00:00 - 17:0017:00 - 23:00

5:02 PM
@CooperCape: as you've probably guessed it was do do with your question.

Yeah - Looking back on it it wasn't really a truly answerable question

I graphed $x^1$ against $x^2$, and over your range (from 0 to 50) the length of the curve isn't that different to the length of a straight line between the start and end points.

Yeah that's how I apporximated it

Unfortunately when you weren't around this morning I deleted the spreadsheet I used to do the calculation.

Oh right - apologies
Wifi at my school broke

5:05 PM
Anyhow, that's why your integral isn't that different from a straight line.

Yeah it wasn't for any useful calculation of sorts just to check if I understood what was going on
One thing did confuse me however - in that it didn't seem as if the line would be spacelike (the units were in metres!) however $\Delta \tau$ was undefined (as the square root is negative)
is there a reason for that?
I thought maybe because I took $c=1$ so using $t^2+t$ put it outside the light-cone

0

Lately I've been wondering about the relation between the symmetries of the energy-momentum tensor and the symmetries of the space-time. In The symmetry of the energy momentum tensor does not necessarily reflect the space-time symmetry: a viscous axially symmetric cosmological solution by Fatemeh...

@JohnRennie What do you make of this?
It seems that since $G=T$ and $G$ inherits symmetries from $g$, the symmetry group of $T$ should be at least as large as the isometry group.

What is @0ßelö7's avatar supposed to be...?
It's somehow unsettling

it's me

@0ßelö7 I'm not sure. It's an interesting question. However I've only skimmed the paper but I'm not sure the paper says what the question claims it says.

5:24 PM
@BalarkaSen If I have a closed manifold and a locally Holder function, it should be globally Holder, right?
There's an argument for loc Lipschitz functions on compact domains in $\Bbb R^n$
A similar proof should work for this
@ACuriousMind How do you say "I don't go out of my way for X" in German?

@SirCumference I searched google for image and it came up with iDubbz who I believe is a youtuber...

@0ßelö7 I don't think we have a direct equivalent for that idiom.

shhhh
@ACuriousMind that's a shame
@ACuriousMind How about "It annoys me when people do X"

Oh okkkaay... damn it's too late to edit/remove :/

@CooperCape nooooo
you ruined my plan

5:32 PM
flag for moderator quick

@CooperCape what, this?
yes, I agree

@EmilioPisanty No I meant my previous reply "Oh okkkaay..." just to keep Sir in the dark but that certainly is an interesting answer holy moly...
It's cool the guy has an intimate relationship with lil' Wayne, however.

@CooperCape not unheard of

I must admit in all of the massive 33 days I've been present I can't say I've seen an answer like that...

@0ßelö7 You can translate that one literally

5:44 PM
@ACuriousMind I'm looking for a more subtle way to say annoy
Not nerven

Then don't say annoy - just say you don't like it

fair enough

@CooperCape well, we clean them up relatively quickly
that's why you don't see them ;-)

Some gooooood moderation then :p
Isn't that what the first post review queue is for? Or something?

@CooperCape Posts like that are usually flagged by everyone who sees them, they don't tend to hang around for long even if no actual moderator intervenes (enough rude/abusive flags also delete a post without moderator intervention)

5:56 PM
hello

Oh wow I didn't know that...

@ACuriousMind who is ur current avatar? :'D

maybe ACM changes his avatar so much because he's an AI and has no self image

@StanShunpike Nines Rodriguez from VtM: Bloodlines

Maybe he's the brother of someone from The Vampire Diaries

6:00 PM
@CooperCape or, in other words, if you see spam or abusive posts, flag them
it really does actually do things

yeah... of course :p
Don't see that many tho

@StanShunpike He is a vampiric AI. Quite dangerous.

@ACuriousMind hmmm probably not someone the girls would go wild over then, but ya never know :'D

So, one recent example:
> DEEZ NUTS!
^ deleted by community flags

Anonymous
Any idea why this C program is printing a couple of garbage characters along with the desired output? The aim of the program is to convert upper case characters to lower case characters and vice versa. A sample output is here.

