The h Bar

9:00 PM

In any case, connecting a property that at first sight should rely on the choice of a metric to a purely topological property of the underlying space is always considered interesting.

0celo7

@ACuriousMind But for flat manifolds one can show that $b_k\le {{n}\choose k}$.

Bah

how does this work

Sanya

physics.stackexchange.com/questions/281989/… why can electronics SE dump their low qual.-questions on us but we can't in reverse :o

0celo7

@ACuriousMind So the first cohomology group $\cong$ first homology group is the abelianization of the fundamental group

what does that actually mean

ACuriousMind

@0celo7 homology. not cohomology

0celo7

@ACuriousMind Typo.

ACuriousMind

9:08 PM

@Sanya I'm not sure whether they have a regular path for that or whether that was mod action - the final close voter on EE was a mod

@0celo7 Uh, what? How is the first cohomology the same as the first homology?

And what about "it's the abelianization of the fundamental group" do you not understand?

Sanya

@ACuriousMind thanks for the info, where do you see that?

0celo7

@ACuriousMind de Rham's theorem

ACuriousMind

@0celo7 What? deRham's theorem is that the deRham cohomology is isomorphic to singular cohomology.

0celo7

Yes, which is isomorphic to the simplicial homology

ACuriousMind

@Sanya Click on the only clickable thing in the banner that says it was migrated

@0celo7 Why does the "co" disappear?

0celo7

9:11 PM

I don't know. That's PhD algebra...

ACuriousMind

No, in this case it's just wrong :P

0celo7

But I know that the dimensions of the homology and cohomology groups are the same

ACuriousMind

Ahhh. If you're taking coefficients in a field then homology and cohomology are indeed isomorphic (if they are finite-dimensional).

0celo7

@ACuriousMind Of course, if I'm working with de Rham theory then that's a given.

And manifolds are compact here

So they're finite-dimensional.

user218912

@0celo7 apparently you're supposed to learn homology before homotopy but nakahara does it backwards, does that mess anything up if you only care about applications to physics?

ACuriousMind

9:14 PM

Yeah, I just needed to figure out what kind of result you were implicitly using here

@IceLord nonsense, there's no "supposed to". I learnt homotopy before homology.

0celo7

@IceLord Don't know, don't care.

@ACuriousMind You probably did not learn higher homotopy theory.

user218912

@ACuriousMind okay good

ACuriousMind

@0celo7 No, but "homotopy theory" doesn't have all that much to do with homotopy groups :P

0celo7

i.e. chapter 4 of Hatcher

@ACuriousMind I don't know. All I know is that Balarka says he doesn't know any. So I'll bet you don't either :P

ACuriousMind

wait, do you just mean "higher homotopy groups" by that?

Because "homotopy theory" has a slightly different meaning nowadays

0celo7

9:16 PM

@ACuriousMind I mean chapter 4 of Hatcher

user218912

guys I have something really important to do right now wish me luck! bye.

0celo7

Fibrations, Postikonov towers, Nerves, etc.

ACuriousMind

@0celo7 Ah, yes. No, I don't know much about that. I never said I did. I'm not sure why we're suddenly talking about this

0celo7

Because the kid just brought it up?

but maybe he's talking about $\pi_1$ homotopy

ACuriousMind

Where?

0celo7

9:18 PM

3 mins ago, by IceLord

@0celo7 apparently you're supposed to learn homology before homotopy but nakahara does it backwards, does that mess anything up if you only care about applications to physics?

are you going crazy?

ACuriousMind

It was pretty clear to me that he was talking about $\pi_1$.

Perhaps the definition of $\pi_n$, but not what's called "homotopy theory"

0celo7

How the hell are you supposed to learn about homology before $\pi_1$?

user218912

wait I made a typo

user218912

i meant the other way around.

user218912

don't kill me

ACuriousMind

9:19 PM

::facepalm::

0celo7

@ACuriousMind I need to know what a "cofactor" is for reasons relating to minimal surfaces. What is it?

@IceLord ...

user218912

i'll just leave now...

ACuriousMind

@0celo7 Uh, no idea

0celo7

@ACuriousMind of a matrix

I'm sure you know

ACuriousMind

ahhhhh

I faintly recall something

@0celo7 Here

0celo7

9:21 PM

I'm taking the determinant of a metric on $N\times(-\epsilon,\epsilon)$

And the write $$g=\sum g_{1i}c_{1i}$$

ACuriousMind

Yes, that's the algorithm for recursively computing determinants

0celo7

I can't handle this PhD level algebra

@ACuriousMind ohhhhh

is that the thingie where you put your finger on the top, then do the thingie of the bottom and cross out the rows and columns of the thingie with the finger?

