The h Bar

Balarka Sen

15:00

I am serious

Shia LaBeouf and Palpatine tell Anakin to DO IT

►

Secret

Well, to begin I have this magazine article
https://areomagazine.com/2017/03/27/how-french-intellectuals-ruined-the-west-postmodernism-and-its-impact-explained/

, and I learn the following from it:

skullpatrol

So both of you want me out?

Secret

Nope, you are fine to stay. I would rather want koolman out (This is why whenever he start asking his JEE questions, I get so annoyed and spam the chat)

Secret

My possibly half backed understanding:

So, in a nutshell, postmordernism is the rejection of consistency, or metanarrative, and favour mutually conflicting stories that only serves the community it is in. It also embraces a hierarchical structure where all individuals are being assigned labels and these labels dictate their role in the society. On top of that is the constant opposition of the status quo and social norms that are currently established and one way to do so is to deconstruct a hierarchy by moving concepts around

but I felt like I am missing something, right?

@BalarkaSen So what exactly are the core values of postmodernism?

skullpatrol

Well, they both posted a vid of "Do it."

Secret

15:03

typo: he start asking his JEE questions with no effort shown

Balarka Sen

@skullpatrol Depends on if you want to take Shia Lebouf serious

ly

LaBeouf, whatever

skullpatrol

JEE drives kids to suicide.

Balarka Sen

@Secret Well, first off, I only get to talk about literary postmodernism. I am no postmodernist philosopher.

Secret

ok

Balarka Sen

One of the emerging themes of literary postmodernism is refutation of objective reality and universal ideologies, ethics, morality, whatnot

Does that answer your question

skullpatrol

15:07

no

Secret

So what do they embrace?

Balarka Sen

I don't see why you think refutation is not embracing. Refuting an idea is embracing the negation of the idea.

shrug

Secret

Well, I guess, what is the negation of universal ideologies, ethics, morality. They seemed quite hard to understand for me as I am not very familar with working outside an established system of concepts

In fact, I don't think I fully understood what subjective reality means

skullpatrol

::runs back to bomb shelter::

Balarka Sen

That's kind of a big question to answer on a few chat messages really

but I am sure there are essays about this

not to mention literature and artistic works

0celo7

15:12

Post-modernists are like nihilists

they should ---- ----------

heather

the post of the wiki page non-sequitur was, I think, a non-sequitur =P

Balarka Sen

how very meta

ACuriousMind

It was also very much doing was he was asked not to do :P

0celo7

why do you keep doing that?

you're gonna get suspended

@ACuriousMind So...how do I overclock. What's a reasonable value?

Secret

well, that magazine article I linked, does mentioned postmodernism is kinda like nihlism, which makes me a bit more confused because there should be a difference between them

0celo7

15:15

@Secret they are both delusional

ACuriousMind

@skullpatrol This was your third kick today, and it's only not for half an hour because you switched accounts. I will consider using any of your accounts to talk in here at all during the next half hour a breach of the policy about using sockpuppets to circumvent system restrictions.

Secret

Claim:

(Claim aborted as I cannot seemed to find that comment about me in the transcript)

vzn

@BalarkaSen trying to understand that comment, is it ref to his recent meltdown? dailymail.co.uk/news/article-4686424/…

Balarka Sen

I didn't know that news, but that makes it 10 times funny

Shia LeBeouf is a total meme

vzn

15:31

@Secret postmodernism is a philosophical and literary concept, quite broad/ abstract/ slippery/ even vague at times... philosophy tends to be inherently confusing sometimes the more one delves into it...

@BalarkaSen yeah a meme, but what is the meme? what was the context of your response?

Balarka Sen

I did not have a particular meme in mind when I said it. There are 10 million memes of him in the internet.

vzn

@Secret recently inquired into this, postmodernists might benefit from en.wikipedia.org/wiki/Logotherapy ... also am reading this right now, think you/ others here would like it amazon.com/Synchronicity-Bridge-Between-Matter-Mind/dp/…

@BalarkaSen so, a meaningless meme? :|

Balarka Sen

i have no clue what that means but i am not going to spend more than 3 messages on analysing why or how Shia LeBeouf is a meme :P

Avantgarde

Just do it?

