<Majiir> egg: Sense was made
<egg|laptop|egg> egg!
<Majiir> Is there any way, even if it has to be a specialized application, to figure out what h to use without doing all that guessing?
<egg|laptop|egg> Majiir: btw, you may have heard the incantation "RK4", that's just a particular fixed-step one-step method (of the Runge-Kutta kind, and developped by Runge and Kutta), of fourth order. It's kind of meh, but common. back to the eggsplanation
<SnoopJeDi> Domain knowledge always helps, Majiir
<egg|laptop|egg> Majiir: well, you can sort of try heuristics depending on your problem, but it's hard to get something good
<Majiir> How would I apply domain knowledge in, say, orbital mechanics (seeing as egg has that knowledge) to do that?
<egg|laptop|egg> Majiir: but the *magically* above is well-understood
<egg|laptop|egg> and works well
<egg|laptop|egg> so I do that for the predictions, rather than applying orbital-mechanics specific stuff
<egg|laptop|egg> because, well, the general algorithms work well enough so that's what people use
<egg|laptop|egg> Majiir: now, there are several ways to go about the *magically*
<egg|laptop|egg> one method is to integrate with the same method two steps at h/2 and one at h
<SnoopJeDi> An example from PIC simulation, you can analytically work out a limit that avoids (some) garbage results: https://en.wikipedia.org/wiki/Courant%E2%80%93Friedrichs%E2%80%93Lewy_condition
<Majiir> egg, that was the method that came to mind immediately
<egg|laptop|egg> the difference between the more accurate and the less accurate approximates the error, so that's your error estimator
<egg|laptop|egg> another is to integrate with a high and a low order integrator, both one step at h
<egg|laptop|egg> same idea then
<egg|laptop|egg> but then there's the smart thing
<egg|laptop|egg> a high and a low order method for the computational cost of one
<egg|laptop|egg> embedded RK methods!
<egg|laptop|egg> you may have heard of Dormand-Prince (DOPRIwhateverorder) that's this sort of stuff
<egg|laptop|egg> we do that (in RKN form rather than RK because our problem is a 2nd order ODE, so RKN methods are possible and better, but details)
<SnoopJeDi> the short answer is that choosing integration step sizes is a very rich problem, and very much an area of ongoing research
<SnoopJeDi> less so for, say, orbital mechanics than for slightly ickier problems like CFD, but things like multigrid methods etc abound
<egg|laptop|egg> the long answer is "principia is a KSP mod whose bibliography fills a square in my library"
<egg|laptop|egg> SnoopJeDi: PDEs are evil
<SnoopJeDi> I cannot dispute this statement
<egg|laptop|egg> Majiir: if your problem is a PDE, you will need to summon greater madness than mine
<egg|laptop|egg> Majiir: I suggest ferram4
<egg|laptop|egg> Majiir: what is your problem?
<ferram4> Depending on the PDE, the situation becomes... special.
<egg|laptop|egg> :D :D :D
<egg|laptop|egg> I have taken a numerical course that distantly touched on that
<egg|laptop|egg> sparse matrix madness
<egg|laptop|egg> givens rotations \o/
<egg|laptop|egg> also iterative methods
<egg|laptop|egg> wheee
* egg|laptop|egg barfs
<Majiir> egg well
<Majiir> The problem is all problems
<Majiir> It's exploratory! :D
<egg|laptop|egg> Majiir: also, I mentioned my bop writeup https://twitter.com/eggleroy/status/831170357973258240
<kmath_> <eggleroy> a while ago @whitequark mentioned "the goddamn numerical blowup in nbody" apropos KSP; the plight of Bop shows that: https://t.co/JGlyKsd6AK
<egg|laptop|egg> Majiir: Eggsploratory!
