The h Bar

0celouvsky

5:00 PM

Wtf

cat's eye

@john i don't have a question at the moment

0celouvsky

Another JEE Indian?

Anonymous

@0celouvsky Lemme verify

Koolman

@blue we can also take it as total

paracetamol

@0celouvsky YES! Mwahahahaha!

Anonymous

5:00 PM

@cat'seye Which grade are you in? :D

gansub

i had a basic question. if the divergence of a closed surface is zero and since the earth is a closed surface - longwave radiation escaping into space would that violate the definition of a closed surface ?

Fawad

Correct time @Kaumudi.H

ACuriousMind

@0celouvsky It's nice you admit that your math is sinister :)

gansub

any idea anyone ?

Koolman

@paracetamol you were also preparing for jee

ACuriousMind

5:02 PM

The Dark Side of Math, upcomung album of my nerd-themed band

0celouvsky

@ACuriousMind I was talking about your algebraic geometry

I don't know what sinister math I do o.O

I only do GR

paracetamol

@Koolman No way -_-

Anonymous

@Koolman Nah, he is the odd one out

Fawad

@Koolman he is medical student

Anonymous

He is a bio guy

gansub

5:02 PM

@blue hello

Anonymous

lol

Anonymous

@gansub Hi

ACuriousMind

@gansub What do you mean by "divergence of a surface"? We usually take divergences of vector fields, not surfaces

Slereah

@0celouvsky What is so GR about sheaves

user228700

Eek, a user from my own city!

gansub

5:03 PM

@ACuriousMind - I meant divergences of vector fields sorry

Koolman

okay got it

gansub

divergence through a closed surface

John Rennie

@gansub You mean the divergence theorem?

gansub

@JohnRennie yes

divergence through a closed surface is zero

John Rennie

I don't think EM radiation leaving the closed surface counts as a net flux of the vector field.

paracetamol

5:04 PM

Tickles everyone

Changes topic: Back to fruits people!

gansub

@JohnRennie - can you explain why not ?

paracetamol

So @Slereah, what fruits d'ya like?

Slereah

@paracetamol lemons

2

paracetamol

:O

rob

@JohnRennie It doesn't, because the fields in radiation are transverse to the propagation direction.

0celouvsky

5:05 PM

@Slereah sheaves are just a nice way to package information

ACuriousMind

@gansub Radiation does not contradict the integral of the divergence being zero - Electromagnetic waves are vacuum solutions of Maxwell's equations, after all.

paracetamol

@Slereah I think we're going to get along really well :D

Currently sipping Lemonade

user228700

In any case, @cat'seye: Welcome! :-)

John Rennie

@gansub elctrodynamics isn't one of my favourite subjects, but if you consider a wave normal to the surface the EM fields are everywhere tangential to the surface.

rob

If the Poynting vector $\vec S \propto \vec E \times \vec B$ is perpedicular to a surface, then $\vec E$ and $\vec B$ are parallel to the surface.

Anonymous

5:06 PM

@paracetamol Ever tried dragon fruit?

dmckee

@paracetamol I am a great lover of baroque and classical music, but you can't talk about Pachelbel's Canon in D without being aware of

[OFFICIAL] Cellist's Pachelbel Rant

►

paracetamol

@blue Long time ago...don't quite remember what it tasted like (kinda bland, I guess)

gansub

@ACuriousMind @JohnRennie occasionally some long wave radiation does leak into space

Anonymous

@paracetamol That's the only fruit which made me vomit.

paracetamol

@dmckee But...that's no cello ._.

0celouvsky

5:09 PM

That's a violin.

paracetamol

@blue That was...graphic...

dmckee

He hasn't always been so cool because he didn't always play guitar. He started out on the cello.

Anonymous

@paracetamol No idea what you were imagining :'D

John Rennie

@gansub yes, the Earth continually radiates into space, but remember that the electric field is normal to the direction of propagation of the wave. So when you integrate the electric field of the escaping radiation over your closed surface it integrates to zero.

