The h Bar

dmckee

12:00 AM

@0celo7 Because you kept telling people facts about your real-life life and person.

Danu

^

Yes, Ryan

0celo7

Yeah, so it's more complicated than simply not using a real name

user129412

@ACuriousMind he hasn't. But as for the question you linked (which I posed), I see what you mean. I figured that perhaps this final part was an easy addition to the actual answer, which is why I included it. It would make sense to make it a follow up question though, once the first one is answered.

Danu

Stop telling people your real name, Ryan

dmckee

If you want to be anonymoous you have to be committed to that in your on-site interactions.

0celo7

12:00 AM

@Danu wtf how do you know who I am

Danu

I heard it from your mom

(jk)

0celo7

@dmckee pls ban Danu he's a stalker

ACuriousMind

He might prefer Mr Unger :P

DanielSank

I actually believe I know his family name too.

^ That

0celo7

ahhh ban all of them

Danu

12:01 AM

welp there we go

ACuriousMind

lol

DanielSank

Anyway, the question is already a difficult one requiring a nontrivial amount of time to answer well. I can some times psych myself up for those, and indeed I really enjoy answering questions like that, but there's no way I'm going to write a tutorial on quantum noise spectral density and answer another question.

Danu

@user129412 just split the posts

user129412

That sounds fair. Shall I edit out the final part?

DanielSank

Please do.

Danu

12:02 AM

Daniel will fulfill all your wishes and desires

DanielSank

I will?

ACuriousMind

You might want to examine my desires first before committing to that

DanielSank

Wait, I'm fulfilling @ACuriousMind's desires?

0celo7

BDSM confirmed

DanielSank

I am confuse.

0celo7

12:03 AM

I knew the latex duck suit was a sign

DanielSank

Also @user129412, as soon as you type "This leads to my first, short question." you should know the question is too broad.

ACuriousMind

@DanielSank Danu didn't specify whose desires

DanielSank

@ACuriousMind ~Sigh~

very well.

ACuriousMind

@0celo7 Your imagination is so...shallow

DanielSank

@user129412 edit the question and ping me.

0celo7

12:04 AM

@ACuriousMind what does that mean

DanielSank

@ACuriousMind Yeah I'm confused. I figured I'd get out that bottle of mead and we'd play a board game or something.

0celo7

I strongly associated with you BDSM, I blame one of your former avatars.

ACuriousMind

@DanielSank Now that does sound nice!

@0celo7 ???

DanielSank

@ACuriousMind See, I know what you like, baby.

ACuriousMind

Which one of my avatars carried that connotation for you?

@DanielSank Careful, you're married

0celo7

12:06 AM

@ACuriousMind I can't remember all of them.

Do you have a list?

DanielSank

@ACuriousMind We're only exclusive about sex, not board games and/or sharing a bottle of hooch.

ACuriousMind

@DanielSank What about affectionate names like "baby"?

DanielSank

@ACuriousMind I don't call her that.

ACuriousMind

@0celo7 ehhhhh, not really

user129412

@DanielSank I have reduced it to a single question.

DanielSank

12:07 AM

@ACuriousMind We call each other "homey" for whatever it's worth.

Danu

@DanielSank Hey... homey

ACuriousMind

Is pronouncing "honey" that hard? ;)

Danu

must make for great pillow talk :3

0celo7

ok this is getting weird...

Danu

Yes, time for me to bow out

cyas

ACuriousMind

12:09 AM

oO

Never seen Danu flee weirdness before :P

Danu

I'm getting out before I'm sucked in too deep

Don't wanna go too deep, homey ;)

ACuriousMind

I think you just duck out because you want to slightly better your sleep schedule

DanielSank

@ACuriousMind Very different meaning.

Danu

you and your logic... GET OUTTA HERE

DanielSank

@Danu Interesting how it sounds so sweet from Anna but so amazingly horrific coming from you.

0celo7

12:11 AM

Ok, let's switch topics.

DanielSank

Must have been the winky face.

