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.
<kmath>
<mbeisen> my postdoc has new variant of the uncertainly principle: it is not possible for him to simultaneous collect good da… https://t.co/QA2hqlUfpF
<kmath>
<NavinPokala> when the journal charges so much the paywall is in exponential notation https://t.co/XCgoPJAjyO
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<SnoopJeDi>
so, this is a slightly embarrassing quesiton because it *seems* like something I should have an answer to, but what the hell even is the interpretation of the 3x3 matrix commonly constructed when teaching the cross product as a determinant?
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<SnoopJeDi>
It never occurred to me before, but it's kinda weird that one row is members of ℝ^2 and the others are members of ℝ, and I'm trying to get my brain around that. Is there some way to interpret it as f:ℝ^3->ℝ^3?
<SnoopJeDi>
nvm hmm no not at all, because it's not acting on ℝ^3
<SnoopJeDi>
...wait, I'm mixing and matching my dimensions. ijk in that case *are* in ℝ^3. I should eat dinner.
<kmath>
<stephentyrone> @RichFelker @UINT_MIN It's the international court of programming languages. The judge will read a list of charges… https://t.co/eNVql80il8
<Ellied>
!wpn egg
* Qboid
gives egg an Ulthar gantlet which strongly resembles a épée
<egg|work|egg>
!wpn Ellied
* Qboid
gives Ellied a tempered vertical (with ground plane)
<egg|work|egg>
Ellied: if you want eggsplanations of the cross product stay tuned, see above :-p
<kmath>
<claudiacicone> After being back to Italy for exactly 13 months, this morning someone thought it was the right time to remind me th… https://t.co/XOtFvMASWg
<egg|work|egg>
!wpn UmbralRaptor
* Qboid
gives UmbralRaptor an expanded register
<egg|work|egg>
UmbralRaptor: so do you understand that Euler angle thing
<egg|work|egg>
or do you require more eggsplanations
<UmbralRaptor>
Schedule wise, I suspect 1800 UTC on Wednesdays?
<UmbralRaptor>
… why did AAS send me an email asking for donations?
<egg|work|egg>
UmbralRaptor: hm, that's within my commute I think
<egg|work|egg>
UmbralRaptor: how about >midnight UTC+1
<Ellied>
well, I got Inception to make my dell laptop freeze solid, but no luck so far on unlocking it
<UmbralRaptor>
Did you set a bios password with non-ascii characters?
<Ellied>
No, I'm just experimenting to see if I can actually get this RDMA exploit working, purely for academic purposes
<Iskierka>
hax
<Ellied>
dumping the memory got to about 2 GB and then failed, says it timed out
<Ellied>
it's possible I got the encryption key, but I don't know how to find it.
UmbralRaptor is now known as NomalRaptor
<egg|work|egg>
!wpn NomalRaptor
* Qboid
gives NomalRaptor a vernacular statistic
<NomalRaptor>
!wpn egg|work|egg
* Qboid
gives egg|work|egg a scary !wpn
<Ellied>
oh, pf, it dropped after 2 GB because the machine only *has* 2 GB
* egg|work|egg
is scared.
<Ellied>
guess the RDMA thing doesn't actually let the requesting host know how big the memory is? weird
<NomalRaptor>
egg|work|egg: after midnight because that way you can us Euler angles to rotate a telescope?
<egg|work|egg>
hah
<egg|work|egg>
(I mean Euler angles are confusing, for a telescope you'd probably use cardano angles?)
<egg|work|egg>
(but to rotate a planet you'd use Euler angles)
<Ellied>
huh, figured out how to activate the IME on this thinkpad (sure enough, it does have one) but it's still not responding in any nmap-detectable way on its ports.
<Ellied>
website for signing up for the GRE: "Your password must be at least 6 characters but not more than 16 characters and must contain a lowercase letter, an uppercase letter, a number, and one of these special characters: !@#$%&*"
<NomalRaptor>
stabbity.
<Ellied>
"We want to make sure that your password is difficult to crack, but not so difficult as to prevent someone with expensive resources from breaking in"
<NomalRaptor>
Also, the key to the PGRE is speed.
