The h Bar

JamalS

20:00

I guess modular forms are partly number theory due to their connections - they are interesting, especially when related to representation theory through monstrous moonshine or to CFTs.

ACuriousMind

@vzn Not a dismissal, just saying. Reading about fractals and never seeing them is boring

0celo7

Show that if $f(x)$ is smooth then for all $x\in\mathbb{R}^n$ we have $f(x)=f(a)+\sum_{i=1}^n(x-a)^i H_i(x)$ and determine $H_i(x)$.

vzn

ok. not all pictures of fractals are "pretty" ofc.

picture work 1k words etc.

ACuriousMind

@0celo7 Uh...either my hangover is worse than I thought, or that's just a Taylor expansion, no?

0celo7

Not infinite

JamalS

20:01

^

ACuriousMind

Ah

I see

user54412

@JamalS I think you might not be 100% familiar with the US college system and its admissions criteria.

JamalS

@ChrisWhite On my applications, I listed roughly 5 extracurriculars, and related most of my essay questions to physics, or some other scientific passion.

user54412

Sure, some colleges want a "smarter" group of students, but most all of them are primarily focused on getting some appropriately diverse cross section of humanity together to expand their collective horizons.

JamalS

My extracurriculars were: student council treasurer (managing finances), human resources aid (actually helped interview faculty for position of head master at my school), student mentoring in math, model united nations club + conference and one more thing I forgot.

user54412

20:05

That's pretty good.

ACuriousMind

I, uh, just walked into my uni and immatriculated. There was no "admissions process" aside from a quite low bar on your math and physics grades.

0celo7

@ACuriousMind Damn commies.

ACuriousMind

And even the masters admission process is more like: "Oh, you have a nice bachelor grade? Come on in, then"

JamalS

@ChrisWhite Obviously you haven't seen my application, but do you think I have a good shot at Princeton then?

In my common app essay I listed all my self-studies, and my Princeton essay was on Edward Witten.

user54412

I think at some level most US schools expect incoming students to not know anything.

JamalS

20:07

Oh, so I have an advantage?

ACuriousMind

@0celo7 Nah, they just haven't got more people wanting to study here than they have capacity, so there's no need to sieve the incoming flock

0celo7

@JamalS are those your undergrad or HS extracurriculars?

JamalS

@0celo7 HS, I'm still in HS...

user54412

@JamalS Mmm, sort of? But it might also not be a heavy consideration. They want to assess potential, broadly defined, and they've gotten used to looking for non-academic indicators for it.

ACuriousMind

@ChrisWhite Is there any indicator that these indicators are any good?

Kyle Kanos

20:09

My ADS RSS feed thing for ArXiv preprints has not been working for me. Anyone else having issues?

JamalS

@0celo7 I know, it seems unusual I actually assessed my teachers :) I got to look at their CVs, tests we did with them, I helped lead a public interview session, etc.

0celo7

@JamalS seriously? that would explain your assignment

user54412

@JamalS As good a shot as anyone who hasn't spent 3 years building houses in 3rd world countries, followed by bringing peace to the middle east. Of course there are far more qualified applicants than openings, so the absolute odds are never too good for anyone.

JamalS

@ChrisWhite What would be a non-academic indicator of potential in physics?

user54412

@JamalS I didn't say they were just looking for potential in your favorite subject area.

JamalS

20:11

But that's going to be important as well, no?

0celo7

@JamalS how have you been learning physics? I can't imagine having all your extracurriculars and reading all those books on your profile

ACuriousMind

@KyleKanos What is an ADS RSS feed thing (I can't decode what ADS means)?

JamalS

I mean, because that's the potential that's actually going to be used.

@0celo7 Well, I did it over 5 years :)

Kyle Kanos

@ACuriousMind: ADS = Astrophysics Data System.

0celo7

i got motivated too late.

JamalS

20:12

And I don't have a social life, or go out, or anything like that, so I have time.

user54412

@KyleKanos they have an arxiv feed?

0celo7

middle of my junior year

JamalS

My reprieve is this chat.

