raptop 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. | We can haz pdf
<SnoopJeDi>
UmbralRaptor, naw I googled it. It's from the beginning of John Carpenter's "The Thing"
<SnoopJeDi>
which is very possibly my favorite movie
<kmath>
<Liv_Lanes> #phdchat What is the upper bound for how many equations are allowed on a slide? I just went to a talk where, I kid you not, I counted 23.
<mofh>
UmbralRaptor: I mean at that point why not just say "just imagine the electroweak Lagrangian here"? :P
<UmbralRaptor>
heh
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<SnoopJeDi>
upper bound? 3
<UmbralRaptor>
I mean, at some point you overflow the hbox…
<SnoopJeDi>
unless you make the text reaaaaallly tiny
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<iximeow>
oops
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<UmbralRaptop>
*poof* out of memory
<UmbralRaptop>
but still nice
<iximeow>
oh is what happened :( whoops
<UmbralRaptop>
clicking links on a phone >_>
* UmbralRaptop
ignores that a laptop with as much ram running, say, Debian would probably not have this problem
<B787_300>
iximeow: what is up with that glow in your image that doesn't reach the egdes
* UmbralRaptop
assumed a lack of flatfielding. (I mean, sky and dome flats may present issues?)
<iximeow>
B787_300: i didn't take flats, so that's a mix of the colors being a bit off, noise not being removed well, and a really harsh light curve
<B787_300>
Ah
<iximeow>
there's vignetting toward the edges because my backfocus is off (hence not bothering with flats) plus some other issues i'm figuring out, so
<B787_300>
Yeah but it is almost like you had reverse vignetting
<B787_300>
Or maybe those few stars where bright enough to punch through
<B787_300>
Did you take darks and biases?
<iximeow>
yes, but i'm using the wrong ones, and that definitely doesn't help the situation
<iximeow>
i've been doing all my processing with some questionable python that's been working well, but not extended to support different sets of calibration images
<iximeow>
i think i used a dark frame built from 120s exposures rather than 60s used in the lights :'D
<iximeow>
the ones that were 120s lights came out great, this is a bit off, so :D
<UmbralRaptop>
(aaaaa)
<UmbralRaptop>
anyway, what filters was M81 in?
<iximeow>
none, actually
<B787_300>
...
<iximeow>
i take it that ... is a ... of approval
<B787_300>
Why not use something like astromagej ?
<B787_300>
No that wasnt
<B787_300>
That was a there are nice free tool out there use them
<B787_300>
Also of you took the correct series of darks use them
<iximeow>
i haven't heard of astroimagej before and most of the nice free tools i've found have been absolutely awful to work with
<iximeow>
B787_300: i ran a python script last night and went to sleep.
<iximeow>
with a setup i know i'm actively going to be changing after an evening i took some decent images for grins
<B787_300>
(I have been known to use old sessions darks and biases before of the temp and exposure was the same to save me time...)
<UmbralRaptop>
Fun fact: recent versions of OSX break astroimagej
<iximeow>
B787_300: i also haven't been able to successfully use any existing nice free tool to even get images out of my camera - oacapture hangs forever for exposures longer than 10 seconds, sharpcap and friends claim my camera is an 8bit mono device and read data incorrectly
<iximeow>
(i suspect that the "hangs forever" is a bad interaction between oacaptue and a bug in the manufacturer sdk but i haven't tracked it down yet)
<B787_300>
Also something I would love to see a study on... with a given telescope and sensor set up how long is a set of flats good for in a normal environment
<iximeow>
oh yeah
<B787_300>
Because aiui flats are for correcting for dust on the lenses/mirrors and any small misalignments
<iximeow>
i'm curious about the same with darks/biases, since those are more for sensor issues which is .. pretty solid state
<iximeow>
darks i've taken months ago are still correct, for the other camera i've used
<B787_300>
Well aiui darks and biases are camera, temp, and integration specific but are good basically until pixels/circuitry start degrading
<B787_300>
I also think flats need to be retaken if you switch sensors on the setup bacause the alignment wont be the same and there might be more dust in the space between the last element and the sensor
<B787_300>
But these are justmusings of an aerospace engineer who has dabbled in astronomy
<B787_300>
Maybe UmbralRaptop could talk an undergrad into doing some research on it...
