The h Bar

12:00 AM

@0ßelö7 Nothing, just making conversation. I once bought Federer's book as well. It is the most difficult math book I have ever seen.

0ßelö7

@WillHunting it's not that bad

people who say Federer is hard/horrible have not read many analysis books

I mean, it is hard, but I don't think there are many easy analysis books

especially considering Hormander exists

Secret

12:44 AM

Last night dream:

Some kind of quantum computing unit involving two very thin quartz crystals and some black conductive material

Unfortunately, I am unable to ask the speaker how will this silicon device be used in information processing in realistic scenarios

There's also a self awareness (which is notated in bright red ink in my notebook) on that question I want to ask, because knowing well that this is a dream, means that unlike in real life, it is impossible to find the speaker for clarification unless there's a sequel dream, which is still unheard of in my case

and that means, it is highly unlikely the question will be clarified for life

I then also thought about that dreams are highly specific mental states of sorts, and that perhaps what the esoterics refer to as planes of existence may be nothing more than specific altered mental states that feels like being in a place

Phase

1:04 AM

Does anyone have any good links for Differential Operators, Eigenfunctions and harmonics?

dmckee

@0ßelö7 I don't know. Why?

We're basically suppose to reserve that for matters which are both important and in need of rapid attention.

vzn

2:00 AM

@heather you might have some )( Computer Science mojo in you if you care, wink =D ... some other notorious physicists eg Mubos Lotl dont give much @#%& lol, others do scottaaronson.com/blog/?p=3409 motls.blogspot.com/2017/08/… vzn1.wordpress.com/2017/08/17/… and hey 75k hits on the Theoretical Computer Science post awesome =D

0ßelö7

2:40 AM

@dmckee I have several questions that are in his mathematical wheelhouse

0ßelö7

3:43 AM

@Phase Davies "Spectral Theory and Differential Operators"

uhoh

4:15 AM

2

Q: How large does refraction become in radioastronomy?

For atmospheric refraction of visible light, Wikipedia gives the order of 1 arc minute at 45° altitude above the horizon, and 5.3 arc minutes at 10°. This is caused by the dielectric polarizability of all of the bound electrons in all the atoms of the atmosphere. At the much lower HF frequencies...

has a +100 bounty

Anonymous

5:34 AM

@JohnRennie Are you free for a while? I have a few Java questions to ask you.

John Rennie

@Blue Morning. Yes, I'm just sitting drinking coffee and watching the Sun rise so now is a good time to ask :-)

Though note that I'm not a Java expert.

Anonymous

Hehe. It's nice to watch the sun rise. :P Alright, I'm coming!

Anonymous

Okay...I've never understood the use of String args[] there

Anonymous

And why args[0] should contain "one"

0ßelö7

5:37 AM

@JohnRennie wake up early for the fight :)

Anonymous

I read the stack overflow posts

Anonymous

But none of them explain the reason as such

Anonymous

"The main method expects us to provide some arguments when we direct our JVM to the class name." ..... Why ?

Anonymous

@JohnRennie

John Rennie

@0ßelö7 Boxing isn't really my thing. I must admit I did Google the result when I got up this morning, and to give MacGregor his due he did better than anyone expected.

@Blue any program has to start running somewhere, and Java apps all start running by the OS calling the main function.

Anonymous

5:45 AM

@JohnRennie I get that. But what is the reason for asking for those parameters (for args[]) ?

Anonymous

Of course it starts executing from the main() function

Anonymous

Or is it just the way the language was made? To differentiate it from ordinary functions by the String parameter?

John Rennie

The OS has to know what the definition of the function it's calling is. So the main function has to have a standard definition.

That definition doesn't have to accept any arguments since Java could provide a function to return the arguments.

But it's convenient to have the main function have the command line args as its arguments.

Anonymous

@JohnRennie Huh. They could have just made the standard definition public static void main(){}instead of public static void main(String a[]){}

John Rennie

Yes they could.

But then if I wanted the command line arguments I'd have to call some other function to get them.

Anonymous

5:49 AM

@JohnRennie Oh. Okay. I see the point.

John Rennie

It's really down to history ...

When the language C was first created its main function had the command line args as its arguments.

Sid

@0ßelö7 The fight is overrated big time

John Rennie

And ever since then every language has done the same.

