The h Bar

${\mathbf E(r,z)} = E_0 \, \hat{x} \, \frac{w_0}{w(z)} \exp \! \left( \! \frac{-r^2}{w(z)^2}\right ) \exp \! \! \left( \! \! -i \! \left(kz +k \frac{r^2}{2R(z)} - \psi(z) \! \right) \! \! \right) $

Danu

So I checked out an undergrad algebra book

Russian style... "because vector addition and multiplication can be expressed geometrically, it is linear"

lol

Balarka Sen

7:57 PM

That's... a proof?

Danu

CLEAR :P

0celouvskyopoulo7

Vinberg is in the "graduate studies in math" series...

Danu

Have you read it?

I could read big parts of it without big problems, without any background knowledge of algebra. So I assumed it was undergrad.

(this was after having taken only 2 math courses in my life, so I really didn't know much)

0celouvskyopoulo7

I have not read it, I just find it surprising you call it an undergrad book

I have several books from that series (they are not undergrad)

Danu

8:14 PM

Mhm

This one starts with super basic definitions etc

ACuriousMind

Is "undergrad" vs. "grad" really the distinction one should make instead of "assumes substantial prior knowledge" vs. "doesn't assume prior knowledge"?

Danu

exactly!

I just call it undergrad if it doesn't assume anything

Also hi ACM

0celouvskyopoulo7

We should teach from Bourbaki then lol

ACuriousMind

We probably shouldn't - but it's much more useful to argue why we shouldn't instead of classifying at as "graduate".

Also hi Danu :P

Phase

I'm honestly confused about closing questions due to them being Homework

I thought that questions relating to homework but ones that are conceptual rather than just asking people to calculate it is fine?

Danu

8:25 PM

In principle something like that is true @Phase

Phase

@ACuriousMind could you explain to me why physics.stackexchange.com/questions/329865/… doesn't fit that criteria?

Just so I better know what not to answer

0celouvskyopoulo7

@Danu Maybe you've encountered someone writing $\iint_\Omega d\omega=\int_{\partial\Omega} \omega$?

Emphasis on the $\iint$

And consistently using $\iint$ throughout two books

ACuriousMind

@Phase I don't see a conceptual question there, nor any evidence of effort. It just poses a standard homework problem and complains about not being given the time. The solution is just to do some straightforward algebra on the standard equations for motion to eliminate time from them. Where's the conceptual question?

Danu

@0celouvskyopoulo7 No.

Slereah

mb it's just because $\textrm{dim}(\Omega) = \textrm{dim}(\partial \Omega) + 1$

Phase

8:28 PM

@ACuriousMind I guess I just interpreted his question more as "is there a way to do A"

reading it again I misread it a bit

Thanks for clearing it up, should I delete me answer or leave it there?

ACuriousMind

It would be better to delete it - all you left for the user is to plug in numbers, so it's a "near-complete solution" in my eyes

0celouvskyopoulo7

For instance we have

But here it's only one integral.

Phase

Oh, are we not meant to answer questions like that? If I was just going to leave a hint for a question I'd put it in a comment, there isn't really much to leave to the imagination with algebra like that anyhoo

ACuriousMind

Well...you are meant to answer on-topic questions like that. But giving complete solutions to off-topic questions just encourages them to come back and ask them anyway.

Phase

@ACuriousMind Ok got it, what about questions like physics.stackexchange.com/questions/329871/…

Should I just flag it as unsalvageable?

ACuriousMind

8:35 PM

I freely admit that the written policy on the whole homework issue is a bit confusing, and that you'll learn its "actual" content much better by just observing what happens on the site. We like to say we're "in the process" of revising it, but I'm actually not sure how optimistic I am for that given what happened (or, rather, didn't happen) at this attempt to reformulate it

Phase

I might just operate under a rule of thumb like "if it can be written in a comment, don't answer"

ACuriousMind

@Phase No such flag as "unsalvagable", but "unclear what you're asking" fits perfectly.

