The h Bar

Sir Cumference

00:01

@0celo7 More generic than "Johnson et al. (20XX)"?

If someone is an active researcher, they'd probably publish several papers with others within a single year

rob

@SirCumference If you're active in the field, you probably know the authors of the papers that are most interesting to you. For instance when I saw this question my first thought was "oh, Geoff wrote those nice review papers about that," which was then how I searched for them.

Sir Cumference

@rob I suppose. But say this arbitrary researcher "Johnson" made a remarkable discovery. Wouldn't it be more clear to refer to the name of the paper instead of the year he made the discovery?

rob

Think about textbooks, where the titles aren't very unique. Looking around my office I have Segre's "Nuclei and Particles," Livesey's "Atomic and Nuclear Physics," and Wong's "Introductory Nuclear Physics." I have two or three books with titles like "quantum mechanics" and two or three books with titles like "electrodynamics."

I can't keep the titles straight, because there's so much overlap in the content, but I can tell the authors apart.

Rumplestillskin

Hey guys is anyone familiar with parts-per notation? I have a table of numbers that are all 10^-5. I want to say "As we can see the differences are only a fews parts in ...." but what is the way to say that? "... a few parts in a hundred thousand"??

rob

@SirCumference For very interesting discoveries, there may not be a concise name for the effect before its discovery. So if Johnson's paper is called "Explanation for such-and-such bizarre effect that occurs under peculiar circumstances," Johnson's colleagues will start calling it "the Johnson effect."

@Rumplestillskin You could do that. I'd convert to parts per million, and say that.

"the differences are only a few tens of ppm"

"the differences are at the $10^{-5}$ level"

Sir Cumference

00:13

@rob Ah, makes sense

Rumplestillskin

Yeah, I might stick with the differences are at the $10^{-5}$ level.. If it was just one order of magnitude less it would sound more compelling though! :) cheers

HsMjstyMstdn

"the water film which occurs at high sliding velocities during skiing is usually produced by friction heating, rather than pressure melting."

Interesting...

rob

@SirCumference Consider the LIGO detection papers.

Apart from the first detection ("Observation of Graviational Waves from a Binary Black Hole Merger") the titles are terrible for mnemonic purposes.

Quick: was GW170104 the second detection, or the fourth one? Was is the 20 solar mass pair, or the 50 solar mass pair?

The titles are great for answering the question "what is the big takeaway from this paper in front of me right now." But if you went to look for them, you'd be looking for "LIGO's first detection," "LIGO's third detection," and so on.

0celo7

00:56

@JohnRennie Made oink oink Schnitzel. Absolutely amazing

Bernardo Meurer

02:05

@EmilioPisanty Shared with you :)

Sorry for the delay, was out today

John Rennie

03:58

@0celo7 My Mum usually makes schweineschnitzel or sometimes she'll use chicken. The one meat she rarely uses is veal. Not for moral reasons but because neither of us find veal that great.

0celo7

@JohnRennie It's been too long since I've had veal

I didn't care for pork as a kid so I was veal all the way

Veal is rather rare in America

and always very expensive

John Rennie

I don't find veal that tasty. And yes it is fracking expensive :-)

0celo7

@JohnRennie I got tenderloin and cut it into very thin disks. Then I fried it until the crust was dark. Amazing

I did less breading this time so it didn't have any oily taste

I'm getting hungry again :)

John Rennie

My Mum hammers it flat rather than slicing it.

0celo7

@JohnRennie That is the traditional method, but I am an analyst. I prefer precision.

John Rennie

04:07

Also you might try using flour instead of breadcrumbs. That still has a nice crisp texture but holds less fat.

0celo7

@JohnRennie I use flour and breadcrumbs.

John Rennie

I forget what it's called, though I can can probably Google it.

Aha, it's pariser schnitzel

0celo7

@JohnRennie Oh, I've been forgetting to salt them. Ketchup is salty enough.

I'll salt it explicitly next time

John Rennie

Do you cook the schnitzel in butter or oil?

0celo7

Oil. No way I could get that much butter without people becoming suspicious

And butter is expensive

John Rennie

04:10

I have to say I think butter is essential for the best flavour.

0celo7

@JohnRennie I might be biased, but what I made tonight was the best I've ever had

John Rennie

It does make a mess though because butter spits when you use it for frying.

HsMjstyMstdn

Don't oils spit, too ?

0celo7

I mean, I'd need at least 2 sticks

@HsMjstyMstdn not if you're careful

HsMjstyMstdn

or isit to do with butter having water content ?