@Sid everyone likes an underdog, and McGregor was certainly the underdog

Anonymous

C doesn't require the command line args to run anymore I guess. I wrote so many C programs without using it. Or does it?

Anonymous

I just start with main()

Sid

5:51 AM

It doesn't really make a difference whether you provide an argument or you don't provide an argument.

John Rennie

@Blue The way that C is designed means you can omit arguments for a function and it will still work.

Anonymous

Right. They should have designed Java in that way. :P

Anonymous

Anyhow...I got it now

Anonymous

Thanks

Sid

The whole argument-providing thing is from History as JR said. Also, because some people were concerned that you "should" provide an argument for getting an output.(According to my Grade 10th Computer teacher)

Anonymous

5:53 AM

I was wondering if there is some technical reason rather than a historical reason. But okay. I got my answer!

Sid

(Also, I hate the fact that there is an insertion.sort function. It just takes away the fun of writing the code yourself..)

John Rennie

I'm surprised colleges are teaching Java these days. Apart from niche enterprise apps it's pretty much faded away.

Anonymous

@Sid That's a pseudo-code probably.

John Rennie

Though Java is a very nicely constructed language so perhaps they teach it for that reason.

Anonymous

And it would be good if java did have that in-built

Anonymous

5:57 AM

I don't like "reinventing the wheel"

Anonymous

And neither do professional programmers

Anonymous

@JohnRennie My college is teaching C

Anonymous

I'm learning java on my own

Anonymous

Also python

Sid

Python is much better than Java

Anonymous

5:57 AM

Because the machine learning course requires python

Anonymous

@Sid I agree.

John Rennie

Python is a good skill to have. There is a high demand for skilled Python developers.

Anonymous

I need to learn java and python as most courses on Coursera use these two languages :'D

Sid

@Blue C sucks. I have that next semester. And I am not going to waste my time doing that now..

John Rennie

@Sid actually I disagree. Java is a very elegant language. Python is quick and easy to use but it's far from elegant.

Sid

5:59 AM

@JohnRennie Quick and easy to use matters far more than "elegant"

John Rennie

@Sid <shrug/>

Anonymous

@Sid C is helpful to teach you the low-level functioning of a computer

Anonymous

Once you move on to learn Assembly languages.... elegance/quick and easy to use is no more valued

Anonymous

C is just a step up from assembly language

Sid

@Blue College students are not professional programmers. For example, it would be an easy way out for guys who haven't seen a code in their life to simply use built-in functions.

They will learn practically nothing.

Anonymous

6:02 AM

@Sid College students will become professional programmers right out of college. Bad excuse.

Anonymous

They need to learn both high-level and low-level coding.

Sid

@Blue You shouldn't be telling college students about built-in functions until they are fit for the industry

At least, not to Freshman year or Sophomore year students

Anonymous

@Sid Of course not. But once they have learned the algorithms of the built-in functions they should use it.

Sid

Yes. Agreed. That is why I tell not to inform newer students about built-in functions. It becomes an easy-way out for people.

Anonymous

If you write all the algorithms by yourself during competitive programming you're sure to be out of the game. :P For example in ACM-ICPC

Anonymous

6:05 AM

@Sid I agree

Sid

@Blue Freshman year students are not going to do competitive programming. They need to first know the basics of stuff.

Anonymous

@Sid The "general" freshman year students. There are always some high-school geeks who seem to know everything about coding. :P But okay, I agree in general.

Anonymous

I do know a few people who were selected in GSoC in their very first year

Sid

"few" people is exactly the point. They would know about built-in functions themselves if they wanted to.

Anonymous

Sure

Sid

6:13 AM

One of the members at Puzzling is a codejam finalist.

Anonymous

BTW I've been deliberating between Matlab and Mathematica

Anonymous

Which one should I learn first? :P

Sid

You will learn MATLAB next year in college, I think

Anonymous

Then I should learn Mathematica

Anonymous

:)

John Rennie

6:21 AM

I think MatLab tends to be used mainly by engineers

user228700

@JohnR: HALP! (Also, hi :-P)

Anonymous

I might need to run some simulations on reflection of magnetic flux this year. So.

Anonymous

@JohnRennie I heard that :)

John Rennie

@Kaumudi.H Morning :-) What's up?

user228700

:-) Does your friend still have Season 2 of Rick & Morty?

