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
<egg|zz|egg>
!acr -add-NIMA National Imagery and Mapping Agency
<galois>
Invalid command. Valid forms: !acr -add:LMAO Lagrange Made Awesome Orbits, !acr -redef:ROFL Rare Occultations for Life, !acr -del:IEEE
<egg|zz|egg>
!acr -add:NIMA National Imagery and Mapping Agency
<galois>
Definition added!
<egg|zz|egg>
"Moreover, with the increasing importance of spacecraft observations, the number of coordinate systems we have to deal with has proliferated." *sobbing*
<egg|zz|egg>
mofh: meoooow
<egg|zz|egg>
(The file can also be read with free FORMAT). << mofh: what's free FORMAT
<egg|zz|egg>
do i want to know
<egg|zz|egg>
!wpn mofh
* galois
gives mofh a plutonium linear explosion
<SnoopJeDi>
!how linear is the explosion please, galois?
<galois>
SnoopJeDi: 876 linears
<SnoopJeDi>
thank you galois
<egg|zz|egg>
!why are Phobos, Deimos, and the GNSS satellites not behaving correctly in Principia?
* UmbralRaptor
wonders why a bus that's normally 2 minutes early is 7 minutes late
<_whitenotifier-3d18>
[Principia] eggrobin labeled pull request #2140: Randomized comparison of the Fortran and C++ geopotentials - https://git.io/fjOMA
<UmbralRaptor>
(I didn't do 4 the first time around because I didn't understand what it was asking)
<SnoopJeDi>
the absolute hardest part of any assignment ha
<SnoopJeDi>
At least the feedback is pretty specific, though. It sucks to just get back a number.
<UmbralRaptor>
Today in class: apparently you can add together two things that aren't tensors and get a tensor
<UmbralRaptor>
Math is fake >_<
<SnoopJeDi>
A thread on precisely that has blown up my twitter mentions this morning actually
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<SnoopJeDi>
UmbralRaptop, a nuclear friend of mine wrote a short book on tensors btw, if you'd be interested in looking through it. It helped me a bit, although I confess I'm still rather bad at thinking in tensors the way physics requires.
<UmbralRaptop>
I mean, if I make it through this class, probably the only place in the next 5 years that I will touch tensors is the Levi-cevita symbol for my QM qual >_>
<UmbralRaptop>
(And I get the impression that it uses a different definition of tensor than GR?)
<SnoopJeDi>
I just figured I'd ask, in case it might be of any assistance :)
<SnoopJeDi>
I should probably bug him about picking an explicit licensing scheme for it and putting it on the web
<egg|zz|egg>
largely just different notation, the underlying algebraic structure is the same
<SnoopJeDi>
which is tragic, since the notation can therefore be such an unnecessary hurdle to clear :(
<SnoopJeDi>
It's weird to me that of all the things we talk about Feynman doing, using notation that worked _for him_ doesn't seem to be very celebrated.
<egg|zz|egg>
but then the two notations highlight different aspects, so knowing both can enlighten one as to the properties of the underlying objects
<SnoopJeDi>
oh yes absolutely
<egg|zz|egg>
UmbralRaptop: but also get your hands on a linear algebra textbook or beat mofh into giving you an introduction, being exposed to bras and kets and upper and lower indices without having an idea what the dual of a vector space is is just irresponsible teaching
<SnoopJeDi>
AGREED
<egg|zz|egg>
(isn't linear algebra a common course for both mathematicians and physicists in the US? here it's given to both for the entire first year, same as calculus and physics)
<SnoopJeDi>
It's quite common yes
<UmbralRaptop>
So, fun fact, I didn't have any idea of what a dual of a vector space was until egg|zz|egg explained it, uh, about a month ago
<SnoopJeDi>
But LA here is probably pretty rubbish by your standards on average I think egg|zz|egg
<egg|zz|egg>
in the mountains of the canton of Bern
<SnoopJeDi>
I had a particularly good course with the guy who eventually became my math advisor, it was very influential on me.