ACuriousMind

Uhhh...perhaps?

It's a bit difficult to describe in words, I'll give you that

0celo7

So, what is $c_{11}$?

ACuriousMind

The determinant of the matrix that's left when you delete the first row and column

0celo7

9:24 PM

Is the cofactor symmetric?

ACuriousMind

It might be if the original matrix was symmetric

0celo7

Yeah, the metric.

ACuriousMind

Yeah, it's symmetric if the original one was

0celo7

Ok, so $g_{ij}(p,0)=\delta_{ij}$

So the second sum collapses to $c'_{11}(p,0)$, that's fine.

But what's with the first sum?

Is $c_{ij}(p,0)=\delta_{ij}$

@ACuriousMind Yes, that's true.

Thanks.

@ACuriousMind I take it back. Don't you need a sign in there?

When we do the determinant trick, we add a sign every other time.

ACuriousMind

Why? $(-1)^{i+j} = (-1)^{j+i}$ last time I checked.

Oh, you mean in front of your $\delta$?

Yes

0celo7

9:33 PM

@ACuriousMind Yes.

Ok, so that makes it less trivial.

$c_{11}'(p,0)$ is the issue.

@ACuriousMind This would probably be easier using the usual determinant derivative rule.

Do you recall it?

ACuriousMind

I'm not exactly sure what you mean

Jacobi's formula?

0celo7

no

I don't know what adj is

aha

$d\det M=\det M \,tr(M^{-1}dM)$

ACuriousMind

That's the same formula :P

0celo7

no?

ACuriousMind

The adjugate is only different from the inverse by the determinant.

0celo7

9:37 PM

:P

nerd

Well, it works!

Because at $t=0$, $g_{ij}=\delta_{ij}$

@ACuriousMind Why is linear algebra so hard?

ACuriousMind

It isn't!

0celo7

ok, then please explain the above computation

I found a better way to do it, so this is not spoon feeding :P

DanielSank

@ACuriousMind Not entirely sure how to explain more than what's in meta.

0celo7

Is $c_{ij}=(-1)^{i+j}\delta_{ij}$?

ACuriousMind

@0celo7 Well, as you already noted, $c_{ij} = (-1)^{i+j}\delta_{ij}$, so the first sum is zero except that $j=1$. Likewise, the second sum is zero except at $j=1$. I'm not sure what there's to explain

0celo7

9:43 PM

Aha...the signs don't matter bc $c_{ii}=(-1)^{2i}\delta_{ii}=1$.

so on the diagonal you just get $1$

I will check this in detail...

ACuriousMind

@DanielSank Well, for one, the description of what allegedly happened to that question doesn't match what I see. Let's step through this in detail:

"The question thus boils down to asking whether D is true, even though the truth value of X is the one presented as the question. Therefore in order to kill this question, D needs to be addressed." - After reading the question again, I agree that that "D" is the issue the question is asking for. So far, so good.

DanielSank

I don't think it's a huge problem, but there is a pattern of questions saying:

"A-->B-->C-->D-->E but we don't see E and A is true, so A --> B must be false."
Then someone says "This is a duplicate of a question that asked 'isn't B obviously True?'".

Which is just logically incorrect.

That's all.

@ACuriousMind very good

Emilio Pisanty

y'all still busy tying y'selves up in loops with that stuff?

ACuriousMind

"The question was then closed as a duplicate. However a detailed look at the comments and the alleged duplicated questions that is suggested to OP, it was found that while they have addressed X or B, D was never addressed." - John Rennie closed the question single-handedly as a duplicate by the power of the gold badge, I'm pretty sure the other two votes were for unclear what you're asking, mine certainly was.

@EmilioPisanty Secret failed to explain to me what exactly the issue is. I'm trying agai with Daniel

0celo7

What's the issue?

Emilio Pisanty

9:48 PM

@ACuriousMind Honestly, the meta question itself was so byzantine and hard to read that I just left it and went to watch Scrubs clips on youtube

DanielSank

@ACuriousMind Ah, so this is yet another case of close reasons lying to us.

@EmilioPisanty Dangit.

