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4:00 PM
Blowing this up to eleven:
7
Q: What's an infinite dimensional or function version of a tensor?

Steven Stewart-GallusA function $f$ is like an infinite dimensional vector with the norm $|f| = \int^b_a f(t)^2 \, \mathrm{d} t $ and dot product $f \cdot g = \int^b_a f(t) g(t) \, \mathrm{d} t $ where appropriate boundaries have to be chosen or you have to restrict functions so that problems with infinities don't p...

 
okay cool
just seemed a little odd to me but thanks :)
 
@Slereah Geroch has a paper on the philosophy of gauge theory and how it relates to GR
You should check it out
 
4:17 PM
@CooperCape because in many cases you don't want to write out that sum?
People work in an arbitrary number of dimensions all the time
 
That's fair... wasn't thinking past 3/4 really
dimensions that is
 
Even 3/4 is a complete pain in the ass to write
 
I think my problem was that I haven't encountered situations where I'd had to extensively write out things such as $a_x\hat i + a_y\hat j + a_z\hat k$
 
If you write out Einsteins equations with classical notation it takes 10 pages
Less if you don't expand the Christoffel symbols
But still
Pages
 
yeah I'm on basic tensors/vectors don't think I'm quite up for that lol
and that's hella pages
okay I wholly agree with it now
just did a question that said expand $A_{ij}x_ix_j$
cikey
 
4:53 PM
Here's an example on how screwed up lengthy if one refuses to write in indices:
 
Sid
What in the fresh hell is that?
 
ugh not working, using screenie instead
Given the following rather nice diagonal metric, the above is what happens when you try to write even one component of the 2nd order partial derivative of it in full
 
is that delta that kronekcer delta or no?
cause that's insane
 
and, don't forget, you have a total of 4 of these in the riemmanian curvature tensor
 
what the...
I think you just made me realise how insane tensors are...
 
4:58 PM
delta there is just a index that runs through 0,1,2,3
 
oh, okay.
how do you denote the kronecker delta then? (I just came across it and it looks delta-ish to me oops)
 
Well, if it appeared inside as one of the components, then it is the kronecker delta, but yeah I should have use other greek letters to minimsie confusion
 
Not your fault... I'm veeeerrrrryyy new at this.
but to clarify... if it's say, $a_i$ and it says $(i = 1,2,3)$ then it's the same as $a_1 + a_2 + a_3$
 
just a single $a_i$ does not imply a sum, you need pairs of indices to imply a sum
 
ahhh I see
that's the diff between free/dummy index
 
5:03 PM
e.g. $a_ib^i$ for the usual vector dot product
 
so $a_i$ is just $a_1, a_2, a_3$.
 
yup
and $a_{\mu}$ is $a_0,a_1,a_2,a_3$. These are conventions used in einstein summation
 
okay... thanks a bunch :)
 
The einstein field equation is a tensor equation, suffice to say you can see how insane it is when you try to write out everything there in full:

$$R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}+\Lambda g_{\mu\nu} = 8\pi G T_{\mu\nu}$$
 
TIL that tensors are phat...
like
a lil' 4x4 box which is secretly maaassive.
 
5:08 PM
Tensors are multilinear maps, meaning they basically act like matrices but can take in more than one vectors and covectors at the same time
and spits out a scalar
 
damn i got a lot to learn.
 
It is kinda like a linear multivariable function where each variable are vector or covectors
 
but neater
 
@Secret Not "kinda"; that's what a tensor is
 
Another question (sorry lol)... If the Kronecker delta is $\delta_{ij}$ and say $(i,j = 1,2...n)$ then is the Kronecker delta an identity matrix of dimensions nxn?
 
5:19 PM
@CooperCape Yes.
 
cool I'm understanding things
 
One should be careful that in relativity there is only $\delta^i_j$ and not $\delta_{ij}$ or $\delta^{ij}$, though.
If you are not doing relativity ignore what I just said :P
 
Okay, cool.
Eventually
but rn ngl I don't understand what it means to have a superscript
 
5:33 PM
tfw you start messaging and using markdown :'(
 
@ACuriousMind Stop using Latin indices for relativity.
 
New favorite Physics Stack Exchange quote (made by someone in response to an answer by Gerard 't Hooft):
> Renormalizing Yang-Mills theory ought to be worth a badge or something.
2
 
6:07 PM
hehehe
 
6:49 PM
@ACuriousMind I am almost done sequencing the potato genome
 
Anonymous
@BernardoMeurer Sounds cool! Was a project or something?
 
@0celóñe7 : "On regular solutions to nonlinear elliptic systems", Charles B. Morrey, ...
 
@Qmechanic i eventually found the English version
It didn't have what I needed
 
7:17 PM
@0celóñe7 : Yeah, I suspected that. Charles B. Morrey doesn't sound Russian...
 
I typed in Charles B. Morrey Russian to google and it came up with the wiki page on him saying "Missing - Russian"
he looks like a g tho
 
7:45 PM
@JohnRennie You around?
 
8:08 PM
eh, I almost always use Latin indices, at least until I write up the paper
turns out it's hard to write letters like mu and nu really tiny...
 
