Mathematics - 2011-08-17

However, for sake of being completely lazy, I am trying to find an even quicker proof than the relatively short one which appears in the literature. :P

J. M.

That sounds more like greed than laziness... :P

Asaf Karagila

What greed? I do want this to be complete. I just don't want to type more than the bare minimum :)

I mean, there are exactly two reasons to study math and stay in the academy.

J. M.

@mixedmath If I were asked about "dazzling, important, and exciting", I could talk quite a bit about it. With the qualifier "to everyday life" however... :D

Asaf Karagila

2:56 AM

1. It is damn interesting!

2. It's a great way to do nothing all day and get paid. :)

J. M.

"even quicker proof than the relatively short one" - sounds like greed to me. I'm not saying it's "bad" in this case, though... :)

Asaf Karagila

Well, the short proof requires me to prove like two and a half lemmas and add various modifications and so on.

It's like a full page of TeX.

My idea is very straightforward and requires no modifications since it uses things I actually did before in this question.

J. M.

"It's like a full page of TeX." - Oh, well... then laziness it is. :P

Asaf Karagila

If it was my descriptive set theory professor a full page would be nothing. That guy requires us to write every last detail. I told him once that if exams were unlimited in time he would ask us to prove that all the definitions are valid in ZFC, or something like that.

The professor who'll be grading this assignment is a lot more relaxed in his approach and requires us to sum up the proofs from class, and more or less use books to guide us in our work.

J. M.

Oh, so he's turning you into a class of tree-killers... :D

Asaf Karagila

3:01 AM

I mean, aside of the first and last question which are three pages together (at the moment), the rest of the six questions (ten if you include sub-questions) fill hardly three pages.

Finally, after hitting the rep limit in [cardinals] and [axiom-of-choice], I finally get some specialist badge in [general-topology]. At least I'm somewhat active in one tag that has enough questions :P

J. M.

Set theory to topology isn't that much of a stretch, no? :P :D

Asaf Karagila

Nope :D

J. M.

Exactly. :P

Asaf Karagila

I didn't say non-set-theoretic... I only said a badge with more than 100 questions :)

lol... my girlfriend just came out of the bedroom wondering where the hell I am.

J. M.

... if it ain't private, what exactly is your gal studying there?

Asaf Karagila

3:14 AM

Linguistics and art history.

Well, she started this year with linguistics and literature, but the latter bored her and she'll start art history next year.

J. M.

Quite interesting...

Asaf Karagila

Ha!

I found this youtube of this drunken chick, drinking and cooking.

J. M.

...I've seen people do that. Now, if she ends up with something actually delicious, that would be new to me. :D

mixedmath

About to finish - grand!

J. M.

finish what?

mixedmath

3:21 AM

Sorry - I was reading back - I was refering to how happy I am for Asaf

that he's about to finish his assignment a mere couple moments late

J. M.

"mere" =))

Asaf Karagila

Well.

Firstly, this chick makes tacos. Not actual cooking, drunken munchies cooking.

Secondly, I told you guys that I have a time machine. The time vortex closes soon though. So I couldn't take my time with it :D

Thirdly, this bastard doesn't want to be proven yet! shakes his fists

mixedmath

Oh, I see.

Asaf Karagila

None of you guys happen to be a very prominent set theorist working in the field of large cardinals, right?

J. M.

...I can't even pretend to be one.

Asaf Karagila

3:28 AM

:P

J. M.

You know what, I'm happy with that. :D :P

Asaf Karagila

lol :)

J. M.

3:40 AM

Wow, apparently Google is celebrating ol' Pierre Fermat today...

Asaf Karagila

Maybe the big brother just knows you are a heavy math.SE user and shows you mathy events.

J. M.

...nono, look at the Google Doodle for today.

Asaf Karagila

It better not be some male genitalia, or else there will be hell to pay!

J. M.

... why would they even do that? :P

Asaf Karagila

To celebrate some day relating to the porn industry?

