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.
<soundnfury> !wpn egg|zzz|egg
* Qboid gives egg|zzz|egg a proactinium gegenschein
<soundnfury> pro*t*actinium?
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* egg|zzz|egg pokes bofh with bop
<egg|zzz|egg> bofh: x coordinates in the jool barycentre frame, 5 a scaled to 1 s https://drive.google.com/drive/folders/0B4y-shYXMH9BblI0QzN4Z3ozQTQ?usp=sharing
<egg|zzz|egg> UmbralRaptor: ^ silly retrobop noises!
<SnoopJeDi> hah, that's amazing!
<egg|zzz|egg> mosquito bop
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<soundnfury> that's better, we don't need two of them
<soundnfury> (one egg is un oeuf!)
oeuf is now known as egg|zzz|egg
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<UmbralRaptor> Bigelow knows what Americans want in tea: https://photos.app.goo.gl/vUwYCg29x3WODdoS2
<SnoopJeDi> 'Mericuppa
<UmbralRaptor> Moar caffeine!
<SnoopJeDi> bofh, your RT of the Rejected Princesses guy taught me that he made a book and I am beside myself with delight over this
<SnoopJeDi> trying to work out exactly how much trouble I'd be in if my 6 y/o niece gets a copy for Christmas
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<egg|zzz|egg> !wpn UmbralRaptor
* Qboid gives UmbralRaptor a smooth pentagon
<egg|zzz|egg> !wpn bofh
* Qboid gives bofh a ½λ pharmacology
<egg|zzz|egg> !wpn Iskierka
* Qboid gives Iskierka an adiabatic metric-like stinger
<Iskierka> metric-like?
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<G-Mobile> it's part of a set that are mostly multiples of 10 apart
<egg|zzz|egg> !seen bofh
<Qboid> egg|zzz|egg: I last saw bofh on [16.09.2017 14:43:46] in #kspacademia saying: "http://www.nhc.noaa.gov/graphics_at4.shtml?cone#contents tropical storm Lee, apparently"
<soundnfury> !wpn egg|zzz|egg
* Qboid gives egg|zzz|egg a prefix-free ring
<kmath> <scanlime> Tuco and Luna are enjoying the birds outside https://t.co/WfCi0x3FKP
<kmath> <scanlime> Tuco has a lot of claws https://t.co/v1M0p6OTZY
<G-Mobile> if you emit a photon at an imperfect reflector, what happens? is the imperfectitudinality of the reflector a representation of non-reflective imperfections in the reflector, some statistical loss in the reflection process, both?
<G-Mobile> egg, have you considered owning more cats?
<kmath> <GeologyCat> GeologyCat is subducting https://t.co/MOTD6iC1Fs
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<kmath> <stuartisett> @JElvisWeinstein @thaicam Something like this? https://t.co/Zw5piPSLYh
<egg|zzz|egg> <egg|zzz|egg> bofh: x coordinates in the jool barycentre frame, 5 a scaled to 1 s https://drive.google.com/drive/folders/0B4y-shYXMH9BblI0QzN4Z3ozQTQ?usp=sharing
<bofh> SnoopJeDi: wait, he made a book? I need to get it
<bofh> egg|zzz|egg: ooh, grabbing
<egg|zzz|egg> bofh: also, speggtra https://i.imgur.com/Xx2U0iL.png
<egg|zzz|egg> guess which one is bop :-p
<bofh> bop is amausing
<bofh> amusing*
<bofh> the yellow one? :P
<bofh> well, orane
<bofh> orange*
<bofh> christ this keyboard
<bofh> holy chaotic orbit, Bop
<bofh> which one is purple, btw?