8:38 PM
@ACuriousMind the amount of GoT possible spoilers/leaks on the internet is insane
 
9:00 PM
@0celóñe7 Summary of the season: The hot girl and the good guy become a couple and win the war
 
@Danu That would be pretty disappointing
They haven't killed any main characters in a while
 
It's a kids show, after all ;-)
 
@Danu they could pull a LOST and say it was all a dream
 
9:30 PM
end of season cuts back to darkness shot of George Martin waking up like "huh! I just got to the good bit"
 
@0celóñe7 I've read a couple of things by a couple of people that reckon as they're running out of main characters due to, well, killing them off, they have to tone down the killing a bit for a season so that there are actually people alive when it gets to the final season...
 
@Mithrandir24601 they have a large main cast right now
there are still four Starks, one or two can die
I'm amazed they haven't killed Gray Worm
not sure he's a main character
 
@0celóñe7 3 Starks, 1 ::cough:: Snow :P and 1 of the Starks seems to not want to admit he's a Stark any more :/
 
@Mithrandir24601 Dany will declare him a Stark by royal decree
maybe
I think Bran should be killed
Puberty + 3 eyed raven makes for a perpetual bad mood
 
@0celóñe7 The way that characters like that usually work out is that they stop caring enough about themselves and so, end up sacrificing themselves 'for the greater good', so it's quite possible
 
9:44 PM
@Mithrandir24601 They already killed Jon once, not sure they'll try twice
Although people can get revived $\ge 6$ times. It is known.
 
@0celóñe7 Personally, I wouldn't consider Grey Worm a main character - he's a good side character, but not ultimately essential to the plot
 
@Mithrandir24601 Hmm, yes. If we want to talk about main characters dying we'd have to list them. For instance, Varyss is basically the core of the plot for 5 seasons but the show isn't about him. Is he a main char?
Is Baelish a main character?
 
@0celóñe7 I'd say he is, because if he dies, there's no-one to replace him that can do what he can do
@0celóñe7 Probably not any more, because if he died, Sansa would probably get his land etc. by right and she now knows how he works, as well as the people of the Vale, so again, there's someone to replace him who can also do what he does (unless there's something he knows that no-one else does, which is possible, although getting less and less likely)
 
@Mithrandir24601 Agreed, Baelish has become less and less important as the show goes on.
I'm not sure what his goal is right now except to marry Sansa (creepy) and get the Iron Throne (not sure how he thinks anyone will support that).
Cersei has proven that ruling through fear isn't going to work in the long-run and he doesn't have the armies to beat Dany. No clue what his plan is, or if it even matters anymore.
 
@0celóñe7 I'm astonished Cersei is still alive... She's done a ton of stupid things since the beginning
 
9:55 PM
@Mithrandir24601 I was expecting her to get assassinated during her walk of shame. Seemed like a good opportunity for that.
 
Oh. Ohhhh :o I think Cersei's no longer the one in control/power. Her 'Meister' is the one that's keeping her there, so he's the one that has the real power...
 
@Mithrandir24601 Really? What has Qyburn done that makes you think that?
He seems like a loyal Hand to me.
 
hate to butt in but he's just a bit too weird imo
 
he is creepy!
He rebuilt the Mountain with body parts
 
then again a step-up from Pycelle... although Pycelle had his humour.
 
10:02 PM
@CooperCape Apparently there's a deleted scene that shows Pycelle's old man spiel is an act.
 
Wait whaaa...
 
@0celóñe7 He's the only one that's actually done anything to keep Cersei in power (including Cersei herself). He's the one that got all the wildfire. He brought Clegane back as that creature, who seems to be the only guard that's truly loyal. However, he's probably loyal to Qyburn, not Cersei. So, Cersei is only ruling because of the Meister. What happens if he decides he wants power? he gets it instantly. So he's the one with the power
 
@0celóñe7 Since I'm not sure how far exactly you are I can't respond to that :P
 
@ACuriousMind I'm up-to-date.
 
@0celóñe7 What do you mean by Pycelle's 'old man spiel'? (so we're on the same lines here)
 
10:03 PM
Well, then whether it was an act or not it didn't help him much :P
 
@ACuriousMind I agree, and was about to comment on that.
 
He was funny being useless though...
 
There are some moments where his "act" could/should have been dropped, but it wasn't. So I'm not sure how to interpret the deleted scene.
@Mithrandir24601 Where he acts slowly and like a fool.
@ACuriousMind lmao does this look like an asymptotically flat manifold to you?
is it supposed to be a line with some disconnected bits?
 
"Yes, the point is that I'm right, so I don't deserve to be on the internet kooks page" ::sigh::
 
or a blob stuck on a half-plane
 
10:14 PM
@0celóñe7 uhhhhhhhhhh
 
@ACuriousMind in the case of the line it's a shit example because all 1-manifolds are flat
 
could use more context
Looks like two eggs in a bag
 
or a geography 'label this meander' exercise.
(dunno why I'm saying that I don't know what it's supposed to be I don't really have rights)
 
@ACuriousMind Oh, apparently it's supposed to be a 3-manifold
¯_(ツ)_/¯
 
@0celóñe7 wat
How?
 
10:18 PM
 
so, as @Slereah said... it literally is a bag...
 
2/10 TikZ drawing skills :P
 
11:21 PM
what an amazing index
 
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