0celo7

04:11

if you throw small things in it does

John Rennie

You shouldn't need that much butter. You're not deep frying it, you just need a film of butter on the sklillet.

0celo7

@JohnRennie Hmm.

HsMjstyMstdn

spits =/= splash ? or am I misunderstanding

John Rennie

@HsMjstyMstdn that's right, and I suspect it is due to the water in the butter.

0celo7

@JohnRennie I'm planning to make Teriyaki chicken tomorrow. Maybe Sunday I'll try butter.

HsMjstyMstdn

04:12

Yeah, just googled it. Tops at around 17% water

John Rennie

Gosh you do eat well :-)

0celo7

@JohnRennie maybe

John Rennie

I was going to have cheese fried in breadcrumbs today

0celo7

Lol

John Rennie

With some bits and bobs to bulk up the meal e.g. garlic bread

0celo7

04:13

@JohnRennie Actually I should find a salad

HsMjstyMstdn

I need to get up early tomorrow to go marketing. Making my weekly hearty soup.

0celo7

I haven't eaten much green lately

John Rennie

Salads, meh.

HsMjstyMstdn

@JohnRennie How dare you

John Rennie

:-)

I love veg in cream sauce, or a veg risotto, but not salads.

I never eat anything that caterpillars have crapped on :-)

0celo7

04:15

lol

John Rennie

This was yesterdays lunch:

Vegetable risotto with green olives.

HsMjstyMstdn

Any salad that isn't washed properly is no true salad, harumph.

John Rennie

Now that's a nice way to eat veg.

HsMjstyMstdn

I always preferred pease that were boiled just so over the ones that were mashed.

John Rennie

Why would you mash peas?

Unless you're making mushy peas, which is a truely awesome dish!

0celo7

04:18

@JohnRennie you really need a better keyboard

HsMjstyMstdn

Aren't those some pease in your dish ?

John Rennie

@0celo7 It's 5 a.m. and I'm not fully awake yet :-)

0celo7

@JohnRennie what does the time of day have to do with your $5 keyboard?

John Rennie

@HsMjstyMstdn yes, but they aren't mashed peas ...

0celo7

get a mechanical one

John Rennie

04:19

@0celo7 do you mind. This is a Dell keyboard.

0celo7

@JohnRennie it's the one that comes with every Dell

John Rennie

True :-)

HsMjstyMstdn

Maybe not mashed but certainly broken, humiliated, crushed and defeated... :..(

John Rennie

Actually not true as Dell have switched to chiclet keyboards like everyone else. It's getting hard to find these older Dell keyboards now.

0celo7

chiclet?

it looks exactly like the standard Dell keyboard

John Rennie

04:21

Chiclet keyboard

A chiclet keyboard, or island-style keyboard, is a type of input device for electronic systems such as personal computers, calculators and remote controls that uses keys in the shape of small squares with rounded corners and straight sides, in the style of Chiclets, an American chewing gum brand. A perforated bezel fills the gaps between the keys. The term has changed meaning in recent years. During the first home computer boom of the 1980s, a chiclet keyboard was synonymous with cheap quality and a poor user experience. Nowadays, the term is neutral and refers to low-profile, low-travel keyboards...

0celo7

huh

I guess my school is behind the times

we only have those like you have

John Rennie

Good, they are much nicer than chiclet keyboards.

0celo7

mechanical ftw

HsMjstyMstdn

^

John Rennie

The keyboard I use is a membrane keyboard not a mechanical one, but it has a nice feel to it all the same.

0celo7

04:23

HsMjstyMstdn

In fact, one of the best mechanical keyboard options you can get comes from our very own Jeff Atwood.

John Rennie

Hmm, Corsair ...

HsMjstyMstdn

codekeyboards.com

0celo7

@HsMjstyMstdn are those meme keyboards? How is it supposed to work without a wrist rest?

John Rennie

$150!!!!!!! My laptop cost less than that.

HsMjstyMstdn

04:25

@0celo7 Wrist rests aren't for everyone.

Sometimes, they just get in the way

0celo7

@JohnRennie mine was similarly priced back in the day

now there's an RGB version that costs what mine cost

@HsMjstyMstdn yikes

HsMjstyMstdn

There are more expensive ones, @JohnRennie. Those keyboards are okay-ish priced if you're going to be bashing away at something for several hours a day.