As the divergence theorem requires.

paracetamol

@dmckee Ah! But I still take offence when anyone pokes fun of my beloved Pachelbel :3

ACuriousMind

5:11 PM

@gansub I'm not quite sure why you call it "leaking", but yes, the earth emits radiation into space. We've tried to explain to you that that does not contradict Gauß' law.

paracetamol

@dmckee Speaking of cellos and Pachelbel, have a look at this one:

Rockelbel's Canon (Pachelbel's Canon in D) - 4 Cellos - The Piano Guys

►

gansub

@ACuriousMind - many thanks. I am not disputing what you say. Just trying to understand your explanation that is all

paracetamol

@ACuriousMind Ooooh! Another eszett!

cat's eye

@curiousmind what kind of radiation earth emits?

gansub

cat's eye - infra red

AccidentalFourierTransform

5:13 PM

whats that fancy beta doing in Gauss' name

paracetamol

@blue I write poetry (hobby). We poets tend to be a bit more imaginative than the average human being ;)

1 min ago, by paracetamol

@ACuriousMind Ooooh! Another eszett!

ß

In German orthography, the grapheme ß, called Eszett (IPA: [ɛsˈtsɛt]) or scharfes S (IPA: [ˈʃaɐ̯.fəs ˈʔɛs], [ˈʃaː.fəs ˈʔɛs]), in English "sharp S", represents the [s] phoneme in Standard German, specifically when following long vowels and diphthongs, while ss is used after short vowels. The name Eszett represents the German pronunciation of the two letters S and Z. It originates as the sz digraph as used in Old High German and Middle High German orthography, represented as a ligature of long s and tailed z in blackletter typography (ſʒ), which became conflated with the ligature for long s and round...

Hullo @Accident o/

John Rennie

@gansub remember you are integrating $\mathbf E \cdot d\mathbf A$. If $\mathbf E$ and $d\mathbf A$ are normal then the dot product is zero.

ACuriousMind

@gansub That's fine, I guess I just didn't understand why you told us again that earth leak radiation - maybe you could be more specific what you don't understand?

AccidentalFourierTransform

no, its a fancy beta and I dont want it anywhere near Gauss

paracetamol

:D

0celouvsky

5:15 PM

Can @ACuriousMind stop being so pretentious

ACuriousMind

@paracetamol You'll need to calibrate your ironymeter better if you want to be in this chat. AFT is perfectly aware what an ß is, he's just being silly :P

@0celouvsky You're just jealous that your keyboard lacks the ß key

paracetamol

@ACuriousMind Whup! Hey! I'm new here...cut me some slack ;)

AccidentalFourierTransform

$\mathscr \beta$

gansub

@ACuriousMind - I did not consider the electric field in my thought process

I only looked at the infrared radation as a "whole"

cat's eye

so the earth is like a spherical infrared source. but Earth isn't really spherical

0celouvsky

5:16 PM

@ACuriousMind Of courße it haß it.

ACuriousMind

@0celouvsky Impreßßive, but you could just have copied that ß from what I posted ;)

paracetamol

@ACuriousMind I'm jealous because mine doesn't have an umlaut A in it :(

John Rennie

@gansub remember that the flux through a surface element $d\mathbf A$ is $\mathbf E \cdot d\mathbf A$.

0celouvsky

I think nöt.

ACuriousMind

@AccidentalFourierTransform Actually, comparing ß and $\beta$, the beta is a fancy ß, not the other way around, no?

paracetamol

5:18 PM

@ACuriousMind That's "Impreßive" with a single eszett to you Mr.Mod ಠ_ಠ

gansub

@JohnRennie - E is the Electric field right ?

John Rennie

@gansub Yes.

AccidentalFourierTransform

no, you dont understand fanciness

gansub

@JohnRennie - so the Electric field of the wave remains within the closed surface because it is perpendicular but what is not perpendicular does escape ?

