@Matt I dunno. From time to time, I do get a bit guilty about women not given their due and stuff. In my undergrad days, I was even contemplating adding my mother's name as a middle initial (my second name is my father's given name). :-)

I haven't acted on it because it seemed (seems) too radical...

That's one reason why I am a bit more careful than usual. Not sure if I am overdoing it.

I think you are. Snowperson is unnatural.

@tb ?

@Matt You would be surprised. Nothing is that unnatural if you use it two-three times. =)

@Matt I was referring to this

(but it felt out of place in between Srivatsan's comments)

snowman ---> man who appears snowy......... snowperson---> man whose personality is like snow ?

@tb I see : ) I ignore badges anyway.

@RajeshD - what nonsense is that? Why should a snowperson be a man in the first place? [Unless that's a joke. :)]

oops...i mean man/woman

@Matt sure, but they still show some appreciation.

i can't edit it now

@Srivatsan Besides complete equality would mean your date will treat you like a buddy and not like a date. Not that I couldn't live with that but I think the other way around is nicer.

@tb I think reputation does that already.

@Matt That doesn't make any sense. =)

@Matt : you are only worried about dates ?

@Srivatsan I heard that in Sweden a woman gets pissed off if a guy holds open the door for her. I can't relate to that.

@Matt Um, I see.

@Matt "I did not open the door for you because you're a lady. I opened the door for you because I am a gentleman."

In case of complete equality of gender ... I do not know what would be the right preference ?

:)

@Matt Depends, I found out that it is dangerous to follow those weird courtesy rules. I once was yelled at by an acquaintance because I entered the restaurant and then later on the bus before her (as I should)...

@JM Well I didn't mean to say I care about holding open doors or not but getting angry because someone treats you nicely is alien to me.

@tb In Sweden?

@Matt I know; I was posting that neat rejoinder I've had to use once. :)

@JM gentleperson =)

@Matt yes, in the Sweden whose capital is Zurich...

My previous comment, that was a joke though.

@tb I was planning a joke about this in the next few minutes. You beat me to it.

@Srivatsan *sbloink*

@Srivatsan Funny : D

@tb Can you elaborate though, I didn't get it. She yelled at you because you didn't hold open the door and got on the bus before her?

@JM But your comment was indeed neat. Might come in handy.

@Srivatsan I have unfortunately forgotten the provenance...

@tb Then that would make sense but what doesn't is the "(as I should)" at the end.

@Matt I didn't act as she expected but according to what I was taught... The door was held open by a waiter and I entered the main hall (slightly) in front of her --- that's the rule --- after all, I made the arrangements and I should talk to the waiter who shows me to the table, etc. After that I figured out that following the courtesy rules is not always the good thing to do...

@tb Oh I see. And that's a reason to yell at you? What a nasty date. Poor you.

@Matt well, it wasn't that bad...

(but that evening ended in a huge fight)

That sucks, t.b.

oH !

@tb Ah, so you had already passed the stage of date. I see.

@tb I still didn't get it. You didn't get yelled at because you didn't hold the door open, right? So why were you yelled at?

@Srivatsan He was yelled at because he entered the restaurant first as opposed to letting her walk in first.

and then the bus...

@Sri don't worry about such things they won't happen in India

...and they say math is hard to understand... :D

@RajeshD I'm certainly not worried. And I don't believe that this won't happen in India.

@tb @Matt : what is the point..is she Sweedish ?

@RajeshD Nothing, we're just discussing how even following norms can be troublesome...

@JM As JvN put it: "If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

(sorry couldn't resist...)

Careful...

Careful what?

@tb Some people get carried away with quotes. I don't think they're here right now though.

i know whoom you are talking about

Skull ?

hahhaha

Well, that guy ain't here, and I had a chuckle at the one time the quote was entirely appropriate... :D

No, this is a good time for it indeed.

@Matt, @tb, @robjohn: I am guessing this question is relevant to your discussion.

Is it?

@Srivatsan That is precisely the Lebesgue number

@robjohn Aw, yes. Even the comment says so.

@Srivatsan So it does :-) We were talking about that earlier today.

I'm sure I've seen that one here before. What is this space called, the comb space, right?

@tb Believe so.

This must have come up before.

Ah, I misremembered

@DylanMoreland I'm looking forward to Gerry's response to that comment...

@Srivatsan Yes, it is relevant. (As robjohn said : )) Thanks Srivatsan!

So there is an unwritten courtesy rule that states that if you go on a date then you have to enter public transport before the girl?