0celo7

I can take mine off and it's awful without it

HsMjstyMstdn

I guess the option of having one or not having one should be there, but I can't stand having a wrist rest. Kills my wrist AND apm...

John Rennie

I type with my arms off the desk, much as you'd hold your arms when playing the piano, so a wrist rest would be pointless.

0celo7

04:29

wtf

HsMjstyMstdn

You must have some really special desks where you come from, or shoulders of steel.

0celo7

is that for upper body strength training?

John Rennie

No, I've just always typed that way

0celo7

@JohnRennie is Arnold

2

HsMjstyMstdn

gg

0celo7

04:30

I thought you looked familiar!

HsMjstyMstdn

hahahaha

John Rennie

:-) Arnold after a crash diet!

John Rennie

04:55

I need a second coffee. Some days these early mornings are hard.

HsMjstyMstdn

Ah, the second coffee. I know it well.

Sid

05:12

@JohnRennie .... What? That's so cheap! My laptop cost me little more than $500

John Rennie

I buy 3-4 year old Dell Latitudes on eBay, and they sell for about £100 - £200 depending on the spec. See this for example.

Laptops have got lighter and with improved battery life in the last three years, but for raw power in many ways things have gone backwards. The 3GHz i7 in the link above is more powerful than the CPU in the vast majority of modern laptops.

Sid

How can I calm myself down? This thing Is nerve wracking

John Rennie

@Sid this thing ??

Sid

In a debate competition. Today is the second (and the most important day)

John Rennie

Ah. Good luck!

Sid

05:22

Well.. Answer??? How am I going to calm down?

HsMjstyMstdn

Deep, steady breaths and the thought that in a few million years, none of it's going to matter anyway.

Sid

@HsMjstyMstdn I am not sure I would be alive in a few million years

HsMjstyMstdn

None of us will

0celo7

heroin

HsMjstyMstdn

wow

actually, no. No wow. Not for Ocelo.

John Rennie

05:26

@Sid breathe into a paper bag?

Isn't that supposed to calm you down because the elevated CO2 levels in the bag have a calming effect?

0celo7

@HsMjstyMstdn what is that supposed to mean?

Sid

@JohnRennie how do I do that in a room full of 100 people without acting weird

John Rennie

Put the bag over your head then no-one will know who you are

HsMjstyMstdn

@0celo7 It means I'm now officially your friend

0celo7

@JohnRennie if I email a random person with a question, should I say that my adivsor suggested I email them?

John Rennie

05:32

@0celo7 I probably would. If you start with xxx suggested I speak to you it at least means you're not some random kook.

rob

@0celo7 Sounds reasonable. "Hello, we haven't met. My advisor Prof. D suggested I write to you and ask about ..."

0celo7

What's a good subject line? Should it be "Question about local causality neighborhoods", "Definition of local causality neighborhoods", ...?

John Rennie

Anything that looks technical I guess. Anything that distinguishes your e-mail from the numerous e-mails academics get from the pseudoscience brigade.

0celo7

@JohnRennie not sure if math people get the same spam

and not from .edu addresses

rob

I like "Question about" with a technical phrase afterward --- makes it more obvious that the body of the email won't be "My groundbreaking theory article written in crayon is attached as a virus-filled youtube pdf"

John Rennie

05:43

Superstition by Stevie Wonder is on the radio! Happy days!

0celo7

06:04

@JohnRennie I sent you what I want to send him

is it ok?

ok time to sleep

bye

John Rennie

Goodnight

Bernardo Meurer

06:56

@JohnRennie Are you around?

John Rennie

Morning :-)

Bernardo Meurer

Morning John :)

So, quick question, I've been needing to ssh into my machine quite often now

but I still don't have sshd running all the time, because I'm a bit afraid

my passwords are very safe

Is it fine to have sshd always enabled? Can I trust ssh's safety?

John Rennie

In principle sshd is fine.

There was the recent bug in sshd that allowed hacks, but that has been fixed.

Unless another bug emerges you should be fine. You might want to move the SSH port to a non-standard one for extra security. We do that when exposing RDP ports to the Internet.

Bernardo Meurer

Alrighty then, I'll just enable it

Hmm, let me investigate how to do that

Could I use 88888?

John Rennie

The port is a 16 bit number

Bernardo Meurer

07:01

Hm

John Rennie

There are restrictions on what ports you're supposed to use, but I can't remember them. Just use a random number between 1024 and 65535.

It might be worth a quick check on serverfault ...

Bernardo Meurer

Done :)

New port

John Rennie

42

Q: Why change default ssh port?