ACuriousMind

@Danu They'll have to carry me out of here feet first!

Danu

@DanielSank You'll get used to it

Anyways, I should stop freaking y'all out

Bye!

0celo7

@ACuriousMind Let $V_p$ be the vertical space of a principal bundle $(P,M,G)$ and let $\bar{ \mathfrak g}$ be the fundamental vector fields evaluated at $p$. I can see that $V_p\cong \bar{ \mathfrak g}$ by arguing that the map $\bar{ \mathfrak g}\to V_p$ is injective, hence surjective since they are of the same dimension. But can one show directly that it's surjective? i.e. given $v\in V_p$ there is a fundamental vector field $\bar X$ such that $\bar X(p)=v$?

0celo7

12:24 AM

So, $p$ injects $G$ into $P$ along the fiber over $\pi(p)$.

Well actually, I think that's a diffeomorphism onto its image

So the differential is an isomorphism onto its image (maybe)

0celo7

12:48 AM

@ACuriousMind Ahhh, I can't prove it's surjective! I have another proof that it's injective

Bishop-Crittenden say that for $t\in V_p$, there exists $\bar X\in\bar{\mathfrak g}$ such that $\bar X(p)=t$, since $p$ maps $G$ onto $\pi^{-1}(\pi(p))$.

Now, I'm pretty sure that map $G\to \pi^{-1}(\pi(p))$ is a difeomorphism, so the dimension of the image of $dp$ must be at least $\dim G$

Since each fundamental vector is vertical, this shows that any vertical vector is a fundamental vector.

Hmm, but we don't know that the vertical space is $\dim G$-dimensional

Eh, work in a trivialization to show that it is.

Bernard Meurer

@kaylagilmour Sup

user218912

@BernardMeurer they don't have enough rep to chat...

Bernard Meurer

@IceLord Shame, she was in like 1000 rooms lols

Bernard Meurer

1:11 AM

@knzhou You're my idol

DanielSank

@BernardMeurer I thought I was.

:(

0celo7

what did he do?

Bernard Meurer

@DanielSank You're more of a god

@0celo7 He helped me with computation theory once

0celo7

I've helped you with math way more than once

Bernard Meurer

@0celo7 Well yeah but you're my friend and you wear hideous shoes

@knzhou Is some dude

meh I mmeeed sleep

0celo7

1:16 AM

hideous shoes my ass

user218912

I still didn't figure out how to take the d'alembert of $e^{-i k \cdot x}$.

0celo7

lol

user218912

I tried things.

user218912

just not the right things.

user218912

can somebody help please :(

0celo7

1:18 AM

what is the definition of the dalembert?

Bernard Meurer

Where's @ChrisWhite? I really miss the guy

0celo7

he deleted his account

dmckee

@BernardMeurer He requested that his account be deleted a few weeks ago.

Bernard Meurer

@dmckee What?

Why?

dmckee

@BernardMeurer If he explained it wasn't to me.

Bernard Meurer

1:19 AM

@dma

0celo7

No one knows

Bernard Meurer

@dmckee That sucks man, I really liked him

0celo7

We can speculate

Bernard Meurer

Nah, not interested in that

dmckee

The most positive spin I could put on it was that he thought it would distract from a job or a job hunt.

Bernard Meurer

1:19 AM

I genuinely appreciated him

dmckee

A less positive spin involves a conflict with another user.

0celo7

@dmckee Yeah right...why delete for that?

Just don't use the site

@dmckee This.

user218912

@0celo7 $\square$

0celo7

@IceLord I can't help you then

I don't know what box means

dmckee

@0celo7 Some people find it very hard to self-regulate their internet usage.

Not that I think there is a high probability of that explanation.

user218912

1:21 AM

@0celo7 sorry it's $\partial_\mu \partial^\mu$

user218912

do you want it expanded form?

0celo7

@dmckee He has a PhD in astrophysics. Somehow I think he has the self-control to not use the internet for a while.