John Rennie

@gansub No, I'm not saying the electric field of the wave remains within the surface.

ACuriousMind

5:19 PM

@gansub That the integral of the divergence is zero does not mean that the electric field itself is zero. There's no reason for the field to be confined inside the surface

@AccidentalFourierTransform Maybe I don't

AccidentalFourierTransform

i seen photos

you clearly dont

gansub

So the perpendicularity of the field and surface makes the divergence zero

Hmmm I need to visualize it

John Rennie

Basically yes.

Though note also that the electric field oscillates in a wave so at any surface element it is alternately positive and negative. When integrated over time this also makes it zero.

In the usual simple examples of a charge at the centre of our spherical Gaussian surface the electric field is parallel to $d\mathbf A$ and is constant i.e. doesn't change with time.

For a radially outgoing EM wave the electric field is normal to $d\mathbf A$ and oscillates with time.

Slereah

So

The most important question

The exterior derivative

$d$ or $\textrm d$

AccidentalFourierTransform

$\mathrm b$

John Rennie

5:28 PM

@Slereah The intersection of me and people who give a damn is the empty set

Slereah

that would be the evitavired roiretxe

AccidentalFourierTransform

why are you speaking french?

Slereah

@JohnRennie is the reason we have ugly notation

AccidentalFourierTransform

and ugly people

Slereah

Also is the hodge star $\star$ or $*$

all important choices

ACuriousMind

5:30 PM

@Slereah Use $\mathrm{d}$ and $\star$.

No debate there

But pay attention to the spacing around $\star$

paracetamol

52

Q: What's the worst thing anyone could do in a fast-food restaurant?

In Johnny and the Bomb (chapter 8) Terry Pratchett writes this: Sir John sat down heavily in a seat, motioned them to sit down as well, and then did the second-worst thing anyone could do in a fast-food restaurant. He snapped his fingers at a waitress. All the staff were watching th...

I like the diagrammatic representation of the Layers of Hell over there :3

John Rennie

Since the only physics conversation n the last hour has now petered out, now seems a good time to repair to my armchair with a book and a beer.

paracetamol

Well then @JohnR, you do that. I'm off to ~~fantasise about peaches in~~ bed. Bye @Acurious @Slereah @blue o/

AccidentalFourierTransform

5 to 10k

almost there peeps

cat's eye

I have a question, how the electrons absorb photons?

AccidentalFourierTransform

5:37 PM

like this

Metal umlaut

A metal umlaut (also known as röck döts) is a diacritic that is sometimes used gratuitously or decoratively over letters in the names of hard rock or heavy metal bands—for example those of Blue Öyster Cult, Queensrÿche, Motörhead, The Accüsed and Mötley Crüe. Among English speakers, the use of umlaut marks and other diacritics with a blackletter style typeface is a form of foreign branding intended to give a band's logo a Teutonic quality—connoting stereotypes of boldness and brutality presumably associated with Germanic and Nordic cultures. Its use has also been attributed to a desire for a "gothic...

Ok sir , with due respect I would follow your orders and write a better answer.Thanks for making me a better human being ,thanks really (I mean it).I would never encourage people ,I promise , Thanks sir thanks. — AMoreCuriousMind Apr 14 at 19:22

> I would never encourage people ,I promise

ACuriousMind

@JohnRennie Did you destroy your armchair during your last drinking session, or why do you need to repair it?

AccidentalFourierTransform

to my chair :-P

ACuriousMind

@cat'seye There's...not really a "how". It's a fact of quantum mechanics that a photon and an electron can interact in such a way that the electron ends up in a higher energy level and the photon is nowhere to be seen, but the theory doesn't really provide a "mechanism" as we would classical understand it.

@AccidentalFourierTransform I feel there might have been a language barrier there :P

AccidentalFourierTransform

can a vector particle eat up a fermion in a Higgs-like mechanism?

that'd be cool

cat's eye

@ACuriousMind so is this any other theory that explains the mechanism?

paracetamol

5:43 PM

@AccidentalFourierTransform Maybe he meant "retire"

He is a Brit after all ._.