Kyle Kanos

I get arXiv preprints sent to me via RSS through ADS. And it hasn't updated since Thursday

@ChrisWhite Yeah, I think it's through myADS. I set it up a few years back

JamalS

@KyleKanos is there a way for new arxiv posts in a particular category to pop up on my desktop?

ACuriousMind

20:14

@0celo7 Considering that most people only start learning this stuff when they study, too late is...not really too late.

Kyle Kanos

On the desktop? No idea. It can be done to your web browser via a RSS feed

0celo7

@ACuriousMind i was shit at math until precalc

alarge

@JamalS Just subscribe to the RSS using your favorite software.

JamalS

@ChrisWhite What do you feel distinguished you on your Princeton app?

0celo7

I couldn't have studied physics 5 years ago

ACuriousMind

20:16

@0celo7 So? There's no obligation to study everything as soon as possible.

user54412

@JamalS For grad school? It's a very different thing. There it was definitely recommendation letters, since my grades were mediocre and I didn't have much research to show.

user54412

Note that Princeton rejected me for undergrad.

JamalS

@ChrisWhite Oh, so for Caltech then.

0celo7

@ACuriousMind Obligation, no. But I sure would liked to have started 5 years ago.

I was saying that I'm impressed by @JamalS.

ACuriousMind

Five years ago I was perfectly content with the vague idea that I might one day study physics :D

JamalS

20:18

@ChrisWhite I thought you went to Princeton as undergrad, but it's the other way round. So what stood out on the Caltech app?

user54412

@JamalS So back when I applied (2006-07), Caltech was still holding out against the common app trend, and they had several things that I think they could use to tell what kind of people would do well there. For example, they asked short essay questions on quirky humor and on demonstrating academic integrity.

user54412

My favorite was "The Box" - a blank page with the instructions "put something interesting in the box"

2

JamalS

What did you put?

0celo7

@ACuriousMind Right now I'm content with the idea that I might go to grad school for physics. I'm set on nuclear engineering right now though.

user54412

Nothing too original -- a landscape drawing where everything was a fractal of some kind. All tediously done by hand with exacting precision. (Yeah, I was bored around that time in my life)

JamalS

20:21

I would have probably written a problem.

infinitesimal

I would have put the word "interesting"

ACuriousMind

@ChrisWhite I really like that instruction.

@infinitesimal The question is - is interesting really interesting? ;)

0celo7

@ACuriousMind What is German high school like? I went to German middle school.

What math does one take?

JamalS

@ACuriousMind Well, the word itself isn't really.

And I think other people would have thought of doing that.

@ChrisWhite How important is the alumni interview?

Kyle Kanos

@ACuriousMind It'd be quite literal to put "something interesting" in the box.

infinitesimal

20:23

Good piont^

0celo7

@JamalS Are you an etymologist?

Kyle Kanos

Some people appreciate literal-ness

JamalS

I have done the MIT one, and Princeton is coming up, but Harvard have said they probably won't be able to for me because of logistics.

ACuriousMind

@0celo7 Uh...We don't really have a separation between middle and high school. There's elementary school, and you then go to one of three kinds of schools, of which the Gymnasium is the one qualifying you for university

JamalS

@0celo7 I like etymology, but no.

infinitesimal

20:24

Like math

0celo7

@ACuriousMind By "high school" I mean grade 9+

I went to Gymnasium

user54412

@JamalS Caltech didn't have one (probably good for me!). I don't think they have enough alums with social skills to do it. Also, us alums are infamous for hating our school :)

0celo7

Up to eighth grade that is.

Jiminion

Let's see, I got into MIT, wait-listed at Princeton, and got the CalTech application but didn't do it.

JamalS

@Jiminion You got into MIT?

Jiminion

20:26

long time ago, back when it was all easier....

ACuriousMind

The math in the upper Gymnasium classes is elementary statistics/stochastics, differentiation/integration, trigonometry, "analytic geometry" (which is mucking about with vectors and planes and stuff), and matrices used for various things

JamalS

Oh

Jiminion

@JamalS Yes, early admission.