John Rennie

6:23 AM

Allegedly :-)

Sid

...lol. I thought she was in trouble or something

Anonymous

@Kaumudi.H Did you find a laundry? :P

John Rennie

@Kaumudi.H maybe we should continue this on gchat ...

@Blue yes, sort of :-)

Anonymous

That's good :p

user228700

@Sid Nah :-) Well, it depends on how you define trouble, I s'pose. If having a hardcore existential crisis everyday counts as trouble, then yeah, man, I'm pretty much dying over here :-P

user228700

6:26 AM

@Blue Laundry=Grandma's place, huzzah!! :-)

user228700

How are you?

Anonymous

@Kaumudi.H Grandma lives near your college?

user228700

@Blue 1.5 hours away by train.

Anonymous

@Kaumudi.H I'm fine. The troubles have subdued. And I'm back into learning new stuff. :) I'm enjoying.

user228700

Oh, that's great news! :-) Have fun!!

Sid

6:32 AM

@Kaumudi.H Your roommate still being a pain?

user228700

A little less of a pain now, thanks :-)

user228700

How's college treating you?

Sid

Fresher's party next week. So, yes. It's treating me pretty good.

Balarka Sen

@Kaumudi you like Ed Sheeran don't you

What Ed Sheeran's Cameo on Game of Thrones felt like

►

this guy is a total meme

10/10

Secret

6:47 AM

0

Q: $\textit{Where}$ is the energy (and momentum) in Electromagnetic Fields?

Using Lorentz force law and Maxwell's equations, one can derive the following relations: $$\dfrac{dW_{\text{mech}}}{dt}=-\dfrac{\partial}{\partial t}\bigg(\dfrac{\epsilon_0 E^2}{2}+\dfrac{B^2}{2\mu_0}\bigg)-\nabla \cdot \bigg(\dfrac{1}{\mu_0}(\vec{E}\times \vec{B})\bigg) \tag{1}$$ $$\dfrac{d\...

energy momentum conservation-laws field-theory maxwell-equations

That illustrate an important consideration on how to figure out which arrangements of maths symbols have physical meaning, and which don't

user228700

7:07 AM

@Sid Wow! What's it going to be like?

user228700

@BalarkaSen I, well, yes, I do like some of his songs.

Sid

We are obviously going to be ragged...

user228700

Ah, what, really?

Sid

Yeah. Heard the metallurgy guys got ragged last Thursday

user228700

Oh, wow, I see.

Sid

7:09 AM

(ragged as in, they were asked to do weird stuff)

Anonymous

I'll enter the freshers party late

user228700

We have no party or anything because our Principal is too afraid of the possibility of us getting ragged after what happened last year.

Sid

Also, we have to introduce ourselves twice. First in English, second in native language, both being mutually exclusive.

Anonymous

When they will be distributing food packets

user228700

@Sid Huh, what weird stuff?

Anonymous

7:10 AM

lol

user228700

@Blue :-P Great plan!

Sid

@Kaumudi.H Asking students to get balloons inside their shirts and burst them without touching it.

Anonymous

@Sid Woah. That's close to hardcore.

Sid

Our seniors(2nd year guys) said to us, that we wouldn't be facing such stuff.

user228700

@Sid That's...what, man, that sucks.

Anonymous

7:13 AM

Anyhow, I think the seniors will catch me since now I'm famous in the campus for protesting against protests. I need to stay careful. :'D

Balarka Sen

he protecc but he also protest

Anonymous

7:52 AM

Shell Sort is going over my head....

John Rennie

8:21 AM

@Kaumudi.H: I need to work for an hour or so, but ping me here if you need anything ...

Alex K Chen

9:02 AM

Anybody here uses vpython for physics simulation ? I have a problem.

Anonymous

9:30 AM

@AlexKChen There is a Python chat room on Stack Overflow

Alex K Chen

@Blue And there's a minimum 20 rep requirement on SO for that.

Anonymous

Create 20 accounts on 20 different SE sites

Anonymous

You'll get 1 rep from each site

Alex K Chen

SO chat account is different from other SE sites.

You can't use your total 20 rep on other SE to talk on SO.

Otherwise, how I'm chatting here ?

