I'm liking the sound of it, @Avant

@0celo7 okay replace that with this.

@BalarkaSen That's good :)

But yeah the death growls looks a little unnecessary

@0celo7 is it your concern about animal rights?

The music itself is very nice

haha, wish you liked them.

@Mostafa it is pornography

And yes, they make interesting music. It's a mix of psychedelic rock and black metal.

So I see

@Slereah is Weinberg GR one of the GOAT books?

I have a feeling, that you will like Ghost @Balarka

So I cannot say

@BalarkaSen youtu.be/4CSFkjPm0A0 (no growls)

@Avantgarde I have never heard of them. Might try that.

Ok, checking out again

Wow this sounds great

Gotcha!

The proof that an irreducible past set is $I^-(\gamma)$ is mildly long

I can see why most books don't reproduce it

not that long but mildly so

Actually I can probably split that proof a bit

Since some of it is generic to past sets

@Avantgarde I really liked Icarus by Monkey3 by the way. I found myself listening to The Fifth Sun in full a few times. If you have anything else to recommend from them I'm totally ears

@Slereah pick a positive number

@0celo7 $$\frac{\pi^\phi + \phi^e}{e^\pi}$$

@Slereah I will use that if you can prove it is rational/irrational

Then 3

lol

thanks

About to simulate something and I need an initial value

that works nicely, one of the initial conditions is $4\pi$ now

Oh wait

Actually that property isn't true for all past sets

Because we have the assumption that the spacetime is distinguishing

damn, trying to type this equation into MMA might kill me.

@Avantgarde Thanks!

Enjoy @balarka

I am not very systematic about music, a strange personal failing

I'm actually not systematic about anything

You were supposed to be doing heat kernel estimates by now @BalarkaSen

But I have been trying really really hard to listen to Eno's works consistently

@0celo7 Yeah :(

Yeah that's fine. Just pick whatever you like (in music, at least haha)

Eno's ambient musics are like very good for sleep

This eg

@Slereah do you have to use * for multiplication in mathematica?

@BalarkaSen Great name for an album

Right?!

I think it was actually played at an airport for a while

It is pretty nice and soothing. Wonder why I had never heard of him before

@0celo7 Depends

It will usually interpret a space as a multiplication

dude he collaborated with three talking heads albums that were just superb

you know Talking Heads right

I've heard of them, yes, but never really got into the music

one yt comment: "When this came out, Eno got it played in actual airports, but they had to stop because people were falling asleep due to its relaxing sound and would miss their flights."

heh lol

The ambience here is very minimal (which is good). I don't think I have come across anything similar. Perhaps some post-rock, but I'm not so much into post-rock anyway. I think you would like post-rock though, the minimal kind. Had I shared the Godspeed You! Black Emperor album with you?

No, I don't think so, actually

Eno spent a long while in his career on minimalist ambient musics

I think when he was a painter he used to kind of blend music and visual arts together by producing minimalist visual pieces with an ambient music going on

That's pretty nice. I'd need those every now and then. Especially when flying, actually, good point

I see, that's cool

I do remember sharing this album before, but maybe you weren't here back then. Anyway, youtu.be/PZwQeZh6rP0

It's not as minimal as Eno's album you shared. At least not everywhere. Some parts are a bit fast, some are minimal. It's a weird album overall, and one of the best of its kind, I'd say.

Oh right you shared this before

ah you've got it then. ok

I liked it.

:)

@EmilioPisanty Please ping me when you're around, NDSolve is giving a 1/0 error.

I'm playing the adventure game of Guardians of the Galaxy

It's mildly disturbing because it's obviously based on the movie but they didn't have the budget to get the voice actors or the likenesses of the actors

So it looks like that scene from Spaceballs when they arrest the body doubles of the protagonist

@SirCumference I need numbers about stars

@0celo7 ok, what numbers

were you lurking

nah, got a notification

@SirCumference So a large mass white dwarf is a polytrope with $\gamma=4/3$. What's a good value for the central density and the radius?

oh god polytropes

i need to remember this, went through hell figuring them out

also if you have exact solutions for the structure equations in full GR for polytropes, that would be good

I would take Newtonian approximations too

@0celo7 ಠ_ಠ

@SirCumference You're an astro student, no?

@0celo7 indeed

So...?

a soon-to-be sophomore

also what should $K$ be

Weinberg says it depends on the entropy per nucleon and the chemical composition

@0celo7 Well you only told me the polytrope, I don't think I can tell you what K is without more info

I was picking $K=1$ but my simulation looks like shit

I doubt any star actually looks like that

@SirCumference what's a reasonable value

@0celo7 So you're asking me for the central density, radius and $K$

At least define some more of those parameters before asking me to solve it

@SirCumference I doubt you can solve it by hand

I am just wanting ballpark numbers

I'm a mathematician, I have no idea what the numbers ought to be

if I give you a radius of 15 light years we know there's an issue

I am trying to write a code that computes the radius

Well, you're dealing with a white dwarf, so $n = 3$

I think the relationship for a white dwarf's mass and $K$ is something like

$$M = \left (\frac{K}{0.3G} \right )^{1.5}$$

latex please

@SirCumference Hmm.

So just find an average mass for a white dwarf

what would that be

I'm just estimating the denominator btw, I don't have it memorized

pls find notes

@0celo7 Wikipedia says usually ~$0.6M_☉$

@0celo7 Found some

I have $$M\approx 4\pi R^{(3\gamma-4)(\gamma-2)}\left(\frac{K\gamma}{4\pi G(\gamma-1)}\right)^{-1/(\gamma-2)}\xi_1^{-(3\gamma-4)(\gamma-2)}\xi_1^2|\theta'‌​(\xi_1)|$$

Dude. Just put in a reasonable mass and you'll get a reasonable $K$

@0celo7 You see this is why I hate dealing with polytropes

It's complicated as hell

@SirCumference this is in the Newtonian approx

I am trying to do this in full GR

I have no clue how natural units work anymore

what should the units of $K$ even be

I'm pretty sure @HDE226868 is better at this than I am

uhhhh, $\rho^\gamma$ doesn't even make sense

I'm running off broken memory

dimensions are wrong

what's a Joule$^\gamma$

plz I have homework

it's summer

I'm taking classes to make my life easier and hopefully graduate faster

ok, go do homework

@HDE226868 ^

see above

@0celo7 K is just a constant of proportionality btw. IIRC it's dimensionless

@SirCumference then $P=K\rho^\gamma$ makes no sense

Well then I don't remember :/

none of the units are right

since when were you interested in stars?

are there some $G$s and $c$s missing?

@SirCumference high school

@0celo7 But I thought you don't care for astronomy?

I like some of it.

Cosmology? :D

@SirCumference cosmology is not astrophysics

@0celo7 Depends on what you call "astrophysics"

@SirCumference waste of tax money?

@0celo7 ...

damn, I was afk

what did you say

why do you keep removing it?

@SirCumference mb $K$ changes units for different $\gamma$?

it converts energy density$^\gamma$ to pressure

@0celo7 Sigh

@SirCumference what?

that website says I need JS

@0celo7 ...You disabled JS?

@SirCumference we've been over this

You can't use this chat if you don't use JS

sigh

idk man

I think I'm using it

might be wrong

www2.astro.psu.edu/users/rbc/a534/lec15.pdf

apparently it is unitful

@SirCumference what is $\mu_e$?