there is a lot of mumbling involved...

the problem is that each flag has to be looked at, read, and asses what caused it

even if in the end one decides that nothing is to be done

that takes a bit of time

not too bad, though

"not an answer" flags, for example, require in lots of cases that one read the question, read the answer and think a bit why exactly it is not an answer

in 99% of the cases, the flagger could have done exactly the same action as we can: add a comment to the answerer suggesting that he expand and/or whatever

those flags contribute to the thermodynamical death of the universe: the flagger presumably has done all that already, but the flag causes us to redo it :)

when I used to maintain a certain piece of highly exposed opensource software, a huge amount of my time went in reading bug reports which in the end were completely useless

:)

Thanks for elaborating. All these town hall meetings and meta questions have made me lose focus of what moderators actually do (not "what I think they should do", like promoting MSE or whatever)

there is also a bit of detective work

«who does this user share IP with?» and that sort of thing

(oh too slow)

and then of course you have to suspend the WM sockpuppet du jour

WM - sorry...

Are those initials, or an acronym?

Wolfgang Mueckenheim

he is sufficiently well known on sci.math as a pest that he has his own acronym

Ahh. So "naming names" is sometimes appropriate :)

(Not that I follow any standard of propriety...)

he is a well known crank

@MarianoSuárezAlvarez Unsurprisingly, he's even better known on de.sci.mathematik.

and professor somewhere in Germany

yeah :/

@MarianoSuárezAlvarez Hochschule Augsburg.

It's sometimes amusing - yet sometimes quite tragic - to see MSE users' ratings on "ratemyprofessor.com" and the like

@TheChaz I made a point of never looking at mine.

I hope that I will choose your path when the time comes.

our students take a poll every semester, with a comments section, so we get to read ours here :)

@MarianoSuárezAlvarez Oh, we did that too.

There are evaluations at my university. I've heard of students being blunt/rude in handwritten evals, but you can imagine the liberties that anonymous internet jerks take on the sites...

sure

And in general it's the students who didn't like an instructor who are most likely to post, though there are exceptions.

@BrianMScott Instructors or books, I would say.

@JM: I posted a different approach to your answer. I converted my page to $\LaTeX$.

@robjohn =)

@N3buchadnezzar That was your question, I see :-)

@JonasTeuwen I was wondering where the mistake in my code was since I got zero everywhere except at four places towards 43. I want to so much facepalm myself. I should've returned reversed(result) in my InverseFourierTransform function.

@BrianMScott Ausburg, you meant?

No, Augsburg.

@JonasTeuwen Should I send you the thing in an email or just post here? I'd rather post here but then you don't get syntax colouring which is rather inconvenient.

@robjohn I like your answer, but how can you say that (1c) converges aboslutely for all non integer z? I am just curious.

Mail it :-).

I'll add a few comments, just a sec. : )

@N3buchadnezzar By comparison to $\sum\frac{1}{n^2}$

@Gigili Augsburg home town of Brecht, and the wonderful Puppenkiste.

@robjohn Of course =)

Would someone explain why the basis elements in a Hilbert space converge weakly to zero? This should mean that if $\{e_n\}$ is a basis that $\left<e_n,y\right>\to 0$ for all $y$ as $n\to\infty$. But can't $y$, say, be $\sum e_n$?

am i misunderstanding the definition of weak convergence?

@tb Oh I see, I pronounced it wrong all the time. I thought it was Ausburg. =|

@EricGregor That series doesn't converge.

@robjohn Okay, I am almost able to follow your proof. But Robjohn you perform black arts between $(4)$ and $(5)$!

@N3buchadnezzar There is nothing between $(4)$ and $(5)$... $(5)$ is just applying the definition $(1c)$ to $if(iy)$

@robjohn i guess i was thinking convergence wasn't important, that i was not really summing up real numbers but declaring $y$ to be the vector with those coordinates

my misunderstanding may be more fundamental

@EricGregor Series in a Hilbert space still need to converge.

Seems like I need to learn some more complex analysis to fully understand your proof, but thanks a lot =)

@robjohn to be technical you mean that elements can only have finite norm? because my sum is a sum of vectors, which do not (as far as i understand) converge or diverge. their norm of course might

@tb: had you deal with harmonic measure?

@N3buchadnezzar There is not much there. Just Riemann sums and Liouville's Theorem.

@Ilya a little, but I forgot most of it.