@Matt well, man enters, looks for an option, chooses one and offers it to the woman who can then accept or decline is a fairly general rule which applies here as well.

@tb I never noticed or realised. Can't be that general : )

@Matt o tempora o mores

@tb If you say that it'll apply to you as well. I'm not much younger than you.

Didn't intend to imply otherwise...

: D

Are you going to answer this? I was about to write an answer and then I realised that I can't actually answer it even though I should be able to.

No, I'm not. It's a bit hairy in the details and I have taken some pains to answer that OP before and didn't see too much appreciation. Also, it's one of those persons who never answers a question...

(or just once a very trivial thing compared to the questions asked)

@tb I am sure you'll love this comment: math.stackexchange.com/q/93062/13425. (See Marc's comment)

yeah, nice...

(forgot to add a smiley at the end of my previous comment)

me too :)

FF is incredibly inconvenient to use : (

: O I'm capped!! First time ever!

@Matt Congrats!

Thanks! : )

congratulations!

Thanks! : )

@Matt I saw the "Mortarboard" about half an hour ago... congrats. :)

I wish people go and upvote Matt's answers like crazy now. =)

:D

@JM Thanks! : )

@Srivatsan : D

1 down, 49 to go...

Hey Henning. Today's your only holiday?

(Re Henning's comment) Oh, Matt needs a lot more of algebra answers for that... =)

@JM Yup. And Monday.

@Matt, BTW, I did not really follow the distinction between your two approaches you mentioned. But: do you have another approach for proving the Lebesgue number lemma? Why don't you add that as an alternate answer?

Good evening.

@AsafKaragila Hey there, I just answered a set theory question : )

Hey Asaf.

@AsafKaragila Howdy!

@Matt I just saw!

@Srivatsan I wasn't proving the Lebesgue number lemma, so: no. Add what to where as an alternative answer?

@Matt Here: math.stackexchange.com/q/82240/13425

@AsafKaragila Noooo, you troll! You up voted my answer even though I'm capped : D

There's at least one more proof (explained in the link in one of the comments). I do think that this lemma deserves both proofs to b explained.

@Matt Muhaha. Congrats on capping out :-)

@AsafKaragila Thanks : )

@Srivatsan Ah, I see, you're asking me to write up one of the proofs in the comments? I can have a go, I guess...

@Matt Well, I meant to say: I know there's at least one more proof since a comment links to them. Of course, if you have a third proof, that will totally be great.

@JM: rendered and added to my old avatar :-)

@Matt, But if you writing it as an answer, write it tomorrow =)

hi

@Srivatsan I doesn't matter so much. I'd like to re-establish the balance between questions and answers of mine.

@VVV Hi VVV.

@Matt What does that mean? More questions or more answers?

@Srivatsan But you're right. I'm a bit tired now.

@Srivatsan I've asked more questions than I gave answers. So I'm catching up with answers.

I have changed my avatar for the holidays again. You may need to refresh to get it :-)

@robjohn The sweet mean square? Or what do you call this work of art? : )

@robjohn Mean and festive. Great! :)

Festivus?

@Matt OK. If you would like to take a shot at it, then please do. I am asking because otherwise I want to add it (just so that both proofs are there in that page).

Who are you??? Frank Constanza?

@Srivatsan Then you should do it. I'll read it and up vote it. I am quite tired right now.

@JM Took a bit of doing to get the rectangular candy-cane and then to merge with the old avatar, I had to figure out how to make Mathematica output transparent backgrounds.

OK. =)

I'm thinking that the ordinal question may be a partial duplicate.

I have answered similar questions before somewhere on the site.

@robjohn Oh, that isn't a Lamé curve that you used as a "torus" base?

@JM no, its four quarters of a torus connected with four cylinders.

@JM How do you use a curve as a torus base?

Well, have a look at equations 2-4 here first.

The $\cos\,u$ and $\sin\,u$ portions are replaceable with some closed curve.

Those are essentially the parametrics I used for the torus

:2802655 it also removes some of the extra space around the '-' sign:

I didn't see the expected difference :(

$a-b$: $a-b$ vs $a{-}b$: $a{-}b$

If you want to vary the cross-section, you can change the $\cos{v}$ and $\sin{v}$ sections as well.

@robjohn yes, that's because {-} is no longer interpreted as operation but as a mere math symbol

@JM Well, that is pretty much what I did, but I changed the pieces by themselves with cut and paste.

In any event, I see no seams! :D Beautifully done.