ACuriousMind

@AccidentalFourierTransform I've never seen anything like it, but I can't exclude some crazy model builder has cooked up something like that

AccidentalFourierTransform

@paracetamol he's not that old

._.

@ACuriousMind Huh?

google.co.in/…

5:45 PM

@JohnRennie Will you have time this weekend? I'm starting a project and I wanted to discuss design (of the code)

0celouvsky

Many people use $h$

Ben Niehoff

@ACuriousMind Hodge star is \DeclareMathOperator*{\hodge}{\star} :P

paracetamol

Pssst Herr @ACuriousMind, can I talk to you a bit? Someplace quieter? ( The Periodic Table chat room)

It's got nothing to do with you being a "sexy, black woman", in case you were wondering ;)

ACuriousMind

@cat'seye Not really, my point was more that asking for a "mechanism" doesn't really make sense. I mean, the electron and the photon have no substructure, and usually when we provide a "mechanism" for how things interact, we explain it in terms of their smaller parts. But when we arrive at the smallest parts, how could we conceivably speak of such mechanisms?

0celouvsky

Why the comma?

ACuriousMind

5:48 PM

@paracetamol I don't like going to another chat with a private conversation, but I have no objection talking to you in another room. Just create a new one.

AccidentalFourierTransform

@ACuriousMind I guess it can work for a massless Rarita-Schwingeron in a Stückelberg-like magical fuckery

0celouvsky

He's a sexy black woman, not a black woman who happens to be sexy

Ben Niehoff

@AccidentalFourierTransform Vector particles can't eat fermions, no, but there might be a way of breaking spacetime SUSY by the gravitino eating a fermion. Not entirely sure, it's not my specialty

ACuriousMind

@AccidentalFourierTransform I dare you to write a paper and include "Stückelberg-like magical fuckery" in there.

2

paracetamol

@ACuriousMind But I won't be needing it afterwards...wait, will you be deleting it?

ACuriousMind

5:49 PM

Also, "Rarita-Schwingeron" :D

AccidentalFourierTransform

challenge accepted friend

ACuriousMind

@paracetamol Why would I? Rooms that aren't used get automatically frozen after a while, but it's not as if there's limited space on chat or anything, we can create as many rooms as we like

0celouvsky

I dare you to write a paper in Weinberg's notation.

ACuriousMind

@AccidentalFourierTransform Language, please.

Slereah

I think the worst particle name I've seen yet was the papapetron

ACuriousMind

5:50 PM

@0celouvsky Man, nothing you could offer me would make me do that

0celouvsky

@ACuriousMind I can give you...a copy of weinberg GR

AccidentalFourierTransform

whats so bad about W.'s notation?

its fine to me

ACuriousMind

@AccidentalFourierTransform At times, I fear the poor letters are going to collapse under the weight of all their decorations

paracetamol

@ACuriousMind Well, I was afraid of clutter...besides, what's to be discussed there is strictly between us. I don't fancy the idea that someone else would come across it. It's nothing incriminating, but all the same, I'm a very private person ._.

0celouvsky

@ACuriousMind man, you would hate PDE

cat's eye

5:53 PM

@ACuriousMind there must be some rules for the photon absorption? if i have a free electron and a photon in vacuum, will the photon disappear immediately?

0celouvsky

The poor norms :(

ACuriousMind

@cat'seye Oh, of course there are rules!

Anonymous

@Kaumudi.H Are you challenging any of the questions in the answer key? There were 5 wrong/ambiguous ones. Man, they are so costly!

0celouvsky

Gotta denote the domain, weight function, power of various things

cat's eye

@ACuriousMind so what are the rules!!?

ACuriousMind

5:55 PM

@cat'seye Well...they are the rules of QM coupled to an electromagnetic field, or even of quantum electrodynamics, which is a subtle field if you want to explore every detail. What sort of rules are you looking for?

