hybrid
<Greys>
a demodulating railgun? sweet googlie mooglie
<Greys>
any of yall know a good study about IR imaging through fabrics? I can only find studies about transmissivity*, and that doesn't really inform clarity
<soundnfury>
!wpn egg|work|egg
* Qboid
gives egg|work|egg a Wasserstein ray
<soundnfury>
hmm... is that a beam of water mugs, or an Australasian fish that lives in water mugs?
<bofh>
whitequark: the "$DRUG, not even once" one presumably.
<bofh>
at this point I'm thankfully mostly keeping it together while wondering what surprises Saturn has in store for us. no guarantees about tomorrow. christ I already miss that probe a bit.
<bofh>
it'd be more visible if they just chucked a bunch of actinides into their star, honestly.
<bofh>
since that'd show up on spectral lines and for much longer.
<Iskierka>
if we were sampling brightness with like second-accuracy a giant nuclear war might be visible for the burst, but I don't think kepler samples that quickly
<UmbralRaptor>
IIRC, the short cadence is 30 minutes.
<Greys>
is that 30 minute exposures or a shorter exposure every 30 minutes?
<Greys>
if the war weren't competing with another sun, it might be distinct on the final output
<UmbralRaptor>
Ah, 6.5 second exposures, binned to either 1 minute or 30 minutes.
<Greys>
angles as area, neat unit
<bofh>
~*~ steradians ~*~
* UmbralRaptor
is bitter that those aren't written as ㎭²
<Iskierka>
if it were exposures on the order of a second and enough burst at one moment in a big war, it might be measurable
<Iskierka>
averaged over a minute pretty sure it's going to be lost in noise
<Iskierka>
though over 1 second the noise might dominate it anyway
<bofh>
doubt it, isn't galactic background noise fairly constant in both amplitude and frequency distribution?
<bofh>
presumably a nuclear burst would be fairly narrowband
<bofh>
UmbralRaptor: same, that would be the perfect unit for them.
<UmbralRaptor>
bofh: AIUI, a steradian *is* a radian^2, and that I learned this relatively recently from egg made some undergrad classes wat harder than they had to be.
<UmbralRaptor>
Oh, right. Zetta erg abbreviates into an entirely different unit.
<egg|work|egg>
UmbralRaptor: undergrad classes? just principia comments
<UmbralRaptor>
egg|work|egg: well, some unit conversions.
<egg>
gosh the notation is daft, that θ is morally a time
<egg>
so ξ is some sort of instantaneous rigid motion I guesss
<egg>
just name the groups instead of dumping everything into coordinates grmlbrlcgh
<egg>
rqou: so do you get the unstated abstractions and the three entries other than the one pointed to by the arrow
<egg>
because I'd say that's the most interesting part, what the formula comes out to be is, well, a calculation
<rqou>
i'm slowly working through it by reviewing the lecture slides
<rqou>
i understand how the hat operator is being used to write cross-products as a matrix multiplication
<rqou>
which is the first formula
<rqou>
the second formula for 2d rotations is pretty obvious to me
<egg>
rqou: like this is a complete mess because they turn everything into "a six-by-one vector" instead of "an element of the Lie algebra and a vector", which means you have to reverse-engineer what the giant array of numbers is supposed to mean
<rqou>
i'm not familiar with Lie algebras (hey, I'm a CS major, not a math major :P )
<egg>
rqou: yeah but they're hiding it from you, thereby removing abstractions that are critical to make sense of this :-p
<rqou>
i have no idea how the third formula works, but i know it's' called the Rodriguez rotation formula
<rqou>
so i guess overall i have no idea what the unstated abstractions are
<egg>
rqou: ok, I'll get back to you after dinner
<egg>
unless bofh wants to do a crash course in Lie algebras first :-p
<rqou>
the TA said that the intuition is (can be) that you pretend you have a differential equation
<rqou>
and then you find its solution, and that's why there's a matrix exponential
<rqou>
and then you just shrug and use matlab or something :P
<kmath>
<katiechironis> @matthewharrison i once had a playtester remark "it seems dumb that hamlet would agree to just duel laertes to the… https://t.co/QkbMiEe7hZ
* egg
pokes bofh with a Lie algebra
<SnoopJeDi>
bofh, LOL
<bofh>
egg: ?
<bofh>
like I've not seen this formulation before but it just looks like the product of a few Householder transforms & a Givens rotation?
<bofh>
I can also give a crash course I suppose but in an hour, have to run now.
<egg>
bofh: sure, but like it seems to me that getting a grasp of the underlying abstractions may be more useful than the specifics of the calculation
<egg>
bofh: that 6*1 vector that stands for an element of V together with an element of so(V) is rather ugly
<UmbralRaptor>
!wpn -add:adj eigen
<Qboid>
UmbralRaptor: Adjective added!