6:02 PM
@Blue Yes, don't use C.

Anonymous
@0ßelö7 I wish

Anonymous
BTW your avatar is cool. This is the type of display picture that suits you ;)

> You are all noobs, my cup of water is less dense than you. Liquids are heavy.
boy, they sure know how to write 'em, down at the bottom end of the barrel

@Blue what the hell does that mean

Anonymous
@0ßelö7 Take it as you wish. :P

6:07 PM
idubbbz is a demigod. I love him.

@BalarkaSen we are scarily similar
stop it

lol
only memetically i think

hmm, yes

I'm a bit confused as to the nature of what a "Lorentz boost" is? Is it simply a translation that doesn't involve rotation or does it transform it to a new set of coordinates which increase $v$?

@CooperCape It is nothing more and nothing less than a change to a reference frame that's moving at constant velocity

6:12 PM
constant velocity $v$?

Okay, thanks :p

@ACuriousMind I just need to convince them to let me give a 10 hour seminar
and restrain everyone in the audience
and hold their eyes open

when your antivirus comes up with "We've detected unsecure passowords (54) on your computer"
I don't even think I have 54 passwords wwhat...

@CooperCape but you should be careful with the term 'translation' - if you use it loosely, in this context, it's unclear whether you mean a translation in 3-space or in four-dimensional spacetime.

6:19 PM
Ahhh okay... so always say 'transformation' or what?

@0ßelö7 Is that you?

@CooperCape no, just specify which one you mean
translation on spacetime
vs
time-dependent translation on 3-space

@Abcd what?

Ahhh okay... thanks :p
Little by little I get there

Does anyone know the name of these? (except The Starry Night)

6:33 PM
I just bought a new computer
Look at how glorious it is

OK found using Google (RAINY NIGHT and VENICE GRAND CANAL by Afremov)

I was wondering if they were by Afremov

7:00 PM
@EmilioPisanty @CooperCape Emilio is absolutely correct, but to use the Lorentz transform as it is usually written in texts you must also have (a) the two coordinate systems have the same orientation (axes are all parallel) and (b) their origins coincide at $t = t' = 0'$.
Dispensing with those requirements makes the math messier without adding any understanding so they are used almost universally.

@dmckee yeah, y'right
here, have a video to compensate

@BalarkaSen are you talking about the h3 meme

@BalarkaSen of course I know
we are on the same level of memes

7:04 PM
digital blackface is exploding on internet
have to catch up with this

digital whiteface too

@dmckee by the phrase "as it is usually written" are we talking about $$x'=\gamma (x-vt)$$ $$t'=\gamma \bigg(t-\frac{vx}{c^2}\bigg)$$

@0ßelö7 yup, what a legend

@BalarkaSen he is now a gif on the internet

there should be a whiteface emoji
of ethan

7:09 PM
💁🏻‍♂️🙅🏻‍♂️🙋🏻‍♂️
that does not render correctly, boo

digital jewface looool

@BalarkaSen Do you know the Yamabe problem

I am afraid not

@0ßelö7 The price usually drops if nobody makes a purchase for a long time. Once someone buys something, the price increases again. I have seen this many times, and I usually wait for the price to drop before ordering.

@Jasper the price raised after I bought the book

7:17 PM
@0ßelö7 There was once I ordered a book for 140 USD and after that it went back to 270 USD.

lol what book?

Oxford Paravia Italian Dictionary.

I see

Turns out that they gave me the wrong edition twice, so I had to spend a huge sum of money returning them.

@Jasper What's the easiest optimal constant Sobolev inequality
I remember there being one that follows easily from Coarea but I can't find which one it was

7:18 PM
But they refunded me everything in the end, as long as you photograph and email them the shipping receipt.
I think I have forgotten all my math, lol.
Anyway, the third edition of that dictionary is now out of print, but I managed to find it in a small online bookstore in the end and got it for about 70 USD brand new.