<B787_300>
Test it by looking at calibration stars throughout the field of view of a sensor
<B787_300>
Would probably teach the student how to post process images as well as how to automate the collects ( if they were smart)
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<oeuf>
!u a̅͏̄͏̅
<galois>
a: U+0061 LATIN SMALL LETTER A
<galois>
̅: U+0305 COMBINING OVERLINE
<galois>
͏: U+034f COMBINING GRAPHEME JOINER
<galois>
̄: U+0304 COMBINING MACRON
<galois>
͏: U+034f COMBINING GRAPHEME JOINER
<galois>
̅: U+0305 COMBINING OVERLINE
<oeuf>
mofh: ^
<oeuf>
!u D̅͏̄͏̅
<galois>
D: U+0044 LATIN CAPITAL LETTER D
<galois>
̅: U+0305 COMBINING OVERLINE
<galois>
͏: U+034f COMBINING GRAPHEME JOINER
<galois>
̄: U+0304 COMBINING MACRON
<galois>
͏: U+034f COMBINING GRAPHEME JOINER
<galois>
̅: U+0305 COMBINING OVERLINE
<oeuf>
whitequark: iirc you like the combining grapheme joiner ^
<oeuf>
mofh: whitequark: nevermind, i am informed the CGJs do nothing here.
<oeuf>
!u D̅̄̅
<galois>
D: U+0044 LATIN CAPITAL LETTER D
<galois>
̅: U+0305 COMBINING OVERLINE
<galois>
̄: U+0304 COMBINING MACRON
<galois>
̅: U+0305 COMBINING OVERLINE
<mofh>
!u Ξ̄̅
<galois>
Ξ: U+039e GREEK CAPITAL LETTER XI
<galois>
̄: U+0304 COMBINING MACRON
<galois>
̅: U+0305 COMBINING OVERLINE
<mofh>
!u Ξ̅̄
<galois>
Ξ: U+039e GREEK CAPITAL LETTER XI
<galois>
̅: U+0305 COMBINING OVERLINE
<galois>
̄: U+0304 COMBINING MACRON
<oeuf>
mofh: i don't have fonts where Ξ̄̅ renders nicely though
<oeuf>
whereas D̅̄̅ works as intended
<mofh>
!u Ξ̄͏̅͏̅
<galois>
Ξ: U+039e GREEK CAPITAL LETTER XI
<galois>
̄: U+0304 COMBINING MACRON
<galois>
͏: U+034f COMBINING GRAPHEME JOINER
<galois>
̅: U+0305 COMBINING OVERLINE
<galois>
͏: U+034f COMBINING GRAPHEME JOINER
<galois>
̅: U+0305 COMBINING OVERLINE
<mofh>
!u Ξ̄͏̅͏̄
<galois>
Ξ: U+039e GREEK CAPITAL LETTER XI
<galois>
̄: U+0304 COMBINING MACRON
<galois>
͏: U+034f COMBINING GRAPHEME JOINER
<galois>
̅: U+0305 COMBINING OVERLINE
<galois>
͏: U+034f COMBINING GRAPHEME JOINER
<galois>
̄: U+0304 COMBINING MACRON
<mofh>
!u Ξ̅͏̄͏̅
<galois>
Ξ: U+039e GREEK CAPITAL LETTER XI
<galois>
̅: U+0305 COMBINING OVERLINE
<galois>
͏: U+034f COMBINING GRAPHEME JOINER
<galois>
̄: U+0304 COMBINING MACRON
<galois>
͏: U+034f COMBINING GRAPHEME JOINER
<oeuf>
aaaaaaaa
<galois>
̅: U+0305 COMBINING OVERLINE
<mofh>
oeuf: so for me the overline renders over the Ξ fine no matter when i put it in the sequence, and the macron never shows up at all
<mofh>
some of that might just be 11-pt terminal font, tho.
<oeuf>
mofh: fancy rendering in terminals invariably fails so *shrug*
<oeuf>
try a proper teggst field
<oeuf>
!seen UmbralRaptop
<galois>
oeuf: I last saw UmbralRaptop at 2019-04-24 - 04:01:36 in here, saying Fun fact: recent versions of OSX break astroimagej
<mofh>
oeuf: depends, this one is decent at anything short of Indic
<oeuf>
mofh: even bidi?