<egg|laptop|egg> Majiir: so in general, you can eggspect things like embedded RK to work well
<egg|laptop|egg> unless you encounter stiffness
<egg|laptop|egg> then things are evil
<Majiir> Just to recap so my simple brain can chew on this
<egg|laptop|egg> chomp
<egg|laptop|egg> chomp chomp
<Majiir> Let's say I wanted to model a spherical object falling through an infinite uniform atmopshere
<Majiir> atmosphere, even
<Majiir> Eventually, no matter what its initial velocity, it's going to basically just be falling down at terminal velocity
<Majiir> I would love for that to approach zero processing power per unit time
<egg|laptop|egg> I think that should?
<Majiir> It sounds like I can do this with an adaptive step size since eventually, numerical issues aside, all integrators are going to just kinda shrug and give me the same result: it's going down.
<egg|laptop|egg> Majiir: methods of order k have the property that they solve exactly a problem whose solution is a polynomial of order k
<Majiir> Neat
<Majiir> Now the solution might not be polynomial here, but with enough floating point error it might eventually become that? :D
<egg|laptop|egg> in a way you can see them as fitting a polynomial to the trajectory
<egg|laptop|egg> Majiir: well, when it reaches terminal velocity, it's a line
<Majiir> Yep
<egg|laptop|egg> you hardly get lower-order than that
<egg|laptop|egg> Euler is exact on that
<SnoopJeDi> yea, you can think of numerical solutions as basically a really convoluted fitting problem
<Majiir> Does it ever *precisely* become a line?
<SnoopJeDi> inasmuch as functions are vectors
<egg|laptop|egg> SnoopJeDi: of course they are
<Majiir> If I had a computer with infinite precision, would I be able to toss a ball sideways in this simulation and ever get a linear solution?
<egg|laptop|egg> hmm
<Majiir> My impression is no, if we're talking simple drag equation sort of stuff
<egg|laptop|egg> ferram4: is terminal velocity reached in finite time in that ideal case
<Majiir> but my horizontal velocity will be so small that eventually I get what I want anyway regardless: the integration step just gets huge
<ferram4> Terminal velocity is never reached in finite time in a uniform atmosphere.
<ferram4> It is approached asymptotic
<egg|laptop|egg> Majiir: but then that's because your solution isn't a line, your asymptotic cost will go down fast
<Majiir> Yep
<egg|laptop|egg> so your step will be finite in proportion of the nonfinite time to terminal velocity
<egg|laptop|egg> where proportion here is sloppy and loose
<egg|laptop|egg> but hey
<egg|laptop|egg> it's ten to two I can be imprecise
<ferram4> In a non-uniform atmosphere and with non-uniform gravity it will become even worse. :P
<Majiir> This has been very helpful! I haven't dived into the maths as deeply as you all, but this is exactly what I was looking for
<Majiir> I am trying to size up how much maths I will need to learn for a project
<Majiir> It sounds like not taking differential equations in college was a big mistake
<egg|laptop|egg> Majiir: now I would like to point out a fun thing.
<SnoopJeDi> the upshot is that any course in differential equations is mostly "here are all the tricks in the bag" anyway
<egg|laptop|egg> you mentioned initially the very naive approach (let's call it the shitty game engine method) of doing physics
<SnoopJeDi> Verlet integration?
<egg|laptop|egg> SnoopJeDi: nah, that's the point I want to make
<egg|laptop|egg> it's so close
<egg|laptop|egg> why not do it :-p
<SnoopJeDi> oops :v
<SnoopJeDi> I accidentally the point
<egg|laptop|egg> Majiir: formally, shittygameengine does x1 += v0 dt; v1 += force(x0, t0) dt
<egg|laptop|egg> and you might, naively
<egg|laptop|egg> but
<egg|laptop|egg> this is forward Euler
<egg|laptop|egg> if you learn one thing, it's that it's literally the shittiest correct thing you can do
<ferram4> "correct"
<Majiir> Yeah I knew that coming in, hence why it was my example :)
<egg|laptop|egg> ok, the technical term is the shittiest *consistent* thing
<ferram4> For very wide definitions of "correct"
<egg|laptop|egg> ferram4: consistent.