Balarka Sen

Do it

vzn

15:38

@BalarkaSen sigh but if you cite him yourself you apparently have some meme in mind? at least you could descr the meme in your mind? but maybe thats the point, that hes pointless? ("oh how the mighty have fallen"?) he seems to be verging on mentally ill lately... (addiction is a mental illness...) o_O

Secret

Superdeterminism

In quantum mechanics, superdeterminism is a hypothetical class of theories that evade Bell's theorem by virtue of being completely deterministic. Bell's theorem depends on the assumption of "free will", which does not apply to deterministic theories. It is conceivable that someone could exploit this loophole to construct a local hidden variable theory that reproduces the predictions of quantum mechanics. Superdeterminists do not recognize the existence of genuine chances or possibilities anywhere in the cosmos. Bell's theorem assumes that the types of measurements performed at each detector can...

I actually did had a superdeteministic dream before

Avantgarde

Dream?

Secret

and believe me, it is pretty much like being in The Matrix... no it's even worse

Imagine a scenario where everything and every action, including moments where you decided to rebel against the dream's intended script, are actually part of the script of the dream, and that you will not aware you are following the script until you wake up

It is a more extreme variation of what Neil Levy called action script, where even the moments you think you have freewill are actually part of a predetemined script

Balarka Sen

I wonder if I am going to spend all my day participating in shit discussions

vzn

@Secret that does not seem to be refd much, had not heard that! thx for the ref... reminds me of "emergent QM", looked into it awhile back, seems to be "emerging" :P vzn1.wordpress.com/2015/01/26/…

@BalarkaSen lol "you get out of it what you put into it" :P

Balarka Sen

15:43

I mean it's tempting and an excellent procrastination technique

vzn

@BalarkaSen agreed! if you have something meaningful to procrastinate about. do you? :)

Balarka Sen

that makes no sense bruh

vzn

@BalarkaSen ?

Balarka Sen

your lol message. the sentence inside the scare quote makes no sense at all

i have read some of the strangest of english sentences, but that's really twisted

vzn

@BalarkaSen its a common english expr. it has lots of positive interpretations. sorry you couldnt find any :(

Balarka Sen

15:50

i actually want to write sentences like that

how high do i need to be to do that?

vzn

← lives in state 1st legalized MJ, does not partake, but marvels at the "change all around me"

Sid

@BalarkaSen I think, that depends on how high you want to be.

vzn

@BalarkaSen 5280ft :P

Secret

Jun 21 at 6:18, by Secret

however, I suspect even my rapid blinking is not really out of my freewill (despite it feels like I am in control), but part of the script of the dream. This is because this event strongly reminds of that most skips in a minute guiness world record video I posted yesterday.

My eye blinking fast may be a symbolism to that skipping

details of that superdeterministic dream

Balarka Sen

@Sid one should always try to maximize dankness

Sid

15:56

@Secret Rapid blinking simply means you have to get your eyes checked. :P

Balarka Sen

so as much high as needed

Secret

@Sid no, the rapid blinking took place within the dream

Sid

@Secret That's your subconscious telling you to get your eyes checked. :P

Balarka Sen

@Secret if Freud found you, I am pretty sure he would not write his big tome called "Interpretation of Dreams"

Secret

O that, I already have a regular eye check schedule since prenisolone can increase eye pressure

@BalarkaSen yeah, for some reason, ever since I watched Cloud Atlas, all my dreams started to have its self contained history, complete with memories for every person including myself, that has nothing to do with my waking life

Yashas

15:59

prenisolone :o

I used to take that too IIRC

for ulcers

anti inflammatory substance

Sid

I used to take anti-histamines for allergy. That's it. Never took steroids

0celo7

Is philosophy a good use of time?

Sid

@0celo7 That would depend on your other activities. :P

This conversation reminds me though, I need to get new glasses. Pretty sure, the power of my lenses will change.

0celo7

@TheRaidersofLasVegas welcome back

The Raiders of Las Vegas

thnx

vzn

16:12

@0celo7 usually

0celo7

Maybe instead of a PoU I should use a cutoff...

Cutoff for a box-shaped neighborhood

@BalarkaSen

Balarka Sen

I don't know what you mean by that

0celo7

@BalarkaSen bah, won't work because I can't control the sides of the box

Someone has to have thought about this before

Balarka Sen

vOv

0celo7

@BalarkaSen do you understand my issue?

Balarka Sen

16:16

Nope

Actually, I have to run now.