<mofh>
plus like, if it's a terminal and you're lazy and not doing shaping, which is likely b/c all terminal writers seem to be lazy, you can still implement arbitrary combining marks relatively decently by just canonically reordering the sequence of combining marks after a glyph, then just rendering them *before* advancing by the advance width of the glyph they're attached to.
<oeuf>
mofh: and if it does the UBA correctly, what about arabic shaping
<oeuf>
yeah also terminal writers seem to think fixed width is a thing
<mofh>
i haven't checked arabic shaping, bidi is a clusterfuck (as in it implements it correctly but just about no terminal application eggspects that and so you often get hilarity).
<oeuf>
which, tbh, is a bit of a mess
<oeuf>
there are places in Principia where we aren't really sure how to align the code
<oeuf>
sadly I have yet to find something that decently renders code that's not aligned under the assumption of fixed width
<oeuf>
I have seen very nice variable-width code *in print*
<oeuf>
(Programming in Ada (83|95|2005) does that)
<mofh>
i mean fixed-width (or at least multiple-fixed-width, where each char width is an integer multiple of the shortest character width in the font, so like single and doublewidth CJKV fonts) fonts *are* a thing, you just have to select them.
<oeuf>
(but then you need some manner of actually-smart tabulation)
<oeuf>
mofh: well, "character"
<oeuf>
EGC probably
<oeuf>
mofh: and then again that works nicely if you're doing non-shaping scripts, and fails afterwards
<oeuf>
mofh: also CJKV tends to be a non-integer multiple of latin if it's going to look remotely nice
<mofh>
oeuf: okay i've never seen a font where the latin wasn't eggsactly half the width of the CJKV
<mofh>
a CJKV font*
<oeuf>
1.5 is a thing
<mofh>
also sure, but at the point you start doing shaping, any conventional assumption of "width" just goes flying out the window with no hope of retrieval,
<oeuf>
well yes
<mofh>
s/assumption/notion/
<galois>
mofh meant to say: also sure, but at the point you start doing shaping, any conventional notion of "width" just goes flying out the window with no hope of retrieval,
<oeuf>
unfortunately IDEs don't understand tabulation so there's no easy answer
<oeuf>
since largely you're using fixed width just to achieve alignment
<mofh>
i mean yes, but in non-shaped scripts you usually *do* want grapheme-to-grapheme alignment, not just tabulation (at least i find it a lot easier to read, esp. quickly).
<oeuf>
do you really? or do you just want *a lot* of tabulation
<galois>
[WIKIPEDIA] Taquet de tabulation | "Le taquet de tabulation sur une machine à écrire est l'emplacement où le chariot s'arrête. Le taquet est placé manuellement et la touche de tabulation permet de sauter au prochain taquet de tabulation. En bureautique, le même concept est utilisé avec des taquets de tabulation fixes, ou ajustable dans..."
<mofh>
i mean sure, but at what point does there stop effectively being a difference between fixed-witdth-grapheme alignment and alignment via an assload of tabulation?
<mofh>
also i'm amused as to how my brain literally tried to treat that as some sort of long-range-order / symmetry-breaking phase transition question
<oeuf>
well, you wouldn't split a token with padding
<oeuf>
you can pretty much align anywhere *between* tokens though, depending on the style and language
<oeuf>
Ada is very aligny
<oeuf>
so for declarations with initializations A : T := V; it is customary to align the colons and :=
<mofh>
I mean how I would eggspect that being aligned is aligning the colons, start of each T, the := and start of each V
<galois>
[WIKIPEDIA] Tab stop#Elastic tab stops | "A tab stop on a typewriter is a location where the carriage movement is halted by an adjustable end stop. Tab stops are set manually, and pressing the tab key causes the carriage to go to the next tab stop. In text editors on a computer, the same concept is implemented simplistically with automatic,..."
<oeuf>
mofh: well, start of each T is aligned by virtue of spaces having constant width
<oeuf>
mofh: i don't think we're proposing justifying code
<mofh>
...point, yeah, justifying code would very rapidly make everything a nightmare to read.