I've noticed that a lot of admins change the default ssh port. Is there any rational reason to do so?

Bernardo Meurer

Oh, keep it under 1024

Oki, done

Cool

Thanks John!

John Rennie

You don't really need to keep it under 1024

Bernardo Meurer

07:06

Well, now it's too late :P

John Rennie

With ports >= 1024 there's a possibility that if a hacker gets onto your server they can hijack your SSH port, but if a hacker gets onto your server you have more problems than they hijacking SSH :-)

The advantage of a high port number is that it makes it impractical for people to port scan for it.

i.e. it's a lot quicker to port scan 1024 ports than to scan 65536 ports!

Bernardo Meurer

Hmm

Okay, changed again :P

John Rennie

:: John hurriedly port scans Bernardo's server ::

Bernardo Meurer

You don't know my IP :P

John Rennie

Damn, how am I going to get on to my BitCoin miner now? :-)

Bernardo Meurer

07:10

Mining bitcoin on this laptop isn't worth it, trust me I've tried

John Rennie

Are you on a college WAN or something like that? Or do you have your own router/firewall?

Bernardo Meurer

It does like 2 hashes per second

I'm at home now, so I have my own router

But otherwise I'm at uni, so their WAN

John Rennie

I guess a firewall doesn't help anyway since you don't know what IP addresses you'll be connecting from.

Bernardo Meurer

I have a fairly restrictive firewall

Oh, damn, I need to update my firewall

Nice reminder

John Rennie

I mean restricting what client addresses can connect to the SSH port ...

We do that for the servers we manage. The RDP port only accepts connections from our office WAN so random hackers can't even connect.

Bernardo Meurer

07:14

That's pretty cool

But yeah, I can't know the IP :/

Anonymous

09:50

How to bookmark a chat conversation?

user84215

By going to the transcript of a message

Anonymous

@MathematicsAminPhysics Thank you

user84215

@Blue You are welcome.

user84215

10:06

The following workshop will be held in the Physics Workshops room (It has nothing to do with the h Bar room): Covariant Electrodynamics in Different Dimensions, at 9:30 GMT on Sunday, October 15, 2017

Martin Sleziak

10:21

@Blue I will add these links - they are not exactly about the question how to bookmark, but maybe the screenshots shown might be helpful: Is it possible to bookmark a conversation in chat, which has messages in two different days? and Take selected parts of a conversation and bookmark it in Chat.

Anonymous

@MartinSleziak Gotcha. Thanks a lot. :) I was able to bookmark the desired conversation

Anonymous

Also, nice to see you in the Physics chat room @MartinSleziak =P

John Doe

11:31

Anyone online?

Qmechanic

@JohnRennie : Be aware that 0celo7 usually only talks about a Russian Arnold :P

ACuriousMind

13:00

@BernardoMeurer hi?

If I seemed to drop in at that time something was wrong because I wasn't online yesterday evening

0celo7

13:36

@Qmechanic yikes

0celo7

13:49

@ACuriousMind Can R^4 be foliated by 3-folds that are not R^3?

Balarka Sen

Sounds like a generalized Reeb foliation works

Ya it does

0celo7

@BalarkaSen I want R^4 = R x S. Is S = R^3 the only possibility? Or is this Reeb thing possible

Balarka Sen

No. Check out Whitehead manifold.

What you're asking is stronger than just asking for a foliation of R^4 by 3-folds, though. But yes, it is possible.

0celo7

@JohnRennie @rob @Slereah He wrote back saying that it's an interesting question and wants page numbers in BEE!

@BalarkaSen Hmm. Is that manifold diffeomorphic to R^3 modulo a compactum?

Balarka Sen

It's complement of a compactum in R^3.

0celo7

13:59

Hmm

Strange that such a thing is contractible

Balarka Sen

It indeed is

0celo7

@BalarkaSen This is the danger with reading mathematical physics. Sometimes they are more physical than mathematical and stuff like this can happen.

Balarka Sen

I think if you force something like simply connected at infinity on $S$ then this shouldn't happen

But don't quote me on that

0celo7

@BalarkaSen I want $S\setminus K\approx\Bbb R^3\setminus B$

Slereah

@0celo7 everytime you have to ask an author about something they never remember the proof!

0celo7

14:13

@Slereah he's not an author of these books

my advisor said he's the friendliest GR guy

Slereah

Who's the least friendly GR guy

0celo7

Hawking

Slereah

I hear he won't even get up to shake your hand

0celo7

rude!