Phase

That's what I flagged it as

When I wrote about unsalvageable I misunderstood the "no editing can save it" tag

ACuriousMind

And even if you think the question is salvagable, please either edit it to actually salvage it, or flag it anyway. If it's flaggable in its current state, it does not matter much what it "could be"

Phase

To be honest if I have a question i just come to the Stackexchange chats

ACuriousMind

8:43 PM

Sometimes that's a good move if the question doesn't fit on the main site (too homeworky, too broad, opinion based, etc.), but I'd urge you to not ask questions in chat that would actually be on-topic on the main site - it's much more useful for others there than buried here in chat

Phase

I'll bear that in mind

0celouvskyopoulo7

@Slereah What is "Bourguignon"

How does one pronounce it?

Phase

Flagging this just makes me feel like a bad person physics.stackexchange.com/questions/329873/…

Bore-gee-nohn? a guess

0celouvskyopoulo7

"We let M be a noncompact Riemannian manifold, of dimension $n\ge 2$, possibly having nonempty boundary, and possibly having compact closure."

...what does compact closure mean for a manifold?

Slereah

@0celouvskyopoulo7 Coming from the region of Bourgogne

It is usually an adjectif for boeuf bourguignon

Beef bourguignon

Beef bourguignon US /ˌbiːf ˌbʊərɡᵻnˈjɔːn/ or bœuf bourguignon (UK /ˌbɜːrf ˈbʊərɡᵻnjɔːn/; French pronunciation: [bœf buʁ.ɡi.ɲɔ̃]), also called beef Burgundy, and bœuf à la Bourguignonne, is a well-known, traditional French recipe. The dish originates from the Burgundy region (in French, Bourgogne) which is in the east of present-day France, as do many other dishes such as coq au vin, escargot, persillé ham, oeufs en meurette, gougères, pain d'épices, etc. It is a stew prepared with beef braised in red wine, traditionally red Burgundy, and beef broth, generally flavoured with garlic, onions and...

@0celouvskyopoulo7 If you add the points of its boundary it's compact?

0celouvskyopoulo7

8:52 PM

@Slereah an abstract manifold does not have a boundary.

to have a boundary in the topological sense you need to be in a bigger space

Slereah

There are definitions of boundaries for manifolds

0celouvskyopoulo7

Simons donated $7 million to Hillary

Jesus

@Slereah It does not make sense to "add the boundary" then.

Slereah

For Riemannian manifolds you can just pick the completion of sequences wrt the metric

So that every Cauchy sequences converge to a point

0celouvskyopoulo7

I think the completion of a manifold would not be well behaved.

peterh

@Slereah I would make it with potato instead carrot, but it is wonderful.

Slereah

8:56 PM

why not

Well, it is possible that you have singularities, in which case the manifold + its boundary doesn't form a manifold anymore

at least not a Riemannian one

Danu

9:14 PM

I just realized that Kähler was a really terrible Nazi supporter... :\

Phase

If you have a wheel that isn't sliding and is rolling, the instantaneous velocity of the point of the wheel in contact with the surface is zero, but what happens if you have a disc that's spinning, and dropped from above with horizontal $v = 0$, how can you model the velocity as a function of time?

not necessarily needing an answer if people don't have time, just a link to relevant things would be great

0celouvskyopoulo7

@Danu hah

Danu

Even in 1988 he was a staunch suppporter. No shame.

That's something pretty exceptional.

0celouvskyopoulo7

He was captured by the allies and Cartan helped him continue studies while captured

amazing

ACuriousMind

@Phase Within the "pure rolling" framework, I think it would just drop and spin in place. You need to "turn on" the sliding friction, I'd say

Phase

9:21 PM

Sorry I forgot to say that, I meant that, without friction there would be no actual force on it so it's net linear momentum wouldn't change

How would one model the velocity or just the instantaneous force as a function of time?

Danu

@0celouvskyopoulo7 Yeah, it confuses me

He volunteered to be a soldier!

I wonder what Cartan thought about this

0celouvskyopoulo7

"That crazy German"

ACuriousMind

@Phase Well, the wheel drops and makes contact with the floor - the point of contact is moving when it does so, and exerts a force on the wheel that makes it start moving.

Phase

Yeah but I mean how would you derive an algebraic expression for the motion? Just standard friction and torque?

ACuriousMind

I guess? I mean, what else could you do?

Phase

9:24 PM

Fair, just haven't really covered Angular momentum properly in my course yet

0celouvskyopoulo7

@Danu haha he had a nazi flag in his office

How the fuck did he get away with that

Slereah

9:41 PM