<Majiir> It's the shittiest passable thing
<egg|laptop|egg> it's consistent
<SnoopJeDi> it's also conceptually simple
<egg|laptop|egg> now
<ferram4> Depends on your system :P
<SnoopJeDi> which has massive value if super-duper accuracy isn't paramount
<egg|laptop|egg> SnoopJeDi: wait a second here
<SnoopJeDi> (which is why it's usually one of the first things you discuss in a numerical methods course)
<egg|laptop|egg> Majiir: for the same cost, and equally simple or simpler code, I can do a massive improvement
<Majiir> Me too, but I'm curious which one you have in mind :D
<egg|laptop|egg> Majiir: x_half = x_minus_half v0 dt; v1 += force(x_half, t0) dt
<egg|laptop|egg> that's a bit confusing because I'm half-functional in my writing here
<Majiir> I get the idea, I've seen this before
<egg|laptop|egg> that's x += v dt; v += f(x, t) dt
<egg|laptop|egg> leapfrog
<egg|laptop|egg> or verlet
<egg|laptop|egg> or Newton, it's in the principia
<egg|laptop|egg> or Delambre
<egg|laptop|egg> or Stoermer
<egg|laptop|egg> ahem
<Majiir> Hehe
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<egg|laptop|egg> Majiir: it's good
<Majiir> So the thing I'm concerned with most isn't accuracy -- not yet
<egg|laptop|egg> well I mean it's 2nd order
<SnoopJeDi> well, Verlet is distinct from leapfrog, the latter means you're updating the position and velocity (or whatever pair you like) at different times
<egg|laptop|egg> better order than Euler's first
<Majiir> It's more about minimizing computation, and also about deferring as much computation as possible
<egg|laptop|egg> SnoopJeDi: they're used interchangeably in various parts of the literature
<SnoopJeDi> There are many ways to be wrong, egg|laptop|egg ;P
<egg|laptop|egg> SnoopJeDi: I will drown you in review articles
<Majiir> I'm willing to accept typical game-physics levels of accuracy, and the systems I expect to model are fairly simple: basic drag models, that sort of thing
<egg|laptop|egg> Majiir: now, this has a very important property
<Majiir> The core thing I'm trying to do is murder fixed timesteps very murderously
<egg|laptop|egg> 2nd order is neat and all
<egg|laptop|egg> but this is symplectic
<SnoopJeDi> The great thing about Verlet Majiir is that it's not really a big step up in complexity, and effectively no change in computational demand, but it gives you such nice stability
<egg|laptop|egg> Majiir: this means that if you give it a pendulum that starts at rest 30 deg off from the vertical, it's not going to fly to 60 deg from the vertical as time goes on
<egg|laptop|egg> which it would with Euler
<egg|laptop|egg> Euler pumps energy into the system
<egg|laptop|egg> this, over the long term, keeps energy sane
<egg|laptop|egg> this is very very important
<ferram4> And allows drag models to somehow cause velocities to increase in certain situations. O_o
<egg|laptop|egg> ferram4: wheeee
<Majiir> Can Verlet be applied to more sophisticated integrators as well, or is that typically part of the definition of the integrator?
<ferram4> Majiir, just remember: fear the long timestep when you're dealing with drag. It is tempting, but sometimes the drag will send your projectile flying back at you faster than it started.