Yes, I agree with that. It looks very nice.

@JM That would mess up the candy striping on the cylinders to do it that way, because the cross sections are radial instead of horizontal and vertical.

@robjohn Yeah, that's a caveat.

@JM I would also think that the cross sections would be slightly elliptical on the cylinders near the corners.

@JM: you probably don't have TGIFriday's restaurants there, but their logo has red and white stripes in it. My wife and I were noticing the candy-cane-like nature the other day. My avatar could almost be considered and advertisement for them.

@robjohn Actually, there's a franchise for them here, but the food is a bit expensive, considering the portions... :D

@JM I made the sides just long enough to be 3 cycles of the swirl.

Indeed, that looks as if it took a fair bit of parameter tweaking!

@JM I get BOGO coupons from them (buy one get one free) so even if they are a bit expensive, it becomes quite reasonable.

No promo like that here, unfortunately. I fondly remember the chocolate mousse and the mud pie I had there...

You chocolate fondue remember a mouse?

Heh.

Anyway, I think this is it for me. Later, you guys...

@JM the antlers get in the way, I've noticed.

@JM: good night.

I have to leave soon to take my son shopping.

I fear the malls with my cold. :-(

We must only fear fear itself!

@AsafKaragila I can't fear disease ruining my Christmas?

@robjohn Fine, I'll make an exception this time.

@AsafKaragila Whew! that takes a load of worry off my mind. :-p

@robjohn Nice avatar!

@robjohn This is my Christmas present to you ;-)

@AsafKaragila Thank you. I will remember you while at our celebration :-)

@DylanMoreland Thanks, I spent a bit of the morning rendering and merging it with my old avatar :-)

Does anyone know anything witty to say to someone who's told you that they're in an open relationship to brush them off?

@robjohn I'm like Santa Claws.

@Matt "Get the f*ck away from me, whore."

I can only deal with people in a nice way if I don't mind them or like them.

@AsafKaragila That was a name we were considering for our kitten for the holidays :-D

@AsafKaragila That's not witty at all.

@robjohn Nice. Call him Satan Claws if he's being mean ;-)

@robjohn Cute : D

@Matt I am closed to open relationships...

@Matt Well... yeah.

@robjohn Good : )

@Matt The chances that a random person would get the reference is minimal, however.

@robjohn Maths major.

@Matt No problem then :-)

So that person is a math student?

Ooh, my new avatar looks great with a snowman in the corner :-)

Yes, or at least I think so. I didn't ask and I don't know their name because I'm not interested in knowing anything about them at all. As a matter of fact I already have much more than I wanted.

How about "Your open relationship is not this person's neighborhood."?

@Matt the fact that they are in an open relationship, for example...

@robjohn That's what I was saying.

Here is what my avatar looks like with a snowman: i.sstatic.net/cAdcO.png

@HaskellElephant: what is a Haskell Elephant, may I ask?

@HaskellElephant: Hello, btw :-)

@robjohn From a distance, the snowman looks like a pipe in your gravatar's mouth.

@Srivatsan Just reading it now and noticing that I still had the arguments messed up.

@Matt Which one?

@Srivatsan Ack, doesn't he know that is bad for his health?

@Srivatsan The Lebesgue number lemma one.

@Matt Yeah, we were talking about that proof and another method that avoids the need for that lemma.

@robjohn What can I say? The mean square likes his smoke. =)

@Srivatsan when he blows smoke rings, do they have corners?

@Srivatsan more importantly, are his smoke rings commutative and do they have zero divisors?

@tb what would a chameleon badge be for?

@robjohn changing the name x times.

:2803262 Ah, or perhaps your avatar. He was talking to JM I think.

@tb Yes, I noticed you were talking to JM :-)

@robjohn (JM asked what the previous usernames field in the profile was good for) but it occurred to me later on that avatar change would be more apt.

@tb The only person I know of who has changed their name is Skullpatrol.

@robjohn I did too (it wouldn't be proper to reveal others)

@robjohn There are others too...

@tb Oops... I probably shouldn't have said what I did.

So, I need to start Christmas orgy-ing, see you all later

The trouble is when somebody changes their name, all existing @Addresses in comments become orphans.

That's right. It shouldn't be encouraged. I think it's a good idea that they allow you to do this at most once a month, which is already a lot.

@HenningMakholm Yes, they should perhaps make @HumptyDumpty point to HumptyDumpty's account directly, so that this will change automatically.