<oeuf>
comments maybe,
<oeuf>
but proportional fonts for code can look nice, if alignment is handled correctly
<oeuf>
unless of course you are choosing your identifiers so they all have the same length
<mofh>
I mean they can look *acceptable*, I'll settle for that for now, not sure about "nice" yet.
<kmath>
<ClementSalviani> Vous DEVEZ voir ça : Les vitraux des chapelles de Notre-Dame de Paris avant l'incendie en très haute définition, da… https://t.co/PQk25Tgiou
<oeuf>
nice
<oeuf>
mofh: so what do you think, re. the umbral tensors
<mofh>
not sure, i'm only getting to that part of the backlog now
<mofh>
oeuf: for the purposes of diffgeo, that looked pretty reasonable as an overview/intro. mlbaker is right in that those objects tend to all be finite-dimensional anyway.
<mofh>
(QM *is* tricky to do rigorously, esp. after a point, but i'm pretty sure you can get thru most of Sakurai/Shankar just by knowing basic functional analysis + POVM's + Stone-von Neumann/Stone's Theorem and maybe \epsilon C^{*}-algebra theory, i'm also prolly being eggscessive still, and regardless those two texts combined are *way* more in-depth than any QM qual i've ever seen)
<mofh>
(but that's prolly better to ask me, like, in about 14 hours b/c more talks in soon and i still want to make it thru this paper and the like)
<mofh>
also continuing in the silliness: i lost one of my hairclips so i just took one of those flowers that fell off my LED blinkenlights headdress from Lyon and crimped it around some of my hair w/needlenose pliers and i actually like how it looks
<oeuf>
mofh: so the Littré says (translating to IPA for clarity) "[sɛ̃tile], several people say [sɛ̃tije]", whereas whichever edition of the Robert I have says (in IPA in the original obviously, it's a modern dictionary) "[sɛ̃tije], Acad. [sɛ̃tile]" (that is, the 8th edition of the dictionnaire de l'Académie says [sɛ̃tile])
<oeuf>
mofh: so this "ill" gradually switched from [il] to [ij]
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<kmath>
<geolizzy> When I took physics in college, I noticed my prof was marking my papers lower than the guys in my class. When I con… https://t.co/V9QBteR1gC
<uovo>
!wpn UmbralRaptop
* galois
gives UmbralRaptop a mercury club with a bread attachment
<UmbralRaptop>
mofh: incidentally, my last attempt at the QM qual uncovered an error in Sakurai
<UmbralRaptop>
!wpn uovo
* galois
gives uovo a circular hyperbolic singularity
<mofh>
UmbralRaptop: ...
<mofh>
UmbralRaptop: I have *questions* about the difficulty level of your institution's quals now.
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<uovo>
mofh: yes but tbh given the lack of background of UmbralRaptop i also have questions as to how the institution's programme is structured
<uovo>
sure we'll teach diffgeo to people who don't know what a vector space is, no problem,
<uovo>
mofh: the common first year between maths and physics makes a lot of sense in hindsight
<uovo>
mofh: the physics did annoy the mathematicians but :-p
<mofh>
uovo: I mean "we'll teach diffgeo to people who don't know what a vector space is" is pretty common, tbh. it's more "we assume that if you're taking a GR course and/or qual, you've had enough linalg somewhere in your undergrad to make sense of our brisk, shitty introduction to tensor calculus & pseudo-Riemannian manifolds, and if not, well, you're SOL, go figure that out on your own somehow I guess?
<mofh>
don't let the Christoffel symbols bite... too much."
<uovo>
mofh: "we assume [...] you've had enough linalg somewhere in your undergrad to make sense of our brisk" << yes, absolutely, a reasonable assumption, the linalg course can't be in the diffgeo course; but how can that assumption not be true
<uovo>
mofh: how is the programme so structured that it is possible to not have that basis
<mofh>
I mean I don't know, the fault there lies with UmbralRaptop's undergraduate institution.
<uovo>
the university of kansas city notkansas iirc?
<UmbralRaptop>
hrm, maybe?