Kyle Kanos

For undergrad, I applied to one University and got in

ACuriousMind

I probably left something out, but that's what I remember right now.

user54412

20:27

@KyleKanos Stress-free much?

Jiminion

@ChrisWhite Ha!

Kyle Kanos

@ChrisWhite No stress. I had better grades & SAT scores than my brother who got in.

user54412

I feel like applying to 1 postdoc. If I don't get it, so be it.

JamalS

@KyleKanos Out of curiosity, what was your SAT score?

0celo7

I supposedly took an analytic geometry class. Didn't see a single vector, plane or matrix. Not even a rotated conic. I hate public school.

Kyle Kanos

20:28

I did it on the 1600 scale and I think I got like an 1150 or so

infinitesimal

Hi @DavidZ

Kyle Kanos

720 in math and shit in verbal

JamalS

My SAT essay got a 9/12, even though I'm normally great at essays.

ACuriousMind

@0celo7 Hmm...we did quite a lot about intersections of planes and lines and so on. My school seems to have been rather thorough in its math education compared to others, though

(which is a bit surprising because its focus is actually dead languages :P )

JamalS

My prompt was something along the lines of 'are complex experiences more valuable than everyday life ones?'

0celo7

20:30

@ACuriousMind My analytic geometry teacher wan an overweight, old guy who either wanted to die or retire.

He's been at the school so long that no one asks him for a syllabus

ACuriousMind

Ah, there are always those teachers who are inventory rather than staff

David Z

@infinitesimal hi

0celo7

@ACuriousMind That's a great way of putting it.

JamalS

Of course they want examples, so I chose on the spot Andrew Wiles' process of proving Fermat's last theorem, Mao in the Chinese civil war, and Humbert from Lolita.

That seemed varied to me :)

0celo7

If anyone is willing to look at this problem, I'd be mega grateful. math.stackexchange.com/questions/1137217/…

ACuriousMind

20:33

@0celo7 "I have made some significant progress while sleeping." lol

3

Unfortunately, I can't help here

infinitesimal

The brain needs sleep.

JamalS

@KyleKanos Verbal? You used to do an oral test?

ACuriousMind

@infinitesimal Though a sleep-deprived brain is a good substitute for most drug effects ;)

infinitesimal

:D

JamalS

Oh, nevermind, that's the critical reasoning.

0celo7

20:35

@JamalS what is your SAT/ACT score?

JamalS

@KyleKanos My worst score was verbal too, but I blame the College board. If one is pedantic, there are multiple correct answers to some questions.

0celo7

@ACuriousMind Thanks for the vote at least.

JamalS

@0celo7 800 math level II, 730 phy

0celo7

Do you even know if I'm on the right track?

ACuriousMind

@0celo7 Uh, I didn't do nuthin'

0celo7

20:37

Oh then thank you kind stranger

Kyle Kanos

@JamalS Verbal's not an oral exam.

0celo7

Still, absolutely no idea?

JamalS

This next one's me

0celo7

Lol I need help not upvotes!

ACuriousMind

@0celo7 No, I'm not at home with these analytical norms

0celo7

20:38

I have no clue what to do with a Sobolev norm

ACuriousMind

Well, that's two of us, then.

0celo7

Its a homework problem though. It shouldn't require intricate knowledge of the subject.

I don't know something that @ACuriousMind doesn't know either?

Cool.

ACuriousMind

I suspect you know some other things I don't know, too, because my GR knowledge is abysmal

0celo7

I used to think I was a genius because I could read and understand. Now that I've started doing problems, however...

Wald is old enough that someone should have a solution manual...

JamalS

Authors really ought to write solutions in the textbooks.

For students tempted to cheat, they're not worth helping. For those that aren't, putting solutions in is fine.

alarge

20:48

Related to yesterday's discussion (Wolfram): features.slashdot.org/story/15/02/17/1838239/…

0celo7

@JamalS Shankar did that, with some "selected" exercises. 10 of them.

David Z

2

Q: How much time would it take for a free-falling ghost-like object to cross the entire Earth?