J. M.

3:45 AM

Great, it would be nice to see the chaos of Google tripping up work filters... :D

Asaf Karagila

You should mail Larry Page, or whatever his name is... :P

J. M.

I think it's Brin and Schmidt doing most of the heavy lifting nowadays...

Asaf Karagila

Nice.

J. M.

It's not showing up in there? Must be the geolocation...

Asaf Karagila

Showing where?

J. M.

3:53 AM

I mean have you tried visiting google.com?

Asaf Karagila

Yeah.

J. M.

..and the doodle isn't showing up there?

Asaf Karagila

Showing up just fine.

I think that at least two of us are having a breakage in communication here :D

J. M.

Oh, somehow I interpreted your words as you not seeing the doodle...

:D

Asaf Karagila

Goddammit.

I found a really good online version of this paper, but now I can't seem to find it.

J. M.

4:00 AM

which paper?

Asaf Karagila

Oh yeaaah, mathscinet saves the day!

"Strong axioms of infinity and elementary embeddings"

MR0482431

J. M.

...Google seems to return it after you hit "I'm Feeling Lucky". :)

Asaf Karagila

Yeah, in the scan appearing on Kanamori's site. Which is totally crappy.

MathSciNet has a link to sciencedirect which got a wonderful quality of a scan.

With OCR!!!

J. M.

Well, Elsevier pays a lot for good scans. :)

mixedmath

"I have discovered a truly marvelous proof of this theorem, which this doodle is too small to contain" - oh Google - how many problems you solve

2

Asaf Karagila

4:03 AM

Elsevier?

J. M.

Elsevier is the publisher behind SD.

Asaf Karagila

Ahh.

J. M.

From what I've been told, most of the scans of old articles are from good Dutch libraries.

so sometimes you'll see a stamp saying that it was the copy of some library.

Asaf Karagila

For the first time since Anne Frank, the Dutch save the day! :P

mixedmath

Dutch libraries? really?

J. M.

4:07 AM

Yep. I've at least two PDFs of articles that say they were from TU Delft, and one from ETH.

mixedmath

I wouldn't have guessed.

J. M.

(so apparently that one was from a Swiss library :P)

Well, that's SD. I don't know about the other publishing houses...

Asaf Karagila

Wow, I have some great tits outside my window!

I haven't seen these birds for a while here.

El'endia Starman

4:28 AM

...is "tits" short for anything? o.O

Asaf Karagila

Great tit is a bird.

Great Tit

The Great Tit (Parus major) is a passerine bird in the tit family Paridae. It is a widespread and common species throughout Europe, the Middle East, Central and Northern Asia, and parts of North Africa in any sort of woodland. It is generally resident, and most Great Tits do not migrate except in extremely harsh winters. Until 2005 this species was lumped with numerous other subspecies. DNA studies have shown these other subspecies to be distinctive from the Great Tit and these have now been separated as two separate species, the Cinereous Tit of southern Asia, and the Japanese Tit of Eas...

yunone

On a more mathematical note, don't forget the Tits group or the Tits Building. en.wikipedia.org/wiki/Tits_group

Asaf Karagila

@yunone: I left you a message earlier but you left without replying...

El'endia Starman

@Asaf: Thanks for the clarification. :P
The only other usage that I had seen was slang for (human) female nipples... >.>

Asaf Karagila

4:43 AM

Yeah, the point was to sound somewhat dirty :D

Well. I had a lovely evening but now I have to go shopping and whatnot.

El'endia Starman

You certainly succeeded in that...until you mentioned "birds". :P

Seeya!

Zhen Lin

5:42 AM

Whenever I look in here there doesn't seem to be any activity. Hmmm hmmm.

J. M.

6:07 AM

...there's always the option of starting an activity; e.g. saying something everybody else can converse about. :)

Zhen Lin

Starting conversation is difficult. :-/

J. M.

I suppose it is sometimes...

