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
<B787_300>
UmbralRaptop: why does it use musical symbols
<UmbralRaptop>
¯\_(ツ)_/¯
<bofh>
oh those are just the musical isomorphisms
<B787_300>
bofh: what do they mean in their mathematical isomorphism
<bofh>
the flat operator defines an isomorphism from the tangent bundle of a (pseudo-)Riemannian manifold to its cotangent bundle, and the flat operator the inverse isomorphism.
<bofh>
they're named b/c the flat operator "lowers" the index when you write your vector field in Einstein summation notation you wind up going from X^je_j to X_je_j (with the inverse for the sharp operator, which raises the corresponding index on your vector field).
<bofh>
like it's perfectly reasonable notation
<B787_300>
i have no idea what you just said although it looks like english
<bofh>
do you know what a riemannian manifold and a tangent bundle are?
<B787_300>
nope
<UmbralRaptop>
Okay, I get the justification for the name, but have no idea what the index moving means. Or what a tangent bundle is. Or a Riemannian manifold beyond you do GR on it.
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<bofh>
I mean the tangent bundle of some manifold M is just the collection of all the tangent vectors to M.
<kmath>
<haya2e_jaxa> [TD1-L08E1] 2/22 at 7:48 JST. We have confirmed the spacecraft began to rise as planned. This was announced by the… https://t.co/AorIL2eXaJ
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<UmbralRaptop>
"Amorphous Magnets in the Spintronics World"
* UmbralRaptop
doesn't feel excited about that colloquium
<UmbralRaptop>
Okay, amorphous magnets sound somewhat intriguing, but it seems like the sort of talk I'd be mostly unable to follow