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11:00 AM
@Ilya I heard in Chinese it's one of the worst swear expressions you can possibly use, right after "his mother" : ) I wonder if he's aware of that.
@Matt such a strange topic you're discussing in this chat ))
@Ilya Maths you mean? : )
@Matt exactly
@Ilya Sort of like grue and bleen?
11:01 AM
@robjohn sort of
@Matt with people from Caucus it's very dangerous to say some blames in the address of their family members, especially mother. They will find you by ip and ride on horses to your house, with sabers in their teeth
@Matt I'm not sure I understand you. I never heard this convention that simple functions are positive. For me a simple function is simply a function taking only finitely many values. Using this we have that $s$ is simple and close to $f$ in $L^1$. So you can without loss of generality assume that $f \geq 0$ in the sequel which makes the argument a bit easier.
@Ilya Saber-toothed Caucasians?
@robjohn well, they train their teeth
@Ilya The Molar Express...
11:08 AM
@tb And you're right. It seems to be my own invention that they have to be non-negative as well.
If doing maths was a video game and being wrong meant death then I'd have already died an infinite number of times.
@robjohn when we were talking to one Armenian guy, he told me some obscene spells ;) some of them are really strange. I mean, very strange blames. I would never say that it is a blame
@Ilya That's why I only use "your mother" when addressing Asaf.
It'll be hilarious if one man's curses are funny to another. Imagine laughing out loud in between...
@Matt welcome to the club :)
@Matt at least in Russian we never use it personally: it's like you came to the street, broke your neck and say: 'your mother' to some meta-mother
@Srivatsan well, let me just spell on of those - and if it is too obscene, please tell me in a minute, I will delete it
11:11 AM
to fap in the mountains
Nope. Just bizarre and arbitrary.
I miss the logic of this at all
@Ilya don't they have lots of goats there?
@tb that's quite funny that you're aware of it. in fact they have a hard situation with girls, so poor young and hot-blood guys. poor them
11:15 AM
Now it's getting bizarre. I think "to fap" is a synonym for "to have a wank" so I don't quite see where the goats come in there.
@Matt so, why does one wank? Hint: because of lack of ... with ...
I know. I'm saying "to fap" is an action that doesn't involve interaction with goats.
But never mind ; )
Just nitpicking.
@Matt well, I think the question was: if they can have a sex with goats, why do they fap? but never mind too
11:18 AM
@Ilya get your mind out of the gutter!
@Srivatsan I won't vote because I read this earlier and I don't understand the question.
Which question did you not understand? Old or new?
@tb done. anyway, I'm leaving
@Srivatsan What's "um" and "al"?
See you, @Ilya! : )
@Ilya enjoy your lunch, then.
11:20 AM
@Matt maximum and maximal, apparently =)
@Ilya Bye, Ilya!
Keep away from the goats please.
What's the question asking?
@Matt What is the difference between a maximal element and the maximum?
@Srivatsan there are niether mountains nor goats, but it's nice that you care )
@tb Oh. Ok... So it's narq.
@Matt Very much ARQ, many students are confused about this.
11:22 AM
@tb thanks, you too. we're going to walk a bit, there is 70 km'h wind with a rain
@tb Like I said: I won't vote on this. : )
@Ilya Wonder if we can look at this movie the same way ever again. =)
@Matt The maximum is $\geq$ every other element while a maximal element is an element for which there is no element $\gneqq$ it.
@tb Thank you, I just read that here : )
This terminology is confusing.
Oh! Now I see what he's asking.
@Matt: do you usually imagine a square in $\mathbb R^2$ with a partial order?
11:29 AM
The words are confusing. Expressing it in symbols would be completely obvious.
@Ilya No, I imagine it with the standard topology and the product measure. Why?
:2871316 No the maximum is the greatest element, i.e. $\geq$ everything else. While maximal elements need not be comparable to everything.
anything, really.
@Matt the RHS of it consists of maximal elements
the right-upper vertex is a maximum
I think I understand. Thanks, @Ilya!
you're welcome
Voted. Although I think this is not a maths problem but a language problem.
11:33 AM
By golly, I had trouble because of the wind to get to the office :D.
A combination of the two, I'd say.
@JonasTeuwen from Aula?
oh. the rain too?
Thanks, tb.
@Srivatsan thwack!
good story
@Ilya Such plentiful rain!
12:04 PM
@Ilya Indeed. I wasn't paying enough attention to the conversation. What I wrote makes no sense in that context.
12:39 PM
@tb It's a little late for this remark but: you're the one to talk : )
@Matt me?! *whistles*
1:03 PM
Argh!! I can't decide how to cook the meat! >:[
@AsafKaragila Get a flamethrower...