Zhen Lin

Firefox is being even more laggy than usual. sigh

anon

Sup.

J. M.

What version are you on?

Hello anon.

Zhen Lin

6:20 AM

FF6, OS X 10.7

J. M.

Oi, you're on bleeding edge? That might be one factor...

Zhen Lin

That was released just today!

anon

@Zhen: There's numerous IRC #math channels on various servers, and chat.mibbit offers in-browser interface.

Zhen Lin

Bleeding edge would be FF8...

anon

They have 8 out now?

Zhen Lin

6:22 AM

Not really. Firefox has changed to a new development model, a bit like Chrome.

J. M.

Okay, make that "cutting edge"... but generally it ain't great to be quickly upgrading with browsers these days.

Zhen Lin

They have 3 channels.

J. M.

"Firefox has changed to a new development model, a bit like Chrome." - and that's one reason

Zhen Lin

Firefox 4 was a huge improvement over 3.5 though. I switched while that was still in beta!

J. M.

That's the thing with betas: they're mixed bags.

If you're the experimental sort, it's dandy to always have the latest version.

anon

6:24 AM

Gmail was beta for so many years...

J. M.

...Google's a different story. :)

El'endia Starman

[chuckles] That's certainly true. :P

J. M.

Anyway, what I was about to say is that if you're using a beta version, you really shouldn't be surprised at nonsmooth behavior...

Zhen Lin

It's not like it's worse than the previous version. Firefox, unfortunately, is generally laggy.

J. M.

It wasn't always that way...

...though I'm in Linux; maybe that's a different tale.

Zhen Lin

6:27 AM

Indeed. But the web was simpler back then.

Nowadays all these Javascript-laden pages demand faster engines.

J. M.

A lot of people are (ab)using Ajax now, yes...

Zhen Lin

Rendering live MathJax previews on large posts is surprisingly slow.

It's a pity it looks worse in Chrome.

(and I'm too lazy to switch anyway.)

J. M.

"(and I'm too lazy to switch anyway.)" - :D

anon

It's not too terrible. Compare with actually LaTeXing a document.

Zhen Lin

That's no excuse really :p

J. M.

6:30 AM

@anon: well there's that.

Zhen Lin

As for LaTeX... one of my complaints about that is how it sometimes requires three full passes to render a document. I wonder if there's a way to work around that somehow.

Or maybe a way to do incremental renders, since documents don't tend to be rewritten from scratch every time it's run.

anon

lol Patrick just called the coth formula a "random shitty identity"

J. M.

...oh boy, I suppose it's subjective :)

yunone

6:47 AM

@AsafKaragila Oh, sorry, I didn't see that. My impression was that Enderton has nice and clear discussion, but the exercises are a bit on the easy side, but the material is relatively simple. I think Levy does a better job of explaining the concepts are a slightly more advanced level, but I didn't really try the exercises in that book.

J. M.

7:05 AM

Bleh, I keep using up comment upvotes too quickly. I know the exact limit is posted somewhere in meta.SO, but I can't be assed to search...

anon

I never knew there was a comment up limit. I knew there was a forced delay though.

J. M.

I think I've hit it thrice this week, counting today.

Jacopo Notarstefano

2:48 PM

Chrome 15.0.854.0 dev on OS X 10.7 does not render the overlines correctly in my comment to the answer posted here: math.stackexchange.com/questions/56352/…

Is anyone else having this problem? I checked that they work correctly in Firefox 6 on Windows XP

Zhen Lin

No overlines in Chrome 13 on OS X 10.7 here.

But MathJax in Chrome is buggy for me in general.

Firefox 6 is fine.

Jacopo Notarstefano

Thank you! That narrows it down.

I guess that filing the bug on meta won't do a thing, since it's a MathJax problem...

Zhen Lin

Same problem in Safari 5.1, so I'd say it's specifically a WebKit problem.

