@0celouvskyopoulo7 Depends on the context

@ACuriousMind "any Cln module is a direct sum of irreducible Cln modules"

Sigh

This is our generation

Your generation, perhaps.

We have the same generation...

Nah.

Back in my day we beat such behavior out of children.

online?

No, parents did.

@0celouvskyopoulo7 Your day was my day tho

Factually incorrect.

@0celouvskyopoulo7 That's not what I would call Wedderburn's theorem, but it's related. I assume Cln is some semisimple algebra?

@ACuriousMind $n$-dimensional Clifford algebra

@SirCumference what are you doing in my swamp

@0celouvskyopoulo7 Yeah, then that follows from "modules over semisimple algebras are semisimple", where semisimple means precisely "decomposes into the direct sum of irreps (or "simple modules, in this language)"

I choose to believe you

How old are you actually, if I may ask @0celouv?

you made me curious by your remark :P

I am 13

haha cool

@0celouvskyopoulo7 Oh, the proof of modules over semisimple algebras are semisimple is easy, but I don't quite recall off-hand how easy it is to show that the Clifford algebra is semi-simple. I think it's simple in even dimensions and something going on with parity should split it into two invariant subspaces in the odd dimensions.

@ShaVuklia He is not 13. :P

Don't assume my age

hahahahahah yea I figured @Acurious :P

actually

first I thought he was maybe a bit old because of his remark. but then after his response, I dropped the age again :P

I am actually 10 but I can't be on this site unless I am 13...

@0celouvskyopoulo7 I find it funny that once upon a time you got upset when people implied you weren't an adult and now you're doing it yourself :P

but I know people who are 18 and behave like old people, so who cares I guess

@ShaVuklia Hint: He is younger than me.

@ACuriousMind Once I started cooking and cleaning for myself I quickly decided that being an adult is too damn hard

@ACuriousMind hm I see

@ACuriousMind You're eternal...

what kinds of music do you all like?

@0celouvskyopoulo7 That is an oddly universal experience, I think :D

@Avant chinese and russian music :P and Simon & Garfunkel. and meme music

@Avantgarde gangster music

@Avantgarde metal, mostly

Dare I ask what "meme music" is?

lol

i don't think it's even a genre, because it's so bad

lol

but it's basically the remixes that people make based on memes. i have a soft spot for memes:P

pls don't judge

meme music?

NOOOOOOOOOOOOOO

NOT AGAIN

I should have known

Hehehehehe

I figured it was that, trololololo, or the Russian Chandram guy

I'm guessing you got rick rolled

^Indeed, you should have known

Curious - metal! :D

me too

stuff like this: youtube.com/watch?v=U5seygQLcsA :P like, I seriously put this on when I do my homework

it just makes me happy because of all the memories:P

oh god

I have no comment to offer.

hahahahaha

guys, it takes time to appreciate this form of art

certainly

XDXDXD

@ShaVuklia You spelled "This stuff takes several hours to brainwash you into liking it" wrong ;)

lol you spelled "years" wrong :P

that Hillary laugh chorus is so irritating

it takes more than just a couple of videos

Trump 2020

it takes a life time of dedication

lol @Avant I thought that was the best part

And you can concentrate while listening to that?

apparently

can you do math while listening to Death Grips?

qn of the week

@BalarkaSen It's not a matter of "can", it's a matter of "should".

@BalarkaSen @ACuriousMind Did you hear the revelation the other day that Kahler was an avid Nazi well through the 80's?

He quit his professorship to volunteer in the army

"The other day" - is it not like two weeks since we talked about that?

Yeah, so?

teichmuller was pro-nazi

"the other day" is, like, yesterday for me, but whatever, carry on with what you actually wanted to say

@ACuriousMind i want to try it actually

Well, I was wondering

@BalarkaSen I'm sure @BernardoMeurer is proud of you.

Weren't there physicists who were shunned becuase of their involvement with the Nazis?

Jordan, especially

There was another

They didn't get the Nobel until the 50s or something

How come Kähler never got a bad reputation for it

It's not like he just ignored it, the guy had a freaking Nazi flag in his office after the war

@ACuriousMind how about death metal

@BalarkaSen melodic death metal is fine

I mean can you imagine the outrage if Witten had a Confederate flag in his office??

@0celouvskyopoulo7 The question is whether that was widely known to people who would have cared and could have done something about it

@ACuriousMind I had Chuck Schuldiner in mind :P

oh wait

@ACuriousMind Done something about it? Report it to the school!

it's just the difference formula

No but you can say $r\cos\phi = A$ and $r\sin \phi = B$ for some $r, \phi$. This is polar coordinates.