(You can optionally laugh maniacally.)
Nah. I bought ribs, they are for slow cooking.
Either use the clay pot or the usual pot.
I have a better prediction on the outcome using the usual pot, and there's the bonus of more food at the end; but the clay... is so tantalizing!!
Clay makes for a nice, slow cooking.
If you really want to bring the juices out, you want clay.
Yeah, but there'll be less food and I don't know how the outcome will be.
It's gonna get soupy, and I'm not sure the clay pot is the one I want to get it souped with.
I'm thinking on less tomatoes this time, though. Which makes the clay a better option.
1:23 PM
@AsafKaragila Good point...
I think I'll run a double scam on my ingredients.
I'll bake the potatoes for 40 minutes, slightly cook the tomatoes and then put it all together for a nice three hours vacation in a pot alongside the beef and the onions and whatnot.
1:49 PM
Rats, foiled by non-trivial sheaf cohomology again...
@Zhen: I'm drawing a blank... what's the name of that graph in your avatar?
It's a hypercube graph.
@AsafKaragila Have you enough whatnot? You've been using a lot recently.
I have another 3 days for a Fanatic badge.
@ZhenLin Thanks! I didn't recognize that embedding at once.
It's my favourite embedding!
1:58 PM
two months overdue
@robjohn Apparently I've got two days to that one myself.
@JM We'll all go up together!
@JM I guess we can't see that stat on others.
It's the only gold badge I have. How embarrassing.
@robjohn Well, at least people won't be able to tell how addicted we are up until the badge actually shows up.
@ZhenLin It will be the only gold badge I have, if I get it.
@JM :-)
Time to make coffee for my wife and then walk the dog. BBL
2:03 PM
Except for "Copy Editor", "Electorate", "Fanatic", and "Marshal", the gold badges look like complete flukes to me.
(...and I dread the day that "Unsung Hero" gets awarded for the first time.)
2:14 PM
Can't we simply declare Goldbach as off-topic?
@tb Oh, you've seen that new one? It's a bit harsh, but seemingly warranted...
...is there a new cash prize that has everybody coming out of the woodwork?
@JM It's the 25% of total that hopefully will prevent it.
I'm surprised that there is Goldbach-related math that's actually meaningful
@robjohn David Mitra was pretty close to getting it...
@QED It's a bit like FLT and Collatz; new ideas will be needed to make headway.
2:19 PM
FLT doesn't seem as stupid as goldbach though
Has Collatz given rise to anything yet?
@QED Only a few dents here and there, I'm told.
I should have known before looking that Arturo was the one Legendary badge.
@robjohn Why, who else could it be? ;P
@JM As I said, I should have known before I looked.
@Srivatsan: welcome back :-)
2:34 PM
Hey @Sri.
Sorry about that.
I was typing "can't chat" with the expectation that I am facing a technical problem.
hi robjohn, JM
well, if you can't chat back, perhaps we can deprecate you without reprisal :-)
I still have my loyal IE. So it won't stay that way for long... :)
@robjohn That sounds deliciously mean... :)
@Srivatsan Do you not experience twinges of revulsion?
@robjohn Maybe we should try it sometime?
2:37 PM
@Srivatsan Chrome not working with MathJax?
@robjohn Not working with chat properly.
I will post in meta one of these days.
@Srivatsan Does it not render properly, or does it not recognize the $...$?
@robjohn Works like a charm.
@robjohn It's got nothing to do with mathjax.
@Gigili with Chrome?
2:39 PM
@robjohn The issue is with chatting - with or without MathJax.
@Srivatsan Oh, I see. Why does Gigili not have trouble?
@JM I have always loved IE from the bottom of my heart, JM. Like a member of the family...
@robjohn Do not know. It's not a problem with chrome either; I occasionally face an identical trouble with FF. It's my computer somehow.
@Srivatsan Okay, then it is not something that I can worry about too much.
Having no way to reproduce or fix.
You needn't worry about it at all right now, robjohn =)
2:42 PM
hi \forall
@NikhilBellarykar try $\forall$
@robjohn That's my problem. I'm trying to observe if there's an pattern.
hi $\forall$
$\exists$ hi
@NikhilBellarykar does that look better? you do have the bookmark?
2:43 PM
@robjohn dint work

@Srivatsan hi :)
@Srivatsan Which OS are you working with?
@robjohn nopes how do I get latex to display here?
@Gigili Windows. 7.
2:45 PM
I have to head out for a while. bbl
@Srivatsan Oh I should have guessed, Windows sucks as hell.