Dylan Moreland

6:01 PM

Lots of browser talk here.

Alexei Averchenko

6:12 PM

rendering is slow as hell

was just editing my 3000+ character question, I just had to disable rendering completely

it's because right now even if I only type one character all latex math is rerendered (almost?) from scratch

anon

Just learn to glance at the preview less frequently. The render doesn't stop from typing, at least in my experience.

Alexei Averchenko

btw is it just me or firefox is incrementing major version every few months now?

anon

Also, exactly how slow is it? I've heard a few people complain about the speed but I've never had it render slower than a second on my end.

Dylan Moreland

@Alexei It does seem like it.

Alexei Averchenko

dunno

i got ubuntu + firefox 5

and a 5yo pc :)

btw what do you think about my question? will i get some activity in it without a bounty?

Dylan Moreland

6:20 PM

Oh, I didn't see that.

Who doesn't love a diagram chase

Alexei Averchenko

what's funniest is that Lang just skips over this topic

anon

Personally I didn't click the question because it's completely outside my knowledge base

Alexei Averchenko

it's just half a page

and i spend two days figuring out details <_<

Zhen Lin

The development model Firefox is using has them pushing out new releases every 6 weeks.

Dylan Moreland

Yikes.

Alexei Averchenko

6:22 PM

crazy, they're gonna inflate their version number

Dylan Moreland

Yes, Firefox 360.

Zhen Lin

Chrome is already at 13–15, and I'm quite sure Opera is also in the double digits

Alexei Averchenko

ie barely hit 8, for crying out loud

and ie 1 was released in 1993

Dylan Moreland

I'll take a look at it if I get sick of Artin-Tate, which won't take long.

Class field theory is a nightmare with beautiful implications.

@Alexei I know that Hatcher pretty much proves this in Ch 2 of his Algebraic Topology. You could look in there, but I don't remember his proof being all that much shorter.

He has diagrams. Diagrams are nice.

Alexei Averchenko

i wish i didn't spend 4 years on applied maths. then i might have understood roughly what this 'class field theory' is about :)

Dylan Moreland

6:33 PM

I would ask questions about it but my advisor is Matt E and I kind of don't want him to know that I'm an idiot.

3

Might be time to go anonymous.

anon

hehe

Alexei Averchenko

is it ok for not to know singular homology after 1 year of master? :)

'cos i'm the one who feels like a sorry late idiot almost 100% of the time :)

i'm 21 and i don't know homology. good luck finding grad school :(

anon

"In mathematics you don't understand things. You just get used to them." - John von Neumann

Alexei Averchenko

i mean i literally know nothing about it

anon

you don't know what it means?

Alexei Averchenko

6:37 PM

nope

just that it involves standard simplices

maps from standard simplices to manifolds

that's about all i know :)

anon

I get from Wikipedia it has to do with how many times closed loops wrap around something, e.g. a torus, and how these can be represented as groups

Jacopo Notarstefano

In my university they made that course required very recently

You're not alone! (I've just read the last chapter of Kosniowski)

Alexei Averchenko

but i bet you're an undergrad

and i'm about to begin my 2nd year master

Jacopo Notarstefano

Yup, albeit an old one :P

Alexei Averchenko

sucks to be me :(

the worst part is that i'll have to somehow find a grad school after this year

and the chances of that happening are slim

maybe in Novosibirsk, unlikely in Moscow, nigh-impossible in a developed country

@DylanMoreland I'm mostly concerned whether or not $\gamma_i$ in my proof is indeed a hom

'cos it's the only thing where i don't know in advance if it's true

Jacopo Notarstefano

6:57 PM

If only I had used Mathscinet earlier!

Jonas Teuwen

@ZhenLin If LaTeX requires multiple passes it usually will tell you so the editor could run it again automatically.

Asaf Karagila

Yes. It is done!

I submitted the unholy assignment!

Jacopo Notarstefano

cheers!