Anonymous

I think they give complimentary 100 rep on SO if you have some min rep on all SE sites combined

Anonymous

9:33 AM

But lol

Alex K Chen

But lol

Anonymous

Instead of trying to find hacks....just go and get some reps

Anonymous

:P

Anonymous

Ask your question on SO

Anonymous

main site

Anonymous

9:40 AM

@BalarkaSen You free?

Secret

10:07 AM

in #!/bin/bash on Stack Overflow Chat, 33 secs ago, by Secret

in #!/bin/bash on Stack Overflow Chat, 27 secs ago, by Secret

bash is saying that my fi after the # is unexpected

Stefan Bischof

11:11 AM

@Secret Unmatched quotes in echo command - might this be the reason?

Jaime Gallego

The quotes seem funky, yeah. @Secret, are you trying to nest double quotes inside other double quotes?

AFAIK you can't. Try to use single quotes inside the double ones.

Ah, but you're trying to pass a variable inside some of these. Check this:

4

Q: Using multiple layers of quotes in bash

I'm trying to write a bash script, and I'm running into a quoting problem. The end result I'm after is for my script to call: lwp-request -U -e -H "Range: bytes=20-30" My script file looks like: CLIENT=lwp-request REQ_HDRS=-U RSP_HDRS=-e RANGE="-H "Range: bytes=20-30"" # Obviously can't do...

linux bash

user228700

12:22 PM

@Balarka: Why do it seem to me that you'd enjoy this particular show:

user228700

Rick and Morty: Nobody belongs anywhere, nobody exists on purpose, everybody's going to die.

►

Balarka Sen

I have been recommended Rick and Morty twice now actually

user228700

Just watch it, man.

Balarka Sen

loool nice

well i have tons of things i should be doing and watching and listening

but will i do any of them? nah

user228700

Ah. Dank memes FTW?

peterh

12:26 PM

@KyleKanos I appreciate your urge to vote everything to down, reject and so on, however, the links are going from http:// to https:// on the whole network, and it is a global rule... :-)

Balarka Sen

I've had enough of the daily healthy dose of memes for today

tryna get some math done

user228700

Cool :-)

user228700

> daily healthy dose

user228700

Man, I wonder how you'd define something like that :-P

Balarka Sen

just the dose that keeps you sane

user228700

12:28 PM

Ah, I see it.

0ßelö7

@Kaumudi.H impossible

It's not on Netflix

user228700

@0ßelö7 What? It is here...

Balarka Sen

It seems most of my favorite music are either ambient music that puts me to sleep or horrid and relatively loud artsy stuff, none of which is good for work

user228700

Besides, I don't want to hint at anything, but I am hinting at something when I say that I don't have a Netflix account :-P

Balarka Sen

I guess I can work with Darude Sandstorm playing on my headphones

user228700

12:33 PM

@BalarkaSen Ah, lol. Does Hans Zimmer do anything for ya?

Balarka Sen

I like Zimmer. They are not on my favorites list or anything.

user228700

Hmm.

Balarka Sen

I guess my favorite musics are a bit too meditative than movie or video game soundtracks

except darude sandstorm. that shit is lit

0ßelö7

@Kaumudi.H in 3rd world countries it is for some reason

skullpatrol

What "world" does that put you in, pal?

0ßelö7

12:39 PM

@BalarkaSen :)

Balarka Sen

Darude - Shooting Sandstorms

►

this is my favorite version of all time

user228700

@Balarka: I thought you were s'posed to be doing Math.

Balarka Sen

I am

skullpatrol

On YouTube?

Balarka Sen

i didn't know you could do math on youtube

peterh

12:42 PM

@DawoodibnKareem How strongly I agree it...

skullpatrol

cool vid

0ßelö7

What math @BalarkaSen

peterh

@DawoodibnKareem I think some system should exist what measures the actual worth of the degrees, essentially the trustability of a University.

0ßelö7

I spent all of yesterday hunting separability stuff

Turns out metrizable Montel spaces are separable

Balarka Sen

@0ßelö7 I understood Hopf-Rinow

0ßelö7

12:45 PM

@BalarkaSen I always though the proof was technical. There are no variations of the proof

It's such a good theorem. @BalarkaSen At Cartan-Hadamard now?

That guy has another proof in Milnor too.

