12:03 AM
Like this problem
Is hard no matter what you guys say:P
Here's the solution in case anyone's interested:

I remember there being a problem in Griffiths that messed up most of our class. I think it was about overlapping spheres or something?

2 hours ago, by Lozansky
perhaps?
the solution uses overlapping cylinders

@danielunderwood There is one with overlapping spheres where you calculate the field in the overlapping region
iirc

@Lozansky those are reasonably ugly, yes
infinitesimally-small separation between regions held at different potentials is tricky territory
all sorts of unphysicality dragons there

This is the one I was thinking of
But it's pretty trivial if you use the hint so I doubt it's the one @danielunderwood is thinking of :P

12:13 AM
@Lozansky for some reason, that makes me think of the French group theorist Jacques T.
... which is probably a very strong sign that I should really go to bed now.

oO
Getting late here as well
I'm off
Thanks for all the help guys

2 hours later…
1:49 AM

1 hour later…
2:58 AM
@EmilioPisanty Heh, the guy who answered that is interning with us :-D

3:19 AM
@DanielSank </3

4:19 AM
@Blue Yes, I am from WB :-)
@Blue No, I think no Institute offers QI in Undergrad level in India, I am doing MOOC by Peter Shor and the Caltech, Q Tech course on Quantum Crypto
@Blue Can I know from which institute you are?
I will like to work on QI later, I heard HRI is a good place for QI in India.

5:01 AM
isn't the center of a group G the normal subgroup of G?

5:12 AM
ncatlab.org/nlab/show/classical+Lie+group It turns out the knowledge I have learnt about Lie group is merely about classical Lie groups. There are still exceptional Lie groups! What on earth are they?
I think I have had some rudimental touch with some of exceptional Lie groups, but I still know too little of them to get a profile of them.
@bolbteppa are exceptional Lie groups closely related to supersymmetry?

5:36 AM
John Baez's page here is suggestive: math.ucr.edu/home/baez/octonions/node13.html

@JohnRennie you around?

@DavidZ morning :-)

To wit: you get the three classical families by constructing algebras based on the reals numbers, the complex numbers, and the quaternions.
The next thing to try would be to pass from the quaternions to the octonions. but those guys are weird

@JohnRennie Hi :-) I had some questions about some homework answers you pointed out recently, could we discuss that either here or in another room? (your choice)

Here is fine. I'm guessing you think I'm being over zealous in criticising people for answering homework questions?

5:39 AM
(octonions aren't even associative, ay yi yi). so it's maybe not surprising that it's harder to create Lie algebras based on them, and that what you get will be 'exceptional'

@JohnRennie Nah, it's not about that. It's more like a couple of the ones you pointed out didn't really seem like "complete answers" in the sense I understand it. I can post a link or two in a minute

c.f. this sentence from his page on F4: "In 1951, Freudenthal embarked upon a long series of papers in which he described not only $F_4$ but also the other exceptional Lie groups using octonionic projective geometry."

which...oooookay

@DavidZ my view is that if you give a helpful answer a homework question then you encourage the asking of homework questions. So it doesn't matter if your answer is complete or not.
The point is that I don't want people to ask HW questions here. It isn't that I don't want them answered, I don't want them asked in the first place.

5:42 AM
@CaptainBohemian oh, forgot to ping you on the above

And note that there is a particular user who seems to make a habit of answering such questions.

@JohnRennie Well, sure, I actually agree that giving a helpful answer to a homework question encourages the asking of homework questions. And I also believe that we don't need to encourage that. But it does matter in the sense that our homework policy makes a distinction between how we mods are supposed to handle complete answers vs other answers.

sup dawgs
anyone know why there's so little data-driven fluid dynamics research?

@DavidZ In my ideal world all answers to homework problems would be deleted, but I appreciate that's a minority view. But I wanted to bring the asnwers to the mods' attention, and in particular the user who is making a habit of answering them.