<UmbralRaptop>
It is, and upper level physics classes put a great deal of effort into using different notations, and possibly terms
<egg|zz|egg>
SnoopJeDi: well it's first year so it doesn't fly high, but it's joint math+physicists, so you avoid lying too much to children
<SnoopJeDi>
UmbralRaptop, I'm coming around to a mindset that teaching physics/math is basically just a foreign language problem.
<egg|zz|egg>
because some of the children are mathematicians and won't take that :-p
<egg|zz|egg>
(I *may* have repeatedly said "you forgot to assume finite dimension")
<egg|zz|egg>
(well, in german)
<SnoopJeDi>
egg|zz|egg, if we're going to avoid lying, let's stop committing intellectual hate crimes and teach kids in HS that no matrices aren't some arbitrary thing they're a wonderful representation of underlying structure
<egg|zz|egg>
wasn't taught about matrices at all in high school
<UmbralRaptop>
SnoopJeDi: there's a related problem of most teaching materials past calc 3 being for the grothendeciks(sp) of the world
<egg|zz|egg>
but they *are* dependent on a choice of basis, they're not canonical
<egg|zz|egg>
teaching matrices are being *the thing* is vile
<SnoopJeDi>
egg|zz|egg, you would have very much enjoyed a lecture I went to last week, incidentally. I'm pretty sure the speaker was arguing that biological evolution is a projection operator on an "information space" (not in so many words, but the language was suggestive)
<SnoopJeDi>
egg|zz|egg, yes, that's what is done in the US
<egg|zz|egg>
because then you forget that there is an underlying structure
<SnoopJeDi>
largely IME because the people teaching it may not really *understand* the notion that a particular matrix is an artifact of a more 'pure' algebraic idea.
<SnoopJeDi>
Stephenson would call it a cnoon :P
<SnoopJeDi>
and I guess mathematicians just call it a map
<SnoopJeDi>
UmbralRaptop, anyway, if you would ever like that, let me know!
<UmbralRaptop>
uh, probably at some point. I'll be bugging my prof in a bit about some seemingly contradictory stuff in a homework problem or 2
<SnoopJeDi>
It's a much simpler dialogue than most mathematical texts, but that's really the whole point anwyay.
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<SnoopJeDi>
You can always keep a more "robust" reference on your shelf etc.
<SnoopJeDi>
hmm, "thorough" is a better word probably. Nathan's work there is good, it's just focused on being a "notation survival guide" moreso than a magnum opus about mathematical beauty or whatever :)
<egg|zz|egg>
oh yiikes this is going to be confusing
<egg|zz|egg>
its approach to tensors is extremely coordinatey, and then it uses the word dual without qualification for the hodge dual later on?
<SnoopJeDi>
Yea it has some things that could use a touch-up. I just pinged him about the possibility that he's made changes, so maybe I have an older copy. I'd be happy to pass along your thoughts egg|zz|egg.
<egg|zz|egg>
It is what it is, and it chooses to do tensors the way it chooses, but I don't think this will be helpful to UmbralRaptop who seems to be lacking mostly when it comes to algebraic concepts
<SnoopJeDi>
The "extremely coordinatey" bit is I think the survival guide thing, and probably the right idea: this is meant for a reader who *gets* that world, but has really no mental map of tensors just yet. "Start where they are and move them towards the idea"
<SnoopJeDi>
Yea it remains to be seen if it's helpful to him specifically. I thought I'd pass it along, which is about all I can really do here anyway, my own understanding is...not great tbqh.
<SnoopJeDi>
tfw maths degree but very lousy mathematician
<SnoopJeDi>
he wrote this I think as a MSc student and has been a prof for some time now, so it's quite possible he'd be _very_ interested in revising it for professional development reasons, so I do mean what I said about being happy to pass along editorial remarks.
<egg|zz|egg>
precisely since UmbralRaptop is dealing with two different notations for the same thing, explaining without motivating one of the notations seems odd
<SnoopJeDi>
If it's not helpful, I hope he will close the file and disregard it.