<soundnfury>
!wpn UmbralRaptor
* Qboid
gives UmbralRaptor an omicron durandal
<UmbralRaptor>
Stabbity! \o/
<UmbralRaptor>
!wpn soundnfury
* Qboid
gives soundnfury a Bourbaki snail
* soundnfury
gives the snail an injection
<UmbralRaptor>
Is the snail sinistral or dextral? (cc: egg)
<Qboid>
Greys: Input string was not in a correct format.
<Greys>
!roll d3.14
<Qboid>
Greys: Input string was not in a correct format.
<Greys>
darn
<egg>
rqou: are you still there?
<rqou>
yes, kinda
<egg>
rqou: ok, so, to take a physical example, the thing that we can look at is a rigid body
<rqou>
ok
<egg>
rqou: we look at the spatial transformations that we can do to a rigid body (while keeping it rigid); it happens that you can represent (the technical term is in fact represent) that with 4*4 matrices, but the important thing is that we're looking at rigid transformations
<egg>
rqou: but further, they have a Lie group structure, that is you can do calculus to those transformations: it makes sense to take a continuous path of rigid transformations
<egg>
rqou: and it makes sense to differentiate them
<rqou>
differentiate a path of transformations?
<egg>
yup
<rqou>
ok
<egg>
rqou: look at just an orientation (without a position), it's perhaps simpler to start there
<egg>
rqou: you have a thing that has an orientation that varies with time
<egg>
rqou: between any two instants t1 and t2, where the thing has two orientations orientation(t1) and orientation(t2), you have a rotation that maps orientation(t1) to orientation(t2)
<rqou>
i can see how that works
<egg>
rqou: now you can define from that a derivative for the rotations (the rotations live in a group called SO(3), the derivatives in ??(3))
<egg>
rqou: now, if you want coordinates, the elements of SO(3) can be represented as rotation matrices, and in that case the derivatives are skew-symmetric matrices
<rqou>
are the derivatives also a group?
<egg>
rqou: well, they're much more
<egg>
rqou: you can add them obviously, if you add two skew-symmetric matrices the result is skew-symmetric
<egg>
and so you get the whole additive group
<egg>
in fact you get a whole vector space
<egg>
but you get more
<egg>
because you have the commutator
<egg>
with that, you get a Lie algebra
<egg>
(SO(3) is a Lie group, i.e. a group that's differentiable, and the derivatives live in a Lie algebra)
<egg>
rqou: now, what is the dimension of the space ??(3) of derivatives of rotations
<egg>
if you look at what a 3*3 skew-symmetric matrix must look like, you come to the conclusion that it's 3d
<rqou>
hmm wait. i thought groups only have one operator. how can you define a derivative?
<egg>
rqou: note: this is special about 3, if you start with SO(n), you end up with n*n skew-symmetric matrices in ??(n), those have dimension n(n-1)/2, which is not n unless n = 3
<egg>
rqou: so your group also has the structure of a manifold, in a way that's consistent with the group
<egg>
rqou: the manifold has tangent spaces, and so your derivatives live there (derivatives of paths on the manifold)
<egg>
rqou: if you take rotations in 2d, the manifold is fairly obvious, it's a circle essentially
<egg>
in 3d it's rather messier to visualize, because the manifold is 3d rather than 1d
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<rqou>
hmm, so why do we use the skew-symmetric matrix representation instead of something else like a vector?
<egg>
rqou: now, since your derivatives-of-rotations are vectors and live in a 3d vector space (of skew-symmetric matrices), you could also write them as triples of numbers, but there's a caveat: you lose some structure by doing that, they don't behave like nice vectors like e.g. velocity, they break down if you go through a mirror; they're really different animals
<egg>
but you *can* write them as vectors (they're actually bivectors though, and I'll use that term from now on because it's shorter than derivative-of-a-rotation)
<egg>
rqou: the thing that turns a bivector into a vector (for a given orientation, i.e. handedness, of your vector space) is called the Hodge star, if you want to dive into confusing parts of Wikipedia
<soundnfury>
!wpn -add:adj Hodge
<Qboid>
soundnfury: Adjective already added!