0celo7

@BalarkaSen to apply elliptic regularity, I have to work in charts. To get boundary regularity, I need to have boundary conditions

ACuriousMind

→ 5 messages moved to Trash

0celo7

But I can't seem to localize the problem while maintaining Neumann boundary conditions

@ACuriousMind any thoughts?

ACuriousMind

Yes, "country conditions" is a very good typo ;)

No thoughts that would help you with the actual problem, though

Sid

@ACuriousMind Is that some sensitive matter due to which you moved the messages to trash?

ACuriousMind

16:29

@Sid Just that they needlessly brought up drama again. Let's just move on.

Sid

Oh, okay.

Secret

On a unrelated note, I think there are at least two trash bins in SE, cause messages in maths chat that are deleted, the trash bin cannot be accessed by ordinary users

0celo7

@ACuriousMind Sobolev embedding certainly holds for a rectangle, right?

ACuriousMind

@Secret Yes, there's a public and a private trash.

0celo7

It's Lipschitz

@ACuriousMind wonder what kinds of things are in the private trash

ACuriousMind

16:33

@0celo7 Uhhhh...I'm not sure I know enough about Sobolev spaces to say anything with certainty

Secret

As far I know, some ordinary level rule violation posts can end up there as it happens when mods clean up trolls in the maths chat in some occassions

ACuriousMind

@0celo7 It's not a consistent distinction because many mods/RO that want to move messages to Trash just pick one of them at random :P

There's also some other trash rooms for specific chatrooms. It's a system definitely lacking in...elegance of design.

Secret

There are also messages that are just deleted by room owners, for a host of reasons from users requesting to have them deleted, or a sensitive information is being shared and etc.

for these, they don't even have "blah blah blah is moved to trash" showing up in the transcript

0celo7

@ACuriousMind see...I want a cutoff function that's constant near the middle of the boundary of the rectangle , then tapers off in the back and the sides. But it should be constant along the n-th direction near the boundary

That way you don't change the normal derivative near the boundary but have a good Dirichlet condition near the back and sides

If you make it decay enough there you can get Neumann all around

Then you get regularity near the boundary. Just have to convert that into charts and a partition of unity

Sid

For some reason, my mouse pointer isn't moving. Anyone knows why?

0celo7

16:43

@ACuriousMind does that make sense :P

PhyMan

@Sid Yeah, it's broken :P

Secret

in Game Development, Jul 3 at 16:56, by doppelgreener

→ 155 messages moved to Trash

Link to private trash example

vzn

@ACuriousMind lol need more elegant trash cans :P ... think there is some reason to have public/ private trash... one is merely offtopic, the other is censored

Secret

Also I need to correct what I said just before: Maths chat uses the public trash

Highly moderated chat rooms such as game development uses the private one

ACuriousMind

@0celo7 sort of, I guess?

I'm really not a formal PDE kind of person :P

0celo7

16:48

@ACuriousMind I'm just running errands thinking about this

Secret

(O and sites like stack overflow, like what acuriousmind mentioned, have their own trash bins chat.stackoverflow.com/rooms/23262/trash-can)

Jan 17 at 8:51, by Secret

O that, while managed to set the record of the most visitors in h bar yesterday, I got myself tempbanned for 2 hours after a gamedev chat user flagged my "spam"

The lesson is that: Some chat room have less tolerance for off topic messages than others, and don't mass post in all chat rooms

From my experience, English language and usage & game development are the two most heavily moderated chat rooms.

Their user culture (especially game development chat) has very very low tolerance for off topicness

Maths chat used to be like that, but now it is relaxed since the general discussion rule is added

Sid

game development=arqade?

Or is that another SE site?

Secret

Game Development

Game development and other polite discussion. Game development...

2

ACuriousMind

@Sid Game Development and Arqade are different sites.

Sid

Oh, Okay..

dmckee

17:04

@0celo7 She mostly eats, sleeps, poops, and exudes an apparently unlimited supply of cute in every direction.

Sid

@dmckee Good luck cleaning poops. :P

Avantgarde

@BalarkaSen @Mostafa Something you'd like? 9gag.com/gag/a9A754j

0celo7

@ACuriousMind amazing, they have a display model of the headphones I was looking at

Physical stores are still the best

dmckee

17:23

@Sid I have to say one thing for waiting until so late in life for this event: diaper technology has improved even comparing against the nineties. Compared to the seventies it's heaven.

AccidentalFourierTransform

@dmckee first kid?

dmckee

Yes.