We have an object of mass $m$ which can go through matter like a ghost. It's only affected by gravity, not by any other force, so it's in free fall. At the instant $t=0$ it is at the surface of the Earth which is assumed to be a perfect sphere of radius $R=6.371 \times 10^6$ m, of mass $M=5.972 ...

Homework-like?

ACuriousMind

@DavidZ Uh, yes?

David Z

Or in other words, suppose we ignore the presence of the homework-and-exercises tag, and also ignore the fact that it had been marked as a duplicate. Is this the sort of question that people think should be put on hold using the no-effort homework close reason?

ACuriousMind

<- This user thinks so.

David Z

20:57

Duly noted

I want to collect some varied inputs, because this also serves as a constraint on any changes we may make to our homework policy in the future

Kyle Kanos

This user thinks so as well

0celo7

How does that close reason work? Do you close if it's clearly a homework question, even if they show effort? Conversely, if they just show no effort, do you cite that close reason?

JamalS

As do I

ACuriousMind

@0celo7 Even effort-showing HW questions are closed if they are simply about obtaining the solution

0celo7

So you won't close a proof-based homework question that shows effort?

David Z

20:59

@0celo7 basically the question has to show two characteristics to not be closed: (1) show effort and (2) ask about a specific concept within the problem that is giving the OP trouble

Anything like "I don't know what to do next" or "Any suggestions would be great" or "Is this right?" or "Can you just give me the answer so I can check it?" or so on fails on point #2

0celo7

So what is OP supposed to do?

ACuriousMind

@0celo7 Not asking that kind of question here, to put it bluntly

Kyle Kanos

Or frame their question such that it's about the concept

David Z

well, yeah, what @ACuriousMind said. The basic idea is that this is not a homework help site.

0celo7

What are self-studiers to do?

David Z

21:02

@KyleKanos that works too, but it's not always easy to pull off

Kyle Kanos

Of course, you do get people who reject your help , saying wonky things like

I'm sure it does, but there really isn't much I can write in your cute template. The purpose of my question was to qualitatively understand why the statement in part two is true, so that I could then translate that knowledge into equations and bounds and do the actual working MYSELF. — user140161 Feb 14 at 19:21

0celo7

I've had questions closed for being homework questions and I really had no clue how to continue.

ACuriousMind

@0celo7 Uh, not asking that kind of question here

Kyle Kanos

@DavidZ I concur that it's difficult. And it probably would get the OP their answer by thinking about what it is that's causing their trouble.

David Z

Indeed. In which case, problem solved ;-)

Kyle Kanos

21:04

I've asked 3 questions. I probably should ask more.

I've thought of two in the last week or so, but just haven't put them down yet

0celo7

@ACuriousMind Take my Sobolev norm question. How should it be phrased to pass this site's closing policy?

ACuriousMind

@0celo7 Closing a question doesn't mean that the question is bad, or should not be asked at all. It just means we do not want it here

David Z

@0celo7 which question is that?

0celo7

3

Q: Application of Cauchy-Schwartz with Sobolev norms

I'm working through the problems in the initial value formulation chapter in Wald's General Relativity. A short summary of the problem. I have to show that $$\sup_{x\in A}|f(x)|\le C||f||_{A,k}$$ where $A\subset \mathbb{R}^n$ satisfies the uniform interior cone condition, $C$ is a constant, $k>...

real-analysis multivariable-calculus inequality pde inner-product-space

ACuriousMind

@0celo7 I don't think it can be phrased such that it would pass muster here.

0celo7

21:06

So what, I just live on, and never figure it out?

David Z

Well in this case you post it on Mathematics ;-)

Kyle Kanos

that is on math?

David Z

@KyleKanos hence the ";-)"

0celo7

Suppose I posted a very similar question with physics content on here.

Kyle Kanos

I see that now

I thought you were telling him to post it on Math and I got confused

0celo7

21:07

You would block that, even though it shows effort?

It's not a homework problem, but that is not obvious I guess.

ACuriousMind

Yes, by the current policy, we would.

David Z

Actually I do see a good question in there. The key phrase is "I just don't see (1) can be used in Cauchy-Schwartz." If you posted a question asking whether there is a way to use that equation in the Cauchy-Schwartz inequality (and not asking for a hint as to what to do next), I think that would satisfy both points of the homework policy.