<soundnfury>
(worth a try)
<egg>
rqou: now, if you do write them as 3-tuples, the matrix commutator on those skew-symmetric matrices (which is an operation that makes sense from the Lie group & Lie algebra perspective) turns into the cross product of the 3-tuples
<egg>
rqou: the matrix commutator of ω1 and ω2 being [ω1,ω2] = ω1ω2-ω2ω1
<egg>
rqou: now there's another bit to rigid transformations, that's the translation bit; it's kind of boring (technically it has the same structure, but everything commutes so it's not very interesting). instead of orientations you have positions, instead of rotations you have translations, their derivatives are velocities; however the group of translations commutes, so the Lie bracket on the velocities vanishes; not much
<egg>
happens there
<rqou>
hmm, i don't quite understand the Lie bracket, but idk if that is important for now
<rqou>
egg: ooh, so the matrix exponential manages to connect together the rotation group and the skew-symmetric matrix vector space
<rqou>
but it's not clear to me why this is "useful"
<egg>
yup, it maps the derivatives to the a path in the rotations
<egg>
rqou: so first to clarify the Lie bracket: there are a bunch of ways to easily define it that require more differential geometry than is convenient here, but there's one that might shed some light: take a path of rotations x(t) and another path of rotations y(t), with derivatives X(t) and Y(t). Now, look at x(t)y(t)x(t)^-1y(t)^-1 (the group commutator of x and y at every time). That's also a time-dependent rotation, and so
<egg>
you can differentiate it; the *second* derivative ends up being [x(t), y(t)], so it sort of tells you how much it doesn't commute back in the group
<egg>
um, I mean [X(t), Y(t)]
<egg>
(and I'm missing a factor of 2, but still the idea is that this is related to the group commutator)
<egg>
rqou: so now, back to the bivectors; they are the derivatives of rotations: what is that, physically
<egg>
assume it's the derivative with respect to time
<soundnfury>
rqou: s/ex/eggs
<Qboid>
soundnfury thinks rqou meant to say: egg: ooh, so the matrix eggsponential manages to connect together the rotation group and the skew-symmetric matrix vector space
<egg>
rqou: that's just the angular velocity right
<rqou>
right
<rqou>
(currently sitting in lecture for a different class that i'll probably have questions about later :P )
<egg>
:D
<rqou>
#kspacademia > office hours :P
<egg>
we have catpics!
<egg>
rqou: so, now, the exp(ω t) turns your angular velocity ω into a one-parameter family of rotations (a path of rotations) where the derivative is ω everywhere
<egg>
rqou: in other words it's uniform rotation with angular velocity ω, which hopefully highlights some usefulness there
<egg>
rqou: now that was looking at the function that maps ω to (the function that maps t to exp(ω t)), rather than looking at exp itself; but from this we can see what exp is
<egg>
rqou: it takes angular velocity * time (which is a bivector with units of angle) to a rotation
<egg>
rqou: i.e., it turns the angle-axis representation into the corresponding rotation
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<rqou>
egg: so are homogeneous coordinates next?
<rqou>
in the equations i posted they generalized the skew-symmetric matrix somehow
<rqou>
for the most part i understand homogeneous coordinates other than the "point at infinity"
<rqou>
but i don't really see how that big mess of an equation appeared
<egg>
rqou: so in those equations you have 4d matrices which look furiously like the representation of the Euclidean group; I talk about them like that, it's probably nicer than if I start talking about projective space (which is where homogeneous coordinates come from)
<egg>
rqou: so, rigid transformations (or Euclidean transformations) form a group
<egg>
rqou: doesn't matter much, the derivatives are the same, and if you drop the S you just get an additional connected component
<egg>
rqou: that's an important point: SO (or SE) are connected, topologically; O and E are not, you can't go continuously from a rotation to a reflection
<egg>
rqou: so, the idea is that you stick your rotation R and translation x in a matrix, ((R, x),(0, 1)), which represents "rotate by R then translate by x"
<rqou>
right, i know that
<egg>
rqou: if you map your positions to the 4-vector (q, 1), you can see that this has the right effect
<egg>
rqou: which means that then multiplying matrices (which is just composing them as functions of vectors) is going to do the right thing to the Euclidean transformations you are representing by those matrices
<egg>
rqou: but now, we know that rotations matrices are things we can derive, and so are translations
<egg>
rqou: so the derivative of this stuff ends up being a matrix of the form ((ω, v), (0, 0))
<egg>
where ω is an angular velocity (a bivector), and v is a velocity (a vector)
<egg>
rqou: angular velocities and velocities are 3d, so the space of the 4*4 matrices of the form ((ω, v), (0, 0)) where ω is skew-symmetric is 6 dimensional
<egg>
rqou: that sheet flattens that into a vector ξ, which is profoundly evil
<egg>
rqou: now again, the special Euclidean group is a Lie group, it has that 6d Lie algebra, it also has an exponential map