AccidentalFourierTransform

conservation of $p$

cat's eye

i'm studying spectroscopy so understand the energy levels of electrons in atoms, molecules. I want to understand the rules for a free electron and photon

AccidentalFourierTransform

a free electron cannot capture a photon because of conservation of energy and momentum

ACuriousMind

Ah, then it appears you're looking for selection rules

John Rennie

@BernardoMeurer I'll be out Saturday lunchtime onwards for a ~~piss up~~ meeting of the Chester science fiction society (in a pub naturally). I'll be around on Sunday but won't be in the best of states.

cat's eye

6:00 PM

@AccidentalFourierTransform can you elaborate that?

John Rennie

@ACuriousMind Middle English repairen (“to return”), from Old French repairier. Used only idiomatically in modern English.

cat's eye

@ACuriousMind no, I'm looking for a theory of single photon and single electron interaction

John Rennie

@cat'seye Compton scattering you mean?

0celouvsky

@ACuriousMind so I've figured out why sobolev spaces on manifolds are a mess, and it's not because analysis sucks

cat's eye

@JohnRennie yes a similar one but for absorption

0celouvsky

6:04 PM

It's because there are two (ultimately equivalent) definitions

And people are pretty inconsistent with the one they use. The definitions are suited for different things

John Rennie

@cat'seye I'm not sure that makes sense. Compton scattering is the trasnfer of some of the photon energy to the electron, so it is partial absorption I suppose. Complte absorption isn't possible because you can't simultaneously conserve both the total energy and the total momentum.

Bernardo Meurer

@JohnRennie Deal! :P

John Rennie

@BernardoMeurer I've written code when well steamed, and it looked great at the time ...

Bernardo Meurer

I've deleted my home folder with a Makefile when I was drunk

twice

0celouvsky

It's confusing because Atiyah had Sobolev spaces on manifolds in 64, but Aubin claimed to have pioneered this stuff in the 70s

gansub

6:07 PM

@JohnRennie - one final question in the radiation divergence question

people do not fall off the earth because earth is a closed surface right ?

0celouvsky

The big issue is that Atiyah's sobolev spaces only worked on compact manifolds, dubiously on ones with boundary, and not at all on noncompact ones

So the literature moved to Aubin's definition but no one bothered to check that everything carries over

cat's eye

@JohnRennie this is really confusing! the electron absorbs photon completely in an atom but not in free space

John Rennie

@gansub that doesn't make sense ...

ACuriousMind

@JohnRennie Interesting, learn something new every day...

John Rennie

@cat'seye in an atom some of the momentum can be transferred to the rest of the atom.

ACuriousMind

6:09 PM

@gansub People do not fall off the earth because gravity points towards the earth's center. What are you talking about?

John Rennie

@ACuriousMind none of it useful :-)

gansub

no I mean I am just trying to visualize fluxes out of closed and open surfaces

and trying to explain to myself the differences

ACuriousMind

@JohnRennie You're talking to a string theorist, "usefulness" does not occupy a top spot in my priority list ;)

John Rennie

@gansub The gravitational field is everywhere (approximately) normal to the surface of the Earth ...

gansub

There is no flux out of a closed surface

but open surfaces do permit fluxes

cat's eye

6:12 PM

@JohnRennie i'm not an expert in quantum mechanics. why the momentum is not conserved in free space?

John Rennie

@gansub there is, because there is mass, i.e. the source of the field, inside the closed surface. So the divergence is non-zero.

Anonymous

@cat'seye If momentum is conserved then energy can't be...

Anonymous

And if energy is conserved then momentum can't be

Anonymous

Try writing down the equations

John Rennie

@cat'seye You'll find the calculation all over the Internet. If you model it as a 2 body collision you'll find that the momentum and energy cannot simultaneously be conserved.

gansub

6:13 PM

@JohnRennie - then that is my problem. i am difficulties with defining an open and closed surface.

if i had an open surface anything can escape out of it as i see it

cat's eye

@all okay thank you :)

gansub

and in a closed surface well i think it cannot . am i wrong ?