But I didn't know it's so easy to use MathJax on Chrome, special thanks to @robjohn.
@Gigili "as hell" is a bit too much; I'm told they've improved things a bit.
wonder who downvoted it and why

(I still maintain that the registry is complete stoofid.)
2:51 PM
The registry is not a bad idea. It actually has some advanced features.
> Downvoted. This question is too vague. – simplicity 20 secs ago
@ZhenLin Sure, but it looks to me like building a skyscraper with a foundation of Jell-O.
Actually, when I read about the technical foundations of Windows, it feels like a building of Jell-O constructed on a foundation of steel and concrete...
They could have created a modern, secure OS. But they didn't.
@robjohn, You were saying something about Riemann and friends?
@JM I wish I could erase my bad memories of it, it reminds me of hang ups.
3:00 PM
@Gigili Frequent BSODs are traumatic, I'll say...
@JM It's much better than what I remember. Touch wood....
@Srivatsan The good thing about Seven is that there's now a mechanism similar to *nix's sudo.
That was in Vista too, except it was apparently very annoying back then.
@JM :-) Just that I never go by that side these days.
I'm not sure how well UAC works, really. Given that all you have to do is press "Yes", users might just train themselves to always click that button to make the annoying dialog box go away...
3:04 PM
@ZhenLin The psychology is a different can of worms. Windows has too many dialog boxes that people do tend to click without reading.
@ZhenLin Very well said, "yes" - "I agree/accept"
@robjohn Oh yeah. I have enough whatnot. Now we play the waiting game for three hours.
IIRC there were a few programs that put in gags like "I also pledge my soul to Hitler" somewhere in installation program's EULAs...
What I heard was that some EULAs had an embedded offer of a prize for anyone who read it...
@JM: Did you read our conversation about non-Euclidean geometry? I was asking something to robjohn...
3:08 PM
@ZhenLin Hah, neat!
@Srivatsan Oh, n-dimensional non-Euclidean geometry? I have a hazy recollection of "hyperbolic polyhedra", but nothing else.
(...and I'm now curious as to what n-dimensional elliptic geometry looks like.)
@Srivatsan what was your question?
@JM OK. Thanks.
In any event, sounds like a nice question for main...
@tb Well, I do not have a precise question because I know pretty much nothing about it.
@JM I considered that, but er, I think it will be justified if I know at least some bits of the theory.
@JM So, what are your musings, then?
3:12 PM
To state my version anyway: is there a notion of dimension in (your brand of) non-Euclidean geometry?
@tb I've always relied on the crutch of knowing how great circles behave; I suppose that's what's impeding me in imagining three-dimensional elliptic geometry, to give one example.
@JM Exactly. That expresses my question.
Or more like, is there even a three-dim elliptic geometry?
@Srivatsan So you're talking about a synthetic approach here?
3:16 PM
@ZhenLin Aha, that's it!
@tb That was my starting point. But I am not too particular.
@JM you should like that. Lots of special functions involved in the determination of their volume, for example. Polylogarithms and the like pop up out of seemingly nowhere.
Is this ignored because it's a lazy question?
Man... I want it to be three hours from now. I'm hungry.
@Matt I guess so. David Mitra posted a link that gave a worked example, but for some reason he removed it.
@Srivatsan One approach is to look at chains of subgeometries of the same type. Definition of dimension by induction, essentially.
3:20 PM
@tb Oh, yes. I think I was reading something by Will Jagy on this months ago...
Q: Value of $\sum\limits_n x^n$

alexBrandWhy is $\displaystyle \sum\limits_{n=0}^{\infty} 0.7^n$ equal $1/(1-0.7) = 10/3$ ? Can we generalize the above to $\displaystyle \sum_{n=0}^{\infty} x^n = \frac{1}{1-x}$ ? Are there some values of $x$ for which the above formula is invalid? What about if we take only a finite number of t...

@tb I see. What does subgeometry mean? For R^n, I imagine it is a subspace...
That's a long answer
@JM You might enjoy this nice note by paul garrett. While it's not quite about hyperbolic stuff and polylogarithms it gives a bit of a taste...
@QED What about it?
3:25 PM
@Srivatsan: I think here what is meant by "geometry" is a space together with the action of a symmetry group.
@QED and vooooooooootes
@ZhenLin So, what is a subgeometry? Subspace with smaller symmetry group?
@ZhenLin that would be a different approach.
@Srivatsan Well, a geometry synthetically consists of a collection of points and relations satisfying some axioms. Now look at a subcollection and restriction of the relations that satisfy the same axioms. Then look at subsubcollections and restrictions of the relations, and one notion of dimension builds on a maximal chain of such subcollections.