@EricGregor It is a sum of elements of the Hilbert space. Such sums follow the same requirements for convergence. $\sum_ne_n$ is not an element of the Hilbert space.

in fact it is not anything :)

let alone an element of that space

@tb I should be more specific that I asked about discrete-time harmonic measures, which arise from kernels

@EricGregor: Unless you have some notion of convergence, you can't sum infinitely many things.

ok, thanks @robjohn, i guess it was a dumb question.

i was thinking of it as a formal sum

@EricGregor It was not a dumb question since you have learned something. :-)

i need to spend more time with infinite dimensional vector spaces

even formal sums have to make sense!

@Ilya as I said, just a little bit (mostly arising from symmetric random walks on groups)

thanks @robjohn :) i still think it's a dumb question, but i am not (excessively) ashamed of asking dumb questions

it is not a dumb question, really

@Ilya I needed nothing more intricate than the backwards martingale theorem and some 0-1 laws to get what I wanted.

Well, you can define your vector space to consist of formal sums if you like. But then there's the question of whether your "real" sums converge to the formal sum!

@EricGregor I think it is a revealing question. It might be one that a lot of people learning about Hilbert spaces might ask.

@Zhen but only of some formal sums

then i stand corrected twice :)

You don't want $\sum_{n\geq1} e_1$, for example

@Mariano: But what if I'm thinking of $\mathbb{R}^\mathbb{N}$? ;)

my example cannot be given a sense there, either

the $1$ in the $e_1$ is there on purpose, not a typo, btw :P

I would argue that's not what I mean by formal sum...

sure

@EricGregor Use Bessel's inequality

Though, does it make sense to talk about a monoid extended with an $\omega$-ary operation? Hmmm.

it does make sense

@JonasTeuwen Sent : )

The trouble would be in formulating an associativity law.

you can have $\aleph_{45}$ arguments to an operation if you really want :)

Porton asked something related to that recently on MO

:D

And MSE.

@MattN I could install matplotlib, can't remember it to be hard...

Took me hours.

due to his usual crypticness, someone observed that it was either trivial or false

@MattN Is it urgent? I need to fix something first.

Due to how python comes with Mac OS...

iirc

@JonasTeuwen No not at all.

If we're only interested in countable sums then we only need to go up to (but not including) $\omega_1$.

usually operations have their arguments simply indexed, though, not ordered

An indexing is an ordering!

no

well, depends

@JonasTeuwen iirc, I tried to do it with macports, installed it for the wrong version of python and got very annoyed. And so on. You get the idea.

@MattN Hmm sudo pacman -S matplotlib seems to work...?

@ZhenLin No, you can index by any set.

Oh... 8-).

@BrianMScott: Sure, but I'm thinking of making sense of infinite sums.

To what end?

but if your sum takes as argument a sequence, then you cannot talk about associativity in general

@tb If they're infinite, there is no end!

Well, isn't that the problem I'm talking about?

if you replace the "second summand" by a sequence, then you changed the order type

@JonasTeuwen Yes but I don't have pacman. And when I did this I also had to re-install macports (since I wiped my laptop) and that took ages too.

well, the problem with associativity is then that it does not make sense to talk about associativity

One merely has to come up with an appropriately generalised version of associativity. :p

you can allow finitely many summands in each summand

that works

if you try to define sums of countable sets as opposed to sequences, then there is no problem

Nah, I think the right way to do it is to have $\alpha$-ary operations for each $\alpha < \omega_1$.

@N3buchadnezzar I added a paragraph break that I did not carry over from the original page. The jump from $(4)$ to $(5)$ is hopefully not so confusing.

and associativity makes sense, and actually holds when sums make sense

@BrianMScott I see. You're probably right... But you can't be sure about the infinite things you're talking about because they're not definite. It would take you infinitely long to communicate it. That's what Gauss objected to Cantor after Cohen forced independence or something like that.

Then it should just be a matter of turning the functor $M \mapsto \coprod_{\alpha < \omega_1} M^{\alpha}$ into a monad.

(as when one defines summable families on an abelian topological group, say)

Brian, you're also comic relief in this soap. : )

@JonasTeuwen I suppose given that the inverse transform works it's likely to be correct.

I agree, it seems easier to extend the theory of commutative monoids with a single $\aleph_0$-ary operation and still have a reasonable notion of associativity.