John Rennie

@gansub I suspect you have the wrong idea of this area of physics.

gansub

@JohnRennie - very likely. some clue in visualizing would help

John Rennie

The surface is just some mathematical object not anything real. We can draw it anwhere we want and any shape we want.

gansub

6:15 PM

ok

how do i tell one is closed and another is open ?

John Rennie

The point is that if you integrate $\mathbf F \cdot d\mathbf A$ over the surface it comes out as proportional to the charge inside the surface.

@gansub a closed surface has the topology of a sphere and an open surface, err, doesn't have the topology of a sphere.

gansub

but both permit matter to pass through right ?

ACuriousMind

@JohnRennie Uhhhhh

E.g. a torus is also a closed surface

John Rennie

@ACuriousMind Uh oh

@ACuriousMind OK - damn! :-)

0celouvsky

@ACuriousMind Also, one couldn't make any sense of "minimal" constants in the old theory. The norms were highly chart-dependent so it didn't make a sense for an embedding to be optimal

ACuriousMind

6:17 PM

It's just not usually useful to consider closed surfaces that are not spheres

0celouvsky

is anyone actually reading this

Emilio Pisanty

@ACuriousMind this is why people hate physicists

ACuriousMind

@0celouvsky Yes, I just had nothing to say. It's interesting, though

John Rennie

@gansub the Gaussian surface isn't a physical object. Asking if things pass through it is somewhat meaningless.

gansub

@JohnRennie ok as a mathematical object what does divergence through a closed surface mean ?

0celouvsky

6:19 PM

@ACuriousMind Basically, on $\Bbb R^n$, one can define Sobolev spaces by saying that $u$ has "rapidly decaying Fourier transform." This makes sense on manifolds if you talk in charts. So you can piece together a Sobolev norm globally using a partition of unity, but that's really unsatisfactory because there's nothing "global" about it.

John Rennie

@gansub As far as I know the phrase divergence through a closed surface is meaningless.

Henke

@blue Physics III

Anonymous

@Henke No idea what that is :P I suppose some Western Uni lingo (Undergrad I guess)

John Rennie

Divergence is a vector operator.

0celouvsky

Aubin tried to fix this in the 70s, but his proofs are really loose. I've talked to people who should know about it but they claim that it's all well known

Henke

6:21 PM

@blue yep

0celouvsky

@ACuriousMind One person said it would be embarrassing to write it all down because everyone already knows it

Anonymous

@Henke Nice :-)

0celouvsky

Except for the fact that they all have no clue how it works in detail

gansub

@JohnRennie - math.stackexchange.com/questions/1689723/…

John Rennie

@gansub: suppose you have a field - we'll make it an electric field for convenience. This field is a function of space so everywhere in 3D space it has some value.

ACuriousMind

6:23 PM

@EmilioPisanty It is?

Emilio Pisanty

@ACuriousMind well, a bit

gansub

@JohnRennie agreed

John Rennie

@gansub: BTW stop me if I'm telling you things you already know.

gansub

sure John Rennie

0celouvsky

wtf

Katana VS Burglar Techniques (Please Read The Video Description)

►

John Rennie

6:24 PM

@gansub Generally speaking the divergence of the field $\nabla \cdot \mathbf E$ at a point is proportional to the density of the charge at that point.

For the EM field the charge is electric charge and for a gravitational field the charge is just mass.

gansub

ok

John Rennie

You can take some region of space, like the inside of a closed surface, and integrate the divergence inside that volume.

gansub

ok

go on

ACuriousMind

@EmilioPisanty What aspect of "this" specifically are you thinking of?

0celouvsky

@JohnRennie nable = french divergence?