@IceLord I don't want anything

Bernard Meurer

@dmckee Both of those seem rather unlikely

@dmckee Man this really sucks

user218912

@0celo7 I do though.

user218912

$\frac{\partial^2}{\partial t^2} - \nabla^2$

dmckee

1:22 AM

@0celo7 No good. I've known too many <s>Spaniards</s> Ph.Ds.

0celo7

Spaniards?

dmckee

Hell. Strikeouts don't work. Meh.

0celo7

@dmckee use --- on either side.

Bernard Meurer

@dmckee ~~they do~~

user218912

@0celo7 are you helping me?

dmckee

1:23 AM

The Princess Bride - I Hate Waiting

►

0celo7

@IceLord you can help yourself

user218912

help me help myself.

0celo7

@dmckee Good movie.

Bernard Meurer

@IceLord He's mine

dmckee

But the wrong clip. I'll try again.

user218912

1:24 AM

@BernardMeurer nah I've known him for longer.

0celo7

@IceLord Just compute the derivatives

I don't see the issue

dmckee

Give you my word as a Spaniard

►

user218912

@0celo7 I know that, but in the answer there is like a $k_\nu$ term.

user218912

I have no idea how that comes from the derivative.

dmckee

@0celo7 Hmmm now I just have to remember that.

0celo7

1:25 AM

@dmckee I still don't get it.

@IceLord is the answer $k^2 e^{-i kx}$

modulo a sign

dmckee

@0celo7 I've known a lot of Ph.Ds. They all have something special going for them, but self-control in the face of an internet interest isn't uniformly one of them.

user218912

@0celo7 no.

0celo7

@IceLord what is the answer then

user218912

@0celo7 the answer is $k^2 \epsilon_\nu$ where the epsilon is the coefficient for the exponential.

user218912

no exponential though

user218912

1:27 AM

i don't get it.

0celo7

is it evaluated at $x=0$ or something

@dmckee Oh, I see.

user218912

maybe... it doesn't say.

user218912

I guess that's the only way.

0celo7

pic

user218912

@0celo7 pic

0celo7

1:28 AM

Are you telling me you can't divide?

Bernard Meurer

@IceLord I've met both his sisters & stayed at one of their houses

0celo7

Because that's sure what it looks like.

Bernard Meurer

@0celo7 M. invited me for thanksgiving lol

But I dunno if I could possibly make it

0celo7

what the fuck, I didn't get invited

user218912

oh fuck

user218912

1:29 AM

they just divided it out

0celo7

I get to drive 9 hours back to virginia

knzhou

@BernardMeurer wat

user218912

@0celo7 so this whole time I thought I was doing it wrong because they divided it out.

0celo7

@IceLord Yes.

How long did you spend on that?

Bernard Meurer

@0celo7 I got invited lol, I wish I could go, I want to meet Kevin

user218912

1:31 AM

like 30 minutes total.

Bernard Meurer

@knzhou You're my idol

0celo7

@BernardMeurer What? Kevin is going to my parents'.

user218912

trying new derivative techniques i invented myself to get the exponential to disappear.

Bernard Meurer

@0celo7 Isn't he?

@0celo7 Also K. I really want to meet her

0celo7

Yes, Kevin and I are going to Virginia.

Bernard Meurer

1:32 AM

@0celo7 Yeah, I want to meet Kevin

user218912

@BernardMeurer how?

0celo7

You're not coming to Virginia...

user218912

that's really weird.

Bernard Meurer

@0celo7 Probably not lol, I',m just saying it'd be nice though lol

@IceLord I'm weird and I really love his sister & her husband

Ron is awesome lol

user218912

@BernardMeurer how did you find them?

user218912

1:33 AM

coincidence?

0celo7

I agree @IceLord it's weird.

Bernard Meurer

@IceLord When I was in LA earlier this year @0celo7 got me in touch with his sister who lives there because she works at GitHub

user218912

oh, makes sense.