0celo7

@EmilioPisanty Byzantine is a new adjective for me

ACuriousMind

OP's follow up comment then want to tell the readers that none of the comments addressed D, however the comments that followed still only addressed X." - what are those "comments that followed"? I see exactly two comments not by OP there: One by Qmechanic saying "related" (and note that Qmechanic writes "duplicate" when he means duplicate), and mine, neither of which accused the question of being a duplicate.

DanielSank

@EmilioPisanty Last night, Secret and I worked through it. It took a while. I was hoping that with the little logic summary it wouldn't be too hard to follow. WE considered making up a fake, simpler example to illustrate the point, but decided to go with the real one for the sake of... reality.

ACuriousMind

"The typical fate of these questions is: D was overlooked, OP wants to clarify D, people lose patience for follow up questions and thus no extra response is given, question was effectively abandoned, result in dissatisfied OP." - Ridiculous accusation, given that I reopened the question as soon as I saw that I had misunderstood the question, which actually the first comment OP addressed to me made clear to me

DanielSank

9:50 PM

Grump grump. This is yet another case of a crapily written meta post. I was talking to DZ about that a few days ago. It is a problem and we should do better.

@ACuriousMind Yes, the meta post is badly written.

You don't have to explain that to me :)

ACuriousMind

So since this entire description of what allegedly happened to the question does not match at all what I see I have no idea wtf the problem is.

Emilio Pisanty

@DanielSank what really got me was that the OP was trying to lord it over everyone and blasting on about how to write correctly ... while doing an astonishingly poor job at communicating what the problem was with the thread at hand.

I was very, very tempted to write a snarky comment to that effect.

But decided it would on balance be a bad idea.

DanielSank

Yes.

Emilio Pisanty

In other news, though, this just got 2.5k views

3

Q: The Paley-Wiener theorem and exponential decay.

Consider a function whose Fourier transform is supported on a half-ray: $$ A(t)=\int_0^\infty \omega(E) e^{-iEt}d E, $$ where I can suppose $\omega(E)\geq 0$ and any suitable regularity conditions on $\omega(E)$ in the limit $E\rightarrow\infty$. I am interested in results constraining the rate o...

I am genuinely puzzled by that

DanielSank

@EmilioPisanty I see no evidence of OP lording anything...

Emilio Pisanty

9:53 PM

@DanielSank maybe not lording

ACuriousMind

Before we talk past each other here: @EmilioPisanty Do you mean the OP of the meta post or of the example question?

Emilio Pisanty

@ACuriousMind OP of the meta post

DanielSank

@EmilioPisanty Oh!

XD

Emilio Pisanty

Takes a pretty hard stance that s/he knows how to answer questions

and has a pretty scathing go at others' responses

DanielSank

@EmilioPisanty That's not at all what I took from it, but then again I spent more than an hour discussing the issue with @Secret before the meta post went up.

Emilio Pisanty

9:55 PM

while also writing a labyrinth of a meta post

DanielSank

@EmilioPisanty I don't understand. @Secret made what... one comment under the original post?

Emilio Pisanty

@DanielSank The meta post itself is plenty

DanielSank

Dude I really think you may be construing personal attack where none exists.

ACuriousMind

@DanielSank The "raising awareness" phrasing comes off as pretty arrogant to some, I guess.

DanielSank

The post says "Here's a pattern that happens. Let's be aware of it".

@ACuriousMind Well that's a damned shame.

Emilio Pisanty

9:57 PM

@DanielSank a.k.a. "Here is one common way that y'all are doing it wrong, I know how to do it right, here's how you do it"

I'm exaggerating

but it's in there

I don't explicitly mind it

DanielSank

@EmilioPisanty No, it's not.

Emilio Pisanty

> The author of the answers and comments must take time to understand why OP is confused. It's not enough to identify one particular (usually the easiest to address) proposition in the chain of logic, say that this proposition is false (and maybe cite stuff) and claimed the question is killed.

DanielSank

That's an unfortunately negative way to consume a post that's trying to communicate information.

@EmilioPisanty I fully agree with that statement, have probably committed the error described there, and do not see any reason to take the post as a personal attack.

Emilio Pisanty

@DanielSank oh, I don't see it as a personal attack

DanielSank

Obviously everyone consumes such things differently, but if there's one thing I've learned about working in a community it's that you have to be ready to consume criticism without getting emotional.

Emilio Pisanty

10:00 PM

I just found the meta post to be so badly constructed that I couldn't make out heads or tails of it, nor did the post communicate clearly to me why I should spend significant amounts of time to puzzle out its byzantine logic

DanielSank

@EmilioPisanty I accept that criticism and thank you for it.