Emilio Pisanty

6:27 PM

@ACuriousMind the obsession with spheres, of course

John Rennie

@gansub That is, take infinitesimal volume elements, $dV$, and the charge inside is then then $\rho dV$, so the divergence is $k \rho dV$ for some constant $k$ (which has epsilon in it for the EM field).

ACuriousMind

@EmilioPisanty Ah

Well, I guess there are some cows who have suffered under it ;)

paracetamol

Hullo @JohnR o/ Back from your beer I see ;)

John Rennie

@gansub Sum up all these volume elements and you get a total divergence for that volume.

gansub

ok

John Rennie

6:29 PM

@gansub Cool. What the divergence theorem tells us is that this total divergence that you have just calculated is related to the integral of the field over the surface that bounds the volume.

gansub

i got that part as well

it is just the difference between open and closed that is the problem i am having visualizing

John Rennie

More precisely if you integrate $\mathbf E \cdot d\mathbf A$ over the surface the result is proportional to the integrated divergence.

@gansub if you have some continuous volume, then the surface of that volume must be a closed surface. Are you OK with that statement?

gansub

ok

how do you define open then ?

John Rennie

An open surface can't enclose anything because it has no separate inside and outside.

So an open surface cannot divide space into two separate parts.

gansub

but a closed surface can right ?

John Rennie

6:32 PM

Yes.

gansub

so the integral of the divergence over a closed surface is zero ?

John Rennie

A closed surface divides space into two regions and it is impossible to go from one region to the other without passing through the surafce.

I don't see how you can integrate the divergence over a 2D surface because the divergence is proportional to $\rho dV$, where $dV$ is a 3d volume element.

The question you link makes no sense to me.

gansub

hmmmmm OK John Rennie

thank you very much for your time

ACuriousMind

Indeed, you integrate the divergence over the volume and the field itself over the surface (I fear I've said something like integrating the divergence over the surface somewhere upthread)

gansub

let me think deeply and maybe get back to you later ?

John Rennie

6:36 PM

You can integrate the flux $\mathbf E \cdot d\mathbf A$ over the surafce because $d\mathbf A$ is a 2D surface element.

@BernardoMeurer are you still around?

0celouvsky

@ACuriousMind Oh and don't even get me started about what $C^k(\bar M)$ is supposed to mean, where $M$ is a $\partial$-manifold

Bernardo Meurer

@JohnRennie yep

0celouvsky

Geometers and analysts think they're different things, and geometric analysts have no fucking clue

John Rennie

Should I buy this?

Answer "yes" :-)

ACuriousMind

@0celouvsky I don't even know what a $\partial$-manifold is :P

gansub

6:38 PM

thank you again @ACuriousMind

and @JohnRennie

your ideas make me want to go deeper

ACuriousMind

@JohnRennie I expected a laptop

John Rennie

@gansub I hope we have helped more than we have confused you :-)

gansub

@JohnRennie - I needed a critical appraisal of my ideas

John Rennie

@ACuriousMind I have my eye on some laptops, but you have to admit that is a cute little PC :-)

gansub

on how I visualize my field

you did just that

i am not a mathematician

i am a fluid dynamicist

John Rennie

6:39 PM

And it's a powerful little beggar as well!

0celouvsky

@ACuriousMind clearly a manifold with $\partial M\ne \emptyset$...

Bernardo Meurer

@JohnRennie Intel i3?

No!

John Rennie

Look at the speed rating‌.

ACuriousMind

@JohnRennie I don't want cute or little. I want...fearsome, strong, towering

John Rennie

@BernardoMeurer: Core for core it's about the same as the CPU in your beast. It's just that you have twice the number of cores!

@ACuriousMind Individual CPU speeds haven't increased much in the last few years. The speed gains have come from having multiple cores. For single threaded apps the latest huge, noisy power hungry computers aren't sigificantly faster.

ACuriousMind

6:43 PM

@JohnRennie I was making an aesthetic, not a rational statement ;)

John Rennie

Ah :-) And presumably it needs glowing lights inside the case and windows for you to admire the lights? :-)

ACuriousMind

These are nice, yes

0celouvsky

@ACuriousMind Does that clear it up for you?