I'm looking but can't find much

5:49 AM
@JohnRennie OK. Well, the way I would suggest bringing that particular issue to our attention is by casting a custom moderator flag and briefly explaining what you've observed.
Though in this case, no need to cast the flag now that you've told me. We'll look into it.

Noted, thanks.

:(
I'm leaving bye

The answers themselves, taken individually, don't all seem to be worthy of moderator action. In general, any time there's a pattern of behavior that looks suspicious or troublesome but the individual instances of it are not flag-worthy on their own, then a custom mod flag is the way to go.
@JohnRennie and thanks for noticing.
On a somewhat separate note: if you don't want people to answer homework questions (in order to minimize the incentive for others to ask them), I think it would be a legitimate response to downvote those answers.
Though I don't always do that myself in recognition of the fact that a non-negligible portion of our community does like having homework-based questions on the site.

6:12 AM
@DavidZ OK. Sorry I guess I was bugging the mods unnecessarily with all the flags. I'm obviously grumpy this morning :-)

Eh, don't worry about it, when in doubt I'd still rather have you flag things to get eyes on it.
And a fair number of those flags were perfectly good ones anyway.

Hi @DavidZ please look at this answer again physics.stackexchange.com/questions/430051/…, it is not a complete answer, the OP has already posted the correct solution and was asking for the error in his own solution. Thanks.

Hm OK let me recheck it

@user7777777 since you're here, I wish you would stop encouraging homework questions by answering them.

@user7777777 So, I think the key thing there is that the question asks, in part, "What average force does the juggler exert on one ball while he is touching it?" and your answer includes $F_J = 5F_g$, which apparently answers that part of the question.

6:27 AM
@taritgoswami JU, 2nd year (electronics)

@JohnRennie I do only answer homework questions if they ask about a concept and show the OP's original effort.
I do not answer questions that are just blatantly pasted onto a post

@taritgoswami HRI takes very few people for their summer program. You could try though. There's a very nice QC group at IISERK under Panigrahi btw.

@DavidZ Alright I see. So is there anything I can do about it (such as editing that part out)?

@BernardoMeurer Why?

@taritgoswami And which institute are you from?

6:30 AM
@user7777777 it's obviously a judgement call about where the boundary is, but I feel you're being a bit generous.

@user7777777 well, since it's still easily accessible in the revision history, we've taken an approach of not undeleting these answers just because they get edited. So... if you're really attached to this answer, we can try to work something out, but I'd suggest just letting this one go.

@DavidZ Alright, it's fine. Thanks for your time.

No problem!
In the future, if you do find yourself answering a homework question, I'd say take a close look to see what the original problem is asking, and double-check the answer you post to make sure it doesn't give that away.
(For what it's worth, I kind of agree with John, but that's just my personal opinion as a contributor. There isn't a site rule that forbids answering homework questions or anything like that.)

Thanks
@JohnRennie I'll take note

@taritgoswami And as for actual "quantum information theory" and "foundations of QM" there are not many people in India who are involved in it right now. The only guy I know of and who works significantly on foundations is Subir Ghosh from ISI, but he isn't really a pleasant guy to talk to (as far as my own experience goes). :P If you really want to work in QI, you're better off going abroad.

6:55 AM
Oops, I actually meant Guruprasad Kar ^. Subir Ghosh is the GR math guy used to stay in the same locality as me. (I'm terrible at remembering names!)

@Blue Where you have learnt QI then? I think you have 2nd highest score in quantumcomputing.SE O_o
@Blue Is it online? or, in their campus?

@taritgoswami I had to dig up some books and papers for my summer project at IISER. Vazirani's lectures are a good start followed by Nielsen and Chuang (that's the gold standard)

@Blue I have appeared for ISI this year, just for 3 marks they I haven't qualified, now in Christian College

@taritgoswami Eeeeh...3 marks :/

@Blue Yeah, :-(

7:07 AM
Which department btw?

Physics
Yeah

Nice :)

@Blue I am following Nilsen and Chuang, can u share ur personal contact ? so that I can contact u?

@taritgoswami I was talking about their summer interns program. HRI, RRI, ISI and IISER all accept QC summer students. But you have better chances of getting in if you talk to the professors directly. Of course, they're offline!