Balarka Sen

I wouldn't say it's technical; it's just starting the geodesic and seeing how it goes from the starting point to the endpoint

It's pictorially pretty clean

@0ßelö7 I don't know Jacobi fields yet, which is what I'm picking up right now

0ßelö7

amazon.com/Fourier-Analysis-Graduate-Studies-Mathematics/dp/…

that poor last name

peterh

-24

Q: If there is no gravity on the moon why is the american flag waving?

If there is no gravity on the moon, how could this flag be flapping in the wind? (see link) http://www.stumbleupon.com/su/2wD6eg/hea-www.harvard.edu/~fine/images/desktops/Armstrong.jpg

space moon

Delete votes are needed

Mithrandir24601

1:19 PM

@peterh This is so subjective though...

skullpatrol

Solar wind?

0ßelö7

@heather you can live here and take classes for free if you clean my house

:)

heather

=)

packing my bags already ;)

0ßelö7

bring a mattress or something

the couch is awful

my back hurts from being on it during the flight last night

@JohnRennie I have some computer doubts (not SSD related)

skullpatrol

1:54 PM

math is the poetry of logical ideas

Wrichik Basu

2:06 PM

I need a small help. I've recently started with Quantum Mechanics deeply. The book that I use is D. J. Griffiths book. But the problem is that, the requirement is that I should at least know the basics of classical formalism like Hamiltonian and Lagrangian operators and use of operators instead of functions in general. Can anyone recommend me a good book that will at least give me a clear idea of these concepts?

I don't want a too deep idea, as I don't want to deviate from my studies much now, but I would surely take time and study if you recommend me a good classical physics book which will act as in intro to quantum mechanics.

Jaime Gallego

@WrichikBasu I've heard good things about Taylor's Classical Mechanics.

heather

I've heard good things about Kleppner and Kolenkow (Daniel Sank recommends it)

0ßelö7

@WrichikBasu Chapter 2 of Shankar's Quantum Mechanics

Mithrandir24601

@WrichikBasu You might think that learning classical Lagrangians and Hamiltonians is deviating from studies in quantum, but studying them is extremely useful in the long run

Wrichik Basu

@Mithrandir24601 that's why I want to learn it.

0ßelö7

2:15 PM

@Mithrandir24601 I think only the high level details are important. He doesn't need to know the spinning top on an oscillating plane

That's why Shankar is a great introduction

Focus on symmetry, symmetry, symmetry

Wrichik Basu

@0ßelö7 is the name of the book "Principles of Quantum mechanics"?

0ßelö7

yes

Mithrandir24601

@0ßelö7 Depending on exactly what you end up doing in QM, yeah

0ßelö7

I think that mathematicians should learn classical mechanics

I can't imagine doing what I'm doing without having started with Lagrangian mechanics

Wrichik Basu

Well, then I'll start with that book. Should I continue with this or return to Griffiths?

0ßelö7

2:18 PM

Griffiths is universally hated by people who actually know quantum mechanics

How it survives is a mystery to me

Wrichik Basu

@0ßelö7 then should I continue with that book or would u recommend something else?

0ßelö7

@WrichikBasu I just recommended Shankar

I like parts of Sakurai too but half of it seems like random special topics he threw in

I like the organization and flow of Shankar. Outstanding (physics) book

Wrichik Basu

@0ßelö7 yes. I'm asking that after doing the classical part, should I read that book in whole?

0ßelö7

@WrichikBasu yes

Wrichik Basu

@0ßelö7 very well. Thanks a lot.

Mithrandir24601

2:22 PM

@0ßelö7 Wasn't that the one that wasn't actually finished by Sakurai though, so the bits that he did are considered to be better than the bits he didn't do

0ßelö7

@Mithrandir24601 I've seen the version that was published without Napolitano's edits and it's somewhat better

there are still random things in there

Mithrandir24601

@0ßelö7 I now have an image of you in the early morning/late night reading large physics textbooks in bed

0ßelö7

@Mithrandir24601 Physics books? I'm a mathematician

Jaime Gallego

Apr 10 at 0:11, by 0celouvsky

I have all five volumes of Spivak next to my bed and I'm proud of it

Mithrandir24601

@0ßelö7 You admitted it! :D

0ßelö7

2:24 PM

@Mithrandir24601 I am a mathematics student...

literally

Mithrandir24601

@0ßelö7 Fair enough then - I've just never heard you say it before :P

Wrichik Basu

@0ßelö7 that's a very good book indeed! :-)

0ßelö7

@Mithrandir24601 I am actually fixing my sleep schedule to be more morning-oriented

@Mithrandir24601 I do have an honorary physics shelf

Jaime Gallego

@0ßelö7 Why is it? Not rigorous enough, I assume?