AccidentalFourierTransform

let me guess her name

hmmm... Elizabeth?

dmckee

Nope. Worse, she ended up with lots of names on account of family politics.

AccidentalFourierTransform

Sarah?

Sid

17:31

@dmckee lol. So, different name from paternal side and different from maternal side?

dmckee

@Sid As well as one for a close friend of ours.

But at least it means I'll have a nuanced set of expressions of displeasure when shouting for her later in life.

Sid

That makes it 3 names. wow. Well, considering I have 3 names too(1 is of course what they call a boy in native language), she wouldn't face too much problems. :P

dmckee

Most kids in the US know that when a parent hauls out all three of their names they are torqued off. I can haul out four if need be.

Sid

@dmckee dude, your girl is just born. Why are you so eager to scold her? :P

AccidentalFourierTransform

because he's a mod. That's what they do

Sid

17:42

I can bet that you won't be able to get angry at her until she reaches double-digit age. Even after that, I doubt you will. :P

dmckee

@Sid We spent a couple of months weighing pros and cons or possible names. I find the politics annoying, so I selected an absurd "pro" to trot out when asked about it.

Laugh or cry, right?

AccidentalFourierTransform

Jul 7 at 20:12, by AccidentalFourierTransform

I want kids too :-(

it must be fun to choose names

I know names, I have the best names

0celo7

@ACuriousMind I got some ridiculous RGB headphones :P

Maybe I should get some RGB RAM

Sid

@dmckee How can prospective names have pros and cons? I mean, a name is a name, right?

0celo7

@Sid e.g. Watermelonisha is a bad name.

AccidentalFourierTransform

17:49

0celo7

@AccidentalFourierTransform How so?

AccidentalFourierTransform

¯\_(ツ)_/¯

Sid

@0celo7 You clearly haven't heard names that are longer than that..

It's pretty smooth though on speaking

0celo7

Uvuvwevwevwe Onyetenyevwe Ugwemuhwem Osas

►

Slereah

18:02

So it turns out the GPK boundary was in HE the whole time

0celo7

fug, something is wrong with the Razer software

it's not updating correctly

of course something had to break

oh shit, up to 38 percent now

the trick is to run it 20 times and restart three times

stuck again

c'mon lil program

Balarka Sen

18:25

@Avantgarde This is very good

Sid

Putin is an artist.

0celo7

Putin might be the greatest person ever

Balarka Sen

He certainly will be after he officially restarts KGB

0celo7

@BalarkaSen I now have a headset w/ mic

We can play GTA5

Balarka Sen

thumbs

0celo7

18:35

@BalarkaSen thumbs?

Balarka Sen

I want to more time for being able to do pretty much literally whatever

@0celo7 I was just giving the new headset and mic a thumbs up

0celo7

@BalarkaSen oh

@BalarkaSen it's summer, why are you so busy?

Balarka Sen

Summer vacation comes and goes pretty earlier in this part of the world

Sid

@0celo7 Well.. here it is monsoon, not summer anymore

Balarka Sen

I am supposed to go to a Riemannian geometry conference

in 4 days

but I still don't know a damn thing about it lol

0celo7

18:38

how the fuck does a high schooler do that

Sid

Wait... what? A conference?

Balarka Sen

sorry a workshop

0celo7

o.O

Who pays for that??

Sid

@BalarkaSen You are in which year of high school?

Balarka Sen

last

Sid

18:41

@0celo7 I think it is either he himself will pay for that.

Balarka Sen

@0celo7 I am going out of peer pressure, not from my own free will

0celo7

@BalarkaSen peer pressure from whom?

Sid

Or if he goes via school, then, maybe the school will give him free transportation

Balarka Sen

a mathematician i know

0celo7

@Sid what high school pays for transportation/food/housing?

Balarka Sen

18:42

and who is conducting the event

0celo7

@BalarkaSen how do you know a mathematician in high school

Balarka Sen

long story man

i pay for travel. they pay for stay and food

Sid

That's a fair deal as long as you are not travelling in a Business Class flight

Slereah

a mathematician in high school sounds sad

Like he gave up on his dreams

0celo7

@BalarkaSen Well when you are there, can you please ask for a reference for regularity theory for elliptic Neumann problems

Slereah

18:43

and settled to teach

Balarka Sen

i have no freaking idea what that means so

0celo7

also existence/uniqueness/regularity for PDE of the form $$S_t =-\frac{1}{S_{xx}+S}$$

Slereah

zdnet.com/article/…

"The laws of Australia prevail in Australia, I can assure you of that," he said on Friday. "The laws of mathematics are very commendable, but the only law that applies in Australia is the law of Australia."