What do you think it means?

ACuriousMind

@0celouvsky What? The $C^k(\bar{M})$ thingy? I dare not guess

0celouvsky

@ACuriousMind What does it mean for a function to be $C^k$ on a manifold with boundary?

John Rennie

6:47 PM

I find it amazing that Dell can squeeze so much power into a case little bigger than a pack of cards. It doesn't have a CD drive because, well, it's too small for a CD to fit into it. That's how small it is.

0celouvsky

why would you need a CD drive o.O

John Rennie

Effectively take a top end ultraportable laptop, discard the keyboard and screen, scrunch what's left together into a rectangle and that's what that PC is.

@0celouvsky play DVDs - that matters when you own shedloads of DVDs.

0celouvsky

huh

John Rennie

I don't own shedloads of DVDs but my niece does. If I were to suggest she have a PC without a DVD drive she would tell me to stick it up ... erm ... lets just say it's a good thing it's so small.

0celouvsky

your niece again

she's like the JEE

can't talk to JR without someone bringing up sheep or his niece

John Rennie

6:51 PM

No, she hates physics - I think she must be a changeling

0celouvsky

Does she like math?

John Rennie

Anyway I make no apologies. When you get middle aged you get sentimental about these things (nieces not sheep).

Anonymous

@JohnRennie That's.....shocking :P Considering she is your niece!

John Rennie

@0celouvsky she gets good marks in maths but she doesn't like it. She wants to be a journalist.

Anonymous

You don't teach her Physics?

Anonymous

6:53 PM

:D

0celouvsky

you need to correct that @JohnRennie

I will send you relevant books

ACuriousMind

@JohnRennie As long as she doesn't become a pop-sci journalist...

John Rennie

@blue I tried. It was one of those you can lead a horse to water but ... moments.

0celouvsky

"Metric Structures in Differential Geometry" is a nice one

@ACuriousMind that was a question for you above, not me being lazy

John Rennie

I treid to explain transfinite numbers to her because I remember being fascinated by them. But, no luck.

0celouvsky

6:54 PM

@JohnRennie If she's anything like me that stuff will bore her

as will school math and math puzzles

ACuriousMind

@0celouvsky How often do I need to tell you my interest in non-smooth things is rather limited? :)

0celouvsky

explain the derivation of the heat equation

ACuriousMind

@0celouvsky Why would his niece be anything like you? oO

0celouvsky

@ACuriousMind Jesus christ, what does $C^\infty$ mean on a manifold with boundary

@ACuriousMind Oh and there's a third Sobolev theory due to Grubb and Palais that looks at embedded tori

John Rennie

@ACuriousMind unless they are secretly brother and sister. So did my brother visit America or did Ryan's dad visit Thames Ditton?

Jaime Gallego

6:57 PM

Howdy y'all

0celouvsky

are you a cowboy?

ACuriousMind

@0celouvsky I'd say "$C^\infty$ on the interior, and existence of the limit towards the boundary" or something like that, but I really don't know what the "right" definition would be

0celouvsky

@ACuriousMind a hunch

@ACuriousMind You're an analyst :D

The analytic definition is smooth in $M^\circ$ and every partial derivative is uniformly continuous in $M^\circ$ (has a continuous extension on the boundary)

John Rennie

@ACuriousMind could you use your moderatorial editing chops on:

33 mins ago, by John Rennie

@gansub Generally speaking the divergence of the field $\nable \cdot \mathbf E$ at a point is proportional to the density of the charge at that point.

ACuriousMind

Ah, the rare nablé operator

John Rennie

6:59 PM

A French differential operator!

0celouvsky

@ACuriousMind The geometric definition is that the function extendß (in charts) to a smooth function on a slightly larger open set.

One implies the other, but I'm not sure about the other way around. There's an argument due to Whitney that seems to hint it, but I'm not sure

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