And the teddy : )

Although, recently I've been thinking that associativity is morally about the possibility of regular representations by endomorphisms. That would make Jacobi the natural analogue of associativity in the skew-commutative case... I'm sure this is part of some established theory though. I remember Martin Hyland trying to say this at a talk last year.

@ZhenLin Isn't an $\kappa$-ary operation supposed to be everywhere defined, usually? How do you reconcile that with convergence or "sense" issues?

@tb Mücken auf einem Misthaufen, oder? :-)

@tb: I don't intend to. What I want to do is make sense of "formal infinite sums/products".

@JonasTeuwen Sent it again, sorry.

@BrianMScott ja, aber ich stelle mir dabei Schmeissfliegen vor :)

@MattN But if you compute the inverse transform you just just get your data back.

Okay, so say I want to be funny. And I bang on a professor (who is from Germany)'s door and shout: "Aufmachen!!!" would that generally be seen as offensive or as funny to a German?

@tb Actually, so do I, though I had to look up Schmeissfliege.

Scheissfliege?

@JonasTeuwen No, that's nothing out of the ordinary.

@JonasTeuwen Sounds pretty peremptory to me.

Yeah, it is.

It actually is already open...

Ah, that makes a difference.

@JonasTeuwen I don't understand. Of course I want my characteristic function back, after I apply the inverse transform to its Fourier transform.

The door is unlocked but closed.

I'll bang it and shout "AUFMACHEN!!!" if I want to speak to him.

I think he will punch me in the face.

@MattN Okay, and that is not the result you obtain? :-).

@JonasTeuwen Yes it is.

@JonasTeuwen Then I misunderstood. To me it would be funny only if the door were actually open.

@JonasTeuwen you only do that if you're a police officer with a warrant or a debt collector.

@BrianMScott It might actually be slightly open. Then I'll do it.

@tb 8-).

@tb Hey, btw, I'm worried: did you check whether the copper who fined you was actually real? Did he give you a fine or did he make you pay in cash?

@MattN I have a wonderful official bill...

@JonasTeuwen Sounds like a grad student's version of ADVENT

@tb Can you check that it's real somehow? 250 seems unrealistic for crossing the street in the wrong place.

@MattN yes, I can and it is (correct Postcheque account), it's no joke, really.

Wow, an actual jaywalking fine? :-|

@MattN well, it counted as ignoring a red light...

@tb So you're an automotive vehicle of some kind? My my.

@tb Still an incredible amount. I thought crossing red lights was around 40.

Sorry, didn't want to remind you of it.

@MattN well, it is what it is and it's annoying enough. See here

@MattN No problem...

@tb But it doesn't say for pedestrians.

@MattN I wish I were poking fun at you. I'm not.

I wondered when you said 250 dollars the other day, but I see now that that's actually very close: 1 CHF = 1.07745 USD.

@tb 250,- CHF for walking?

Yes, yes and yes, can we please change topic, this is too annoying!

I'm sorry. That sucks! 8-).

Is it normal that you're doing mathematics for days.

And then you figure out you made an error on page 1?

Yes! Someone who doesn't like Bill D read the post I last answered and upvoted everyone except Bill.

Make that into months.

@JonasTeuwen I thought that was normal.

Good.

I guess they won't be voting for him in the elections either...

It sometimes happens that you have a bad misconception. But if something looks too good to be true consistently I'd guess I'd grow suspicious rather sooner than one or two weeks into it.

I actually couldn't until I had the result :-(.

Or maybe I could, but I was too stupid.

But on a positive side: Now I do know more combinatorics! 8-).

Nothing at all salvageable from this work?

The method is okay :-).

So, it's not too bad, is it. It sucks but if you have a method and some new tools to take away from this, I think it's not the end of the world.

Na, I know it isn't, I was just wondering if I was the only one that is this stupid.

@MattN I won't be voting for him in the election, but it's a good answer.

Then usually in the end I have a result which I basically did in a day and been messing for weeks with nonsense.

Then he says something like: "Wow, you've worked quite fast!".

And then I feel like: "What?", but probably I also have to take the struggle into account 8-).

@BrianMScott I didn't either : ) Thanks for the plus one.

@MattN What are you tokkin' about?

@JonasTeuwen The elections (sort of) and Bill's and my latest (algebra) answer.

@JonasTeuwen It sometimes helps to be honest with yourself in such situations. If you had started from scratch, would you really have been able to establish that result in one day?