<egg|zz|egg>
UmbralRaptop: mathworld is good at relating the various things to each other (e.g. here the "contravariant" wording which generally comes with index notation and the "ket" wording), but is unfortunately scattered across tiny articles http://mathworld.wolfram.com/ContravariantVector.html
<UmbralRaptop>
Also, today we ran into a "covariant derivative" which uses a ∇ for some reason
<SnoopJeDi>
I wish "the web's most extensive mathematics resource" had more suggestions for further reading
<SnoopJeDi>
Although the page for "contravariant tensor" is much better on that matter.
<galois>
[WIKIPEDIA] Covariant derivative#Formal definition | "In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by..."
<UmbralRaptop>
!w manifold (mathematics)
<galois>
[WIKIPEDIA] Manifold | "In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. In this more precise terminology, a manifold is referred to..." | https://en.wikipedia.org/wiki/Manifold
<egg|zz|egg>
UmbralRaptop: well, here you have a pseudo-riemannian manifold
<galois>
[WIKIPEDIA] Pseudo-Riemannian manifold | "In differential geometry, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the requirement of positive-definiteness is relaxed. Every tangent..."
<egg|zz|egg>
UmbralRaptop: the g in that article is the g_μν you know
<UmbralRaptop>
g_{\mu \nu}
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<egg|zz|egg>
and the tensors you manipulate all the time live in tensor products of T_p M (upper indices) and its dual T*_p M (lower indices)
* SnoopJeDi
🔪 index gymnastics
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<_whitenotifier-3d18>
[Principia] pleroy closed pull request #2140: Randomized comparison of the Fortran and C++ geopotentials - https://git.io/fjOMA
<_whitenotifier-3d18>
[Principia] pleroy pushed 3 commits to master [+0/-0/±5] https://git.io/fj3cl
<_whitenotifier-3d18>
[Principia] pleroy 15560f4 - Factor out C++ and F90 computations.
<_whitenotifier-3d18>
[Principia] pleroy 2309c2e - Randomized comparison of the Fortran and C++ implementations of the geopotential.
<_whitenotifier-3d18>
[Principia] pleroy 97a9607 - Merge pull request #2140 from pleroy/GeopotentialTest Randomized comparison of the Fortran and C++ geopotentials
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<UmbralRaptop>
And now some belated responses
<UmbralRaptop>
"<SnoopJeDi> It's weird to me that of all the things we talk about Feynman doing, using notation that worked _for him_ doesn't seem to be very celebrated." <-- "we" largely celebrate clever quips and dickery, really
<UmbralRaptop>
<SnoopJeDi> UmbralRaptop, I'm coming around to a mindset that teaching physics/math is basically just a foreign language problem. <-- I hope not, given my language struggles >_<
<egg|zz|egg>
CHAMP?
<galois>
CHAMP: CHAllenging Minisatellite Payload
<SnoopJeDi>
UmbralRaptop, it's an idea I've been toying with because I've personally found that teaching students to "translate" equations into plain English sentences helps engage them in active reasoning.
<SnoopJeDi>
most recently because of grading some inclined plane problems and seeing the classic sin(θ)/cos(θ) errors, which are so easy to avoid if you just "wiggle the knobs" on what those functions do to your result and see if it makes sense (i.e. does it behave correctly for θ=0, π/2, or more generally any extreme values?)
<SnoopJeDi>
so many students fall into the trap of thinking pushing symbols around is inherently virtuous
<egg|zz|egg>
!seen mofh
<galois>
egg|zz|egg: I last saw mofh at 2019-04-21 - 20:14:55 in here, saying Yes but I've forgotten a lot of background/techniques that I need to figure this out :P
<UmbralRaptop>
!time
<UmbralRaptop>
!seen UmbralRaptop
<galois>
UmbralRaptop: I last saw UmbralRaptop at 2019-04-22 - 17:51:38 in here, saying !time
<UmbralRaptop>
Ah, UTC
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* UmbralRaptop
wonders if Christoffel symbols and Killing vectors just sort of happening represent similar teaching issues
<SnoopJeDi>
probably!
