Mathematics - 2012-08-10 (page 3 of 3)

Jonas Teuwen

21:18

Hi guys.

MeAndMath

Hello!

Old John

@JonasTeuwen Hej Jonas

Jonas Teuwen

@OldJohn Hi :-).

Old John

If anyone is going to be in the UK at the end of the month, we are having a party (myself and my wife are both retired and both have important birthdays this month) - and any MSE member is invited :)

MeAndMath

Thanks @OldJohn!

Old John

21:25

when I say "any MSE member", I might have to exclude one or two people on the site :P

Jonas Teuwen

@OldJohn I am in Helsinki :-(.

@OldJohn I will remember it for next year! 8-). But I might be in Australia...

Old John

@JonasTeuwen I am sure you will have a great time there - I always have!

MeAndMath

@OldJohn oh...

Jonas Teuwen

@OldJohn Maybe you should give your party in Helsinki eh...

Old John

I would love to - but have already agreed to povide beds for people from ireland

Jonas Teuwen

21:27

@OldJohn So you have two extra beds then! 8-).

Old John

@JonasTeuwen at least

MeAndMath

Where in the UK?

Old John

@MeAndMath halfway between Manchester and Liverpool

user19161

@JonasTeuwen You mean you will be, not am.

user19161

So @jonas if finding a girlfriend is not the holy grail, then what do you consider the holy grail of mathematics?

Jonas Teuwen

21:30

@JasperLoy What do girls have to do with math?

user19161

@JonasTeuwen Nothing, but my question still is valid.

MeAndMath

@OldJohn Nice.I really would like to go...pity that i can´t...But thanks!

Jonas Teuwen

@JasperLoy How precise do you want the answer?

user19161

@JonasTeuwen Anything. I just want to know what you think.

Old John

@JasperLoy when did girls have anything to do with the holy grail of maths ???

Jonas Teuwen

21:31

@JasperLoy I can't answer it.

@OldJohn They ruin your quest in looking for it! 8-).

user19161

@OldJohn Well, I just make random associations!

Old John

@JonasTeuwen :)

user19161

@JonasTeuwen Not really. They might even help you. See A Beautiful Mind.

Old John

@MeAndMath well - if you are ever in our part of the UK - drop me an email

Jonas Teuwen

@OldJohn I am reasonably often in the UK 8-).

@JasperLoy That's fiction...?

user19161

21:33

@JonasTeuwen It is possible though. Art mirrors life and life mirrors art.

Old John

@JonasTeuwen just let me know - I now have a decent supply of whisky :)

Jonas Teuwen

@OldJohn Purrrfect.

MeAndMath

@OldJohn Unfortunately I´m not...I really would like to be!

user19161

@OldJohn You spelled whisky the way I like.

user19161

@MeAndMath Another time then, another time.

MeAndMath

21:36

a party with mathematicians:Awesome!

user19161

You can always come to chat. It's also a party.

Henry T. Horton

<walks in wearing nothing but cowboy boots> Howdy y'all

MeAndMath

YAY!That´s why I love being here!

Old John

back shortly - just going to look for meteorites :)

user19161

@HenryT.Horton Erm, luckily Peter is not here or he will faint.

user19161

21:38

@OldJohn Are there real ones where you are?

Henry T. Horton

Poor Peter... The blood rushes straight away from his head in these situations

user19161

@HenryT.Horton You are really a drama queen.

skullpatrol

I will faint in his place ...

Henry T. Horton

Thanks.

skullpatrol

np

user19161

21:40

@HenryT.Horton Pics or it did not happen.

Old John

@JasperLoy it appears not - at least tonight

user19161

@OldJohn But did you ever see any?

skullpatrol

@HenryT.Horton BTW do your cowboy boots have spurs?

Old John

@JasperLoy I have seen plenty in the past

user19161

Ah, I have never seen one.

MeAndMath

21:41

me neither:-(

Old John

@JasperLoy don't worry - they only last for a fraction of a second usually - not that great, really

skullpatrol

Meteor showers are neat to watch.

Henry T. Horton

I don't have time for showers

MeAndMath

LOL

Old John

more important - I think I now understand the relevance of $p$-adics :)

user19161

21:44

@HenryT.Horton You need to shower before you meet me.

skullpatrol

@HenryT.Horton I wondered where that smell was coming from.

Henry T. Horton

@JasperLoy You need to accept my natural scent if you really love me.

3

user19161

@HenryT.Horton OK. I will let you know when I am there.

MeAndMath

how cute

Henry T. Horton

@skullpatrol That's probably one of the hamburgers that got lost in my rolls of fat...