<egg|laptop|egg> SnoopJeDi: I'd argue it's less code complexity if you don't require dense output on both v and x (or are ok with having one of them at half-steps)
<egg|laptop|egg> Majiir: there are more sophisticated symplectic or conjugate symplectic integrators
<egg|laptop|egg> Majiir: Principia has 37 of them
<egg|laptop|egg> Majiir: however
<egg|laptop|egg> sadly
<egg|laptop|egg> tragically
<egg|laptop|egg> horresco referens
<SnoopJeDi> egg|laptop|egg, I meant algorithmic complexity anyhow, since code complexity is going to depend on the expressivity of your language, heh
<Majiir> ferram4, I initially asked because I want to make the timestep long when I *can* and then very short when I *must* -- and I'm curious what techniques there are for that
<egg|laptop|egg> variable stepsize breaks symplecticity
<Majiir> Ahh
<egg|laptop|egg> which is why principia's histories are fixed stepsize
<egg|laptop|egg> we care about not exploding energy
<Majiir> Can I tune my error bounds so that the energy error is also bounded..?
<Majiir> or is this a different mess entirely
<egg|laptop|egg> Majiir: your error bounds on what?
<Majiir> On each integration step
<egg|laptop|egg> you really need symplecticity if you want time-independent energy bounds
<Majiir> Well, I wasn't thinking time-independent
<egg|laptop|egg> now, what you could do is break symplecticity ~not too often~
<Majiir> Again, thinking objects falling here, not orbits
<Majiir> Oh that sounds interesting
<egg|laptop|egg> maybe have a stepsize for low orbits, one for interplanetary stuff?
<egg|laptop|egg> I'm throwing ideas at the wall here
<egg|laptop|egg> there are papers by the shovelload
<Majiir> I would also accept bounded power
<SnoopJeDi> Majiir, is this game-specific
<egg|laptop|egg> doing various things that may be slightly related to what I want
<Majiir> SnoopJeDi, nope
<Majiir> Well, okay, yes
<Majiir> It's specific to games
<Majiir> It's not specific to any particular game :)
<SnoopJeDi> ^ REALLY great articles
<Majiir> I'll take a look, thanks
<SnoopJeDi> http://gafferongames.com/networked-physics/deterministic-lockstep/ remains my favorite "networked games are hard" article
<ferram4> And symplecticity for drag: don't bother, you're basically ignoring the energy removed from drag anyway, so the error isn't that big a deal. Still not nice, but you've basically got a system (your object) that's constantly bleeding energy anyway.
<egg|laptop|egg> that seems overly implementation-oriented and not aiming very far though
<egg|laptop|egg> RK4 is meh :-p
<egg|laptop|egg> and Majiir seems interested is things that border on researchy
* egg|laptop|egg emerges from a sea of numerical integration papers
<Majiir> I am interested in borderline researchy things, but really I'm trying to do my own research on a thing and I don't have all the foundational not-even-that-researchy stuff :D
<SnoopJeDi> the two are not mutually exclusive
<egg|laptop|egg> Majiir: yeah, feel free to ask me, I am very much into that sort of stuff
<Majiir> Like I said, I'm trying to murder fixed timesteps very murderously. That's about all that's set in stone at this point, and the rest is hand-wavey ideas
<egg|laptop|egg> Majiir: btw, I have 138 papers into my papers dir; most of them are principia-related
<egg|laptop|egg> I am pretty much swimming in a sea of numerics papers
<SnoopJeDi> papers dir D:
* SnoopJeDi hugs EndNote
<Majiir> My hunch is that murdering fixed timesteps murderously leads to a whole lot of computational advantages
<egg|laptop|egg> Majiir: it does, but it breaks one of the very few hard guarantees that you can get in that field
<egg|laptop|egg> it all depends on the sort of thing you want to do
<Majiir> Yeah
<egg|laptop|egg> if you're doing orbits, symplecticity is very attractive
<egg|laptop|egg> because the truth is pretty much a cute Hamiltonian that you can pet