<egg|zzz|egg> laythe I think
<bofh> yeah that corresponds to what I hear, too (just listened to all of them now)
<egg|zzz|egg> jool is obviously a weighted mix of the 3 heavy moons
<egg|zzz|egg> bofh: fun thing with that spectrum is that it's really hard to give a meaningful mean orbital period for retrobop
<egg|zzz|egg> whereas the other moons are quite sharp
<bofh> https://science.energy.gov/news/doe-science-at-40/ what the fuck, Quark-Gluon Plasma is essentially superfluidic instead of weakly-interacting?!
* egg|zzz|egg pokes whitequark with a gluon
<bofh> egg|zzz|egg: well yes, it seems retrobop has orbital behaviour roughly comparable to Hyperion's axial rotation
<egg|zzz|egg> :D
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<egg|zzz|egg> bofh: as a function of period (in days), https://i.imgur.com/A5NtbkV.png and logarithmic https://i.imgur.com/8HrjNPE.png
<egg|zzz|egg> um, swapped the links
<egg|zzz|egg> bofh: interestingly Tylo's interaction with retrobop seems to have a fairly sharp period
<egg|zzz|egg> although retrobop itself doesn't Ꙩ_ꙩ
<bofh> what the. that's interesting.
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<egg|zzz|egg> VIMS?
<egg|zzz|egg> !acr -add:VIMS Visible and Infrared Mapping Spectrometer
<Qboid> egg|zzz|egg: I added the explanation for this acronym.
<whitequark> egg|zzz|egg: hi
<egg|zzz|egg> !wpn whitequark
* Qboid gives whitequark a stabbity checker
<egg|zzz|egg> whitequark: retrobop is weird! https://i.imgur.com/A5NtbkV.png
<soundnfury> egg|zzz|egg: what's that, a spectrogram?
<egg|zzz|egg> bofh: wait no that's not even Tylo, that's *Vall*'s interaction with retrobop? wtf
<soundnfury> (I can't tell, because someone didn't label their axes)
<egg|zzz|egg> yeah, Fourier transform of the x coordinate
<egg|zzz|egg> x axis is the period in days
<soundnfury> that is gloriously insane
<bofh> retrobop is fittingly insane
<soundnfury> how come our solar system doesn't have any chaotic multibody systems like that? :(
<egg|zzz|egg> I'll need to write a follow up with those spectra some day
<egg|zzz|egg> also eventually I'd like to estimate the ляпунов eggsponents of that mess
<egg|zzz|egg> (and maybe some statistics about how likely things are to break down?)
<egg|zzz|egg> whitequark: how is котя doing
<soundnfury> !wpn bofh
* Qboid gives bofh an invertible sickle
<bofh> !wpn soundnfury
* Qboid gives soundnfury a torx LART
<soundnfury> seems more like something you should have…
<bofh> egg|zzz|egg: yeah, some proper dynamical systems analysis sounds in order, but is tricky
<bofh> soundnfury: LOL indeed
<egg|zzz|egg> bofh: I'm utterly puzzled by this apparent interaction between vall and retrobop Ꙩ_ꙩ
<APlayer> Phew. Okay, vectors in JS are implemented. Next goes the rest of the RK4 maths crap
<egg|zzz|egg> bofh: wait it looks like this has the right period for being that spike in the frequency graph? Ꙩ_ꙩ
<egg|zzz|egg> period whatever
<bofh> sec
<bofh> what the hell is the red stuff at 5*10^7?
<egg|zzz|egg> bofh: so that's the apsides of everything as a function of time
<egg|zzz|egg> bofh: red is vall, as always
<egg|zzz|egg> bofh: yes, the eccentricity of vall oscillates on a weekly basis
<egg|zzz|egg> no, this makes no sense
<egg|zzz|egg> bofh: that's also why vall's orbit is so wide on the 5-year trace
<bofh> I was about to say, the eggsentricity is oscillating on that short of a period?