0ßelö7

@JaimeGallego The focus in quantum mechanics (for physicists!) is on the algebraic aspects (Hilbert spaces, operators, etc.) and Griffiths uses the wave function approach

So from that perspective Griffiths kind of muddles the linear algebraic simplicity

I don't think it's possible to have too little rigor for a physics book. When you're doing stuff with infinite dimensional spaces and "topology" doesn't get mentioned (ever), it's not rigorous

And topology never gets mentioned in quantum mechanics when physicists do it

Not saying that's a bad thing, in fact I can't ascertain if anyone knows if it even matters

Jaime Gallego

2:32 PM

@0ßelö7 That makes sense.

0ßelö7

The reality is that "rigorous" quantum mechanics uses a combination of linear algebra and differential equation theory

Phase

2:45 PM

is it correct to say that if you let $D$ denote the differential operator $\frac{d}{dx}$, $D^{-1} = \int dx -k$ where k is the constant of integration?

0ßelö7

No, because $k$ is arbitrary. That's ill-defined.

You need to impose some kind of condition on the space of functions $D$ acts on (and maps into) so you can properly define the inverse.

Phase

Does the linear operator $D^-1$ have to be injective to be usable?

0ßelö7

Usable?

Phase

Idk, Im just trying to do a lot of coursework rn and I cant be assed to write out the full integration symbols

Im just trying to define something a bit quicker to write

0ßelö7

I have no idea what you're trying to do here.

Phase

2:49 PM

:[

Can $D^{-1}$ not map a function to a space of functions?

0ßelö7

@Phase what?

I just said that operator is ill-defined without more information

If you want $D^{-1}$ to mean $\int dx+C$, fine

But unless you define $C$ that's not really an operator

Phase

Why is it ill defined to just have it omit the constant of integration?

0ßelö7

What?

Phase

:| Am i really making that little sense? by $\int dx - k$ I meant integrating, and then getting rid of the constant of integration

0ßelö7

I don't think you understand what "constant of integration" means

We're taught to put it in by hand in calculus

Phase

2:57 PM

I thought it's just some scalar variable that is more general, and allows the integration to describe a family of functions

0ßelö7

But there is literally no difference between $x^2+1$ and $x^2+2$ in terms of being antiderivatives of $2x$

Secret

[Warning, superrandom nonsensical phrase from my 2014 scifi reviews]

> I am starting to felt ok about this crazy idea because a simialr situation exist for the big bang: The universe expands, but without a centre, it expands everywhere at once.

Using the mindset of a mathematician plus a tourist who explore foreign places (i.e. doing maths is like exploring an alien space), this can be understood as the separation between entities simply become bigger

> The spacetime manifold itself evolves with time, whose rate is dependent on the observers within it and the matter-energy distribution

The universal past and present is encoded in the way the causal discontinuities are related relative to each other

Meanwhile in the present:

Nope, all of these make no sense in GR as we have discussed in the past as the spacetime topology is not allowed to change and there is only one history

It is however, consistent with GR to have spacetimes where the spatial topology changes, c.f. trouser spacetimes, wormholes and many others

GR, however is agnostic about the mechanism on that. It is still an open question whether the spatial topology is physically possible or can only remain as merely a solution to EFE

All of this will be settled once we have quantum gravity

Master Yushi

"A simple pulley has two unequal variable masses hanging from it, the masses vary such that their sum is constant. The breaking tension of the rope is 15/32 of the weight of the sum of masses of the blocks. Find the minimum acceleration and the least value of the greater mass"

Shouldn't the minimum acceleration be zero

John Rennie

@MasterYushi the acceleration can't be zero because then the masses would be equal, the tension would be 16/32 of the weight of the sum of masses of the blocks and the string would break.

Master Yushi

@JohnRennie right, so the acceleration would be least when the tension in max?

When T=Tmax, one of the masses will be 3c/4 and the other will be c/4, c being the sum of masses

Comes out to be g/4

Jaime Gallego

3:41 PM

Bee Gees - Holiday (1967) [High Quality Stereo Sound, Subtitled]

►

Transcript for