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<egg>
rqou: and exp((ωt, vt), (0, 0)) is a one-parameter family of Euclidean transformations, whose derivative is ((ω, v), (0, 0)) everywhere, i.e., a rigid motion with constant velocity and constant angular velocity
<rqou>
so this is a "screw axis"
<egg>
rqou: they call t θ here, which is also quite evil
<egg>
rqou: nah, it's only screwing if ω and v are aligned
<rqou>
ah ok
<egg>
rqou: this is just a rigid homogeneous spherical cow tumbling along happily in an otherwise empty universe
<egg>
I insist that the cow be spherical, so that its rotation isn't chaotic, let us not summon джанибеков
<egg>
rqou: oh btw, obviously physically ω and v being aligned makes sense, but ω and v pointing in the same direction doesn't (it depends what handedness you choose for your screws). The way you can check whether they are aligned is, by taking ω as a matrix, seeing whether the product ωv (whose result is a vector) vanishes
<egg>
rqou: wait no, I got that backwards, with this exponential the velocity gets rotated too of course
<egg>
rqou: so yeah, it's much less physically nice than what I said, I guess it's the Frenet frame of a helix
<egg>
rqou: so then that term with the arrow is the displacement (along a helix)
<egg>
rqou: the second term is how much you travelled along the axis, it's vt (how much you travelled along the helix at your constant speed of v) projected on the axis ω
<egg>
s/speed/velocity/
<Qboid>
egg meant to say: rqou: the second term is how much you travelled along the axis, it's vt (how much you travelled along the helix at your constant velocity of v) projected on the axis ω
<egg>
rqou: the first term is what happens in a plane orthogonal to the axis of the helix (ωv is orthogonal to the axis), you can see the rotation (the exponential)
<egg>
rqou: intuitively, the identity-minus business is there because this is the displacement from a point on the helix to another point on the helix, rather than from a point on the axis, so this accounts for the rotation not being centred where you are (the displacement from that first term vanishes when the rotation is the identity)
<egg>
rqou: I'm using a somewhat different notation, but one that doesn't erase abstractions (it took me way too long to figure out how ω ω transpose v was something sensible)
<egg>
(ω transpose v is actually the wedge of a bivector and a vector, yielding a trivector (aka a pseudoscalar), which is then multiplied (something something interior product something) by a bivector to get a vector again and everything is nice)
<rqou>
egg: sorry, got distracted by something else
<rqou>
reading...
<rqou>
i'm not sure i completely get it, but i probably understand enough to do the problem set
<rqou>
egg: stand by until i finish this problem set, and then I will ask you about adjoints :P
<egg>
"i probably understand enough to do the problem set" << that's clearly not enough, more eggsplanation is needed :-p
<rqou>
you can explain more after i finish this problem set
<rqou>
and after i ask you about adjoints for the next problem set :P
<egg>
:D
<rqou>
problem set catch up, whee!
* rqou
swears he will do the next problem set sooner :P
<bofh>
That's a pretty good introduction to Lie Groups/Lie Algebras va SO(n). Going to save that for the future.
<rqou>
yeah, i know relatively little "advanced" math
<rqou>
i'm just a CS major who plugs numbers into formulas :P
<UmbralRaptor>
"This homework is of course supposed to cause some pain and suffering."
<UmbralRaptor>
(My QM prof)
<egg>
UmbralRaptor: :D
<rqou>
i don't get it, my intuition for linear algebra is "good enough" but i have close to no intuition about rotations at all
<egg>
rqou: that's because there's so much more to them than linear algebra
<egg>
they're a Lie group, and you can't understand that without differential geometry (and it's a lot on top of differential geometry)
<rqou>
yup, never studied that
<egg>
differential geometry and Lie group being stuff that you typically get to properly learn about in MSc level courses in math
<bofh>
UmbralRaptor: hey, it
<bofh>
UmbralRaptor: hey, it's QM. no pain, no gain :P
<egg>
bofh: sounds like a Trubowitz course
<UmbralRaptor>
egg, bofh: primary textbook author is Sakurai. I think Landau is suggested?
<bofh>
GOOD.
<bofh>
That's honestly my standard req for advanced QM textbook (Sakurai).
<UmbralRaptor>
hm
<egg>
rqou: so does that figure I showed you make sense
<egg>
!wpn UmbralRaptor
* Qboid
gives UmbralRaptor a cinematic radix
<egg>
!wpn rqou
* Qboid
gives rqou a pyrolytic self-adjoint memory
<egg>
!wpn bofh
* Qboid
gives bofh a zeta vertex
<UmbralRaptor>
!wpn egg
* Qboid
gives egg a thermometer
<UmbralRaptor>
!choose Classical Mechanics|Make anime^Wbatch RV&exptime calcs real
<Qboid>
UmbralRaptor: Your options are: Classical Mechanics, Make anime^Wbatch RV&exptime calcs real. My choice: Make anime^Wbatch RV&exptime calcs real
<UmbralRaptor>
;choose Classical Mechanics|Make anime^Wbatch RV&exptime calcs real
<kmath>
UmbralRaptor: Classical Mechanics
<UmbralRaptor>
eggchoose Classical Mechanics|Make anime^Wbatch RV&exptime calcs real
<kmath>
<elakdawalla> I posted that and instantly realized something was wrong. It's summer in the northern hemisphere. It's upside down!… https://t.co/0AxfQolzjp