<egg|zzz|egg> :D
<bofh> OH. that would do it
<APlayer> egg broke the universe
<bofh> purple is remarkably stable in comparison
<egg|zzz|egg> yup
<egg|zzz|egg> bofh: doesn't seem to obviously correspond to a harmonic of something else
<egg|zzz|egg> ;rpn 2 5 /
<kmath> egg|zzz|egg: 0.4
<egg|zzz|egg> bofh: um, Tylo and Vall seem uncomfortably close to a 2:5 resonance?
<bofh> interesting. they quite possibly are, up to perturbation at least
<egg|zzz|egg> ... as are vall and laythe?
<egg|zzz|egg> ;rpn 1.618 4 /
<kmath> egg|zzz|egg: 0.4045
<egg|zzz|egg> bofh: ah right, I put their osculating orbits rather close to that resonance :-p
<bofh> ...*facepalm*
<egg|zzz|egg> bofh: well I had tried to make them dissonant by shoving a φ in there :-p
<whitequark> egg|zzz|egg: sleeping
<egg|zzz|egg> whitequark: does she try to fend off эта хуйня now?
<egg|zzz|egg> bofh: well, still the 4:10:25 resonance is much better behaved than the stock 1:2:4
<egg|zzz|egg> bofh: there's a very strange spike in the spectra of laythe and vall, which is not at 5 laythe periods but slightly above that somehow
<egg|zzz|egg> (there's also a tiny spike in Laythe's spectrum exactly at 5 laythe periods, but that's to be eggspected)
<egg|zzz|egg> bofh: :-p
<kmath> <bofh453> *facepalm*. https://t.co/4WLm1KpOvS
<kmath> <stephentyrone> @apontious https://t.co/O6ZE8RY65H
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<whitequark> egg|zzz|egg: yeah, she does it pretty well, actually
<whitequark> what helped is taking эта хуйня by the scabbard and pointedly slapping in front of котя
<whitequark> so she understood that she is, in fact, allowed to do that too
<egg|zzz|egg> :D
<egg|zzz|egg> !wpn bofh
* Qboid gives bofh a lead diprotodon
<soundnfury> !wpn egg|zzz|egg
* Qboid gives egg|zzz|egg a sonic screwdriver/compactification hybrid
<soundnfury> ah! both can be used to solve contrived problems in unexplained ways!
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<bofh> touché
<APlayer> Uh, I may need some help
<APlayer> Some may remember when I was working on a tool to simulate low thrust maneuvers and you guys taught me that RK4 is a thing...
<APlayer> Now, for RK4, I need a t0 and a t1, right? That is, t1 has to be defined, or may I omit that?
<egg|zzz|egg> bofh: so that spike in Vall's spectrum near Bop doesn't seem to be a resonance with anything else that I can see Ꙩ_ꙩ
<egg|zzz|egg> but then I'm also seeing nothing at 2 tylo periods = 5 vall periods in the spectra?
<egg|zzz|egg> bofh: oh, there's a lot of 4/φ weirdness in those spectra, that laythe/vall weird spike is 4/φ from the spike in vall's spectrum near bop...
<bofh> heh. next time, don't cram a φ into your orbital elements :P
<UmbralRaptor> Use a more safely transcendental number?
<UmbralRaptor> APlayer: t1 is the time you're finding the values for and t0 is the tine you already know them, I assume? Notation varies. But if I'm correct, t1 is just t0 plus your time step.
<UmbralRaptor> Greys: blarg, everything I did with reflection was purely classical. >_>
<APlayer> t0 is the time when the simulation starts, t1 is the time when the simulation ends.
<UmbralRaptor> That makes t1 sound unnecessary.
<APlayer> Okay, that solves my problem. Thanks!
<UmbralRaptor> Though for testing, you probably wan it to stop after a few tinesteps?
<UmbralRaptor> *timesteps
<soundnfury> Greys: at least for radio waves reflecting off metal, I believe the loss is in the form of resistive heating in the reflector (due to the evanescent-wave currents flowing therein)
<soundnfury> optical frequencies may be more complicated, because the wavelength is small enough for Weird Quantum Shit™ to happen with the atoms of the reflector
<UmbralRaptor> It's possible that properly quantum stuff is more a feature of xray optics.