<Ellied>
yeah, I understand. I'm not expecting to do super well but I'm hoping I'll at least do well enough to get accepted somewhere :I
<Ellied>
we have a prof here who hardly ever talks about anything but the PGRE
<Ellied>
are there any conceptual questions, or is it all numerical problems, or what?
<NomalRaptor>
Pretty numerical, but sometimes you can use conceptual stuff to rapidly select a choice. Check out the practice exams.
<Ellied>
hunf. Still haven't found any way of remotely detecting the presence of an IME (or locally detecting one if it's not activated)
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<SnoopJeDi>
egg|cell|egg, after I brain-dumped in here, I had a vague notion that this was scraping up against wedge products and other differential geometry, so I yanked my book off the shelf to re-read the formal stuff about frames and so on, but I'd be interested in any interpretation of the determinant itself, and even moreso with the map defined by that matrix
<SnoopJeDi>
I presume cell is not an eggcellent medium, but it proved a pretty decent question to chew on last night. (A friend has students who asked him what a determinant *means*)
<egg|cell|egg>
Yeah will reply when I'm home
<SnoopJeDi>
?
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<egg>
moo
<SnoopJeDi>
μ
<egg>
!wpn SnoopJeDi
* Qboid
gives SnoopJeDi an aluminium metallic etalon
<egg>
so the cross product is fake actually
* SnoopJeDi
band-stops
<SnoopJeDi>
!wpn egg
* Qboid
gives egg a neptunium wolf
<egg>
unless you have an orientation, then it's the hodge star of the wedge
<egg>
but mostly it's the wedge that you really care about and you're orientation-free
<egg>
now, the determinant
<egg>
the determinant is only an element of the field for endomorphisms, not linear maps between different vector spaces
<egg>
SnoopJeDi: there, det A is the scalar that has the property that (det A) (v_1 ∧ ... ∧ v_n) = A v_1 ∧ ... ∧ A v_n
<SnoopJeDi>
your "mostly" is very different from our "mostly" but okay :P
<egg>
SnoopJeDi: well, almost always really
<SnoopJeDi>
almost always orientation-free?
<egg>
(okay if you're doing fancy QM thingies)
<egg>
for anything classical you never truly want a cross product
<SnoopJeDi>
right I'm not getting off into the deep-end of GR where you *actually* use differential geometry and have to think about the manifolds themselves
<SnoopJeDi>
it's rather unceremoniously plopped in our laps along with "look the only space is ℝ³ okay?" and then maybe you gain the fluency later to start questioning it (IME most people in physics/eng. probably don't?)
<SnoopJeDi>
but I think I follow your point about the wedge being the thing-underneath
<egg>
SnoopJeDi: no but I mean GR is not a concern here, unless you lose chiral symmetry because QM magic, what you are *really* doing is wedges, never cross products
<SnoopJeDi>
and the cross-product emerges as a sort of artifact of your stipulation that there is an orientation
<egg>
yeah, it's the thing-underneath :-p
<egg>
the thing-in-itself?
<egg>
:-p
<SnoopJeDi>
pretty apropos for wedge products
<SnoopJeDi>
!wpn -add:adj bootstrapped
<Qboid>
SnoopJeDi: Adjective added!
<egg>
das Wedgeprodukt an sich
<SnoopJeDi>
I'm probably just going to have to re-read some of O'Neill if I hope to get my head around "why does the determinant show up in this definition"
<egg>
SnoopJeDi: okay so the definition of the determinant *is* "what the endomorphism does to the highest grade of wedges"
<SnoopJeDi>
still unsure of what to make of one row of a "matrix" being a frame and the other two rows being scalar coordinates
<SnoopJeDi>
in the sense that the coordinates aren't coordinates and we're just being notationally lazy?