<Majiir> So far I'm thinking games, and very particularly excluding the case of orbital simulation games
<egg|laptop|egg> if you're in the ferram4 sector
<egg|laptop|egg> well
<egg|laptop|egg> that's madness
<egg|laptop|egg> there's no Hamiltonian worth mentioning
<Majiir> I figured if I tried to tackle orbit games I'd have to just become an egg anyway
<egg|laptop|egg> no need to even try symplecticity
<egg|laptop|egg> Majiir: well, only a part of egg
<egg|laptop|egg> Majiir: a lot of my madness is just that I have strongly typed myself into many layers of insanity
<egg|laptop|egg> which is good
<SnoopJeDi> With games, it's usually best to just go do something
<egg|laptop|egg> it catches bugs in that physicsy code all the time
<SnoopJeDi> What you build usually sucks and you consider why and you learn a lot in the process
<egg|laptop|egg> SnoopJeDi: nonsense
<egg|laptop|egg> SnoopJeDi: it is good to get stuck building libraries
<Majiir> SnoopJeDi, in this case I am not trying to write any particular game -- but what you say is true about software projects in general
<egg|laptop|egg> for the fun lies in the writing of abstractions
<Majiir> I'm trying to bound my problem a bit, because I've struggled to really develop the idea
<SnoopJeDi> egg|laptop|egg, you are the local authority on writing libraries ;P
<SnoopJeDi> I meant it is best to learn-by-doing with games
<Majiir> I was half hoping egg would tell me that what I want is just impossible and here's a theorem proving it
<Majiir> It's both fortunate and not that he gave me a solution instead :D
<SnoopJeDi> You can read AABB articles all day long and not relaly "get" it
<egg|laptop|egg> Majiir: I can show you my abstractions; they can help perhaps with understanding what is what
<Majiir> show me ur abstractions gurl
<egg|laptop|egg> hah
<ferram4> Ultimately a lot of what you want exactly depends on what your requirements are... which are dependent on what you're trying to do.
<Majiir> Yep
<Majiir> This does help me figure out what to even think about tackling though
<ferram4> Building an integrator is a lot like any other kind of engineering. :P
<egg|laptop|egg> PDE man strikes again :D
<Majiir> It's really helpful to know that fixed timesteps are necessary for simpl..simplececiticity that one
<ferram4> And as a result, they all suck, just to different degrees. :P
<Majiir> It stops me from going down the rabbit hole of trying to figure that out on my own :|
<egg|laptop|egg> Majiir: yeah, it's a fun theorem, I can find you that paper
<egg|laptop|egg> Majiir: welp, first we have the equation (it's the specific kind of equation I care about, 2nd order ODE; good for physics, you have forces) https://github.com/mockingbirdnest/Principia/blob/master/integrators/ordinary_differential_equations.hpp#L42-L72
<ferram4> Fortunately, this is math, and so things can be proven.
<egg|laptop|egg> Majiir: oh note
<egg|laptop|egg> DoublePrecision
<Majiir> I really am imagining egg just drowning in a sea of papers
<ferram4> Also, you have gotten the egg to throw papers at you, take cover.
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<SnoopJeDi> ferram4, which is, after all, just a specific application of Sturgeon's Law
<egg|laptop|egg> your state is a DoublePrecision
<egg|laptop|egg> this is Very Important
<egg|laptop|egg> without compensated summation you will be engulfed by a tidal wave of roundoffs in long-time integration
<ferram4> Nah, we can just simplify things to shorts. It'll be all good.
<Majiir> ^ that was my next question
<Majiir> How does fixed-point do?
<Majiir> (in general)
<Majiir> ...well, in general with integrators
<egg|laptop|egg> it doesn't. Nobody does numerics in fixed point that I know of.
<Majiir> And everybody uses fixed timesteps in game engines with shittygameintegration :D
<Majiir> Is there a reason it's always floating-point?