<soundnfury> well, quantum stuff with the atom size near λ is an xray thing, but quantum stuff with electron jumps near hf is a feature of visible-light optics
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<egg|zzz|egg> bofh: well why is φ such a bad choice though, doesn't its continued fraction make it the best choice to prevent resonances?
<bofh> erm, I was under the impression resonances are *desired* :P
<bofh> it's not a bad choice if you explicitly want to prevent them
<egg|zzz|egg> bofh: not really
<bofh> tho now I'm curious how something transcendental would fare instead
<egg|zzz|egg> bofh: the galilean moons suggest that of course, and that's why the devs (well nova) went with 1:2:4
<bofh> (but not π for obvious reasons
<bofh> +)*
<egg|zzz|egg> but jool is a couple of orders of magnitude too light
<egg|zzz|egg> the resonance destabilizes things
<bofh> what's jool's GM?
<egg|zzz|egg> UmbralRaptor: you remember numbers iirc
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<egg|zzz|egg> bofh: well our astronomer is afk, but https://wiki.kerbalspaceprogram.com/wiki/Jool
<egg|zzz|egg> bofh: <UmbralRaptor> If you take Kerbin to be Earth, Jool is an underweight Saturn orbited by 3 terrestrial planets.
<bofh> ahh.
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<UmbralRaptor> egg: not the eggsact numbers, but see above quote.
<UmbralRaptor> Jool's 80 kerbins, Saturn is 90ish Earths.
<kmath> <PHDcomics> Inner voices https://t.co/0DT45kk9Yy https://t.co/qkbma0VVEC
<bofh> Ahh.
<bofh> also 3 terrestrial planets + Bop & Pol, no?
<UmbralRaptor> Yeah.
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<egg|zzz|egg> UmbralRaptor: also what do you think of those boppy sounds
<egg|zzz|egg> bofh: but besides jool being tiny, resonances generally get messy
<egg|zzz|egg> something something Nice
<UmbralRaptor> Bop and Pol are on the light end for "normal" gas giant moons IIRC.
<UmbralRaptor> So they're monsters for captured asteroids.
<egg|zzz|egg> :D
<UmbralRaptor> Uh, I'd need to be relinked the sounds?
UmbralRaptor is now known as SpreadsheetRaptor
<egg|zzz|egg> SpreadsheetRaptor: x coordinates in the jool barycentre frame, 5 a scaled to 1 s https://drive.google.com/drive/folders/0B4y-shYXMH9BblI0QzN4Z3ozQTQ?usp=sharing
<egg|zzz|egg> bofh: hm, I'd need to compute the spectra absent bop, or with 2:5 resonances instead of 1:4ф dissonances to see how things change...
<egg|zzz|egg> so many simulations to run
<egg|zzz|egg> s/4φ/4\/φ/
<SpreadsheetRaptor> Bop is actually an insect.
<egg|zzz|egg> !u фφ
<Qboid> U+0444 CYRILLIC SMALL LETTER EF (ф)
<Qboid> U+03C6 GREEK SMALL LETTER PHI (φ)
<SpreadsheetRaptor> Also, ow at Laythe.
<egg|zzz|egg> argh so many keyboald layouts
<egg|zzz|egg> SpreadsheetRaptor: ah yes it does get high-frequency
<bofh> it's the innermost moon, so that makes sense
<egg|zzz|egg> bofh: thing is φ itself has a messy continued fraction of course, but 4/φ has a fairly good convergent with 5/2
<soundnfury> yeah, you want something that's just not near any small-number ratios or products thereof. √2 is surprisingly good for that (cf. wolf fifth)
<Ellied> Easy: Use Google's network location service. Hard: Replace it with a third-party middleware and backend that uses Mozilla's location service. Ellie: Carry around a 5 GB database of every known cell tower in the world.