<egg>
yeah
<egg>
SnoopJeDi: but the wedge is a wedge of n-1 vectors, and the determinant is what happens to a wedge of n vectors, so there is a connection
<egg>
you can take ijk as your v_i in the above, and then (det A) (i∧j∧k) = (Ai∧Aj∧Ak), the wedge of the columns of the matrix
<SnoopJeDi>
The smell of anticommutation alone is enough to convince me there's a connetion heh
<SnoopJeDi>
I just grok the algebraic bits sufficiently poorly to follow it beyond a gut feeling, I think
<egg>
now wedge associates (contrary to the cross product), so that's (Ai∧Aj)∧Ak
<SnoopJeDi>
which stands to reason since I never had "real" algebra ever
<SnoopJeDi>
I am very unsurprised to see Spivak's name pop up in the googline I've been doing though :P
<egg>
SnoopJeDi: so what do we make of (Ai∧Aj)∧Ak = (det A) (i∧j∧k)? well let Ak = k, the wedge of the other two columns becomes the determinant of A in its kth coordinate; then permute ijk and shove signs around
<egg>
this shows that with the determinant you can compute lower wedges, I don't have a satisfactory explanation of the fact that you can shove vectors in the entries to get the above
<SnoopJeDi>
(the person who brought this Very Good Question to me has no exposure to D.G. beyond what we incidentally get rubbing shoulders with cosmo)
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<egg>
it's not differential geometry
<egg>
no manifolds were harmed in the making of this eggsplanation
<SnoopJeDi>
abstract algebra, then
<egg>
barely abstract :-p
<egg>
and just linear
<SnoopJeDi>
(ﾉಥ益ಥ）ﾉ ƃƃǝ
<egg>
wheee!
<SnoopJeDi>
you assume far too much knowledge in all of the above on the part of garden variety physicists :P
<SnoopJeDi>
at the risk of calling out my colleague, I did have to remind him that the most pragmatic way to think about the determinant is in terms of the invertible matrix theorem
<SnoopJeDi>
hence the name
<egg>
SnoopJeDi: so I call the cross product *(v∧w)_k
<egg>
um
<egg>
*(v∧w)
<egg>
and _k for its kth coordinate
<egg>
um I should not call my basis vectors ijk that's just annoying
<egg>
let's go with e_1, e_2, e_3
<SnoopJeDi>
yea that's what O'Neill uses and I think it's idiomatic
<SnoopJeDi>
egg, the reason I keep mentioning differential geometry btw is because that's the only (formal) exposure I've had to exterior products
<SnoopJeDi>
exterior/wedge
<SnoopJeDi>
and notions of duality and...
<SnoopJeDi>
It was a good class but I understood rather little of it :P
<egg>
yeah okay you never had a half-decent linear algebra class :-p
* egg
pets the physicist
<SnoopJeDi>
I had two, actually!
<SnoopJeDi>
the differential geometry being the second :)
<SnoopJeDi>
but I freely confess that my math degree is decidedly applied and kind of undeserved, at that
<SnoopJeDi>
learning to be comfortable with saying the holy words "I don't know" is pretty freeing, though :D
<egg>
SnoopJeDi: well uh, long story short, there's this thing called the wedge and it takes vectors and gives you things that get wedgier and wedgier and it's cool and you should look it up; in 3d, the wedge of two vectors is 3d (but not the same thing as the starting vectors), the wedge of three is 1d (but not a scalar)
<egg>
wedgy things are vectors that can be written as sums of "pure" wedges, so you can say what happens to pure wedges and be happy
<SnoopJeDi>
sure I remember wedge products and expressing the FTC as d²=0 and all that
<SnoopJeDi>
just not well enough to do much more than wave my hand and be confident in the silhouette of what I don't know :P
<egg>
a linear endomorphism A from V to V gives you a natural map from the nth wedge of V to itself (wedge everything in the pure wedges)
<SnoopJeDi>
but even knowing about Frenet frames puts me ahead of most of my colleagues in that matter
<egg>
since it's a linear map, and the wedgiest wedge is 1d, it's really a scalar
<SnoopJeDi>
which is actually pretty surprising to me considering how mechanics-y it is, but I guess we don't often get into the realm of say attitude control?
<egg>
(linear endomorphisms of 1d vector spaces are field elements!)
<SnoopJeDi>
everything in accelerators starts with the Frenet frame though, because we decompose our 6D space into longitudinal/transverse and then pray to the appropriate machine gods that the two don't couple
<SnoopJeDi>
synchro-betatron coupling is hairy stuff
<egg>
SnoopJeDi: so back to the subject at hand, the *definition* of the determinant of A is that it's this scalar
<egg>
"the thing that happens to the wedgiest wedges under A"
<SnoopJeDi>
is it at all accurate to say that's "norm-y" in some sense?