Taking the piss?
-2

So, a few days ago scientists registered a very powerful Solar flare. It will reach Earth very soon (Saturday I beleive). I think I won't be able to build a Faraday cage. Should I use foil hat instead? I heard it can actually increase the effect of a flare.

@CooperCape Yep.

@0ßelö7 By the way, thanks for calling me a ninja that day. I think you look like a ninja too now. =D

Solar flairs? Umbrella :)

Anonymous
@Avantgarde Nah. That won't work. Better start building a 12,742 km deep hole to hide within the next 12 hrs.

Anonymous
7:26 PM
;)

@Blue Are you willing to invest?

@JohnRennie I want to believe it is. I really want to believe that.

Anonymous
@Avantgarde It doesn't need much investment. Just you need this:

Anonymous

Anonymous
Pretty cheap

7:27 PM
@Blue for ~12k kilometers?!?!?

Anonymous
@Avantgarde Well, you should carry some food with you so that you don't feel hungry while digging the hole. Oh, and it might be hot there. Beware. :P

mmm

hi @Avant

@BalarkaSen yello there

how's it going

Anonymous
7:37 PM
@Avantgarde Plenty. Plenty! I like most dishes containing meat. The usual pizza, burger, blah blah. My favorite cuisines would be Indian, Chinese and Italian. I love spicy dishes.

Anonymous
I hate veggies btw.

@BalarkaSen Good, what'sup with you?

tryna do some math

@Blue Very predictable :| I was hoping you'd say some obscure, elusive Ethiopian soup
@BalarkaSen You should send him a fan mail

Anonymous
@Avantgarde If you want those type of answers, @BalarkaSen is the right person :P

7:41 PM
@Avantgarde lol
i like art not artists

aw
@Blue Still trying to get to understand meat.

he was attractive back in the 60s though, so maybe i would have then
roxy music skitz

Anonymous
@Avantgarde Haw?

@BalarkaSen Roxy Music? You like em?
@Blue Haw? lol
Roxy Music is so chill.

Anonymous
Well, the tastiest food ever is surely the one you get hidden in your refrigerator at midnight

7:45 PM
they were good

Good music, but weird expressions. Typical 80s
@Blue Been staying away from the fridge for a while. The cough and cold isn't good. Made me miss my swimming. I feel like a fish out of water

@Avantgarde Typical 80s? ORLY?

Anonymous
@Avantgarde Hmm. I hardly swim.

Anonymous
@BalarkaSen Is that music? lol

@Blue Yes.
It is explosive music
brain = explode music

Anonymous
7:49 PM
Our tastes vary wildly :P

dab to you then

@BalarkaSen What year is that from?

@BalarkaSen dab on him. hard
@Jasper I must be thinking of the isoperimetric inequality

@Blue Cricket? Or wait, Football?

@Avantgarde exactly 1980. He wrapped up 70's with that album

7:52 PM
haha

Anonymous
@Avantgarde Mostly football :P

@Blue knew it
Mohun Bagan

Anonymous
@Avantgarde Nah. Never watched a single match of theirs

@Blue :(

Anonymous
I don't watch sports much

Anonymous
7:54 PM
Except IPL

Same here

Anonymous
That too very less

I like fidget spinning. Does that count as a sport?
(Not really)

Anonymous
I'm an expert in pen fighting.

Anonymous
XD

7:55 PM
I've seen that thing everywhere now. It really went viral

Anonymous
And sharpener fight too

Anonymous
Pen and sharpener fighting should be international level sports, really. Chess and stuff is crap.

Anonymous
lol

I plan to watch this movie

@Blue Chess is great. I'm assuming you didn't do pretty good at it? :P

Anonymous
7:57 PM
@Avantgarde Too boring for me

Anonymous
I like games where I have to move my hands, fingers, legs, etc

@BalarkaSen What the? Now they got a movie coming out?