<bofh> egg|zzz|egg/soundnfury: you'll still hit one eventually, the rationals are dense in the reals after all.
<egg|zzz|egg> bofh: the question being how early, 2 and 5 are still fairly smol numbers
<soundnfury> yeah see φ:1 sounds like a slightly sharp minor sixth, whereas √2:1 sounds like the actual devil
<soundnfury> (the best intonation I've been able to find for it is 45/32)
<soundnfury> egg|zzz|egg: maybe you should have used Farey sequences.
<egg|zzz|egg> soundnfury: what about 7/5 for √2?
<soundnfury> that's not quite as close
<soundnfury> but point taken
<soundnfury> that _is_ the interval between a justly intoned major third (5:4) and minor seventh (7:4), which _is_ six semitones.
<egg|zzz|egg> soundnfury: and even failing that you have the next convergent, 17/12, and here you're getting really close
<soundnfury> egg|zzz|egg: yes but 17 isn't a number
<egg|zzz|egg> :D
<soundnfury> (at least as far as musical intonation is concerned :P)
<soundnfury> I mean, you show me a string or pipe playing its 17th harmonic
<bofh> Ellied: where does one get this 5GiB database?
<egg|zzz|egg> !wpn bofh
* Qboid gives bofh a hafnium ?
<bofh> *a* hafnium? like are we talking 1 atom, 1 mol, what?
<egg|zzz|egg> bofh: it says a hafnium ?, is the ? not rendering for you?
<soundnfury> !u ?
<Qboid> U+1F4A9 PILE OF POO (?)
<egg|zzz|egg> bofh: also, still no news from atlas on rootn vs squareRoot?
<bofh> ahh. yeah, it inexplicably failed to render here. *glares at fonts on this machine*
* egg|zzz|egg stares at atlas's fluffiness https://twitter.com/stephentyrone/status/909246104331538433
<kmath> <stephentyrone> @apontious https://t.co/O6ZE8RY65H
<bofh> egg|zzz|egg: no reply in-thread, guess I'll poke in PM now
<egg|zzz|egg> <soundnfury> that _is_ the interval between a justly intoned major third (5:4) and minor seventh (7:4), which _is_ six semitones.<<< also sounds like you want http://organ-au-logis.pagesperso-orange.fr/Images/Mersenne/Mersenne23p48.gif or maybe http://organ-au-logis.pagesperso-orange.fr/Images/Mersenne/Mersenne23p49.gif
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* soundnfury gives egg|zzz|egg a logic piano
<Ellied> bofh: OpenCellID and Mozilla. F-Droid has a "Local GSM" location backend for microg that will download from both.
<Ellied> (for the former you need to give them your name and email for an API key)
<Ellied> so "every known cell tower in the world" is a stretch to say the least, but they at least appear to have quite good coverage in major population centers.
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<bofh> tbh I just use gps, but this is still useful info to have
<Ellied> I spend a lot of time inside buildings, and for some reason it doesn't seem to want to save GPS data for last-known-position stuff
<egg|zzz|egg> !wpn u
* Qboid gives u a serpentine radius
<egg|zzz|egg> um
<egg|zzz|egg> !wpn SpreadsheetRaptor
* Qboid gives SpreadsheetRaptor a radon surjective bomb
<Ellied> There is also a backend that will use GPS data to maintain a local database of wifi networks for location
<Ellied> that is, wifi AP BSSIDs.
SpreadsheetRaptor is now known as UmbralRaptor
<UmbralRaptor> attwifi location: everywhere
<egg|zzz|egg> !wpn UmbralRaptor
* Qboid gives UmbralRaptor a postorder pharmacy/ideal hybrid
<Ellied> UmbralRaptor: well, that's why I corrected myself to BSSIDs, because it's keying in on the individual broadcast stations instead of the whole network.