<SnoopJeDi>
emphasis on -y
<egg>
not sure what that means
<egg>
SnoopJeDi: now, bivector wedge vector is, in coordinates, the dot product; so (v cross w)_k = (v∧w)∧e_k
<egg>
wedge associates so drop the parentheses, that's v∧w∧e_k, which is a wedge of the wedgiest sort
<egg>
construct the beautiful matrix (v|w|e_k), which has the property that (v|w|e_k)e_1 = v, (v|w|e_k)e_2 = w, (v|w|e_k)e_3 = e_k
<SnoopJeDi>
a wedge of the wedgiest sort because we're in 3-dimensional space, yes?
<egg>
yes
* SnoopJeDi
nods
<egg>
SnoopJeDi: now this beautiful matrix has as its determinant the number w such that w (e_1 ∧ e_2 ∧ e_3) = v ∧ w ∧ e_k, because that's what the determinant is
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<egg>
so the e_1 ∧ e_2 ∧ e_3 coordinate (and the only coordinate, 1d space) of (v∧w)∧e_k is that determinant
<egg>
that's (v cross w)_k
<egg>
as you said, plonking vectors into the matrix is just mapping
<egg>
you do the same or all three values of k
<egg>
SnoopJeDi: it's kind of sneaky in that the e_k I'm injecting here is not the e_k you put in your matrix, it's really the kth coordinate of all three vectors you've injected
<SnoopJeDi>
ahhh
<egg>
also I was sloppy, (*(v∧w))_k (e_1∧e_2∧e_3) = (v∧w)∧e_k = (det (v|w|e_k)) (e_1∧e_2∧e_3) is what I meant (thus (*(v∧w))_k = det (v|w|e_k) which is what you're using and mapping over k)
<egg>
bofh: ^ the above line might amuse you if you've not worked this one out already
<bofh>
This is tedious as shit tbh :P There's a reason (several, actually) why I've not liked diffgeo much :P
<SnoopJeDi>
I think that's a big part of why I enjoyed the course I took on it so much, the prof (who was my advisor and also taught me linear algebra) emphasized the mental image much more than the tedium
<SnoopJeDi>
...he let us smash our heads into more than a few good problems, mind, but classtime was pretty much literally about http://www.smbc-comics.com/comic/2014-02-24
<egg>
bofh: it's not differential geometry damn it
<SnoopJeDi>
it's close enough to that wheelhouse
<egg>
bofh: you know this stupid trick where to compute the cross product you put basis vectors in a matrix?
<egg>
bofh: that's the proof
<SnoopJeDi>
unless you are egg and have a strong iron curtain between the algebra bits and the calculus bits :P
<egg>
this is all first-year linear algebra!
<SnoopJeDi>
the subject matter is, the trappings are most certainly not
<SnoopJeDi>
not as taught in contexts I know, that is
<egg>
differential geometry was 4th year for me I think?
<SnoopJeDi>
maybe in fancy-pants Europe it's different ;P
<egg>
SnoopJeDi: it's 1st year linalg, but 2nd semester towards the end
* egg
pokes bofh with a weird matrix
<SnoopJeDi>
egg, incidentally, if I asked you to name your favorite introductory linear algebra (english-language) text, what would you name, if anything?
<bofh>
egg: okay I was taught that proof in second-year linalg and it was tedious then :p
<SnoopJeDi>
egg, you learned wedge products in those courses? huh.
<egg>
bofh: oh, I was never taught that :-p
<bofh>
SnoopJeDi: I'm a fan of Axler tbh, dunno about egg.
<SnoopJeDi>
same
<egg>
never had a proper textbook for linalg
<egg>
only Knoerrer's elucubrations
<SnoopJeDi>
that. is a good word.
<bofh>
indeed.
<SnoopJeDi>
that prof is the one who taught me the rule of thumb that you never properly learn something until you've forgotten it twice
<egg>
(might be another case of a word being more frequent in french)
<bofh>
SnoopJeDi: that's not a bad rule of thumb from personal experience.