Anonymous
Similarly I find cricket boring

It's a joke movie trailer. Watch the full thing

Anonymous
(playing cricket)

8:00 PM
@BalarkaSen You know German?
@Blue It is boring

no but i know how to put subtitles on
:p

:P I listened to some German rap the other day. Interesting journey, that

well I can brag about having listened to Norwegian black metal thanks to Ulver
Bergtatt is really good. I looked up the translations of their lyrics; very artistic
both musically and lyrically
Ok, cool I got "Reflections" downloaded. I can play this while doing math or some shit now

Wow, you liked that? Bergtatt is one of their best. But they quickly moved far from black metal into experimental electronic. In that genre, Perdition City is very good.

Anonymous
Anyone went to watch It ?

8:07 PM

I have heard of It
's a horror movie

Anonymous
It (Also Known As It Chapter One : The Losers Club) is a 2017 American supernatural horror film based on Stephen King's 1986 novel of the same name. Produced by New Line Cinema, KatzSmith Productions, Lin Pictures and Vertigo Entertainment, and distributed by Warner Bros. Pictures, it is intended to be the first installment in a planned duology. The novel was previously adapted into a 1990 miniseries. The film tells the story of seven children in Derry, Maine, who are terrorized by the eponymous being, only to face their own personal demons in the process. The film is directed by Andy Muschietti...

@Avantgarde Of course, I was absolutely mesmerized by it. Great music. I'll check out Perdition City

mm I like me some horror. Let me check their trailer

Anonymous
I like horror movies. Was planning to watch it

8:09 PM
@BalarkaSen Sure. Ulver are one of a kind in what they do.

Anonymous
Annabelle Creation was nice XD

Anonymous
@Avantgarde The trailer is disappointing

There's too too many buzzphrases flying around about new horror movies
"one of the best Stephen Kind adaptations" really?
The Shining is a classic
come on

Anonymous
Mirrors was one of my favourite

Anonymous

8:11 PM
@Blue It really was
Last horror I watched was Babadook. It was nice

@Blue Cronenberg's movie? Well it's admitted as one of the classic works in the genre of horror movies
so I am afraid you'll find yourself in the minority on that

Anonymous
They didn't let me enter the hall to watch to watch Conjuring 2 as I was under 18. It wasn't that scary.

Never watched Shining

Anonymous
I wonder why they put such age rules

@Balarka Try this and tell me if you like it

8:16 PM
high grossing horror movies on big halls tend to be more of a popcorn flying flick than actual horrors

@Avantgarde Can't listen right now, but I will. Thanks.

@BalarkaSen alrighty

Anonymous
@BalarkaSen Umm, I didn't like the ending actually. Otherwise it was okay. Not bad.

@0ßelö7 lol nope

8:19 PM
@BalarkaSen it might be a trivial lemma, I can't really tell
I'm not 100% sure what it's saying

@Blue Roger Ebert hates Cronenberg but gave that movie a praise as one of the best King adaptations of all time

what's wrong with taking $\Omega_i=B_{p_i}(\gamma)$, where one selects $p_i$ by second countability?
and $\gamma=\delta/3$
Hmm. Does "partition" mean disjoint?

I suspect for compact manifolds it's trivial

@BalarkaSen I mean, it really depends on what exactly "partition" means. If it's $M=\coprod \Omega_i$, then there is work to be done
But if it's just $M=\bigcup\Omega_i$, I think it's trivial
I should see how it's used

@0ßelö7 What if $\delta/3$ is greater than the injectivity radius?

8:27 PM
@BalarkaSen I thought $\delta$ was the injectivity radius

$\delta_0$ is

Oh shit, for all $\delta>0$
Ah, well. I missed that.

right.
you need control on the radius you need to exponentiate and stuff
and for noncompact manifold that's gonna be a mess

Hmm. So is everything dependent on $\delta$?