Anonymous

What does $\int d^3p$ mean ? This notation is confusing. Does it mean the integration of momentum space elements ? Can we write it as $\int 4\pi p^2 dp$ ?

0celo7

14:17

$\int_{R^3}d\mathbf p$

@Blue only if your integrand is rotationally invariant

Anonymous

@0celo7 What does that mean ? :P

Anonymous

Explain in words please XD

0celo7

@Blue An integral of a vector variable over $R^3$

Anonymous

So, say we have the $p_x,p_y,p_z$ axes. We are integrating infinitesimal elements in that 3-D space to get the volume (given some constraint) ?

Slereah

It means that it should only depend on the radius

$p_x^2 + p_y^2 + p_z^2$

Anonymous

14:21

What did you mean by rotationally invariant though?

Anonymous

@Slereah Right. Momentum follows that

0celo7

@Slereah Huh?

$\int d^3p$ does not imply that stuff is rotationally invariant

@Blue you integrated out the angular variables

you can only do that if the integrand is rotationally invariant

Balarka Sen

@0celo7 Probably not true for Whitehead

John Rennie

@0celo7 Result! :-)

Anonymous

@0celo7 Which is the angular variable here? And what does a variable being angular mean? Does it refer to the angle it forms with the coordinate axes?

Secret

14:24

Chaitin's constant

In the computer science subfield of algorithmic information theory, a Chaitin constant (Chaitin omega number) or halting probability is a real number that, informally speaking, represents the probability that a randomly constructed program will halt. These numbers are formed from a construction due to Gregory Chaitin. Although there are infinitely many halting probabilities, it is common to use the letter Ω to refer to them as if there were only one. Because Ω depends on the program encoding used, it is sometimes called Chaitin's construction instead of Chaitin's constant when not referring to...

One of the most random possible probability, you cannot even compute it in the absence of an oracle!

[Random]

Now imagine a quantum state with a normalisation constant of $\sqrt{\Omega_F}$

Balarka Sen

@0celo7 There's no integrand in $\int d^3 p$, which is probably the source of confusion

It's $1$

0celo7

@BalarkaSen Physicists write integrals like $\int d^3p \, f(p)$

Balarka Sen

ugh

Anonymous

To make it clear....$d^3p$ just means $(dp)^3$ ? Or no?

0celo7

@Blue Do you not know multivariable calculus?

Anonymous

14:28

@0celo7 Not fully

Anonymous

I don't know what the notation $d^3p$ means

0celo7

it's the measure for a triple integral

Balarka Sen

$d^3 p$ is a volume element in the 3d space of momentums

0celo7

if that means nothing to you then learn more calculus

Balarka Sen

It's $dp_x dp_y dp_z$ to be more precise

@0celo7 Eh, it's a 3-form :3

0celo7

14:30

@BalarkaSen You take your abstract math elsewhere

Balarka Sen

lmao

0celo7

In this room we only do measure theoretic calculus

Anonymous

@BalarkaSen Okay, so basically it should be $dp_xdp_ydp_z=(dp)^3$, which people write as $d^3p$. Now, under what condition can we write $dp_xdp_ydp_z=(dp)^3$ ?

Anonymous

Rotational invariance?

Balarka Sen

@Blue Look, $(dp)^3$ is not a thing

0celo7

14:31

No. Rotational invariance gives $d^3p = 4\pi p^2dp$

Balarka Sen

$d^3p$ is by definition $dp_x dp_y dp_z$. There's no arithmetic going on here, it's just notation.

0celo7

If you knew integration theory this would be trivial

Anonymous

@BalarkaSen Ooo

Anonymous

Okay, now when can we write $dp_xdp_ydp_z$ as $4\pi p^2 dp$ ? What does rotational invariance mean? It looks similar about each axis ?

Balarka Sen

Please don't write that.

0celo7

14:33

@BalarkaSen He's a physicist

Balarka Sen

(Those two are not even equivalent objects, one is a 3-form and the other is a 1-form.)

0celo7

I TOLD YOU TO STOP THAT

Balarka Sen

@Blue Say you're looking at $\int f(p) d^3p$

That's $\iiint f(p_x, p_y, p_z) dp_x dp_y dp_z$

Anonymous

@BalarkaSen Yep. Then?

0celo7

@JohnRennie Do you know the proof that ADM mass is conserved?