Old John

21:46

yesterday, I had enough showers/steamings/massages/dunkings-in-warm-water ... to last me a month :)

Henry T. Horton

At least it's a free meal if I find it later.

user19161

@HenryT.Horton WTF!

MeAndMath

@OldJohn :-D

skullpatrol

U has a smell.

user19161

Hey this Chrome seems to be working better in chat now.

user19161

21:50

@skullpatrol Is that a dog or cat?

MeAndMath

looks like a cat...

skullpatrol

@JasperLoy Yep, from the nose it looks like a cat to me.

user19161

@skullpatrol Actually it looks like a tiger.

MeAndMath

Wow!

Old John

looks like a deformed rat to me :(

MeAndMath

21:53

how does it look like a tiger?

Old John

vicious polar bear attack :)

MeAndMath

polar bears are normal bears after a coordinates change

8

skullpatrol

@MeAndMath And if they existed at the South pole would that make them bipolar?

MeAndMath

:-D

skullpatrol

hi @robjohn

robjohn

22:08

@skullpatrol hello

Jonas Teuwen

@robjohn How do you feel; as moderator?

skullpatrol

@HenryT.Horton Put your clothes back on the Konig of Style is here :0)

robjohn

@JonasTeuwen pretty much as I always feel.

skullpatrol

hi @mixedmath

mixedmath

hiya

Jonas Teuwen

22:11

@robjohn It did not enrich your life...? That's good!

skullpatrol

hi @Norbert

robjohn

@mixedmath howzitgoin?

Norbert

hi guys

robjohn

@JonasTeuwen I still have a lot to learn

Jonas Teuwen

@robjohn How to be sneaky...?

mixedmath

22:12

@robjohn I'm pretty well. I did one of those MRI study bits that colleges are always doing, and so I got to look at pictures of my brain today.

Norbert

I've got an easy question for you

mixedmath

ok

Norbert

Can you help me?

skullpatrol

$\Huge\text{A real twisted mean square.}$

robjohn

@mixedmath: was it interesting or freaky? It's probably different for everyone.

mixedmath

22:13

@Norbert I don't know, but I can listen to the problem.

Norbert

is it true that $s_n(RS)\leq s_n(R) s_n(S)$ where $s_n$ is the n-th singular value

robjohn

@mixedmath: you were already a mod, right? So you probably don't have too much to learn about the process.

mixedmath

@robjohn It was really cool! I apparently have a very wrinkly brain. That's exciting.

@robjohn yes, that's right. I'm a mod at Philosophy. Although there are a thousand times more flags at MSE

robjohn

@mixedmath I think it is very bad if it is not wrinkly. So that's good.

Henry T. Horton

Dang... my brain is a perfect sphere

3

robjohn

22:15

@mixedmath Yeah, but you know how to handle things. I still don't know exactly how to handle certain things.

Norbert

I think I have a prove, but it uses a serious sledgehammer

robjohn

@Norbert 15 or 30 pound?

Norbert

32

mixedmath

@Norbert I'm afraid to say that I've forgotten everything about singular value bits. So it turns out that I'm useless to you :(

Norbert

Well in this case I'll just show you a proof and I'll say is correct or not

ok?

Thanks to Allakhverdiev we know that $$s_n(T)=\inf\{\Vert T-F\Vert: \mathrm{dim}(F)<n\}$$ Take arbitrary $F$ with $\mathrm{dim}(F)<n$

then $-R F-SF+F^2$ have rank $<n$

so $$s_n(RS)\leq \Vert RS-FS-RF+F^2\Vert$$

but $$s_n(RS)\leq \Vert RS-FS-RF+F^2\Vert\leq \Vert R-F\Vert \Vert S-F\Vert$$

Since $F$ is arbitrary we apply Allakhverdiev result to get $$s_(RS)\leq s_n(R) s_n(S)$$

right?

skullpatrol

22:27

@HenryT.Horton If your brain was a perfect sphere every point on it would be bipolar ;-D

Henry T. Horton

Identify antipodal points on my brain to get the real projective brain

Norbert

@mixedmath what do you think about this proof

it seems to me correct

MeAndMath

22:43

Funny!

LOL

Peter Tamaroff

@MarianoSuárez-Alvarez Ahh! What a pity! I didn't expect that! =P

MeAndMath

@PeterTamaroff Hola,Peter!

Old John

@MeAndMath Funniest thing I have seen for a long time was "What is an anagram of Banach-Tarski?"

Peter Tamaroff

@MeAndMath Hello.

MeAndMath

@OldJohn what´s the answer?

Old John

22:49

Banach-Tarski Banach-Tarski

MeAndMath

@OldJohn GREAT!

@PeterTamaroff What´s up?