Bernard Meurer

@IceLord And idk I thought she was super cool so we became friends lol

user218912

I will definitely meet 0celo7 irl someday.

user218912

1:35 AM

idk how but I will

Bernard Meurer

I've also had extended conversations with his father

0celo7

that's creepy af

both of you are creepy af

Bernard Meurer

@IceLord He has the shittiest shoes

user218912

@0celo7 no, isn't it fair to see the person you probably messaged 5k times irl.

0celo7

no, it's not

@BernardMeurer You and R should just form the "hate on Ryan's shoes club"

Bernard Meurer

1:37 AM

@0celo7 Come on, I've lived for a few days with your sister lol

user218912

@BernardMeurer okay... that is creepy af if anything.

0celo7

yes it's very creepy

Bernard Meurer

@0celo7 Me and R made talked about you for a long time back in LA lol

user218912

@0celo7 you got yourself into it xD

0celo7

what does that sentence mean

@IceLord regretting it

Bernard Meurer

1:38 AM

@0celo7 K and M have adopted me basically lol

0celo7

ok wait

Bernard Meurer

@0celo7 It means we mocked you

0celo7

my R not M's R

@BernardMeurer I don't see what there is to mock.

wait who is K?

I have two Ks in my family

Bernard Meurer

@0celo7 Your sister

0celo7

also there's 3 Rs

well, 2 Rs and one B

Bernard Meurer

1:39 AM

@0celo7 R is M's R

0celo7

did you congratulate him today?

Bernard Meurer

@0celo7 Why?

0celo7

Michigan is 5-0

Bernard Meurer

Sweet, I'll congratulate him lol

0celo7

do you even know wha I mean

Bernard Meurer

1:41 AM

@0celo7 That's wrong man lol

@0celo7 yes, Michigan Wolverines

user218912

@0celo7 how about the second term?

user218912

why is there a $k_\nu$ and $k$ dotted with $\epsilon$

user218912

how does that come out of a derivative?

0celo7

not telling you, sorry

user218912

why? :(

0celo7

1:51 AM

cuz I can do it in my head

it's e-z

user218912

idk how to do it though, if I see it once I'll be able to do it again easily.

0celo7

just take the derivative

what more do you want?

user218912

please show me the steps.

user218912

please

user218912

this isn't homework.

0celo7

1:53 AM

@BernardMeurer what do you think?

user218912

@0celo7 you big meanie

user218912

how am I supposed to learn

Bernard Meurer

@0celo7 About what?

0celo7

should I help him?

Bernard Meurer

Hmm

@IceLord What have you tried?

user218912

1:58 AM

@BernardMeurer I took the derivative of the exponential and used chainrule.

user218912

I don't get that answer.

Bernard Meurer

@IceLord let me see what you got

user218912

I got the same thing as the first term.

user218912

means I'm using indices wrong.

0celo7

SHOW ME

Bernard Meurer

2:00 AM

^ that

0celo7

I can't read your mind

user218912

I got $k^2\epsilon_\nu$

user218912

again

user218912

idk how indices work in this situation

Bernard Meurer

@IceLord Dude how did you get that

Show your development

0celo7

2:01 AM

@BernardMeurer Good!

Bernard Meurer

@IceLord It's pointless to help you if we can't point what you're doing wrong

We need to see your mistake to understand what you're not getting

0celo7

Exactly.

user218912

I did $\partial_\nu \partial_\mu \epsilon_\nu e^{-i k\cdot x}$

0celo7

@IceLord I will no longer help until I see every single step

Bernard Meurer

@dmckee Do you have a contact email? I want to ask you some site-related things

user218912

2:04 AM

from that I first took $\partial_\mu$ of it

user218912

and I got $\epsilon_\nu ke^{-ik\cdot x}$

user218912

but idk how to take the $\partial_\nu$

user218912

does it contract with the epsilon?

0celo7

hmm

what's the problem statement

user218912

to do $\partial_\nu \partial_\mu \epsilon_\nu e^{-i k\cdot x}$

0celo7

2:06 AM

I want to check my answer

I will tend to help if I cannot get the right answer

user218912

fuck I'm retarded.