@tb Oh, I see. Can you give a concrete example? How does this work for euclidean space?
@tb Neat; I think I'll add hyperbolic stuff to my bucket list...
3:30 PM
I am adding making a bucket list to my bucket list now.
isn't bucket list for before you die?
Yay, the Riemann tensor of the 3-sphere has vanishing covariant derivative.
@QED Yes, it's a short life after all. =)
You guys checked this out, right?
@QED Precisely. Life's short, as Sri says.
Check this as well.
@JM Let's spend it making and comparing our bucket lists! =)
3:35 PM
Uhu, which film was that? I watched it, and I forgot.
@Srivatsan Well, even before I joined math.SE I already had a bucket list as long as my arm.
Now, thanks to this damn site, the length has tripled...
@JM :-)
@Srivatsan $\mathbb{R}^n \supset \mathbb{R}^{n-1} \supset \cdots \supset \mathbb{R}^{2}$. You have collections of points and of lines, and various axioms that relate them together (incidence, parallelism, congruence, etc.) Restricting those to $\mathbb{R}^k$ gives you a subgeometry. Now you'd have to prove that this chain is maximal.
@JM Just for fun, I added the interesting references (mostly books) in my Amazon. My wish list size is now 300 after 3 months are so. =)
@tb Sounds interesting. In fact, you should also show that this is the longest chain also, right?
@Srivatsan "Now you'd have to prove that this chain is maximal." :)
3:39 PM
Because if there is a longer chain of length $n$, I will think that the dimension is $n+1$.
@tb What does that sentence mean?
Essentially what you said. You can probably set up an induction. Note that you start with $\mathbb{R}^n$, so you have a concrete model. Then you should try to prove that every proper subgeometry can be embedded into $\mathbb{R}^{n-1}$.
(but I'm hazy on the details)
@tb Nice.
@tb As a side note, what subject would this come under? Keywords?
@QED: Why in the world is that website garbage? Because of its style? Many stars in it?
@Srivatsan I have no idea. I would start looking under incidence geometry. I know that people studying buildings think about similar ideas.
@tb Fine, thanks.
It seems Paul Garrett has some papers on buildings =)
Book, actually.
3:49 PM
@Srivatsan Sure, he also has a book which I want to look at more closely at some point.
Buildings are quite cool. There's lot of nice language going on there: there are appartments, aisles, there's the rainy day lemma and so on...
@Gigili, yes that's part of it
@Gigili, the post got downvoted because it links to rubbish site
@Srivatsan See this:
@QED We're in no position to judge.
that's not true
3:54 PM
@tb Hmmm. That sounds far too combinatorial. I'd rather deal with stalks and sheaves and germs and kernels...
I have to leave now.
@Srivatsan Noooo!
@tb I'll catch you again later tb. Thanks for the pointers.
@Srivatsan See you. Thanks for the diversion yesterday.
3:55 PM
@Gigili, timecube.com
@ZhenLin well, and at some point you'll study algebraic groups...
@Gigili, I claim this site has some of the most important mathematical insights of the century
That excerpt looks very picturesque. Now if only I could understand the terms properly...
@robjohn Do you mean the puzzle or the question about nonEuclidean geometry? :)
@Srivatsan The puzzle. I still don't know how to answer the NE question.
3:56 PM
I have like two hours until this is ready. I think I'll bake some bread too!
@JM: Got any good recipes for breads that go well with beef stew?
@AsafKaragila what's taking 2 hours? beef stew?
@robjohn I suppose you didn't have to answer it for it to be a distraction =)
... bread in 2 hours? What?
The stew has at least two more hours until it's ready.
Anyway, thanks to you too, @rob. See you.
3:57 PM
@Srivatsan Mariano?
@Srivatsan Ah, but I thought about it and did feel I did a significant bit. Enough to make it worthwhile. Ah, but the last remark was about the NE question...
Heckmann? =)
See you!
See you
@AsafKaragila In two hours? I don't think so...
@QED And I'd say it's garbage.
3:59 PM
so you understand
@JM Focaccia?
@AsafKaragila I haven't done that in a while. That has a short baking time?
I think so... and a relatively short time before baking too.
@tb Maybe the proofreaders were tired... :)
At least if you go for the half-assed recipes and not those with "now put in the fridge for 24 hours or more."
Yeah. I found a recipe with 40 minutes leavening and 25 minutes in the oven.