ACuriousMind

@0celo7 That's irrelevant, it's really the type of question this is about, regardless of whether or not we are helping someone cheat

0celo7

@DavidZ I'm pretty sure I wasn't supposed to use Cauchy-Schwarz with (1).

But then it becomes a "check my work" problem.

David Z

Not if you ask whether it's possible to use one equation with another

Check my work problems are the sort where someone posts a question, a complete answer to the question, and just wants confirmation of it being correct

and furthermore, where the OP doesn't even have any particular reason to think it's not correct

0celo7

21:10

In my problem, I'm stuck on the last inequality $$||\partial^k_r(\psi f)||_{L^2}\le C_4 ||f||_{Q,k}$$

How do I phrase the question to ask about it?

And have it be acceptable?

David Z

Well, what about it are you stuck on?

0celo7

No clue how to go about proving it.

It's an a) b) c) problem and this is part c).

David Z

Personally, I think it might be fine if you showed that you consulted some references, searched the web, etc. and couldn't find any discussion of how to prove that inequality. But that's just me.

0celo7

How are self-studiers recommended going about answering their questions that don't meet this site's approval? /r/physics is cracking down on questions, /r/askscience is dead and Physics Forums are shit.

David Z

The honest answer is that you find another site or venue that is accepting of the kinds of questions you want to ask. Personally I would point people to Physics Forums first, but only as a courtesy. We're not obligated to direct people to the right place to get their questions answered. If you don't like PF, maybe try /r/askphysics?

0celo7

21:18

@DavidZ It's really hard to search for questions online. For example, my research turned up something about the Sobolev imbedding theorem, but that's buried 200 pages in an analysis book and should not be required for a GR homework problem.

David Z

@0celo7 yeah you don't have to find it, just point out that you made an effort and the information isn't readily accessible.

0celo7

@DavidZ Perhaps I don't understand why "homework-like" questions that show significant effort are disallowed. If I had any choice in the matter, I would allow them.

ACuriousMind

Have you read the endless meta debates about this?

0celo7

TIL there are endless meta debates about this.

JamalS

@0celo7 Regarding your linear algebra problem: $\det (1+\epsilon M) = \prod_i (1+\epsilon \lambda_i) = \exp \left[ \sum_i \log(1+\epsilon \lambda_i)\right] = 1+ \sum_i \log(1+\epsilon \lambda_i) + \mathcal{O}(\log^2)$. Using $\log(1+x) \approx x + \dots$, $=1+ \epsilon \sum_i \lambda_i = 1+ \epsilon \mathrm{Tr} M$.

Kyle Kanos

21:23

@0celo7 meta.physics.stackexchange.com/search?q=homework+is%3Aquestion

0celo7

@JamalS Oh, that's different than the method I used, if I'm not mistaken. I forget, can we diagonalize a matrix such that its diagonal elements are its eigenvalues?

ACuriousMind

@0celo7 Not in general

JamalS

^

ACuriousMind

But physicists like to assume they can

JamalS

Aye, my method is quick and dirty.

0celo7

21:27

So how is the first step justified?

And what is the condition on the matrix such that we can diagonalize using the eigenvalues?

ACuriousMind

@0celo7 It isn't, strictly speaking.

@0celo7 Being Hermitian is sufficient, for example

0celo7

But @JamalS did use such a diagonalization technique in his first step, right?

ACuriousMind

Yes, that's why he calls this method "quick and dirty"

0celo7

Good to know I at least know some linear algebra.

ACuriousMind

Wait

I think this proof might work even for non-diagonalisable matrices

0celo7

21:33

@ACuriousMind does the log det M= tr log M identity hold for all diagonalizable $M$?

ACuriousMind

The determinant is always the product of eigenvalues, and the trace is always the sum

That doesn't depend on it being diagonal or not

JamalS

Yeah, so what are you objecting to?

0celo7

Scratch that knowing linear algebra bit.

I have to review.