People get in major trouble for not using made-up gender pronouns

@BalarkaSen You want to try death metal?

@Balarka but why don't they consider $r$?

@Avantgarde Nah. I just stumbled upon "Death" by chance.

It's not my thing.

@0celouvskyopoulo7 In post-war Germany, even with denazification, I think the chance of the person you report to just being another Nazi supporter who tells you to shut up would have been non-neglegible, especially considering that someone must've hired Kähler in the first place.

haha ok. I would've suggested a song or 2 then

You can freely suggest :)

I am open minded about pretty much literally whatever

but being avant garde I am not open minded about my opinions of them

:P

And finally, he probably had tenure and would have been very difficult to get rid of even if the complaint stuck. Not really what most students want to get involved with.

Ok, I'll suggest some softer death metal youtu.be/rYBgWgjjgxQ

@ShaVuklia Is $(\omega^2 - \omega_d^2)^2 + (2\gamma \omega_d)^2 = 1$?

yes

wait

let me check

@ACuriousMind Maybe in the <80s, you're right

no

But I don't think tenure would stop anyone from firing Witten if he had a Nazi flag in his office

@Sha Sorry, I meant $ = R^2$

yes

oh okay

@0celouvskyopoulo7 He retired in 1974.

so if their squares add to 1

we know that we can find $\phi$

@ACuriousMind 1974<1980.

??

!!

@ShaVuklia A'right. I apologize. Then $(A, B) = ((\omega^2 - \omega^2_d)/R, 2\gamma\omega_d/R)$ is a point in $\Bbb R^2$ of magnitude 1, so can be represented as $(\cos \phi, \sin \phi)$ for some $\phi$ in polar coordinates.

And yeah

¡¡

@ACuriousMind Have you seen this notion of infinitesimal stability of a field configuration under $\mathrm{Diff}$?

but why can it be represented as a polar point, when there is no $i$ in front of $\sin$ ?

@0celouvskyopoulo7 Yes, I agree that it would probably not be something you'd get away with today. The past is a different country.

@0celouvskyopoulo7 I don't know what "this" refers to, but probably not

oh in $\mathbb R^2$

@ACuriousMind First of all, what does $T_e\mathrm{Diff}(\Sigma)$ mean?

Polar coordinate is not just for complex plane. It's a map $f : \Bbb R^2 \to \Bbb R^2$ given by $f(r, \theta) = (r\cos \theta, r \sin \theta)$.

oh right

As a map $f : \Bbb R^2 \to \Bbb C$ you can write it as $f(r, \theta) = r\cos \theta + ir\sin \theta$

@0celouvskyopoulo7 That should be the vector fields, going by my dirty physicist's intuition :P

@ACuriousMind ...vector fields on what?

On $\Sigma$

(Which is also equivalently written as $f(r, \theta) = r\exp(i\theta)$ by Euler's formula but whatever)

An infinitesimal diffeomorphism should be a vector field

It's supposed to be the tangent space at the identity diffeomorphism

Yes, I assumed you were not asking whether I knew what the notation meant, but what it "is"

So that's a good point, from the physics PoV that's exactly what it is

But I was looking for a rigorous definition

Good luck.

But I recall you saying you're not familiar with classical mathematical field theory

Not with the mathematical variant, no

It's seriously complicated to say in which sense Diff(M) is a smooth manifold.

@BalarkaSen Well, I think I need to understand it

"Good luck"

@BalarkaSen So you don't know?

nah

mike does

infinite dimensional frechet stuff

sorry last thing @Balarka. so we know that $(A,B)$ is on the unit circle of $\mathbb R^2$. but how does it follow then that we can write $\cos(\omega t+\phi)$?

I'll read the paper and see how much I can piece together. But I really don't want to have to learn a whole other field of mathematics

because that is again in $\mathbb R$

@BalarkaSen Mike will tell me to read Kriegel & Michor, which is pretty damn scary

oh i see why

we first "try" $\cos \phi$ and $\sin \phi$

and because the squares add up to 1

we know it's well defined

Mhm. So you can solve for $\phi$.

and we'll find the right angle with $\tan\phi$

right, thanks!

Yep.

And (A, B) being on the unit circle means A = cos(phi), B = sin(phi). That means your expression is Acos(wt) + Bsin(wt) = cos(phi)cos(wt) + sin(phi)sin(wt) = cos(wt - phi)

wowwwww

thanks man

bornologification? you can come up with better terminology

I got so much better with sines/cosines and complex exp ever since I started studying vibrations :P

it's a good exercise

The bornologification of a locally convex space is the finest locally convex topology with the same bounded sets,

Oh. Is that really a thing.