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<SnoopJeDi>
upshot: once you start that wondering, you're on the way to figuring out what notation _does_ make sense for you, and from there you know what the target for translation is >:D
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<egg|zz|egg>
UmbralRaptop: this stuff has a lot of theoretical baggage behind it; you can't really talk about GR without talking about differential geometry so it appears, but making differential geometry appear when you don't have a solid first-year mathematics foundation is utter madness
<egg|zz|egg>
is mofh around
* egg|zz|egg
swats mofh
<egg|zz|egg>
!wpn
* galois
gives egg|zz|egg a !wpn -add:adj scandium javelin
<SnoopJeDi>
yea, it really is >:(
<egg|zz|egg>
!wpn whitequark
* galois
gives whitequark a logarithmic 𒄈
<UmbralRaptop>
AAAAAAAAAⒶⒶⒶⒶ
<egg|zz|egg>
UmbralRaptop: i wonder whether i can inflict a crash course in linalg upon you
<UmbralRaptop>
Also, index notation + Einstein summation is a good way to make endless mistakes in problems, and have *impossible* to translate equations
<SnoopJeDi>
not quite impossible, but it can be extremely audience-inappropriate to be sure.
<oeuf>
well
<oeuf>
it does solve a problem
<SnoopJeDi>
unless you mean "they can be used wrong"
<oeuf>
generally when you have to resort to it, the alternative is unappealing
<oeuf>
but again, behind it is a theoretical framework
<oeuf>
if you don't see that the indices correspond to Vs and V*s in the tensor product, and that their summing together is a natural operation, it's just pushing piles of chalk around
<oeuf>
which then leads to mistakes because nothing makes sense to start with
<oeuf>
Kreidehaufen (phrase stolen from Herr Professor Struwe)
<oeuf>
s/or/or Doktor/
<UmbralRaptop>
I mean, this was eggsplicitly introduced so that we'd have shorter equations… ¯\_(ツ)_/¯
<galois>
oeuf meant to say: Kreidehaufen (phrase stolen from Herr Professor Doktor Struwe)
<oeuf>
UmbralRaptop: well, yes, but why is sensible to sum a^i_j b^j and why a^ij b^j is an abomination doesn't seem to have been communicated to you
<UmbralRaptop>
correct
<UmbralRaptop>
And the textbook / lectures suggest that I'm supposed to know this intuitively
<oeuf>
it makes sense for a textbook or lectures to assume you have been through introductory linalg; less so for the programme to put you through GR (or diffgeo, effectively) without having been through it
<UmbralRaptop>
introductory as in a freshman or sophomore level class, or first/second year head student? This matters because the class is mostly undergrads
<oeuf>
i don't know what makes a man fresh or what a sophomore is, or how you end up separating the head from the rest of the student, and the concept of (under)grad doesn't fully apply here
<oeuf>
introductory as in first year at university in continental european systems
<oeuf>
non-french
<oeuf>
let's not bring the french systems into the discussion, lest sanity be lost forever
<UmbralRaptop>
s/head/grad/
<galois>
UmbralRaptop meant to say: introductory as in a freshman or sophomore level class, or first/second year grad student? This matters because the class is mostly undergrads
<oeuf>
i think i mean undergrad
<UmbralRaptop>
ah
<UmbralRaptop>
>_<
<oeuf>
as in, the year wot you teach calculus and linalg
<UmbralRaptop>
literally every matrix I ran into before this class was A_ij, and those were usually not written >_<
<oeuf>
the notation is one thing, i don't necessarily expect ^i _j except at the end in the very tensoriest bit of the linalg course
<oeuf>
but familiarity with V* or the tensor product (both in coordinates and in the abstract)
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<egg|zz|egg>
mofh: miaou
<mlbaker>
ya-ong
* UmbralRaptor
chirps at mlbaker in confusion
<UmbralRaptor>
a pseudo-Riemannian manifold,[1][2] also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate.
<UmbralRaptor>
I'm now having nightmares about a manifold that uses weirstrass functions
<oeuf>
UmbralRaptor: without the pseudo- it says positive definite instead of nondegenerate
<oeuf>
UmbralRaptor: you can say positive semidefinite instead of nondegenerate, which makes things more eggsplicit
<mlbaker>
the most interesting case is prolly the lorentzian case though, which is indefinite
<mlbaker>
UmbralRaptor: ya-ong is the sound korean cats make