<UmbralRaptor> !wpn egg|zzz|egg
* Qboid gives egg|zzz|egg a Sturm-Liouville license
<UmbralRaptor> Ellied: ah
<Ellied> I don't know if it actually triangulates or just assumes "hey, I can see that one, I must be within a few meters of it"
<FluffyFoxeh> pretty
<soundnfury> egg|zzz|egg: if I drop you in a lake, do you become an œ?
<Ellied> UmbralRaptor: so, another step towards understanding trans health care as well as 1930s Germany did?
<UmbralRaptor> Something like that.
<egg|zzz|egg> !wpn котя
* Qboid gives котя a praesiodymium homomorphism
<egg|zzz|egg> !wpn whitequark
* Qboid gives whitequark a cone
<UmbralRaptor> Ellied: though hopefully without the destruction of records part this time. =S
<UmbralRaptor> !wpn egg|zzz|egg
* Qboid gives egg|zzz|egg a basilect
<Ellied> Hopefully.
<Ellied> Granted, destroying records is considerably harder in the modern age than it was back then.
<Ellied> All they had to do was set a library on fire and it was over. Nowadays most records are not only multi-site-redundant, but also often stored on media with a better-than-even chance of surviving a building fire.
<Ellied> OTOH, destroying data from said media can now be accomplished in a very short time and can be initiated remotely. :I
<Ellied> I keep thinking about those EPA climate scientists who started backing up all the climate data they could reach onto personal drives a year or so ago in case the administration decided to order its destruction.
<egg|zzz|egg> !wpn UmbralRaptor
* Qboid gives UmbralRaptor a nefarious cow
<egg|zzz|egg> !wpn Ellied
* Qboid gives Ellied a symmetric spiral cut product
<egg|zzz|egg> !wpn rqou
* Qboid gives rqou a trihexaflexagon
<rqou> !wpn egg|zzz|egg
* Qboid gives egg|zzz|egg an arsenic overclocked † which vaguely resembles a banana
<egg|zzz|egg> rqou!
<egg|zzz|egg> rqou: did the eggsplanation make some amount of sense
<UmbralRaptor> "nefarious cow" sounds very Swiss.
<rqou> somewhat
<soundnfury> UmbralRaptor: the nefarious cow is being observed through a sneaky telescope
<soundnfury> !wpn UmbralRaptor
* Qboid gives UmbralRaptor an Ebers-Moll torpedo
<UmbralRaptor> !wpn soundnfury && egg|zzz|egg
* Qboid gives soundnfury && egg|zzz|egg a gregarious polytrope
<egg|zzz|egg> rqou: so <egg|zzz* = (zzz|egg>)*
<rqou> er, so i vaguely know that the QM bra and ket notation is somehow related to adjoints and/or dual spaces, but i don't know anything beyond that
<egg|zzz|egg> rqou: so, typically you write the inner product of vectors v and w <v,w>
<egg|zzz|egg> rqou: sometimes you might see the notation <v|w>
<egg|zzz|egg> rqou: now, <v|.> (. being a placeholder) is a linear function that returns a scalar, aka an element of the dual
<egg|zzz|egg> and then you can apply it to a vector w and get <v|w>
<soundnfury> egg|zzz|egg: "linear form"
<egg|zzz|egg> yes I know soundnfury
<egg|zzz|egg> rqou: the physicists write <v| for <v|.>, and then |w> for a vector w
<soundnfury> (I thought I'd mention it in case that was what he knew it as)
<egg|zzz|egg> good point
<egg|zzz|egg> rqou: so then <v| applied to |w> is <v|w>, which is a fairly neat notation
<egg|zzz|egg> rqou: now say you have a matrix (linear endomorphism, whatever) A; you can multiply A and w, instead of writing that Aw you write it A|w> since you call your vector |w>
<soundnfury> (if you're a co-ordinates thinker like me, <v| is just vᵀ)
* egg|zzz|egg throws soundnfury in an infinite-dimensional vector space without the axiom of choice
* soundnfury stabs egg|zzz|egg with a lemon
<egg|zzz|egg> or v*, we're in a Hilbert space (or v dagger depending whether you're feeling stabbity)
<egg|zzz|egg> well <v| = |v>* really
<soundnfury> egg|zzz|egg: we're _always_ feeling stabbity in here
<egg|zzz|egg> rqou: anyway, the nice thing with that is that you can use an arbitrary matrix as your bilinear form and it looks like you're using a bilinear form: <v|A|w>, which means v* A w, but it clearly looks like we're doing a bilinear thing, whereas v* A w has this weird asymmetry
<egg|zzz|egg> (the proper thing to do would be to not use an endomorphism as a bilinear form of course, and to say that A is a bilinear form that you apply to v and w, A(v,w), but then the coordinated people get annoyed
* UmbralRaptor stabs soundnfury with an orange.
