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
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<egg|cell|egg>
Meow
* UmbralRaptop
pets egg|cell|egg
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* egg|cell|egg
Lorenz contracts UmbralRaptor
<egg|cell|egg>
s/z/tz/
<galois>
egg|cell|egg meant to say: Lorentz contracts UmbralRaptor
<egg|cell|egg>
s/tz/ꜩ/
<galois>
egg|cell|egg meant to say: Lorenꜩ contracts UmbralRaptor
* egg|cell|egg
dilates UmbralRaptop
<egg|cell|egg>
ＵｍｂｒａｌＲａｐｔｏｐ
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* oeuf
meows at UmbralRaptop
* oeuf
stares at Odonatoptera
<egg|laptop|egg>
bofh: UmbralRaptop: I wonder whether starting with differential geometry would make teaching special relativity saner
<bofh>
egg|laptop|egg: possibly? I don't think it's necessary for SR, all you care about is Minkowski space there
<egg|laptop|egg>
bofh: sure, obviously it's only needed for GR, but otherwise you don't really have the vocabulary to talk about the underlying concepts in special relativity
<egg|laptop|egg>
see UmbralRaptop's confusion at quadrivectors
<egg|laptop|egg>
in particular quadrivelocity being a unit vector in the tangent space
<egg|laptop|egg>
which only makes sense if you have tangent spaces and geodesics thereon
<bofh>
I mean okay, true, but like I think a lot of this is
<bofh>
"tangent spaces and geodesics" is what I consider like, basic vector calculus
<bofh>
so I guess I agree with you here
* egg|laptop|egg
slaps bofh's coordinates
<egg|laptop|egg>
bofh: tbh I'd say differential geometry helps even with classical physics, because a lot of things that happen to be vector spaces are better handled as reference frames anyway
<bofh>
"The introduction of numbers as coordinates is an act of violence" :p
<bofh>
(~ Hermann Weyl)
<egg|laptop|egg>
oh I didn't show you the Hermann Weyl Zimmer at ETHZ
<bofh>
I mean yes. In fact I'd say it helps even more with classical mechanics tbh
<bofh>
Like I guess my issue is I consider "differential geometry" to mean "Riemannian geometry" and "vector calculus" to mean "smooth manifolds theory"
<bofh>
...which prolly explains some of my frustration at trying to explain certain concepts to others, oops.
<bofh>
>_<
<egg|laptop|egg>
bofh: ...
<egg|laptop|egg>
bofh: but anyway for GR you want *pseudo*-Riemannian geometry :-p
<egg|laptop|egg>
In fact I'd say it helps even more with classical mechanics tbh << well in relativity it is quickly necessary, so that's rather stronger than helping
<bofh>
true
<egg|laptop|egg>
bofh: I wonder how hard it would be to make Principia's reference frame formalism GR-compatible
<bofh>
I mean for starters I'm not sure how Principia implements the notion of spacetime metrics and geodesics.
<egg|laptop|egg>
bofh: yeah, so the inner product is assumed to be canonical, there is no explicit dual space
<egg|laptop|egg>
that's obviously something that would need to change
<egg|laptop|egg>
and we have only one time type
<egg|laptop|egg>
Instant
<egg|laptop|egg>
(which is TT)
<bofh>
that strikes me as a fairly nontrivial change to begin with
<egg|laptop|egg>
but space coordinates are typed by reference frame
<egg|laptop|egg>
bofh: also obviously we would need namespace feldgleichungen = principia;
<bofh>
LOL
<egg|laptop|egg>
bofh: also I have found more eggsciting typesettings of degrees, minutes, and seconds
<egg|laptop|egg>
bofh: in Kepler (1609)
<egg|laptop|egg>
it seems some angles are broken down with a unit larger than the degree though, and I'm not sure what that is
<egg|laptop|egg>
the abbreviation for it is s
<egg|laptop|egg>
bofh: ah, a longer abbreviation is sign.
<egg|laptop|egg>
bofh: so it's 30 deg
<bofh>
huh. i was going to guess spatium/arclength but that wouldn't make any sense.
<bofh>
also that kinda seems reasonable tbh
<egg|laptop|egg>
bofh: so e.g. p. 335:
<egg|laptop|egg>
Tunc longitudo Solis a corde Leonis eſt 5 ſign. 27 grad. 33 minut. 20 ſecund. differens a longitudine Martis eccentrica 1ᷤ.26̊.35́.7̋. per 4ᷤ.0̊.58́.13̋. qua diſtantia arcuali [...]
<egg|laptop|egg>
bofh: ^
<egg|laptop|egg>
bofh: so the sign, degree, minute, second symbols are set above the digits
<egg|laptop|egg>
and the parts are separated by full stops
<bofh>
wait, set *above* the digits? what's the line spacing like then
<egg|laptop|egg>
normal
<egg|laptop|egg>
bofh: diacritics are a thing, you don't need to space lines to set those
<bofh>
oh, so it basically is treated like an offset ring above?
<egg|laptop|egg>
yeah
<egg|laptop|egg>
for three-digit degree counts it's over the middle digit
<bofh>
that... actually seems sensible, honestly.
<egg|laptop|egg>
note that longitudes have a sign, but other angles may go above 30 degrees
<egg|laptop|egg>
bofh: and in some tables, you just have a heading SGMS or GMS and then the sexagesimal digits are simply separated by full stops, without degree minute second symbols atop them
<egg|laptop|egg>
at low altitudes in KSP, KSP rotates the world (so that it operates in the surface frame)
<egg|laptop|egg>
that's well-known
<egg|laptop|egg>
but
<egg|laptop|egg>
that means that a vessel in low Kerbin orbit spins as the planet does :D
<whitequark>
uh
<egg|laptop|egg>
whitequark: you know how in timewarp things don't spin in stock KSP?
<egg|laptop|egg>
whitequark: well, they don't spin in KSP world coordinates
<egg|laptop|egg>
whitequark: so if you timewarp along a low kerbin orbit, your vessel spins like Kerbin does :D
<egg|laptop|egg>
this finding brought to you by thinking about https://github.com/mockingbirdnest/Principia/issues/1639 and realizing that since KSP also rotates the universe (albeit continuously along a single axis, rather than arbitrarily at SoI transitions like Principia), it has to solve the same problem
<egg|laptop|egg>
which it doesn't
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<galois>
[WIKIPEDIA] Free variables and bound variables#/media/File:Binary math expression tree.svg | "In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older..."
<egg|cell|egg>
!u 🜄🜂
<galois>
🜄: U+1f704 ALCHEMICAL SYMBOL FOR WATER
<galois>
🜂: U+1f702 ALCHEMICAL SYMBOL FOR FIRE
* UmbralRaptop
pokes covariant and contravariant vectors with a cat
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<UmbralRaptop>
1.6 and 1.7 have the best QoL features since 0.17 (maneuver nodes)
<UmbralRaptop>
Which in turn had the best since map mode and timewarp