<egg|laptop|egg> Majiir: note that here, what happens is that lest you fuck up missing a compensated summation, the truncation error (from using an integrator rather than formal integration) will dominate FP error
<Majiir> I understand what you are saying, but I don't follow why that's the case
<egg|laptop|egg> so you use FP because it allows you fancy things like multiplying and understanding what comes out of that, and it's fast, and all glory to our dark Lord Kahan
<egg|laptop|egg> Majiir: well
<egg|laptop|egg> Majiir: I can only give you a conceptual wishywashy answer
<Majiir> That's acceptable
<egg|laptop|egg> if you multiply matrices, the operations you do, in infinite precision, give you the matrix product; exactly. It's a bit convoluted, and the convolutions are there to appease our Lord Kahan. But you're really multiplying matrices.
<egg|laptop|egg> but if you integrate with a fixed step of finite size, and do your computation in infinite precision, then you get a shitty error
<egg|laptop|egg> that you can estimate, and say "it's order k in the size of the step"
<egg|laptop|egg> but still, you have an error
<egg|laptop|egg> formally
<egg|laptop|egg> even if you do it with reals that don't exist
<Majiir> That makes 900% sense
<Majiir> but how do we know those errors dominate?
<egg|laptop|egg> because the steps are kinda large, compared to the sort of things that are FP errors :-p
<Majiir> Haha okay
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<egg|laptop|egg> or because we plot the thing, and we see where we hit the floor of FP
<Majiir> That wasn't as uber cool mathy as I was hoping, but it works :D
<egg|laptop|egg> and there, yes, what limits you is FP
<egg|laptop|egg> but above that floor it behaves like the pretty theoretical polynomials
<Majiir> So basically either you're bound by the integrator which you'd expect, or you're bound by FP which means your integrator is just super good anyway
<egg|laptop|egg> yeah
<egg|laptop|egg> Majiir: or you fuck up FP
<Majiir> That's likely to happen
<Majiir> You will be there to shame me
<egg|laptop|egg> Majiir: that's what plotting is for: behold fucking up FP https://twitter.com/eggleroy/status/815719741990072321
<kmath_> <eggleroy> Double-double sum vs. ill-conditioned compensated summation in multistep integrators: hitting the floor vs. going u… https://t.co/0C7k1P7sUm
<egg|laptop|egg> Majiir: back to abstractions
<egg|laptop|egg> Majiir: we have an ODE
<egg|laptop|egg> those words are useful to know if you come across a paper
<Majiir> egg this is super helpful but I am dressed and need to get foods :X
<egg|laptop|egg> Majiir: then, we have the sort of things we give an adaptive integrator as tunable settings https://github.com/mockingbirdnest/Principia/blob/master/integrators/ordinary_differential_equations.hpp#L94-L117
<egg|laptop|egg> Majiir: ack
<Majiir> syn?
<egg|laptop|egg> Majiir: how long does it take you to get foods
<Majiir> I don't know, like 30-60 minutes
<Majiir> You should sleep
<egg|laptop|egg> ok, say egg when you're back, if I'm awake I'll keep throwing code and papers at you
<Majiir> Okay :D
<Majiir> Seriously, really helpful, I appreciate it a lot. Will try to process my own thoughts and dump them in here for feedback
<ferram4> And now, let's make things interesting. Nonlinear PDEs for everyone \o/
<egg|laptop|egg> hahah
<egg|laptop|egg> oooh wait it's possible
<egg|laptop|egg> Majiir is going to love Hairer and Söderlind 2005
<egg|laptop|egg> muahahaha
<ferram4> Ooh, very nice.
<egg|laptop|egg> yes it was in my papers directory of course :-p
<egg|laptop|egg> I propably have a printout of it somewhere
* egg|laptop|egg swims in the sea of papers
<egg|laptop|egg> this just came to my attention (reshared by eevee), relevant to the discussion https://twitter.com/fermatslibrary/status/838392423063687168
<kmath_> <fermatslibrary> A visualization of chaos: 41 triple pendulums with very slightly different initial conditions https://t.co/CTiABFVWHW
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<egg> !tell majiir tell me to poke you with Hairer and Söderlind; also bring back Soozee.