Tell me it's not.

I wanna be ultrabornologified when I die.

@BalarkaSen It's in the appendix of Kriegl & Michor

I wanted to get this book but then I read that sentence and noped out

ncatlab.org/nlab/show/bornological+topological+vector+space

I like functional analysis but damn

What the actual

I mean

What

Bornological is fine

Topological vector spaces are just so technical

> The name was coined by Bourbaki.

That explains everything man

amazon.com/Convenient-Setting-Global-Analysis/dp/0821807803

I wonder if the name makes sense in French

because in English it makes no sense

alright guys, i'm out. thanks a lot for all the help today!

"bornivorous"

@0celouvskyopoulo7 Why not? I mean, it's not a great title, but it's saying that its topic is "global analysis" and that it's a convenient setting (to do math in, presumably). What's non-sensical about it?

@ACuriousMind So I'm looking at some space of field configurations $\mathscr S$ (with some initial $U$), and the obvious map $\psi_U:\mathrm{Diff}(\Sigma)\to \mathscr S$. Then "stability" is phrased in terms of $d\psi_U:T_e\mathrm{Diff}(\Sigma)\to T_U\mathscr S$

@ACuriousMind I was talking about the word bornologic, because Bourbaki are French

So it's not clear to me what either of those tangent spaces are

or what that differential is supposed to be

::shrug::

handwave

@0celouvskyopoulo7 Ah. I think 'borne' means "bounded"? @Slereah?

$\mathscr S$ has the $C^2(\Sigma)$ Frechet topology from what I surmise

Well, if $\mathscr{S}$ is a vector space I would assume its tangent space can just be identified with itself, so that's a map from vector fields to field configurations that should be thought of as "small perturbations" of $U$. Don't ask me to make that rigorous.

k i'm going to log out and do some actual work

@ACuriousMind I think that he's just using the 'curve' definition of tangent spaces, which makes sense in this context

Oh well, need to read this instead of talk

@ACuriousMind do you know of a place called "DFT"

think physics

dft.if.uerj.br

The link I have for this paper is dead

What do?

reddit.com/r/technology/comments/6adipo/…

Well...fduck

@SirCumference I must say I don't understand the whole fuss over net neutrality. I see why people want it, but I don't see why people should get it or deserve it.

@0celouvskyopoulo7 Why ya say that?

@SirCumference Surely the ISPs should decide how things are priced and how traffic flows.

If you say so. From a consumer standpoint, I just enjoy faster internet. Website owners will feel the same way.

Of course it's better for the consumers, but they are not relevant

The only weapon the consumers have is their wallet, anything else is made up

@0celouvskyopoulo7 That reminds me of a quote: "You are not Google's consumer, you are its product."

Yeah, and you don't have to pay for google

@ACuriousMind are you around

@Slereah Your knowledge of Visser is required

@0celouvskyopoulo7 somewhat

@ACuriousMind I'm probably goofing, what is the "orthonormal frame attached to a particular coordinate system"

I'd say the frame attached to it is just $\partial_\mu$, but I don't see why that'd be orthonormal

Exactly...

@ACuriousMind i think it's a tetrad derived from the $\partial_\mu$, somehow

It's just $\partial_\mu$ rescaled by the appropriate metric coefficients to become orthonormal.

sorry @0celouvskyopoulo7, saw your post of the picture of the drawing a couple minutes ago - I've got most of the drawing done, just need to add the text now

@heather uhhh

i know, i know, i'm an idiot

Hate to ruin it for you, but I turned my hand drawing in on monday

I got an A on the exam

yeah, it's a pretty nice drawing

Well the drawing was not the key, lol

well, it still is a nice one

thanks

urgh, i can't believe i didn't see it until now

what are you doing these days

finishing up the school year - had a spanish and math test today

and a social studies project due yesterday

and next monday is a quiz in health

oh god, health class

that was so awkward

I had to do a project on cocaine

yeah, so, it's a co-ed class, and we're in that unit

and the teacher is uber-bubbly/way too happy all the time

it's...interesting.

@heather you have the disposition of a single mother lol

what does being a single mother have to do with it?

I really, really enjoyed my high school health class.

The teacher actually went into some stuff about interpersonal relationships that I remember to this day.

Must you make a point of always contradicting me and disagreeing?

No, of course not. You're wrong to say that.

ironically, you contradicted him in saying that

@DanielSank, okay, you must've had a great teacher and a less awkward curriculum, because I hate health

^ Not an accident.

That was intentional.

^

@DanielSank Stop agreeing with me!

@heather Perhaps. Also, this was high school that I'm talking about.