JamalS

Regardless of the matrix, it's going to have eigenvalues $\in \mathbb C$, and those identities hold.

And that identity for the log, tr, etc. just comes from the property of logs.

@0celo7 Since you're into norms at the moment, have a look at #5 of mathworld.wolfram.com/…

0celo7

@JamalS You sure? I swear you have to put $M$ into a diagonal (or at least upper-triangular) form.

JamalS

21:38

@0celo7 Why?

Just find the eigenvalues, and that's it.

0celo7

No no, the log det one.

Also I found really neat proof. We know that $|A-aI|$ is a polynomial of eigenvalues, so $|A|$ is just the product.

ACuriousMind

@0celo7 Triangularisability is not a constraint over $\mathbb{R}$ or $\mathbb{C}$ - every matrix is triangularisable

0celo7

@ACuriousMind Do I remember correctly that the determinant of an upper-triangular matrix is the product of its diagonal elements?

ACuriousMind

@0celo7 Yes, that is correct

0celo7

@ACuriousMind Also proof that triangularibility is not a constraint?

ACuriousMind

21:43

@0celo7 Every complex matrix has a Jordan normal form

Jiminion

Louis Jourdan RIP

0celo7

@ACuriousMind Maybe I'm just bad at linear algebra, but that proof seems highly nontrivial.

Am I wrong to have expected it to be easy?

ACuriousMind

@0celo7 The proof is not really that difficult, but it is not trivial, yes. Why would you expect a strong statement like "Every matrix is almost diagonalizable" to be easy to prove?

0celo7

I don't know, I just did.

David Z

@0celo7 the gist of the reason is that this is not a homework help site

ACuriousMind

21:50

Well, if you are a French algebraist, the preferred method of proving difficult statements is to break them down into a series of lemmata which each seem trivial, so, at the end, you have the non-trivial result without having done anything :D

0celo7

@DavidZ Aren't physics concepts taught in part through homework?

Kyle Kanos

@0celo7 One can hope that is the case. But for many students, the homeworks are "plug-and-chug"

0celo7

@ACuriousMind I'm only vaguely familiar with the rank-nullity theorem. Therein lies my confusion.

JamalS

@ACuriousMind When that's done, I'm left at the end feeling like, 'Erm... wait... what? Let me go back and check...'

ACuriousMind

@JamalS Yeah, it's beautiful and very annoying at once

David Z

21:53

@0celo7 yes, usually, but I don't see how that's relevant

0celo7

Like the dozen lemmas (lematas) used in proving anything to do with inverses or determinants?

@DavidZ In one sentence, what is Phys.SE?

JamalS

@0celo7 A website with a physics community comprised of everyone from high school students to researchers that aims to answer physics-related questions abiding by specific guidelines.

David Z

@0celo7 the description from the tour is probably a good start: "Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics and astronomy."

0celo7

I think @JamalS 's "specific guidelines" piece is good.

Kyle Kanos

Really...

-1

Q: How many shades of grey are there?

We can distinguish a limited number of colors, or shades. But, physically, how many shades are there? Photons' color depends on their frequency (okay, grey is not a single color, but, if needed, we can consider blue for simplicity). And those frequencies depend on the energies of the transitions ...

optics photons quantization photon-emission

There's at least 50, right?

ACuriousMind

21:58

I actually groaned when I read that question title. Not a groan of pleasure, mind you.

JamalS

@KyleKanos Have you read any excerpts?

It's really filth; badly written filth.

0celo7

@ACuriousMind would only say that if he had something to hide.

Kyle Kanos

No

And I have no interest in reading it either

0celo7

@JamalS link to your favorite part?

Not that I'm interested mind you

JamalS

I didn't read the book, just a few quotations in a news article.

0celo7

22:01

It's relevant to physics

ACuriousMind

@0celo7 I have many dark secrets to hide. Liking that book is not one of them.

0celo7

@ACuriousMind definitely has skeletons in his closet.

JamalS

Don't we all?

0celo7

@JamalS skull $\implies$ skeletons

JamalS

Oh god, my cold is insufferable. My nose literally spewed mucus all over my keyboard.