@Blue Yeah I also think so, but this winter I got selected for BARC research intern under Dr. Zafar Ahmed

7:10 AM
The nuclear physics guy?

@Blue Yeah, but,I will work on Mathematical Physics

Awesome :)
BARC is a great place indeed

Thanks :-)
Yeah
How you know him?

@taritgoswami blue.stackexchange98@gmail.com
@taritgoswami Had browsed through the BARC pages last year and contacted a few people there. That time I was more into physics :P

@Blue Ooh, I will contact you

7:15 AM
@Blue you created a gmail account just to handle the SE mail. That's a good idea! I'll put that on my list of things to think about doing.

@JohnRennie Yeah, I had a few people on QSE who wanted to talk to me privately but I didn't want to give out my real email (at least not immediately). It's quite helpful, yes :)
@taritgoswami Sure, no worries

@Blue yes indeed. These days I guard my main e-mail account!

3 hours later…
10:21 AM
"It swiftly becomes apparent that Quantum Mechanics and Relativity are merely mind games that have zero basis in actual reality. They are repackaged Kabbalistic Occult ideas being hammered together with spurious and incomprehensibly obtuse and speculative mathematics."
He's onto us

1 hour later…
11:31 AM
What is temperature?

11:50 AM
the inverse of the derivative of entropy w.r.t. internal energy

what is entropy?

i think i might be close to reach a record. in my last 14 answers, only 1 recieved votes
@LeakyNun I suggest getting a copy of Callen's book

what is the book?

it's a function that contains all the info of the considered system, which is assumed to exist when the system is at equilibrium. it must satisfy certain properties

12:10 PM
What is the meaning of life?

@CaptainBohemian I don't think they are closely related to susy, they come up in string theory

learning as much physics as one can before dying

@coniferous_smellerULPBG-W8ZgjR sedlyf

@coniferous_smellerULPBG-W8ZgjR which chapter / page?

12:27 PM
@bolbteppa Haha what is that

@coniferous_smellerULPBG-W8ZgjR you said that temperature is "the inverse of the derivative of entropy w.r.t. internal energy". no doubt that's how temperature is defined. but is that the best way to understand what temperature is?

You can think of temperature as a measure of the kinetic energy of the constituents. Higher the temperature, more vigorous is the jiggling of molecules.

Congress doing it's job :p

12:44 PM
I don't care about "the best way to understand what temperature is" because the answer is subjective, while the def of it, in principles, should be objective
i dont remember the page number. but it's at the beginning of the book
callen starts with defs a bit as axioms and then builds thermodynamics up
from ground zero up to the sky

Which theory should I know to understand caters reversible pendulum? I just wanna get some suggestion to learn where or in which chapter I should be able to understand it's mechanism in details?

@coniferous_smellerULPBG-W8ZgjR I'm trying to learn
instead of trying to be objective

The definition in terms of entropy is the most general one. And yes, that is indeed the best way to understand it.

@LeakyNun You need to understand why that definition is the definition of something useful: It is because it means that inverse temperature is the Lagrange multiplier for maximizing entropy at fixed energy, cf. e.g. physics.stackexchange.com/a/231065/50583

Which theory should I know to understand caters reversible pendulum? I just wanna get some suggestion to learn where or in which chapter I should be able to understand it's mechanism in details? Can someone help me ?

12:59 PM
> This merely shows the complicated man behind the heroic stereotype—one with sufficient diplomatic skill to soften his words without diluting his science.

@EmilioPisanty Is that a misspelling of "in plain sight" as "in plain site" there in the URL? :P

Kinda reminds me of an erstwhile contributor on this site who occasionally struggled with that area
@ACuriousMind looks like. Good catch.
I hope I'm still around on 2092
See the fireworks light up again

@ACuriousMind that brings me to asking, what does the lagrange multiplier actually mean?