<UmbralRaptop>
University of Missouri - Kansas City
<uovo>
mofh: why are you liking me a thing for high school teachers
<uovo>
UmbralRaptop: ah, university of notkansas kansas city, not university of kansas city notkansas,
<mofh>
uovo: wrong link >_<
<uovo>
tbh with the tendency of meow city not to be in meow state in the US I am very confused that new york city is in the appropriate state
<UmbralRaptop>
Yeah, part of the University of Missouri system
<mofh>
basically X11 copybuffers suck
<uovo>
mofh: s/copybuffers //
<galois>
uovo thinks mofh meant to say: basically X11 suck
<uovo>
the word copybuffer reminds me of capybary
<uovo>
s/.$/a/
<galois>
uovo meant to say: the word copybuffer reminds me of capybara
<uovo>
have you tried replacing the copybuffer with a capybara
<mofh>
i'm not sure that would be an improvement, pretty sure the capybara would get very annoyed very quickly at being used to store text temporarily repeatedly,
<B787_300>
UmbralRaptop: i think a vampire would be seen in the relfector unless they were using a silver coated mirror
<UmbralRaptop>
hrm
<UmbralRaptop>
What are the alchemical properties of aluminum?
<B787_300>
as that was why the myth started... most old mirrors were silvered and they thought silver was a "pure" metal and wouldnt reflect the "impure" vampires
<B787_300>
expensive...
<B787_300>
like i am pretty sure they knew of aluminium but it was so expensive most didnt bother with it
<Iskierka>
aluminium was first isolated in 1824
<UmbralRaptop>
Aluminum causes UB on vampires then, I guess?
<uovo>
Iskierka!
<uovo>
!wpn Iskierka
* galois
gives Iskierka a lorenz katyusha
<uovo>
<mofh> uovo: wrong link >_< <<< okay but what was the right link then,
<mofh>
poke me in a few hrs, have to run off to more talks now
<Iskierka>
meow
<uovo>
*scritch*
<e_14159>
If vampires are not reflected in mirrors, doesn't that mean that they're immune to sunglight as long as they're in front of a mirror?
<galois>
e_14159: 2019-04-04 - 14:22:38 <SnoopJeDi> tell e_14159 it's a constant struggle. humility is hard :\
<e_14159>
o_O
<e_14159>
I haven't written anything in a long time.
<uovo>
!wpn whitequark
* galois
gives whitequark a hyperbolic divergent railgun
<uovo>
!wpn e_14159
* galois
gives e_14159 a keen rectangle
<e_14159>
I feel like I might have gotten the short stick.
* e_14159
gives uovo a short stick
<uovo>
standoff stick
<UmbralRaptop>
The mirror immunity also means that vampires are unaffected by moonlight
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<UmbralRaptop>
… why is my relativity final scheduled for 0730?
<SnoopJeDi>
If devs could speak English, we would not understand what they had to say
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<UmbralRaptor>
Thing I heard about today: student does really clever reverberation mapping with YSOs. Student is now unemployed (searching for postdocs)
<galois>
[WIKIPEDIA] Luna moth | "The Luna moth (Actias luna) is a Nearctic moth in the family Saturniidae, subfamily Saturniinae, a group commonly known as giant silk moths. It has lime-green colored wings and a white body. The larvae (caterpillars) are also green. Typically, it has a wingspan of roughly 114 mm (4.5 in), but can exceed..."
<uovo>
> A parasitic fly deliberately introduced to North America to be a biological control for the invasive species gypsy moth appears to have had a negative impact on Luna moths and other native moths.
<SnoopJeDi>
UmbralRaptor, wait they did something clever and got fired? WTF?
<UmbralRaptor>
SnoopJeDi: No, they graduated successfully. Just no jobs in their subfield
<SnoopJeDi>
OH, okay
<UmbralRaptor>
It's still just… ow
<uovo>
UmbralRaptor: okay so let v and w be elements of V, ц and щ elements of V*. For concreteness, let's say v = x^17 - x^2 + 1, w = x^3 - 2, ц = (evaluate at 1), щ = (integrate from -1 to 1).