Balarka Sen

14:36

@Blue If $f$ only depended on the distance from origin $(0, 0, 0)$ to a point $(p_x, p_y, p_z)$ in the momentum space, and not on the individual coordinates, you could write $f(p_x, p_y, p_z) = g(\sqrt{p_x^2 + p_y^2 + p_z^2})$.

Anonymous

@BalarkaSen Okay, I can agree

0celo7

aka $f(|p|)$

Balarka Sen

(This is the "rotation invariance" everyone is talking about)

Right, @0celo7

John Rennie

@0celo7 No

Slereah

Chaitin's constant isn't random

0celo7

14:38

@Slereah check skype

Slereah

It's 100% definable

0celo7

I need to send that

Anonymous

I basically wanted to find out $\iiint f(p_x, p_y, p_z) dp_x dp_y dp_z$ such that $p_x^2+p_y^2+p_x^2 \leq 2mE$.

Slereah

And is semi recursively enumerble

0celo7

@Blue is $f$ rotationally invariant!!?

is it at least separable in polar coordinates?

Anonymous

14:39

@0celo7 It's just $1$ :P

0celo7

...

I'm done!

Anonymous

So, in this video (youtube.com/…) the lecturer writes that as $\int_{0}^{\sqrt{2mE}} 4\pi p^2dp$

0celo7

that is correct

Balarka Sen

My internet is a bit glitchy

heather

would anyone mind taking a look at this question of mine?

Anonymous

14:41

So my question is, is $dp_xdp_ydp_z=4\pi p^2 dp$ by notation or is there something more to it?

Balarka Sen

@Blue No, it is not by notation or by anything

It is garbage.

0celo7

@Blue See page 244 of Federer [sarcasm but if you do it will explain]

For $f\equiv 1$, you get what you want.

Anonymous

@0celo7 I guess I have to take that on faith now. That professor uses it without explaining and even ends up with the correct answer. Lol

Anonymous

(It's around 13 minutes into the video I linked)

Balarka Sen

You don't have to take it on faith. You have to be patient for 5 minutes instead of referring constantly to whatever video you have that uses it without explaining

So that we can explain it to you

Anonymous

14:46

@BalarkaSen Okay? Well, you said that it's garbage...so I stopped asking

0celo7

I assumed you knew calculus. Ignore what I said earlier

Balarka Sen

The thing about differentials is indeed garbage. The correct statement is what 0celo7 wrote above

0celo7

When you really understand what's going on you can hand wave like I do

Balarka Sen

In any case, when $f(p) := f(p_x, p_y, p_z)$ can be written as $g(\|\mathbf{p}\|)$, you can do the following

Do a change of variables so you parametrize everything in spherical coordinates

Then $r = \|p\|$ and the other components in spherical coordinates parametrize the sphere of radius $r$ in $\Bbb R^3$

But $f(p)$ is constant on every sphere $p_x^2 + p_y^2 + p_z^2 = r^2$ because it's a function of $r$.

Anonymous

@BalarkaSen Alright so far

Anonymous

14:52

So we are changing the coordinate system from $p_x,p_y,p_z$ to $r,\theta,\phi$

Balarka Sen

So, explicitly written, $\iiint f(p_x, p_y, p_z) dp_x dp_y dp_z = \iiint f(r) r^2 d\theta d\varphi dr$ where $(r, \theta, \varphi)$ are the spherical coordinates.

0celo7

you're missing an $r^2$

Balarka Sen

@0celo7 $4\pi $ comes when integrating $\iint d\theta d\varphi$

Anonymous

@BalarkaSen Is the Jacobian 1?

Balarka Sen

That's the surface area of the sphere of radius $1$.

Oh, I see. Sorry.

0celo7

14:53

@BalarkaSen Better.

@BalarkaSen I didn't say anything about $4\pi$.

Anonymous

When converting that to spherical coordinates isn't the Jacobian $r^2\sin(\phi)$ or something?

Balarka Sen

Yeah I got it. I was doing a different parametrization by scaling the spheres.

0celo7

@Blue Yeah, he's missing more stuff.

Way to go @BalarkaSen

Balarka Sen

... Huh, the determinant of the Jacobian is $r^2 \sin(\varphi)$, indeed.

0celo7

@Blue so if you know that why are you confused about any of this?

Anonymous

14:56

@0celo7 I'm still trying to connect the dots

Balarka Sen

So the inner integral is $\iint \sin(\varphi) d\theta d\varphi$

Does this give me $4\pi$ when integrating over the sphere of radius $1$?

Anonymous

It's just finding the surface area, isn't it?

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