I doubt it! But it actually feels like I've done nothing. The comment just makes me think: So actually I have done something.

Well, the thing just is whether you were imagining having a great idea and follow up on that belief: Yeah, the disappointment is big, I understand. On the other hand I believe that it's a very small percentage of my actual work that really feels like making progress. But that progress would not be possible without the bulk of the time spent on getting a feeling of what's going on which of course involves a lot of rubbish.

:-). Okay thanks.

99% transpiration and 1% inspiration...?

well, you need to fit the headache somewhere :)

:D.

What's GEdgar's point here?

Wasnt it perspiration? :P @JonasTeuwen

@tb I don't know. He trolled me before.

@FortuonPaendrag The Edison quote?

He often is somewhat ... cryptic.

@JonasTeuwen Maybe. The one with success and inspiration perspiration exasperation etc

@tb One time he asked me to do a simpler case. So I tried and failed. Then he said: Exactly. Then why would you try your general case?

I felt trolled. Bigtime.

I even told my supervisor. "Gerald Edgar trolled me!". Then he said: "He what?".

@JonasTeuwen Thats funny!

@JonasTeuwen I remember that. Darn Bessel thingies :)

He often is deliberately terse...

@tb The young whipper-snapper comment? He's saying that anyone who doesn't remember Anderson must be young. It's a response to TonyK's comment.

Mr. Anderson?

My exact thought, Matt.

: )

You know what nearly made me cry when I saw it today? It means the demise of the site.

Visit the users page and sort them according to monthly score.

Then look at the 7th row from the top.

@tb: Theo, you've got to pick up an upvote somewhere! :-)

@MattN tb?

: )

@MattN What shocked me is Arturo's position.

@BrianMScott Hah! : O Congratulations! (on the roundhouse kick)

@BrianMScott As it did me, Brian. But, congratulations :D

Thanks, both. But I doubt that it will last.

What are you guys talking about?

I think I'll take one of my excellent beers... Not yet certain which one.

@Jonas About Brian's monthly reputation gain exceeding Arturo's.

@Brian Nice :-).

@BrianMScott Did you know that professor (van) Mill is also retired?

@JonasTeuwen I'm pretty sure that I did, yes. I know that he's older than I.

But there's still KP to carry on.

And KP told his PhD student (jointly with van Mill) after that student asked KP if it was common to bring space cake for your birthday that he shouldn't listen so much to me. "Jonas is full of ..." then the guy said: "hokum?".

@BrianMScott Brian, do you teach mathematics?

@PeterTamaroff I did for many years, but I retired a year ago.

@JonasTeuwen Sounds like KP knows you well. :-)

Yes... 8-).

@BrianMScott Do you mind readig this answer of mine? I just want to be sure there is nothing wrong there, since I tried to be a little explanatory, but maybe there is something missing or whatever. =)

@PeterTamaroff I think Thomas is speaking hokum there.

@PeterTamaroff Hang on, and I'll look.

@JonasTeuwen Would hokum mean the same as "gibberish"?

@PeterTamaroff Yep.

@JonasTeuwen What course of action do you see fit, captain?

@PeterTamaroff Nothing.

I'm pretty sure that if the limit exists then normal Riemann integral will also exist.

I will retire to bed now. See you guys around!

@PeterTamaroff Not quite. Gibberish is non-words or random words making no sense of any kind; hokum is intelligble bullshit. What Thomas is saying could be hokum, but it's not gibberish.

@FortuonPaendrag Good night!

@PeterTamaroff Looks okay to me.

@JonasTeuwen Yes. But he assumes one particular case of both $\Delta x_i$ and $x_i$s which does not honor Riemann's approach. Particularily, one interesting property is we can choose $x_i$ to be arbitrary as long as it is in the $\Delta$ intervals and the limit will do the job.

@BrianMScott Yes... True. How do you know?

@JonasTeuwen He's a (retired) professor.

From the US! "Hokum" is something they say in NZ.

@JonasTeuwen How do I know what?

@BrianMScott What "hokum" means :-).

@JonasTeuwen Large vocabulary!

@JonasTeuwen It's pretty international....

I heard it many times in US sitcoms.

@PeterTamaroff I'm pretty sure that it's of U.S. origin.

Oh :-).

Do I need usepackage{} of something to use tabular in latex? Getting a bit tired and my tabular doesn't want to compile.

@MattN Oh no, a table. I think it is a LaTeX primitive.