0celo7

22:04

Ok, that joke wasn't that bad, was it?

@JamalS I was healthy until I shoveled this snow.

JamalS

I didn't really get it, to be honest.

ACuriousMind

No, it wasn't

JamalS

What was it? Someone explain it?

dmckee

FSM spare me from philosophers who think their subject covers fields other than the human condition!

0celo7

@ACuriousMind 's avatar is a skull

ACuriousMind

22:05

@JamalS I currently am a skull. The rest of it has to be somewhere, no?

JamalS

Aaaah

Well, shouldn't be skeleton, singular?

Kyle Kanos

@JamalS Kinda gross

ACuriousMind

(Actually, I am a demon from the plane of Baator, and there never was a body I was attached to, but how should you know)

JamalS

He shouldn't be expected to have more than one of his own.

0celo7

@JamalS, @ACuriousMind has definitely mastered cloning

JamalS

22:06

@KyleKanos And embarrassing. It happened to me in one of my final exams last year.

0celo7

Yeah he's a clopen set you see.

ACuriousMind

@dmckee I'd take that sentence as truth even without the relative clause :P

0celo7

(Shitty inside joke.)

JamalS

When I have a cold, it gets really bad.

0celo7

(Didn't even make sense to me.)

JamalS

22:06

Speaking of clopen, everyone's seen that Hitler learns topology video, right?

0celo7

Yeah I linked it yesterday

@ACuriousMind was helping me with some topology

JamalS

@ACuriousMind Have you done any knot theory, by the way?

ACuriousMind

It's really distracting if you also understand the actual words he's saying, though

JamalS

^ I know, I can understand German, so I muted it.

ACuriousMind

@JamalS Only brushed it when I heard that Chern-Simons theory has some links to it, but no, I don't really know anything about knots

JamalS

22:08

ok

0celo7

@JamalS are there any really good online resources for CFT that don't require me to magic $140 for Di Francesco?

I've read Polchinski's summary in his ST book but I didn't get all of it

And BBS assumes you know it

dmckee

@ACuriousMind Well, as I grow older I'm more and more interested in learning what other people might have learned about the human condition. Maybe I can learn some of those lessons the easy way.

ACuriousMind

@KyleKanos I think the question has actually become on-topic now

ACuriousMind

22:28

@0celo7 Even I must obey the no-cloning theorem

0celo7

@ACuriousMind TIL that's a thing...

Apparently no school tomorrow either.

I could do something productive.

Like learn CFT!!

@ACuriousMind @JamalS I'm begging for good online resources.

ACuriousMind

@0celo7 Have you read the intro in Tong's notes?

0celo7

@ACuriousMind do you mean the intro to CFT or the intro to the notes?

Yes to both.

But when I hit Kac-Moody in BBS I exploded

dmckee

Ah ... now we have the layman telling us what the evidence for [theory he's suspicious of] is. ::sigh:: I'm in a foul mood today.

0celo7

I don't want to shell out $140 for a textbook and I haven't...stumbled..upon a PDF of Di Francesco

@dmckee Who are you talking about?

ACuriousMind

22:34

Hm, well, I got nothing. I learned CFT in a lecture that didn't use any particular book

dmckee

1

Q: Big bang red shift verification

So I have read on proofs for the Big Bang theory as it appears to be a bit far-fetched to me (the layman). I mean, definitely there is some genius mathematics behind the fancy yet inaccurate linguistic description, but for me, physics can only be real physics (and not philosophy) if it can be ver...

big-bang gravitational-redshift

It's not like we haven't answer layman question on this stuff before, but they don't search and then they come to tell us our business.

0celo7

@dmckee Is it still thought that the singularity theorems are evidence of the BB?

Or does the presence of dark energy complicate things?

dmckee

Like I said, I'm in an unforgiving mood.

Oh, there are the nuclear abundances, and BAO and the CMB, too.

And I'm not even in the cosmology business.

0celo7

I know, but in Wald and Hawking & Ellis they use the singularity theorems coupled with redshift as evidence.

user54412

@0celo7 Singularity theorems are proof that classical GR has a singularity under generic hypotheses. The Big Bang model is really only about what came after any hypothetical singularity.