That's not the same thing you were saying thirty seconds ago though.

Emilio Pisanty

@DanielSank That is the additional layer that I found it ironic that a post that was that confusing then goes on to instruct others about how to communicate

0celo7

@Americans What exactly is an "unofficial transcript"

DanielSank

@EmilioPisanty Ok! I get it.

Emilio Pisanty

I don't think I can communicate that irony all that precisely, though

DanielSank

10:02 PM

@0celo7 It's a transcript that you didn't pay the uni to stamp saying "we promise this is real".

@EmilioPisanty I get it, dude.

I really get it.

Emilio Pisanty

which is why I refrained from writing said snarky comment

DanielSank

The post is crappily written.

Emilio Pisanty

@DanielSank writing is hard

ACuriousMind

You have to pay your university to stamp transcripts?

DanielSank

@EmilioPisanty Yes it is.

@ACuriousMind Yes.

Emilio Pisanty

10:03 PM

@ACuriousMind this is the country of "you have to pay for us to tell your uni your GRE results, and we will only do it for five years", remember?

0celo7

@DanielSank Well, how do I get this transcript

i found the place where I give them $10

Do I make a PDF of my academic history?

ACuriousMind

@EmilioPisanty Well, I guess I'm not really surprised.

DanielSank

I find it slightly funny that this meta post got so much flak, while other meta posts we've had over the last few years, which are equally terrible, have gotten lots of answers and upvotes. It's rather interesting to speculate on why that happens.

@0celo7 I don't know how to get an official transcript at your university.

Try something called the "registrar's office".

0celo7

@DanielSank Unofficial!

ACuriousMind

@DanielSank Well, it got flak from me because I felt that it took an honest mistake I made and promptly corrected as soon as I become aware of it and...accused it as being representative of some pattern I could not fully determine what it was.

DanielSank

10:07 PM

@0celo7 I don't know how to get an unofficial transcript at your university.

ACuriousMind

I'm willing to be criticized, but I dislike being criticized without being able to tell exactly for what

DanielSank

@ACuriousMind What's wrong with saying that an honest mistake is part of a pattern?

It's not like anyone said that the pattern is you.

0celo7

Huh, I'm on the dean's list. I found that, but can't find the fucking transcript page

DanielSank

@ACuriousMind Indeed that is frustrating. Perhaps you were not being criticised?

Perhaps @Secret was pointing to a pattern so that we will be aware of it.

Note that no usernames were included in the meta post.

ACuriousMind

@DanielSank No - it's fine if there is an overarching pattern that's clearly delineated and shown with evidence.

DanielSank

10:09 PM

@ACuriousMind So the post is crappily written. Yeah ok.

I feel like the reaction to this meta post was considerably different from the reactions to other (more important) meta posts which are equally crappily written.

0celo7

@ACuriousMind They charge $10-43 depending on where the transcript is being sent.

DanielSank

I won't link them though, because then people will think I'm making personal criticism ;)

ACuriousMind

@DanielSank I had a rather long chat with him earlier today. He laid out a pattern and then produced a post as an example of it in which I couldn't find any parts of that alleged pattern. Then suddenly there were two different patterns, but no example. Then I gave up.

DanielSank

@ACuriousMind Well that's frustrating.

ACuriousMind

So I still don't really know what aside from the rather general and undisputed "people misread posts" the problem is.

Emilio Pisanty

10:12 PM

@ACuriousMind that is such a German sentence

DanielSank

@ACuriousMind Yeah, that's it. The message is "People misread posts. Here's an example of a way that I (Secret) think I see happen with some frequency. Keep this in mind please. Have a nice day."

I should probably edit the post to say that.

ACuriousMind

@EmilioPisanty It's the verb at the end of the sentence, isn't it?

DanielSank

Because clearly something about the wording has brought out the pitchforks.

Emilio Pisanty

@ACuriousMind that and the general awkwardness =P

DanielSank

@ACuriousMind Long noun clause, late verb.

ACuriousMind

10:14 PM

lol

Emilio Pisanty

@DanielSank Not sure I see the pitchforks

DanielSank

@EmilioPisanty I exaggerated for effect.

0celo7

@ACuriousMind It's...not English.

ACuriousMind

We Germans are masters of linguistic awkwardness :P

DanielSank

Typical American English sentence, eh?

Emilio Pisanty

10:14 PM

@DanielSank German verbs do tend to be late.

0celo7

But Germans are generally pretty punctual.