4:03 PM
@JM It's a very cool paper. But marred by two things: 1) wrong order of names, 2) misspelling
@QED Of course I understand! But "NAAS (USA) Awarded A++ = Excellent Grade to article of prime numbers formula by Prof. S.M.R.Hashemi Moosavi"
Well then the NAAS are clueless too
@AsafKaragila Okay, tell me how it goes... :)
They are if you say!
I may go for Ciabatta instead.
4:05 PM
Don't get sarcastic
Which of those prime formulae isn't just Wilson in heavy disguise?
@Gigili, I don't understand why you're defending this nonsense, you haven't even read it have you?
@Gigili 1) What is a NAAS (USA) award? 2) Can you find an official source for that?
@tb Honestly, I don't know but I wouldn't judge as they did.
I couldn't find any official source by now.
@Gigili, that "They are if you say!" is really rude because you're basically just disagreeing with me by sarcastically pointing out that I don't have absolute authority - I never claimed to anyway - without making any definite statement, which means you have no responsibility to back up anything up.
4:15 PM
Still... I'm doubtful that it's anything more than a heavily disguised version of Wilson's theorem...
I've decided not to bake bread now.
@Gigili, the only reason I responded to your objections to this was for your own benefit, so I think you should try to be a bit nicer about it. If you really think there's something to this website (which you haven't read) maybe point it out?
@QED Rude?! Sorry if you got offended by my response!
why the question marks? I explained in detail why I found it rude
It's fine, I just don't understand why you want people to think "Just maybe there's something to this" about this cranks work
@Gigili: I hate to break it to you, but the format on the site is indeed off-putting, even if the mathematics might have some use...
4:20 PM
I guess you're exaggerating, I said you cannot judge when you're not sure about it. Calling a website garbage or rubbish like that is not rude? consider - one percent - there's some efforts behind that. I'm certainly not going to continue this discussion with you @QED.
(whatever "use" means.)
@Gigili, I don't think either of learned anything from the discussion then
I like that analogy by Aaronson: it's a bit hard to seriously look at a scientific paper written entirely in crayon.
@JM Very true, painfully true. My point is we're not allowed to publish our comments in public.
4:25 PM
@Gigili There are many problems with that site, but for a start, it doesn't actually answer the question. Section (5) talks about finding the $k$th prime, but if you look carefully, you can see that the function needs two variables, a k and an n, and it will tell you if n is the $k$th prime. So you need to find the $k$th prime, n, in order to find the $k$th prime!
@Zhen: Maybe I'm being obtuse but I don't understand your complaint about non-exactness in degree zero.
Degree zero of the de Rham complex, not the sequence!
Hmmm. Although my description of the failure is incorrect.
I'm still not following.
Someone please make it an hour and a half from now!
I mean you're just applying the Mayer Vietoris sequence which is explicitly done in Bott and Tu, for example.
4:29 PM
Well, suppose I am given a smooth function $h$ on $U \cap V$. How do I find functions $f : U \to \mathbb{R}$, $g : V \to \mathbb{R}$ such that $h = f - g$?
I'm starving.
@lewist I didn't read it. Seems you're right.
@ZhenLin See here
This is the crucial picture:
Ah, those partitions of unity thingies again.
Exactly :)
4:35 PM
I had it stuck in my head that I needed a $H^1(S^n, \Omega^\bullet)$ on the right...
but I guess I should have remembered that $\Omega^\bullet$ has vanishing sheaf cohomology.
Yes, those partitions of unity thingies again :)
And meanwhile I resolved my complex analysis confusion: it's just the open mapping theorem.
(plus a bit of plane topology)
@Zhen: I object again... The intersection $U \cap V$ is diffeomorphic to $S^{n-1} \times (0,1)$.
Yes, but directly establishing that it has the same de Rham cohomology seems troublesome.
Using a bump function $f$ on $(0,1)$ you can send a closed $k$-form on $S^{k-1}$ to a $k$ form on $S^{n}$ (just write it down in coordinates)
Indeed. But why does this induce an isomorphism in cohomology?
4:53 PM
@ZhenLin I think you need the Poincaré lemma for that, so yes, you need a little bit more, but again this is rather explicit.
(I'm sure this is done somewhere in Bott and Tu)
Ah. Thanks.
5:34 PM
Oh boy, it is almost ready!
The beef is soooooo good.
I like it when French people say "the beef" when they want to say "the cow".
Or "the pork".
Oh, those faux-amis!
So... who wants to buy me a 6L clay pot?
5:43 PM
So I can cook similar amounts in the oven, it's a whole other world when you cooking in clay pots.
I'm a graduate student. I don't have the money. Sorry.
looking at the non-grad students

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