0celo7

22:37

I'm not doubting the BB, just wondering about one of the methods.

user54412

I'd say its furthest-back-in-time empirical evidence lies in nucleosynthesis

0celo7

@ChrisWhite but our universe is still thought to fulfill the conditions of the singularity theorems?

@ChrisWhite Wald was written/published in 1984 after all

user54412

@0celo7 Sure. But it's trendy these days to qualify all such statements with "but of course everything might change with a quantum theory of gravity"

user54412

sorry, gtg -- bus to catch.

0celo7

@ChrisWhite I figured as much. So dark energy doesn't change the theorems?

@ACuriousMind How does one reconcile Poincare recurrence with the Second Law? Is it the "almost always" clause in the Second Law?

ACuriousMind

22:48

1

Q: Is there really such a thing as an irreversible process?

If an isolated system goes from a state A to B, will it always eventually fluctuate back to state A? If not, give an simple example. Is it right to say that entropy only says that the probability for reversal is very low, but not actually 0, ie that it will take a very long time for some proces...

thermodynamics statistical-mechanics entropy

tl;dr: Yes, it is the almost always

0celo7

@ACuriousMind ty

usukidoll

hi hi

user54412

23:23

@0celo7 Hmm, dark energy violates the strong energy condition, which is what is used in the standard theorem (at least as phrased by Wald). It also saturates all the other standard energy conditions.

user54412

But I feel this has been addressed more recently and still doesn't get rid of singularities

0celo7

@ChrisWhite Dark energy has negative pressure, right?

user54412

Yeah, $p = -\rho$

user54412

with $\rho > 0$

0celo7

Are there any recent (1998+) books that discuss causal structure and the singularity theorems?

user54412

23:27

If there are, I've never used them.

0celo7

@ChrisWhite How familiar are you with Wald? Any chance you've done Problem 10.1? (I'm majorly stuck.)

user54412

My GR course used Wald for all causal structure.

0celo7

Ch. 10 is the initial value formulation

user54412

There's a small chance I've done that problem (most of the GR problems I've done were made up by the prof), but I'm looking at it now

user54412

I saw that Math.SE post

user54412

23:30

uniform interior cone condition -- now I wonder what that is

0celo7

Right under (10.1.15)

user54412

are Wald's cones hollow or filled?

0celo7

@ChrisWhite Solid.

@ChrisWhite Wald credits two guys for the argument. One is unpublished, and the other is a very dense analysis text.

I tried to follow the argument in the analysis text but it was 100+ pages inside. No way you're supposed to know all that for a GR exercise.

@ChrisWhite: Parts a) and b) are easy and I did them right away. I've been suck on c) since.

Danu

23:54

@0celo7 As in the norm in $H^1 $ (or $H^2$?)

0celo7

@Danu I'm not sure what you mean by $H^1$

Danu

The first Sobolev space

0celo7

Yeah all I know about Sobolev spaces is from Wald.

Danu

Is there something you need?

I took a course where they popped up all the time

0celo7

Which is pretty much nothing.

I need help with math.stackexchange.com/questions/1137217/…

Danu

23:56

That doesn't mean I know anything serious about them either but yeah, maybe

0celo7

I don't think you need anything in-depth though.

I doubt Wald would require in-depth knowledge.

Danu

Oh

I know the k=1 case I think

user54412

Wald uses the term in passing. He wants the (square of the) norm of a function to be the integral of the sum of the squares of the function and all its partial derivatives up to $k$-th order.

0celo7

@ChrisWhite Yeah, that's why I didn't think the proper analysis was necessary. (It has something to do with the Sobolev imbedding theorem.)

Danu

Chapter 8 of Lieb & Loss - Analysis gives relevant inequalities

0celo7

23:58

@ChrisWhite Did you take a look at it?

user54412

I'm looking now

0celo7

@Danu I've seen a related proof that used tools Wald doesn't assume you have.

Danu

right

Yeah, it seems very odd that one would need these things in GR

Transcript for