<uovo>
UmbralRaptor: now define ц⊗щ as the rational-valued function of two elements of V, (ц⊗щ)(v, w) := ц(v) * щ(w)
<uovo>
UmbralRaptor: "⊗" is read "tensor"
<uovo>
UmbralRaptor: recall that one of the names for the elements of V* (like ц and щ) was "linear form"
<uovo>
UmbralRaptor: ц⊗щ is a "bilinear form"
<uovo>
UmbralRaptor: (it is left as an eggsercise to the reader to compute ц(v) * щ(w) with the eggsample values of v, w, ц, and щ)
<uovo>
-4 i think?
<uovo>
UmbralRaptor: anyway
<mlbaker>
UmbralRaptor: so now seeing this bilinear form thing, you're like 'wait, so it's not a linear map?' and you wonder whether you have to take a whole other course on 'multi-linear algebra' now
<mlbaker>
UmbralRaptor: and the tensor product is the thing that reduces multilinear algebra to linear algebra
<uovo>
indeed
<uovo>
UmbralRaptor: and first of all, you can look at what happens if you feed only one vector to (ц⊗щ) instead of two
<uovo>
(ц⊗щ)(v, _)
<uovo>
it's hungry for another vector
<uovo>
you get something that will take a vector and will give you a scalar
<uovo>
but, we know what that is
<uovo>
that's an element of V*
<uovo>
specifically, it's ц(v) * щ
<uovo>
UmbralRaptor: so, ц⊗щ is a bilinear form on V, and by virtue of being that, it's also a linear map from V to V*
<UmbralRaptor>
* is • ?
<uovo>
* here is just scalar * vector
<uovo>
I should probably drop it
<uovo>
it induces confusion
<uovo>
well, scalar times linear form here
<SnoopJeDi>
I love watching uovo talk about math
<uovo>
ц(v)щ
<mlbaker>
(ц⊗щ)(v, _) sends w to ц(v)щ(w)
<uovo>
and that's by definition ц(v)щ, as you can see in your backlog
<uovo>
though last time we used greek for the dual space
<uovo>
but cyrillic is nicer
<uovo>
UmbralRaptor: now, that bilinear form isn't just a linear map from V to V*, it is a linear map from V to V* in two different ways for the same price!
<uovo>
UmbralRaptor: namely, (ц⊗щ)(_, w), you can play the same trick with the other parameter
<uovo>
and then you get щ(w)ц
<uovo>
UmbralRaptor: does that make sense
<UmbralRaptor>
because щ(w) and ц(v) are scalars?
<uovo>
yup
<uovo>
because ц and щ are scalar-valued linear functions of V, aka elements of V*
<uovo>
UmbralRaptor: now the astute diapsid way notice that in the definition (ц⊗щ)(v, w) := ц(v)щ(w), the right-hand side is rational-by-rational multiplication, which commutes
<uovo>
not sure where i'm going with that though, so nevermind
<uovo>
UmbralRaptor: so, ц⊗щ is a bilinear form on V (and bilinear forms on V are linear maps from V to V* in two ways).
<uovo>
UmbralRaptor: there are bilinear forms that can't be written as ц⊗щ for some ц and щ though
<uovo>
UmbralRaptor: those things that can be written ц⊗щ are called "pure tensors"
<UmbralRaptor>
Not to be confused with "pure states"
<uovo>
UmbralRaptor: precisely, they are the same thing
<uovo>
the density matrix for a pure state is a pure tensor
* UmbralRaptor
blinks
<uovo>
for a mixed state, it may not be written ц⊗ц for any state ц
<uovo>
(modulo some kets and bras, we'll get to braket notation later)
<uovo>
UmbralRaptor: have you heard about the density matrix
<uovo>
it's called ρ a lot of the time
<UmbralRaptor>
yes, I think. How to get it/density of states was rather unclear
<galois>
[WIKIPEDIA] Density matrix#Definition | "A density matrix is a matrix that describes the statistical state of a system in quantum mechanics. The density matrix is especially helpful for dealing with mixed states, which consist of a statistical ensemble of several different quantum systems. The opposite of a mixed state is a pure state. State..."
<uovo>
UmbralRaptor: okay, so how do you get those mixed tensors
<UmbralRaptor>
uovo: weighted sums of the pure states?