Wonder why the verbs are late.

Emilio Pisanty

@EmilioPisanty: I agree with what you said about me not knowing stuff. I want to only scrutinize this data and if it passes the scrutiny, I am done. If it doesn't pass the scrutiny, then also I am done. I respect your advice on learning QM and statistics, but hope I can scrutinize this experiment's data without doing that. Please forget the last chat, I promise I will do as you say with this data, within my capability and if I am not capable of doing something, I will let you know. I was stuck on the outcome and that must have given impression I was disregarding your advice without meaning it. — kpv 7 mins ago

!!!

"I hope I can scrutinize this Bell's inequality experiment's data without learning any QM or statistics"

ACuriousMind

That was kpv's attitude from the beginning, did you expect it to suddenly change?

0celo7

@EmilioPisanty Hmm?

Emilio Pisanty

@ACuriousMind I guess it was kinda foolish of me but I did at some point hope for some appreciation of the magnitude of the problems involved

0celo7

10:22 PM

Ah.

Similar to JD's attitude of being a master physicist without knowing basic high school calculus.

Emilio Pisanty

@0celo7 I will refrain for the moment from commenting on JD.

0celo7

@EmilioPisanty Scared?

If my account gets deleted because of him, my productivity will double.

If I were smart, I'd delete it anyway.

ACuriousMind

@0celo7 Accounts don't get deleted against the will of their owner, only suspended. (Except in the case of spammers)

0celo7

Do Einstein quotes count as spamming :P

Emilio Pisanty

@0celo7 No, but JD has a habit of engaging in particularly exhausting discussions, which I have no patience for at the moment.

0celo7

10:28 PM

@EmilioPisanty Just block him...

Emilio Pisanty

@ACuriousMind I was also kinda hoping that kpv would take at least some of the advice here to heart

124

A: I believe I have solved a famous open problem. How do I convince people in the field that I am not a crank?

First, make sure you are not really a crank before trying to convince others. Read these common characteristics of cranks. If they apply to you then get professional help. For the rest of the answer I will assume that you have really solved a famous open problem. In the following "he" refers...

not sure it happened, though, and I won't try again.

@0celo7 Indeed I have. I'm happy to block you too if you insist on talking about this.

0celo7

@EmilioPisanty Chill.

Emilio Pisanty

@0celo7 I am chill. This was not appropriate, though.

0celo7

Appropriate?

I don't think I understand that concept. (Only half kidding.)

"Perhaps surprisingly, many cranks may appear quite normal when they are not passionately expounding their cranky belief, and they may even be successful in careers unrelated to their cranky beliefs."

That Wiki page is awesome.

@ACuriousMind Is any topological group a Lie group?

ACuriousMind

@0celo7 no

0celo7

10:39 PM

can you give an example?

ACuriousMind

Yes. Hint: Look at subgroups of $\mathbb{R}$.

0celo7

Ahh

Where's my spoon!?

ACuriousMind

There is no spoon.

0celo7

Ah! I get that reference!

It's mentioned in Hamilton's Ricci Flow!

DanielSank

@ACuriousMind Significantly changed tone

ACuriousMind

10:42 PM

@0celo7 lolwut

0celo7

@ACuriousMind Yes. The "inspirational" quote on chapter...let me see

10

ACuriousMind

huh.

0celo7

@ACuriousMind I didn't know you read Ricci flow

@ACuriousMind Ok. Take $\Bbb Q\subset\Bbb R$. It's a group, but not a manifold.

Hmm. Maybe I should give $C(T_pM,TM)$ the compact-open topology.

Otherwise this makes 0 sense.

0celo7

11:03 PM

@ACuriousMind I should note that I have watched the Matrix many times.

I do know where the quote is from

bolbteppa

11:43 PM

Hmm, if you calculate the arc length of an ellipse in parametric coordinates $x = c \cos(t), y = d \sin(t)$ you work out $s = \int ds = \int_0^t \sqrt{(dx/dt)^2+(dy/dt)^2}dt$ and get a complete elliptic integral of the second kind, where $t$ is the parameter on two circles that generate the ellipse $z = pe^{it} + qe^{-it} = c \cos(t) + i d \sin(t)$, but if you work out $s = \int_0^{\phi} r d \phi$ where $\phi$ is the angle between the radius and the x-axis of the ellipse,

you get a complete elliptic integral of the first kind, but what the f**k is $s = \int_0^{\phi} r d \phi$, can't remember

bolbteppa

11:53 PM

Transcript for