Peter Tamaroff

@MeAndMath Nothing now, but today I met a field medallist.

Henry T. Horton

You never said what the talk was or who gave it...

MeAndMath

@PeterTamaroff Incredible!who is?

Peter Tamaroff

@HenryT.Horton This guy

MeAndMath

22:53

Nice!

Henry T. Horton

That bowtie... THAT BOWTIE

Jaakko Seppälä

Still unsolved. math.stackexchange.com/questions/8698/…

MeAndMath

Hey,@PeterTamaroff, tell me something,what lin.alg book do you use?

Peter Tamaroff

@MeAndMath No one at the moment. I'll finish my topology book first. People seem to praise "Hoffman and Kunze"

MeAndMath

@PeterTamaroffI have it

I think so funny Tamaroff studuying topology.

there are so many off in topology.

Henry T. Horton

22:57

What are you saying here

MeAndMath

who´s saying?

Henry T. Horton

You´s saying

MeAndMath

what am I saying?

Fortuon Paendrag

Any Algebraic Geometers around? Are there sufficient conditions for when the solutions to a polynomial in multiple variables can be parametrized?

Henry T. Horton

@MeAndMath What are you saying?

MeAndMath

23:05

@Henry About what?topology,Tamaroff?NOW,I`m not saying anything.

Henry T. Horton

About topology

MeAndMath

did you that there is a Hausdorff space in Bonn university?

Henry T. Horton

No :(

MeAndMath

In the Mathematics Institute of at the University of Bonn, in which Felix Hausdorff researched and lectured, there is a certain room designated the Hausdorff-Raum (German for Hausdorff Space).

Jaakko Seppälä

I read basics of algebraic geometry when I wrote my master's thesis but I don't know an answer to your question.

David Wheeler

23:13

i supposed married points aren't allowed in

Peter Tamaroff

@HenryT.Horton Henry.

Henry T. Horton

Henry?

Peter Tamaroff

@HenryT.Horton Could you help me with something?

Like, get serious.

Henry T. Horton

Not now

Peter Tamaroff

Just for a while.

It's quite fast. =P

Henry T. Horton

23:16

Bastardo

Peter Tamaroff

@HenryT.Horton Figlio di puttana!

Fortuon Paendrag

wow. It's getting wild in here. What are you working on, @Peter?

MeAndMath

Henry,eu não deixava...

Henry T. Horton

Gana un mundial...

Peter Tamaroff

@HenryT.Horton 78' 86'

Henry T. Horton

23:18

lol

Peter Tamaroff

@FortuonPaendrag Identification topologies.

Fortuon Paendrag

Any question in particular?

Maybe I can be of service.. :P

Peter Tamaroff

@FortuonPaendrag OK.

Say $p:E\to B$ is an identification.

Say $G:E\to Y$ is continuous.

Let $p,G$ be such that for every $x,x'\in E$ such that $p(x)=p(x')$ then it follows $G(x)=G(x')$.

The idea is to construct a continuous function $g:B\to Y$

By defining $g(b)=G(x)$ for each $x\in p^{-1}(\{b\})$, $B\in B$.

Now, I want to put that in terms of the equivalence relation $x\sim x'\iff p(x)=p(x')$

Note that $g$ will be well defined since whenever $x,x'\in p^{-1}(\{a\})$ for some $a$; it will follow that $x\sim x'$, so $G(x)=G(x')$

That's because we're defining $g$ in fact in terms of equivalence classes, right?

Fortuon Paendrag

Yes, yes. I follow that part.

This is similar to the path-lifting lemma. A more general case, I think.

So, what is your question?

Peter Tamaroff

How can the construction of $g:B\to Y$ be put in terms of the equivalence relation?

Fortuon Paendrag

23:28

I cannot think of anything..

I mean, isnt $\sim$ just establishing the structure of the quotient space

Peter Tamaroff

@FortuonPaendrag Basically, for each $x\in E$, let $\widehat x$ be its equivalence class.

Fortuon Paendrag

$g$ exists if and only if each equivalence class is mapped to the same element in $Y$ by $G$, right?

Peter Tamaroff

Those are all the points "identified" together by $p(x)=p(x')$

Sorry I misread.

Fortuon Paendrag

So, do you accept my statement?

Peter Tamaroff

@FortuonPaendrag But the equivalence class will indeed do that. Note that $x\sim x'\Rightarrow G(x')=G(x)$

Fortuon Paendrag

23:32

Ah right. I was stupid. You put that in the Hypotheses.

Peter Tamaroff

@FortuonPaendrag I'm not proving anything. Just that the author doesn't mention any equivalence relation explicitly. I think I should wait. He does it in the next paragraph.