0celo7

@BalarkaSen Elliptic means the differential operator $L=a^{ij}\nabla_{ij}+\cdots$ satisfies $a^{ij}\xi_i\xi_j\ge \lambda |\xi|^2\ge 0$, Neumann means we want $\partial u/\partial n=0$ on the boundary, and regularity means $f\in C^\infty(\bar M)\implies u\in C^\infty(\bar M)$ if $Lu=f$.

Balarka Sen

@0celo7 Yo, you want to teach me Riemannian geometry in, uh, 4 days?

0celo7

18:48

@BalarkaSen What is the workshop on?

Balarka Sen

a bunch of things; complex differential geometry, geodesic flows, h-principle, Yang-Mills. I suspect these are all introductory talks and they say they are aiming at students with a background in Riemannian geometry

I personally asked the convener and he said I should at least know curvature. Maybe Jacobi fields.

0celo7

Yang-Mills should be up your alley

Complex differential geometry could mean algebraic geometry hell

Balarka Sen

Basics of Riemann surfaces, holomorphic differentials and harmonic forms, Riemann bilinear relations, the period map, Siegel upper half space, Teichmuller space, quasiconformal maps, Bers embedding, Bers Simultaneous Uniformization, Quasifuchsian groups, complex Fenchel-Nielsen coordinates and the relation to the complex symplectic structure, etc.

Complex manifolds, holomorphic vector bundles, Kahler manifolds, dbar equation, Kodaira embedding, Kodaira vanishing, algebraic geometry from a differential perspective.

that's the syllabi

0celo7

If you had a week I would suggest reading Wells' "Differential Analysis on Complex Manifolds"

Since you have a good knowledge of sheaves, maybe you only need four days.

Balarka Sen

I don't think I particularly need to know any of that. I just think I should know curvature :P

The talks are apparently self-contained

0celo7

18:53

@BalarkaSen Ok, well let me explain why curvature is the way it is. Do you know the Frobenius theorem for foliations?

Rhetorical, of course you do.

Balarka Sen

Right.

0celo7

It's actually a much older theorem, and the original purpose was a necessary and sufficient condition for certain first order matrix PDE to have unique solutions.

Spivak has a whole chapter about how foliations and first order PDE are related.

Balarka Sen

Yah, foliations on $M$ are the same thing as differential ideals of $C^*(M)$, I believe

0celo7

@BalarkaSen $C^*(M)$?

Balarka Sen

$\Omega^*(M)$: graded ring of differential forms on $M$

typo.

by differential ideal i mean an ideal which is a graded ideal of that graded ring

a distrubution naturally gives rise to such an ideal: forms vanishing on that distribution

0celo7

18:59

Anyway, the relevant result is: Let $U$ be an open set in $\Bbb R^k\times\Bbb R^m$ and let $(A^i_j)$ be an $m\times k$ matrix of smooth functions on $U$. Then the following are equivalent: (i) For every $(x_0,z_0)\in U$, there is a nbhd $V$ of $x_0$ in $\Bbb R^k$ and a unique smooth map $f:V\to\Bbb R^m$ with $f(x_0)=z_0$ such that $$\partial_j f_i(x)=A^i_j(x,f(x))$$ for all $i,j$. (ii) The functions $A^i_j$ satisfy the following system of equations in $U$:

$$\partial^x_k A^i_j+A^l_k\partial_l^z A^i_j=\partial^x_j A^i_k+A^l_j\partial^z_j A^i_k.$$

@BalarkaSen The proof is little more than showing the PDE defines an involutive distribution, then you get an integral manifold and it's a graph that gives the desired function $f$.

Balarka Sen

Gotcha

bolbteppa

A lot of that is in GSW and Griffiths Alg Geom

Why are mass and spin conserved in the Poincare Group

0celo7

@BalarkaSen Natural question in Riemannian geometry: We have a manifold $(M,g)$. Pick $p\in M$. When does there exist a nbhd $U\ni p$ such that $(U,g|_U)$ is isometric to an open set in $\Bbb R^n$ with the standard metric?

Balarka Sen

Right, that's a completely fair question.