<egg|zzz|egg> or we could use Einstein notation and indices)
<rqou> so one thing that seems a bit weird: if <v| is supposed to be a linear functional, what basis is used to turn it into a vector of numbers?
<egg|zzz|egg> rqou: you don't need a basis, just an inner product
<egg|zzz|egg> the inner product turns v=|v> into <v|, by saying <v| = <v|,.>
<rqou> right, but then there is that "<v| is just vᵀ" thing
<egg|zzz|egg> that's because ᵀ is just that
<egg|zzz|egg> you don't need a basis to transpose
<rqou> i thought transpose is supposed to take a vector and give me a new vector, but the inner product takes a vector and gives me a function
<egg|zzz|egg> you merely need an inner product, vᵀ = <v,.>
<SnoopJeDi> rqou, it's perhaps more accurate to say that the transpose is the operation egg|zzz|egg is describing
<egg|zzz|egg> rqou: a row vector is a linear functional
<SnoopJeDi> i.e. tranposition as she is taught is not the more fundamental concept
<egg|zzz|egg> rqou: or rather it's the coordinates of a linear functional
<soundnfury> UmbralRaptor: but Zorn doesn't have an orange!
<rqou> ah ok
<egg|zzz|egg> rqou: now, in coordinates vᵀ(in the turn the vector sense) = <v,.> is true only taking the inner product which is consistent with the coordinates
<egg|zzz|egg> rqou: which you probably know you can compute as <v,w>=vᵀw
<soundnfury> rqou: if you do want a co-ordinate thinking: (<v|e_x>, <v|e_y>, <v|e_z>)
<egg|zzz|egg> rqou: (and there it's quite obvious that vᵀ = <v,.> since <v,w>=vᵀw right)
<soundnfury> that's how you turn a linear form into a row-vector with a basis
<rqou> but that only works if you're using the standard inner product, right? not some weird one just for lulz
<kmath> <stephentyrone> Twitter truly does not understand its audience. https://t.co/NVk2cy2G80
<egg|zzz|egg> rqou: if you're using an inner product that's inconsistent with your coordinates, then you shouldn't be using the transpose that comes from your coordinates :-p
<egg|zzz|egg> (or at least you should be careful)
<soundnfury> I think it works as long as your inner product distributes?
* soundnfury shrugs
<egg|zzz|egg> rqou: say you're using some other inner product which, in your coordinates, is computed as <v,w>_B = vᵀBw; then in those coordinates, the linear functional induced by <.,.>_B from v is vᵀB
<rqou> ah i see
<egg|zzz|egg> rqou: but let's say you can go to <.,.>_B-orthonormal coordinates with the matrix A: (Av)ᵀ(Aw)=vᵀBw (so that B=AᵀA), then in those coordinates the transpose is as above, and in fact to get the B-transpose of v, you go to those coordinates, get Av, transpose, (Av)ᵀ=vᵀAᵀ, and now use the coordinate transformation for row vectors to go back, vᵀAᵀA)
<egg|zzz|egg> rqou: which is exactly vᵀB