You'll break the system

It's important to learn about things that matter in your life. Forced ignorance because a subject is taboo would seem, IMHO, to not serve a good purpose.

Some people grow up very uninformed about how things really work and it can lead to interesting problems.

@DanielSank In my class people kept asking about anal sex. It wasn't a good class.

I will probably get banned for that.

You might. I can imagine there could be very useful questions though.

Not sure I should repeat them here.

Frankly, people need to be able to get information somewhere, so why not school?

@0celouvskyopoulo7 You can comment on their utility.

@heather how's your Spanish?

@DanielSank It was clearly guys who didn't want to use condoms and had thought of a dozen ways to not get their girls pregnant.

I've been doing Duolingo in Greek and Russian recently. I like it. Installed it on my phone so I can practice during those five minute gaps everyone finds throughout the day!

@0celouvskyopoulo7 Well then it's good that they were able to ask their questions!

@DanielSank The teacher had an anonymous question box

And it's good that the girls could hear the answers too. Everyone should have the same information so nobody is left having to rely on trust in a difficult situation.

@0celouvskyopoulo7 That is an enlightened idea.

I recall my middle school health teacher insisting that a certain phenomenon that happens only to men were a myth, invented by men to cajole women into doing various things they wouldn't otherwise do.

Imagine my horror (both because I didn't know what was going on and because I realized I'd been lied to) a few years later when I suffered the condition.

Keeping this stuff secret and taboo serves nobody, IMHO.

I actually have no idea what you're talking about.

ED?

I probably can't say without incurring the wrath of the mods.

@0celouvskyopoulo7 What's ED? Link?

@DanielSank Viagra cures ED.

Ah. No not that.

You can't link what you're talking about?

.

I am so confused. Men don't have those.

:-P

How would that even work?

I think I'll not respond out of respect for chat rules.

happy to chat on another site's room though

@DanielSank mas o menos/pobre

bien

Hay que practicar, no?

si, si.

me gusta hablo en espanol - es divertida

Ven a Santa Barbara de vacaciones. Puedes hablar Espanol aqui ^^

no comprendo - 'go to santa barbara for vacation - can talk spanish here'?

lo siento - mi espanol es malo =P

I'm pretty sure "lo siento" is not used in that way.

I believe you want "disculpe".

Can we please talk physics, not spanish

"Lo siento" is much more of an expression of emotional empathy with someone who is suffering.

@EmilioPisanty right?

@0celouvskyopoulo7 At least it's not French... :P

oh, and disculpe is kind of a "i was rude, whoops" or "my mistake" sort of?

how about...physics in spanish?

@heather Yeah it's more of an "excuse me" or "pardon me".

@heather Chevere!

@DanielSank i was kidding, i don't know any words related to physics.

disculpar = to excuse

disculpe is a command.

did i do 'me gusta hablo en espanol - es divertida' (specifically the conjugation of hablar) correctly?

Los equatios einsteinos

You would say "Me gusta hablar espanol".

huh, i thought that you had to change -ar to -o

You make that change to say "I speak".

oh.

But you're trying to say "I like to speak..."

oh....that makes sense.

i only conjugate when i'm using it actively, sort of - right?

@Mithrandir24601 French is the language of Bourbaki and Berger

Hence it's the third best language.

@0celouvskyopoulo7, why do a lot of people say Bourbaki is bad?

@0celouvskyopoulo7 Mathematicians? I'm a physicist... So... Doesn't really change my mind about not liking French...

@heather use the -ar form whenever you'd say "to xxx" in English.

Bourbaki is hard to read, I have only read certain sections

As far as I am concerned it's a reference work

But they did a lot for modern mathematical structure

I don't know why people dislike them, honestly. They'll say something about being too abstract and then go do stuff with affinoid varieties.

Maybe it's the lack of pictures that triggers people. Not sure.

Certain math deserves pictures, some does not.

By the way, @heather, if you haven't discovered it yet, one of my (Spanish) friends mentioned this translation site as being particularly good for individual words

thanks @Mithrandir24601

i have not seen that.

@Slereah Got the 50 years of Cauchy book...

Literally everything in it looks good

@heather ¡de nada!

@ACuriousMind wtf :P

And it's now after midnight here, so I'm off to bed - buenas noches

buenas noches

got to go myself, have a good day everyone

@0celouvskyopoulo7 It's not the side effects of the cocaine / I'm thinking that it must be love

cocaine is great man

@BalarkaSen When you say you log off to "do some actual work", are you just dealing drugs? :P

Good idea. Maybe I was.

I'm a big believer in drugs

meh why's the chat transcript about health. drugs cure health, man. talk about drugs, not health

solution >>> issue