<uovo>
yeah, linear combinations of pure tensors
<uovo>
UmbralRaptor: for two bilinear forms β and γ, and a rational p, define (pβ+γ)(v, w) the obvious way, := p β(v, w) + γ(v, w)
<uovo>
UmbralRaptor: eggsercise: prove that for all ч,ц,щ in V*, (ч+ц)⊗щ = ч⊗щ + ц⊗щ
<mlbaker>
one thing that might help here is noting the 'standard bilinear form on Q^n'
<mlbaker>
is e^1⊗e^1 + e^2⊗e^2 + ... + e^n⊗e^n
<uovo>
well, yes, but right now we don't have a basis :D
<uovo>
and our main eggsample space is infinite-dimensional muahahaha
<UmbralRaptor>
very large n
<uovo>
(I will make the space finite and introduce a basis sooner or later though)
<mlbaker>
point is just that the pure ones are somehow a very small set
<uovo>
yeah
<mlbaker>
because linear forms kill a lot of stuff (a codimension 1 subspace)
<UmbralRaptor>
This looks like the sort of thing where my proof attempt would get killed by a trap in the order of operations
<galois>
[WIKIPEDIA] Russian cursive#/media/File:Russian Cursive Cyrillic.svg | "Russian cursive is a printed variant of the Russian cursive (when it is reproduced in ABC books and other places) and is typically referred to as (ру́сский) рукопи́сный шрифт, "(Russian) handwritten font". It is the handwritten form of the modern Russian Cyrillic script, used instead of the block letters..."
<UmbralRaptor>
Cursive is what you teach people if you think they write too much
<egg>
UmbralRaptor: see the letters involved here are handwritten as handwritten y, u with a loop, and a double u with a loop,
<egg>
UmbralRaptor: okay now consider the following function of two polynomials v and w
<egg>
β(v, w) := v(0)w(0) + v'(0)w'(0)
<egg>
UmbralRaptor: with ц := evaluate at 0 and щ := evaluate the derivative at 0, β = ц⊗ц + щ⊗щ
<whitequark>
UmbralRaptor: whaat
<whitequark>
re cursive
<egg>
whitequark: UmbralRaptor dislikes writing in cursive i suppose
<UmbralRaptor>
Last I checked, I wrote ~1.5x as fast printing instead of using cursive
<UmbralRaptor>
Quite aside from the sizing and symbol availability problems
<UmbralRaptor>
egg: does d/dx(ц⊗ц) follow the chain rule?
<UmbralRaptor>
uh, product rule
<egg>
uh what
<egg>
ц⊗ц isn't a function of x, it's a bilinear form on V
<egg>
the elements of V can be seen as functions of x (they're polynomials in x)
<egg>
but once you're in V* or in V*⊗V* you have other animals
<dx>
uwu
<egg>
UmbralRaptor: ц⊗ц is "evaluate the product at 0" effectively
<UmbralRaptor>
dx: yeah, this is rather emoticon adjacent
<UmbralRaptor>
egg: ah
<egg>
цщц
<egg>
^ whitequark
<egg>
UmbralRaptor: ц⊗ц + щ⊗щ (evaluate the product at 0, evalute the product of the derivatives at 0, take the sum) is an eggsample of a mixed tensor
<egg>
UmbralRaptor: this is because щ and ц are linearly independent, so you can't use the property that you just proved to turn that into a pure tensor
<egg>
UmbralRaptor: another eggsample: v(0)w'(0) + v'(0)w(0), aka "evaluate the derivative of the product at 0", which can be written ц⊗щ + ц⊗щ
<egg>
um
<egg>
s/ц⊗щ$/щ⊗ц/
<galois>
egg meant to say: UmbralRaptor: another eggsample: v(0)w'(0) + v'(0)w(0), aka "evaluate the derivative of the product at 0", which can be written ц⊗щ + щ⊗ц
<egg>
UmbralRaptor: you should bite when i say absurd things
<egg>
UmbralRaptor: do things make some amount of sense up to now
<UmbralRaptor>
I think so
<egg>
!seen mofh
<galois>
egg: I last saw mofh at 2019-04-24 - 13:06:14 in here, saying poke me in a few hrs, have to run off to more talks now
<UmbralRaptor>
!seen Ellied
<galois>
UmbralRaptor: I last saw Ellied at 2019-04-07 - 01:50:11 in here, saying ah.