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> 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>
Eggstreme UV
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<egg|laptop|egg>
mlbaker: hm, a symmetric linear map/bilinear form on (V, ⟨_, _⟩) yields one on V∧V as I^: V∧V → V∧V, ω ↦ {I, ω}; I think an eigenbasis of I yields an eigenbasis of I^ under ∧, but how are the eigenvalues of I and I^ related?
<egg|laptop|egg>
(where I merrily identify V and V* above, and V∧V and 𝔰𝔬(V), since I gave V an inner product)
<egg|laptop|egg>
ah it's just λ1 + λ2 for v1 ∧ v2
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<egg|laptop|egg>
INTERNATIONAL EARTH ROTATION AND REFERENCE SYSTEMS SERVICE (IERS)
<egg|laptop|egg>
SERVICE INTERNATIONAL DE LA ROTATION TERRESTRE ET DES SYSTEMES DE REFERENCE
<egg|laptop|egg>
Paris, 7 January 2020
<egg|laptop|egg>
Bulletin C 59
<egg|laptop|egg>
To authorities responsible
<egg|laptop|egg>
for the measurement and
<egg|laptop|egg>
distribution of time
<egg|laptop|egg>
INFORMATION ON UTC - TAI
<egg|laptop|egg>
NO leap second will be introduced at the end of June 2020.
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<egg|cell|egg>
Can that be extended to trivectors?
<mlbaker>
i feel like your thing probably just comes from applying the /\^k functor where k=2
<mlbaker>
along with the duality identifications you mentioned
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<egg|work|egg>
mlbaker: I don't think so?
<egg|work|egg>
let v in V be an eigenvector of I in End(V), with eigenvalue λ
<egg|work|egg>
then (I∧I)(v∧v) =: Iv∧Iv = λ² v∧v, thus v∧v is an eigenvector of I∧I with eigenvalue λ², rather than 2λ
<egg|work|egg>
Another way to look at this is slapping some dimensional analysis on it, the units on I∧I are the square of those on I, where as those on {I, _} are the same
<egg|work|egg>
mlbaker: or did I get the definition of I∧I wrong?
<egg|work|egg>
OK I'm evidently not awake since v∧v=0, but the same argument holds for, say, v∧w
<egg|work|egg>
you get the product of the eigenvalues as the eigenvalue for the wedge of the eigenvectors
<egg|work|egg>
rather than the sum
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<egg|work|egg>
mlbaker: in particular if V is 2-dimensional, I∧I = det I, whereas {I,_} = tr I
<egg|work|egg>
(the underlying motivation here is that if I is (sum over the particles at r of the r_i r_j m), {I, _} is the moment of inertia, and (sum over the particles at r of the r_i r_j m) is a much nicer expression than the one usually given for the moment of inertia (which fails to generalize to dimensions other than 3))
<egg|work|egg>
(in particular that I is m r⊗r for a point mass m at r, rather than m (r²𝟙 - r⊗r) for the matrix for {I, _})
<egg|work|egg>
!wpn whitequark
* galois
gives whitequark an aura with a study attachment
<egg|work|egg>
!wpn mlbaker
* galois
gives mlbaker a thermonyaacular regular disaster with an aura attachment
<galois>
title: "That man was not included in the simulation" on Twitter: "another tragic consequence of someone attempting to pip install without using @anacondainc @pwang… "
<galois>
title: Probability Fact on Twitter: ""Monte Carlo is an extremely bad method; it should only be used when all alternative methods are worse." -- Alan Sokal(And often all alternative methods /are/ worse.)"
<SnoopJeDi>
I was thinking of an elderstein because tardigrades are so nearly eternal
<SnoopJeDi>
probably
<SnoopJeDi>
!wpn UmbralRaptop
* galois
gives UmbralRaptop a purple t-test
<egg|laptop|egg>
!wpn
* galois
gives egg|laptop|egg a fermium Джанибеков cat with a saber attachment
<egg|laptop|egg>
tumbling cat
<SnoopJeDi>
UmbralRaptop, so I hadn't heard about this "maybe the Ia supernovae observations were biased and dark energy doesn't real" paper until today o.O