I think partition simply means union here, like any sane person would use it

8:28 PM
Like is $\{p_i\}$ dependent on $\delta$

Oh yeah very likely
If $\delta$ is small you'd need more and more points to cover all of $M$
Becuase $\Omega_i$ has radius less than $\delta$

so choose $\gamma<\min\{\delta_0,\delta\}$?

@BalarkaSen Yeah, just choose $0<\beta<\min\{\delta_0,\delta\}$, $\gamma=\beta/2$ and $\Omega_i=B_{p_i}(\gamma)$ for some sequence $\{p_i\}$

Strange. That should work.

8:38 PM
not sure what the hell curvature has to do with anything

i was thinking the same

but that's the stuff that makes Riem geo interesting, imo

maybe the uniform bound on the locally finite covering
I don't easily see how that comes

I think it's a comparison geometry thing.
Curvature bounds control volume growth of balls

ah
I should learn shit

8:42 PM
because $\sqrt g\sim something+ curvature +O(r^3)$ or something

yeah

(that's the intuition, the proof does not use expansions)
That growth theorem should be in GHL

It's been a while since I read GHL
let's see

page 168 ff.

tnx

8:47 PM
yeah, theorem 3.101 looks like a typical result

ah my copy must be a different edition because page numbers don't match
Bishop-Gunther?

yeah

Gottem
Ah cute so bound on curvature from above controls growth on balls from below
That should be exactly what you need
The bigger the balls, the lesser the overlaps in local finiteness

there is another result that should be in this book but I can't find
Oh, it's the same result
nvm
@BalarkaSen that result is sometimes attributed to Gromov

I see
makes sense to me!
he's a growth fanatic

8:51 PM
otoh I have Bishop's original book
he doesn't mention Gromov
@BalarkaSen Cheng used the theorem to show that if $\mathrm{Ric}\ge (n-1)K$, for $K>0$, and $\mathrm{diam}(M)=\pi/\sqrt K$, then $M=S^n$.

wow snoop dawg
that's cool

@BalarkaSen You basically show that M has constant curvature IIRC. The point is that the classification of constant curvature manifolds is sorcery

9:26 PM
@Blue Because when you're under ~18, it means you can't decide what's right and what's wrong, and therefore may hurt yourself :P

10:03 PM
@Jasper Ah, it was on page 81 of Ziemer

10:20 PM
@0ßelö7 from my reference frame when I shove you into a black hole at some point do you go wrapped around the entire thing?

@GPhys You mean if I'm large compared to the black hole?

no I mean in particular if you are small

I don't understand how a point should get wrapped around the entire thing

not a point, you

small usually means pointlike
I don't know; why do you think so?
@GPhys It depends on if you are falling with me or if you're trying to escape
If you're an infalling person then you won't see anything strange. The weirdness comes when you try to hover far away from the black hole and look in.

10:34 PM
yes the latter I think in the latter you wrap around

@GPhys So I go...behind it?
That doesn't seem like an observer dependent thing

Poincare-Birkhoff-Witt obvious to anyone?

@0ßelö7 well imagine I throw you in so many times that I'm appreciably increasing the black hole mass

If you're hovering at say $r=4m$, will you even see me go in or will I get frozen at the horizon?

from the point of view of the outside observer, the effective mass (and size) of the black hole is increasing
but the technical outside description of this is just you getting spread around the entire surface I'm assuming

10:43 PM
@GPhys I don't know the answer, and I think you're using your gut here, not any math. So I'm not sure if that's trustworthy
But here is a similar interesting question. Suppose we feed a steel rod into the black hole so the mass increase is appreciable

of course, that's why I asked wondering if you knew the answer
I was just giving my motivation for the question and not attempting to give anything resembling a proof

Well first, there is that question about putting a stick in a black hole
Does it suck in the stick or cut it clean off?
@GPhys Nah, these black hole gedankenexperimenten are a mystery to math people
@JohnRennie might have a better feeling

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