@LeakyNun It gives the rate of change of the quantity being extremized when the constraint changes (that's why it is the derivative of entropy w.r.t. energy in this case), i.e. it tells you how much entropy the system gains or loses when you change its internal energy

oh!
I mean, I haven't done much calculus and I don't really understand the meaning of the multiplier
but I don't really understand how it gives us the minimum
can't you always change lambda to make the quantity smaller if you're away from the constraint?

1:15 PM
I'm not sure what you mean by that

let's say you want to minimize $f(x)$ subject to the constraint $h(x) = b$
how is that equivalent to minimizing $L(x,\lambda) = f(x) - \lambda (h(x) - b)$?

Ah. The minimization of $L(x,\lambda)$ w.r.t. $\lambda$ just gives you $\partial L/\partial \lambda = h(x) - b = 0$, so when you minimize $L(x,\lambda)$, all its minima/extrema have $h(x) = b$ automatically.

Hey folks
do you remember what SE post was like
where it was regression to order N of the US population
which was all good, but then at order 4, the US population collapses in 20 years

I'm guessing that wasn't a physics.SE post?

@LeakyNun It's a bit easier to understand in terms of gradients (direction of steepest ascent) I think
Basically you need to keep moving on the constraint curve
Until you reach an extremum for $f$

1:22 PM
@ACuriousMind maybe I'm being thick. If you fix $x$, then you get something like $L(\lambda) = A - \lambda B$. If $B \ne 0$ then $L$ is unbounded below right
how can it then have a minimum?

@ACuriousMind No
Not sure where
Maybe crossvalidated or math or mathematica

@LeakyNun Ah! Well, we're not looking for minima of $L(x,\lambda)$, we're looking for stationary points.

I guess I don't really have a good intuition for what in the world $\lambda$ is doing

@LeakyNun It is just a constant which indicates how many times larger the gradient of $f$ is w.r.t the gradient of $g$.
Provided they are pointing in the same direction (that's a necessary codition)
There's a nice picture on Wikipedia

right, but that's just the intuition for when $x$ staisfies the constraint

1:33 PM
What? We are always moving on the constraint curve!
Until the directions of those two gradients match

do you know lagrange duality?

@LeakyNun I don't

@LeakyNun I have a feeling you're trying to ascribe a generic meaning to $\lambda$ in $L(x,\lambda)$ when the constraint is not satisfied. There is none.

@ACuriousMind well I'm learning Langrange duality

This is actually mirrored in temperature: A system that is not in equilibrium, i.e. has not maximized its entropy, has no well-defined temperature
@LeakyNun Huh? What's that and how did we get there from temperature and Lagrange multipliers?

1:40 PM
> In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem
hmm

@ACuriousMind in Lagrange duality, we set $g(\lambda) = \inf_x L(x,\lambda) = \inf_x [f(x) - \lambda(h(x)-b)]$
and find the maximum of $g$ instead
and the maximum of $g$ is always smaller than the minimum of $f$; sometimes they're equal

Interesting

@ACuriousMind for example?

The point is that that temperature is not well defined unless the system is in equilibrium. Consider an exothermic chemical reaction.

why is that temperature not defined?

1:50 PM
@LeakyNun An example of a system that's not in equilibrium? Actually, almost all real-world systems are probably examples of that, but most are close enough to equilibrium that we can ignore that :P

@ACuriousMind well that's not very helpful...

But yeah, a chemical reaction that's just starting is a good example

I mean, I can stick a thermometer inside the chemicals surely

@LeakyNun If it's a large enough system, you'll notice the fluctuations in the thermometer
Exothermic reactions are chaotic
So if you sample random regions
You wouldn't get similar temperatures

that just means the temperature is not uniform?

1:53 PM
Yeah, sorta

@LeakyNun A thermometer does not measure temperature directly. It measures some indirect quantity, that, assuming the thermometer is equilibrated with the system being measured and the system being measured is in equilibrium, is an indicator of temperature.

hmm

Temperature is not even defined for such systems, yeah

I think what one has to realize is that the modern statistical notion of temperature does not exactly line up with our intuitive notions of "hot" and "cold".