0celo7

I could flag that and get you suspended

user218912

it's $\partial_\nu \partial_\mu \epsilon^\nu e^{-i k\cdot x}$

0celo7

lol

user218912

@0celo7 wanna bet.

user218912

2:07 AM

that won't get me suspended.

0celo7

remove it, I'm being triggered

user218912

even worse now.

0celo7

the r word offends me

user218912

@0celo7 lol?

user218912

it's directed at ME.

user218912

2:08 AM

it doesn't offend anyone.

0celo7

I won't flag because we have too many flags already and we don't want Shog to show up and ban everyone

but I've gotten suspended for saying I like a little pain with my women

anything can get you suspended here

user218912

no because that's offensive.

user218912

mine is not offensive to anyone.

0celo7

to whom?

user218912

idk what you mean by that so idk.

user218912

2:12 AM

it just sounds offensive.

user218912

probably to feminists.

0celo7

ok so are you done now?

Mikhail

Hey guys, anybody know what an equation of the form u_xx-u_tt=1 is called? Its almost the famous diffusion equation, but that would be u_xx-x_t =1...

0celo7

=1?

user218912

@0celo7 $\partial_\nu \epsilon^\nu$ is 0 right?

user218912

2:14 AM

because epsilon is constant.

0celo7

I don't know.

user218912

but you said you could do it in your head.

Mikhail

@0celo7 I just choose some kind of constant

0celo7

@Mikhail I'm unfamiliar with the equation you are calling a diffusion equation

Usually diffusion is u_xx=u_t

@IceLord no this is PhD calc 3

user218912

@0celo7 ._.

user218912

2:18 AM

I just don't get how a $k_\nu$ appears.

user218912

how does it get an index?

user218912

oh shit

0celo7

what bothers me is that no one had to explain this to me. I'm not trying to be an asshole, but I am really confused how you're confused

user218912

I figured it out.

user218912

well part of it.

user218912

2:29 AM

now I don't know how the dot product term appears.

0celo7

I give you...2 minutes to show all your work

user218912

$\partial_\nu \partial_\mu \epsilon^\mu e^{-ik\cdot x} = \partial_\mu k_\nu \epsilon^\mu e^{-ik\cdot x}$

user218912

then idk how to proceed.

user218912

oh I know

user218912

are you taking $\partial_\mu(\epsilon^\mu e^{-i k\cdot x})$

user218912

2:36 AM

because then it becomes $k\cdot \epsilon$ i think.

user218912

which is what I wanted.

user218912

am I right or wrong? @0celo7

0celo7

dude show me the answer

let me make sure what I'm doing is right

user218912

the answer is $k_\nu k\cdot \epsilon$

0celo7

the FULL answer

ok as I thought

you're doing the chain rule wrong

user218912

2:39 AM

:(

0celo7

that's not your issue here, but you are doing it wrong

user218912

where did I make a mistake?

0celo7

you need some $i$s

user218912

but don't you remove them in the end?

0celo7

no

they go away my themselves

and you need to prove that

user218912

2:50 AM

k I give up

user218912

@0celo7 i know

0celo7

what did you try?

god dammit that's the last time I'm asking that

I just won't respond any more

user218912

21 mins ago, by IceLord

$\partial_\nu \partial_\mu \epsilon^\mu e^{-ik\cdot x} = \partial_\mu k_\nu \epsilon^\mu e^{-ik\cdot x}$

user218912

is this right so far?

0celo7

no

user218912

2:55 AM

which part is wrong?

0celo7

Last chance. Let $f:\Bbb R\to\Bbb C, x\mapsto \exp(-\mathrm ixk), k\in\Bbb R$. Find $f'$.

user218912

$-ike^{-ikx}$

0celo7

Ok, so you do know the chain rule.

user218912

yes...

0celo7

Now figure out the rest, no more help from me.

user218912

2:57 AM

wat...

user218912

but there are indices.

user218912

just tell me how to treat them

user218912

use 1 example

0celo7

See you tomorrow.

user218912

:|

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