Dylan Moreland

7:13 PM

@Alexei I feel like the chain complex stuff is just getting in the way.

Alexei Averchenko

of what?

Dylan Moreland

7:30 PM

It's not so bad in the end.

Nevermind!

I just thought the indices were unnecessary because you're just looking at two rows, but it wasn't any harm in the end.

Alexei Averchenko

three rows, actually :)

well, two if you ignore the meaning of Bs and Zs

Dylan Moreland

It looks good to me. gamma_1 should indeed be a homomorphism.

Woops, three. I guess I consider the snake lemma to be the map Ker d'' -> Coker d.

And then you do a little bit more chasing and get the map on homology.

Brandon_R

what up guys

Alexei Averchenko

dylan is looking at my question, and i'm weeping about my wasted life :)

Dylan Moreland

I don't see anything here to fix. And it's doubtful that you can do better with a diagram chase.

Alexei Averchenko

7:39 PM

@DylanMoreland actually, i don't know snake lemma yet. did i mention how much i suck?

Dylan Moreland

Oh, this is pretty much the snake lemma.

It's more advanced, really.

I did learn a really neat proof of this from Kevin Costello.

Asaf Karagila

Snake lemma?

I should pass a law against algebra in here as well :P

Alexei Averchenko

@DylanMoreland link plz

Dylan Moreland

@Alexei Unfortunately I don't have this written up anywhere. It's one of those things that I say I'll scan and then never get around to.

Asaf Karagila

I think I will start allowing only set theoretic chat in here. Yes, that sounds like a reasonable idea.

anon

7:43 PM

Let X denote the set of all chat which is not set theoretic...

Alexei Averchenko

@AsafKaragila won't you at least allow pullbacks, please?

Asaf Karagila

@AlexeiAverchenko Fine. But only in topos related categories.

Alexei Averchenko

awwwwww

Dylan Moreland

Get Harry in here.

Asaf Karagila

@anon Let P be a notion of forcing and G a generic filter such that some p in G forces that X is empty.

I got a new chair, this 300$ piece of machinery. Pretty nifty thing.

@DylanMoreland What Harry?

Also, non mathematical chat is allowed :P

Dylan Moreland

7:48 PM

My friend from Michigan. He's kind of famous on MathOverflow; less so here. Actually, I think he was banned from here for life.

Asaf Karagila

What's the username on MO?

Alexei Averchenko

i can only recall harry hindy or something like that

Asaf Karagila

Gindy

Dylan Moreland

mathoverflow.net/users/1353/harry-gindi

He loves the topoi.

Alexei Averchenko

gindi :)

Asaf Karagila

7:49 PM

I was closer :P

I don't really know much about topoi, I just approve that if you insist on doing algebra :)

Alexei Averchenko

why was he banned?

Asaf Karagila

Good question.

Alexei Averchenko

i don't insist on doing algebra, but i need to learn something about singular homology fast :D

'cos i got an assignment to read husmoller's 'fiber bundles'

Asaf Karagila

Why? D:

Alexei Averchenko

and i don't think it's a good idea to do k-theory before singular homology

actually, i suck at homotopy too, so i'm in a weird place now

soft homotopy lifting is a bitch

broke my brain real good

or was it soft homotopy extension?

'soft extension of covering homotopy' - i hope i translated it right

Asaf Karagila

7:55 PM

Now I must leave. Behave or else...

Jonas Teuwen

9:34 PM

@AsafKaragila Y so srs?

Jacopo Notarstefano

9:47 PM

Ouch. Found a flaw in an assignment due tomorrow. A baaad flaw.

Jonas Teuwen

9:59 PM

The bars are still open I reckon.

I seem to like Pseudo-differential operators.

Willie Wong

11:07 PM

@DylanMoreland Just for another year or so.

Dylan Moreland

11:31 PM

@WillieWong Aha. Good to know.

It is probably good for him, in the end.

Transcript for

$Mathematics$ Mathematics