(I know the answer but not how it's done)

bolbteppa

I mean there is some nonsense about group theory showing you about mass and spin being conserved, but it seems you can also get spin and the Pauli Lubanski from treating spin as a density matrix which is awesome

and this thing shows up in the propagator which is shocking

0celo7

19:07

@BalarkaSen It is good enough to find a coordinte sytstem $(y^i)$ about $p$ such that $$\nabla \frac{\partial}{\partial y^i}=0$$ everywhere (where they are defined) for all $i$.

Do you see why?

Balarka Sen

That means $\partial/\partial y^i$ are geodesics starting at $p$, right? That should mean the exponential map should be an isometry under that parametrization, am I right?

Well, actually, you mean $\nabla_v \partial/\partial y^i =0$ for all $v$ on $T_pM$ wherever that makes sense. That means the exponential map is an isometry, I guess

0celo7

You are, but the reason I had in mind is a little easier. By a linear change of coordinates we may assume that $g_{ij}(p)=g(\partial^y_i,\partial_j^y)(p)=\delta_{ij}$. Then use the definition of the LC connection: $$X g(\partial^y_i,\partial_j^y)=g(\nabla_X\partial^y_i,\partial_j^y)+g(\partial^y_i‌,\nabla_X\partial_j^y)=0$$ for any vector field $X$ defined in $U$. So the metric coefficients are $\delta_{ij}$ everywhere, i.e. the Euclidean metric.

bolbteppa

@BalarkaSen That syllabus is very specific, you don't need to waste time on diff geom, lecture 11 "Complex Manifolds" of the string theory course here: perimeterinstitute.ca/training/perimeter-scholars-international/… will set up the complex diff geom for the second half up to Kahler, to motivate the first half find out what a Fuchsian group and what Uniformization is, but the lecture is going beyond that and looks crazy heh

Balarka Sen

@bolbteppa The syllabus is not complex differential geometry. That's just like a quarter of the talks.

It's just a broad overview of the various applications of differential geometry, of which CDG is a specific part.

No prior knowledge of CDG is actually needed, according to the convener.

bolbteppa

Cool well that's only an hour but maybe the lectures will do the same thing

I wish I could sit down with Griffiths and get up to Kodiara etc

0celo7

19:18

@BalarkaSen Clear?

Balarka Sen

@0celo7 Oh yeah that made sense.

That's much easier.

0celo7

@BalarkaSen So the goal is to construct those coordinates out of a given one. That's a common technique: pick some coordinate system and derive a PDE that you need to solve for the ones you actually want.

Let $(x^i)$ be some coordinate system around $p$. We want to find functions $\mu_i$ such that $$\nabla(\mu_i dx^i)=0.$$

This is eqivalent to $$\partial_j^x\mu_i+\Gamma^k_{ji}\mu_k=0.$$

Note that I actually have not assumed that the connection is torsion free yet...

So this equation if of the form covered by the Frobenius theorem. The necessary and sufficient condition that this can be solved for $\mu$ is $$\partial_i^x\Gamma^k_{jl}-\partial_j^x\Gamma^k_{il}+\Gamma^k_{im}\Gamma^m_{jl}‌-\Gamma^k_{jm}\Gamma^m_{il}=0.$$

@BalarkaSen Three guesses what tensor that is...

Balarka Sen

Looks like the Riemann curvature tensor. $\nabla_X\nabla_Y - \nabla_Y\nabla_X + \nabla_{[X, Y]}$

Maybe $[X, Y]$ should be $[Y, X]$

0celo7

@BalarkaSen I can never remember, but that's exactly right.

Balarka Sen

Yeah. That's a very fun perspective there (about using the Frobenius theorem)

0celo7

19:26

So we have these $\mu_i$, which are actually vector-valued.

But we're not done yet.

Finally, we want coordinates $y$ such that $dy=\mu_i dx^i$. So we need $$\mu_i=\frac{\partial y}{\partial x^i}.$$

Balarka Sen

Mhm

0celo7

And again the Frobenius theorem gives the necessary and sufficient condition as $$\partial_i^x\mu_j=\partial_j^x\mu_i.$$ Using the other equation this is just $$\Gamma^k_{ij}=\Gamma^k_{ji}.$$

So zero torsion + zero curvature implies locally flat.

Balarka Sen

Ah, got it

0celo7

@BalarkaSen Does that clear it up?