I guess I'll have to use array then.

@PeterTamaroff It seems to have begun as vaudeville jargon, meaning 'a time-worn gag, speech, situation, or piece of business that is known to wring applause or tears from any audience'.

The problem is, with all the stuff I have to put into it it looks crappy : /

@BrianMScott Where did you used to work before you retired?

@MattN Yeah. Don't.

@BrianMScott Interesting.

@JonasTeuwen Well tabular apparently doesn't want to work.

@JonasTeuwen Cleveland State University.

@MattN Don't you have to nest it within some other... thing?

@BrianMScott Cool. Thanks.

@JonasTeuwen Inside a table maybe. Let me try.

@MattN Yeah I think you have to do that.

Still "Missing $ inserted.".

A MWE? :-).

it is impossible to help debug a tex table without seeing the code

\begin{table}
\begin{tabular}{ c c c }
\alpha & Spec_\alpha (A) & Spec_\alpha (B) \\
0.95 & 0, 21, 22 & 0 \\
0.9   & 0, 1, 21, 22, 42 & 0 \\
0.8 & 0, 1, 20, 21, 22, 23, 42 & 0 \\
0.5 & 0 & 1 \\
\end{tabular}
\end{table}

Have you tried tabular*[\textwidth]{ c c c } ?

Meh :-).

ops

tabular is not a math construct

you need to wrap every table item in dollar signs

I have in my file, of course.

well

I have this in my file:

the point of seeing the tex table was to debug it

Or you could enclose the entire thing in a math enviroment, but I believe that is bad syntax-

if what you showed us is not your problematic table, then posting it does not help much :D

do not do that

a table inside math makes the universe cringe

It is and do you agree that scrolling and having it in one line doesn't help debug?

I don't know what you mean...

@MarianoSuárezAlvarez You're cryptic, Mr. Cheshire cat.

I mean this:

@MattN Matt, also remove the last \\ in your code =)

@BrianMScott oh, thanks, I wasn't aware of the meaning of whipper-snapper.

Huh. Not even the university library has "An extension of the Galois theory of Grothendieck"

that is not what I see

@MattN Oh, and the code snippet you posted works fine here.

@BrianMScott No, actually I'm proving the point that soft questions are overrated :)

I mean in my latex editor, I have no problems with your table. Is this for the site, or some larger project MAtt?

post it at pastebin.com or some other such place

Here it is.

or maybe I don't know how to search for books-that-aren't-books... :-/

Shall I have this beer, this, this or this beer?

as I said, do not wrap the table within $$

wrap each entry in the table with $ ... $

what you probably want to achieve is centering the tabular

then wrap it in a \begin{center} \end{center}

@MattN MWE!

@MarianoSuárezAlvarez Thanks, that worked.

I know :)

@MarianoSuárezAlvarez Do not use \begin{center}use \begin{table} \centering...

But I think I have to have it left aligned.

it is prbably better if you left align the third column and right align the other two

@N3buchadnezzar, it depends on what you want to achieve

the two are different...

They are?

Or multirow it...

I'll have a Mooi & Meedogenloos I think.

@MattN pastebin.com/H7PqwL4j :$

@ZhenLin The Memoirs of the AMS are usually filed as a Journal, so you should probably look for the journal title first.

@tb Thanks for the suggestion!

I guess that means I'll have to actually pay a visit to the library to find out if they've got it...

I don't remember: are you in Cambridge or in Oxford?

Cambridge.

Aye.

Thanks.

At least at the Isaac Newton Institute it doesn't look too promising. Joyal-Tierney is from the mid-eighties, right?

1984, apparently.

HOLY MONKEY! This beer smells promising. And it is like 30cm away.

But the main library for mathematics is the Moore Library, and they seem to have all issues from 1950. I think. I don't understand the catalogue wholly.

Well, somewhere in this University, err city, they must have all issues :)

Hah, I certainly hope so. Especially given that Johnstone wrote the MathReview for that memoir.

Oh yeah.

@JonasTeuwen Doing that should be unlawful!

What should?

It looks too dark to be nice.

It ain't friggin' limonade! 8-).

@JonasTeuwen Showing off your beer with no consideration of your fellow users.

Sure, come over. I have more for you!

@JonasTeuwen That is true. Argentine beer is rather tasteless. I like Warsteiner

Warsteiner? Holy monkey.

You need to try this.