<Qboid> egg: I'll redirect this as soon as they are around.
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<Qboid> egg: I'll redirect this as soon as they are around.
<kmath_> <eggleroy> <Majiir> I really am imagining egg just drowning in a sea of papers https://t.co/P2iqkDT7CN
<egg> Norgg: egg!
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<UmbralRaptor> "The main focus of this paper is to search Tardigrade water-life on exoplanets…"
<egg> UmbralRaptor: O_o
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<Iskierka> a bit ambitious?
<egg|principia|egg> !wpn UmbralRaptor
* Qboid gives UmbralRaptor a silver yxala
* UmbralRaptor puts the yxala to work on micronerva.
<egg|principia|egg> UmbralRaptor: I am drowning in a sea of mad KSP reference frames and principia pointers in the boonies instead of drowning in a sea of papers
<egg|principia|egg> can I go back to drowning in the sea of papers :'(
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* e_14159 hands egg|principia|egg a bunch of cluster software frameworks.
<e_14159> How about drowning in that instead?
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<kmath_> <eggleroy> <Majiir> I really am imagining egg just drowning in a sea of papers https://t.co/P2iqkDT7CN
<e_14159> egg|principia|egg: Please add a bibliography for that picture.
<egg|principia|egg> hah
<egg|principia|egg> I should update the principia bibliography
<egg|principia|egg> but not today
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<e_14159> What do we say to deadlines?
<egg|principia|egg> :D
<e_14159> But really, there appears to be almost no cluster software nor instructions for my usecase :-/
<UmbralRaptor> Egg should probably use that as a header image on twitter.
<egg|principia|egg> UmbralRaptor: hmm
<egg|principia|egg> UmbralRaptor: that wants a weird shape though, I should take another one perhaps
<UmbralRaptor> blarg
<egg|principia|egg> UmbralRaptor: meh, good enough
<egg|principia|egg> UmbralRaptor: and that way we don't see that the foreground paper was a rather dull one :D
<UmbralRaptor> hah
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<kmath_> <eggleroy> <Majiir> I really am imagining egg just drowning in a sea of papers https://t.co/P2iqkDT7CN
<ferram4> heh
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<kmath_> <FakeUnicode> Accurate solar system model hurtling through space ⚵♁☄☿ ⚶ ♃♄☀♅♂︎ ♀︎⚴ ?⚳♆♇ ⚷ ⚶⚴♂︎♇ ♁♆?☿⛅ ⚳♀︎♅♄ ⚷ ♃⚵☄ ⚵ ♆☄ ♄ ♀︎♁⚴ ♂︎⚳ ♅♇☀?⚶♃ ⚷☿
<egg|principia|egg> !u ♅
<Qboid> U+2645 URANUS (♅)
<egg|principia|egg> they're using the one with the Herschel monogram
<egg|principia|egg> clearly the neptune one should be the LV >_>
<egg|principia|egg> UmbralRaptor: you don't have a header image?
<egg|principia|egg> something something spectra
<UmbralRaptor> Maybe.
<soundnfury> egg|principia|egg: that egg isn't drowning, it's _floating on_ a sea of papers.
<soundnfury> (Apparently egg is less dense than paper)
* UmbralRaptor ? poorly defined wavelength cutoffs for typical magnitudes.
<egg|principia|egg> soundnfury: you're seeing but a still frame! it sinks deeper at every wave of printouts
<soundnfury> nonsense, the majority of its volume is above the papers
<soundnfury> so as more papers are added, it will rise
<soundnfury> (the egg shall rise again!)
<egg|principia|egg> UmbralRaptor: hmm, try setting the theme colour to that of the egg in that picture, not sure if it looks good https://twitter.com/eggleroy
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<egg> s/try/tried
<Qboid> egg meant to say: also I am rather busy with trieding to update principia to 1.2 anyway
<egg> uh wat
<egg> right I /nicked
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