Balarka Sen

@0celo7 That's a lot helpful, yeah. Thanks!

Mostafa

19:40

@Avantgarde Nice. Putin is The man

One of the main papers that brought Mirzakhani the Fields Medal is 204 pages!!

0celo7

???

Slereah

20:01

"Since $P$ is a past set, $$P = I^-(P \cap I^+(p)) \cup I^-(P \setminus I^+(p))$$"

Is it that obvious???

0celo7

What is $p$?

Slereah

A point in $P$

0celo7

let's draw a picture.

Slereah

I don't trust pictures

0celo7

Yes.

It is trivial.

Slereah

20:02

they do not reveal the weird topological exceptions

0celo7

$P=I^-(P)$ and $(I^+(p)\cap P)\cup (P\setminus I^+(p))=P$.

Slereah

Yes, but is $I^-(A \cup B) = I^-(A) \cup I^-(B)$?

Hm

Thinking about it

By the definition of $I^-$ for sets

I guess it is

0celo7

Of course.

It is a functor

Slereah

$$I^-(S) = \bigcup_{p \in S} I^-(p)$$

0celo7

Exactly.

Slereah

20:05

Aight

thx

I wonder what the rule is for intersections

I guess I need some De Morgan law there

0celo7

@Slereah PhD set theory

Slereah

De Morgan law is just ring properties man

0celo7

20:20

@Slereah PhD algebra then

Slereah

I actually can't find a theorem for it

I don't know what gives $$\bigcup_{p \in A \cap B} I^+(p)$$

0celo7

what gives what

Slereah

I think it's $I^+(A) \cap I^+(B)$ but I'm not 100% sure

0celo7

I would believe it...does that not follow from $$I^+(p)=\bigcup_{p\in A}I^+(p)$$

Slereah

Does it

It's not too hard with union because you just enlarge the domain of definition

but I'm not sure about intersection

If I take two spacelike separated points $p$ and $q$, $I^+(p \cap q)$ is the empty set

But $I^+(p) \cap I^+(q)$ isn't necessarily empty

0celo7

20:36

@BalarkaSen How does Whitney's embedding $M\to \Bbb R^{2n}$ work?

Balarka Sen

@0celo7 I think the actual proof is complicated, but you can immerse $M$ in $\Bbb R^{2n}$ so that you only have transverse double points in the image right?

You can look at paths based at the double points, fit disks inside them and "push" the immersed submanifold along the disks to desingularize it

That gives an embedding of $M$

0celo7

@BalarkaSen Uh, I guess I believe you on that?

Was that in GP?

Balarka Sen

Yeah it's true. Embed $M$ in $\Bbb R^{2n+1}$ by usual Whitney argument, then pick a generic hyperplane and project along it

It's the same trick. I think it's mentioned in GP

0celo7

@BalarkaSen And that gives only transverse double points?

For "almost all" planes?

@Slereah wonder what happens if you put the EFE into mathematica

Slereah

probably not much

0celo7

20:43

@BalarkaSen Btw, I am taking a measure theory-based probability course next semester. Pls send prayers

Slereah

1 like = 1 prayer

0celo7

1 star = 1 prayer

6

Balarka Sen

Prayers sent

0celo7

thx

@Slereah what is $p\cap q$?

Mostafa

Putin riding a bear toy is available for $47.99
http://www.ebay.ca/itm/221868418003

0celo7

20:50

@Mostafa too expensive

Slereah

@0celo7 $\{ p \} \cap \{ q \}$

if you prefer

0celo7

@Slereah so...nothing if they're different points?

Slereah

Yes

On the other hand, $I^+(p) \cap I^+(q)$ isn't necessarily empty

Mostafa

@0celo7 The size:

Slereah

I'm not sure there's really a simple formula for $I^+(A \cap B)$

Mostafa

20:51

0celo7

god, tag that NSFW

Slereah

Nothing shameful about the human form

0celo7

you're a Europoor

over here we have finer sensibilities

Mostafa

@0celo7 Is this about Putin or the bear?

what about this?

Avantgarde

@BalarkaSen New music? (ignore the growls if you can) youtu.be/MWlg4xzrLP4

0celo7

20:58

@Mostafa amazing

Putin saving Western Civilization and Freedom

Mostafa

@0celo7 yeah.

Balarka Sen

@Avantgarde On it

0celo7

@Mostafa that's obscene

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