<egg>
(see also whitequark and that paper written by a french guy about the oneiric behaviour of the cat)
<SnoopJeDi>
he's also Jim Simons's academic grandson :D
<SnoopJeDi>
I owe him a thank you card as well, or at least a "hi how ya doin" email, he's a good guy
<kmath>
<whitequark> paper's so heavy on jargon I understand nothing. the fuck are "ponto-geniculo-occipital waves". why "oneiric behavior" you can say "dream"
<egg>
my conjecture is "in french it doesn't sound that weird"
<SnoopJeDi>
academia: "just because you can means you shouldn't"
<SnoopJeDi>
yea egg I'm assuming the pronunciation is much less cumbersome in French
<kmath>
<AcademiaObscura> I just read a peer-reviewed academic paper that only used the active voice and now there is a rift in the space-time continuum.
<egg>
SnoopJeDi: [ɔniʁik]
<egg>
(onirique)
<egg>
SnoopJeDi: but mostly it's not quite as uncommon a word as it is in english
<kmath>
<0xAmit> @gangrif @Cannibal Unlock system preferences with root and a blank password. First time fails, second doesn't. Enjoy.
<SnoopJeDi>
It Just Works
<awang>
How does that even happen
<UmbralRaptor>
Security is apparently impossible.
<SnoopJeDi>
There are only two problems in computer science: cache invalidation, sorting a list, and off-by-one error.
<awang>
I always heard it with the second item being "naming things"
<SnoopJeDi>
(I have no idea what the mechanics of this bug are but they're guaranteed to be stupid)
<SnoopJeDi>
OTOH we're talking about the company that screwed up SSL because typing braces is apparently hard
<SnoopJeDi>
programmers are stupid and the fewer preferences you allow them to have the better it is for everyone
<awang>
Apple seems to have made quite a few very silly mistakes recently
<awang>
Wonder what's going on
<icefire>
bleeding talent
<egg>
!wpn whitequark
* Qboid
gives whitequark a spring insulator which strongly resembles a merge conflict
<icefire>
SnoopJeDi honestly the thing that bothered me about that SSL bug was that it got past code review (if there was any code review)
<icefire>
if there wasn't well thats really bad and indicates a poor release process
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<UmbralRaptor>
Apparently I have a reason to ? past UmbralRaptor after all.
* UmbralRaptor
? UmbralRaptor for leaving a bad weighting function in the dispatch scheduler.
<Ellied>
I'm super pumped about this mac vuln because not having admin access on the school machines is really frustrating :D
<egg>
!wpn UmbralRaptor
* Qboid
gives UmbralRaptor a ferroelectric curl
<egg>
that's a kind of cat right
<egg>
so it's a stabbing implement
<egg>
!wpn Ellied
* Qboid
gives Ellied a quacking creole
<UmbralRaptor>
A vector stabber?
<UmbralRaptor>
!wpn Ellied
* Qboid
gives Ellied a Saturnian radix
<UmbralRaptor>
!wpn egg
* Qboid
gives egg a sulfur metric
<UmbralRaptor>
Ellied: Watch the machines be on Lion, or something.
<xShadowx>
any math geniuses? not sure what terms to google :| trying to find the formula for how much pulling force on a rope to raise/tilt a tower on the ground to vertical, like have tower on ground on its side _ anchored/pivot on the left, length 10ft, basicly all th weight is at the right (top) end 400lb, then rope connected at that 10ft top end, pully 10ft above the anchor/pivot, raise to / and | :)
<kmath>
YouTube - Doodling in Math Class: Triangle Party
<UmbralRaptor>
:Δ
<UmbralRaptor>
: ∇
* UmbralRaptor
stares at the latest observation sim.
<UmbralRaptor>
Only 7/50 stars got any spectra. (This was a 5 year survey!)
<UmbralRaptor>
Those 7 range from 61 to 734 spectra. o_O
* egg
pokes UmbralRaptor in the Euler angles
* egg
stabs Cohen and Fornberg
* egg
stabs egg
<egg>
bofh: pull request of the day: #1636
<Qboid>
[#1636] title: Interpolation is not trivial when we are not interpolating at a node | Emit the table for evaluating the 0th derivative by finite difference (aka interpolation). | https://github.com/mockingbirdnest/principia/issues/1636