Fortuon Paendrag

Then you basically define g as follows. if $x \sim x'$ by your equivalence relation, then $g(x)=g(x')=G(p^{-1}(x))$

Is that a construction in terms of the equivalence relation? Or is this too obvious?

Peter Tamaroff

@FortuonPaendrag It's OK. That's what the author does.

But he makes no mention of an eq rel. He is about to do it now

Fortuon Paendrag

@Peter Were you looking for something more explicit?

Peter Tamaroff

@FortuonPaendrag Nah, its OK.

Fortuon Paendrag

23:37

:)

MeAndMath

Henry got upset...

Gotta go!meal time!

user19161

@MeAndMath Nope.

David Wheeler

basically, if you have a surjection p (any surjection), then there is a "canonical" bijection between E/~ (where ~ is induced by the surjection p) and p(E).

Jonas Teuwen

I need more xmonad.

user19161

I need more wine.

Jonas Teuwen

23:41

@JasperLoy Easy!

user19161

@JonasTeuwen sudo apt-get install wine!

user19161

Hey @ben!

David Wheeler

of course, if we want to have continuity of the maps involved, that means we have to restrict how many open sets we wind up with in the image.

Jonas Teuwen

@OldJohn @robjohn Also bearded mathematician!

Henry T. Horton

It's the Duistermaat-Heckman formula guy

robjohn

23:46

@JonasTeuwen I have to read back in the transcript to get some context.

Jonas Teuwen

@robjohn There is none - other than two beard mathematicians named John.

Easy eh... If only that math was so easy.

He was a very famous Dutch one - for Dutch standards.

robjohn

@JonasTeuwen okay

Jonas Teuwen

And I am reading one of his books as we speak!

user19161

@robjohn There is no context other than who has beards in this chat!

user19161

@JonasTeuwen Which?

Jonas Teuwen

23:47

@JasperLoy And named John...

Because Hans is named Johannes (= John in English).

David Wheeler

ok, is the space compact? check. simply connected? check. do i have a beard? check. good to go.

Jonas Teuwen

Yes.

user19161

@JonasTeuwen Does it mean you should get a beard too?

Jonas Teuwen

@JasperLoy It seems like I have no other choice.

user19161

@JonasTeuwen I am not getting one, no way.

Jonas Teuwen

23:49

You are not named John and are no analyst.

Henning Makholm

@JasperLoy It's not a matter of "getting" as much as just stop actively suppressing it.

Henry T. Horton

He is an analist though.

Jonas Teuwen

@HenningMakholm He is Asian, you know...

Henry T. Horton

No beard for Jassy...

user19161

@HenryT.Horton Erm, no. I don't do that.

Jonas Teuwen

23:51

@HenningMakholm Then one needs Pokon.

Henning Makholm

@JonasTeuwen Not a hyperintelligent shade of the color blue? Aw, shucks.

user19161

@JonasTeuwen I hope to be an analyst though, but maybe a geometer.

Jonas Teuwen

@JasperLoy Duistermaat was both!

And a pretty damn good one!

Henry T. Horton

But he had a beard to contribute to his power

user19161

@HenryT.Horton I have a beard down there though.

Henry T. Horton

23:54

Yes Jasper, we know you're asian

Jonas Teuwen

A beard makes you a better mathematician. No doubt about that.

I bet @JM has a beard.

user19161

@HenryT.Horton Oh come on, even non-Asians have beards down there...

Henry T. Horton

I imagine JM has a double chin with a beard on each one

Jonas Teuwen

And I a moron if I use compiler-compilers in Haskell?

user19161

I just realized that Henning has a beard as well!

Jonas Teuwen

23:56

You know what is scary? A lexical analyser for Haskell is maintained by some dude with an @microsoft.com e-mail address.

Henning Makholm

@JonasTeuwen What is your alternative? Compiler-compilers in Visual Basic or compiler-compiler-compilers in Haskell?

user19161

@JonasTeuwen Why is that scary?

Peter Tamaroff

Why do we have do distinguish between strong and weak induction? Arent they basically the same?

Henning Makholm

@JonasTeuwen Um, Simon Peyton-Jones is at Microsoft.

user19161

@PeterTamaroff Well, sometimes in a proof we make use of one and not the other.

Henning Makholm

23:58

@PeterTamaroff Yes they are, but they are distinguished for the benefit of beginning students who cannot yet handle them as instances of the same thing.

Peter Tamaroff

@HenningMakholm OK.

Jonas Teuwen

@HenningMakholm As a double spy?

Wait. Should I go back to Lisp?

user19161

@JonasTeuwen You should just go back to your books.

BenjaLim

@JasperLoy hey

Transcript for

$Mathematics$ Mathematics