That kind of happens in chat when you reply to a particular message. [Yet another advantage of replying to previous messages. Yay!]

@tb E.g., JM's old name persists in many places till date.

[Ah, there is another example of someone who changed their name, @robjohn.]

Okay, FF 3.0.6 does not like snowmen at all: henning.makholm.net/misc/snowman.png

@HenningMakholm I have noticed that.

@tb Have fun! : )

@HenningMakholm Yikes, he doesn't look well.

@HenningMakholm Woah! that is bizarre...

@HenningMakholm I have Firefox 3.5.15, which is pretty old in itself, but it renders the snowman properly.

@HenningMakholm Ouch! the current version is 9.0.1!

Perhaps I ought to upgrade. Still running Debian "lenny" here.

@robjohn , sorry for going away without answering you earlier!

@HaskellElephant no problem; we all have to go afk from time to time.

@robjohn , my inspiration for the name comes from Haskell Curry, and well Elephants, thats pretty self explainatory (elephants are awsome).

@robjohn , and "learn you a haskell" has an elephant on the front =D learnyouahaskell.com .

@HaskellElephant Holy shit! It says "H*ly Sh*t" on that page

Hi

@QED hey there

Hello there.

hi folks

@Bullmoose what's up?

hey @robjoh n

Hello

deriving the variance of a entropy of a Gaussian r.v. and got this nonsensical answer

3/4 + (1/2) log (2 pi sigma^2)

I think there is either a minus instead of a plus or sigma^2 missing in front of 3/4

argh

heh

Answers that don't require you to think are good too.

don't think that gets as many votes though

hi

@VVV

QED i can't read your message

test

hmmm

this is very strange

(the variance of the entropy)

I'm gonna post it as a question

just write out all the definitions and calculations in full

the mistake will become obvious

oh!

@Bullmoose What's the question, exactly?

trying to derive the variance of entropy

Your answer does not make sense "dimensionally"...

(and if you don't spot the mistake in doing that, it just means you've written all the details of your question comprehensively)

yeah

Bullmoose, have you got this bookmarklet (for MathJax support in chat) installed?

no, i don't know how to do TeX in chat

but i think i'll just write it up a question

one of two things will happen

OK.

1) I'll spot my mistake

The easiest way to get to the installer page is to go to my profile and click on the $\LaTeX$ Support for Chat link.

2) someone will get a credit for spotting my mistake

Off to run errands, and spread my cold. bbl

Going to be afk for a while. @Srivatsan I had to have dinner, I'll read and up vote the Lebesgue number lemma proofs later.

Huh... Hugh Laurie is OBE.

@Matt Sure.

this is a test of @robjohn's MathJax code $$f(n)=\mathcal{O}(\sqrt{n})$$

and it works... wow, @robjohn is the man!

@AsafKaragila That's not exactly a hot-off-the-press news, is it?

@Srivatsan Hitler was a Nazi!

@AsafKaragila Now that is hot news, yes.

I call Godwin. Asaf has lost!

What does that refer to, Henning?

Look at the problem please: math.stackexchange.com/questions/92962/…. Simple proof until no.

@Srivatsan Godwin's Law

@HenningMakholm Aw right. Thanks.

@brainail, you didn't like the answers given?

@HenningMakholm That seems too creepy actually, considering that Asaf could've picked pretty much any random fact: like my favorite "Lincoln was the 16th President of the US".

e^(-x^(2))

it can be calculated by

differentiation

the integral

is that right??

"creepy"?

@brainail I didn't understand what you meant. Did you mean that you want a simple proof? Do you have any reason to believe that there's a simple proof?

@HenningMakholm Creepy that Godwin's law worked here.

hi again folks

hi

@Srivatsan I think it fits the definition. This is an online discussion, and Asaf made a comparison that involved Hitler or the Nazis (namely, comparing the hot-off-the-pressness of various facts).

@QED There are not all obvious...

@QED i think i spotted my mistake writing the derivation of variance of entropy of Gaussian

@brainail, it would probably be better to try to understand one of the answers than finding a new one: Even if it means learning new stuff

@Bullmoose, excellent -

the interesting part is that it doesn't depend on the variance of the distribution....

i wonder why that is...

@HenningMakholm Yes, I agree that Godwin's law worked out to be right. I am just saying Asaf had a lot of choice (no pun intended) of random facts , and yet he managed to choose an allusion to Hitler. Which I find interesting.

Perhaps this is what happens in every online forum, I do not have much experience with that.

@Bullmoose Dimensionally it makes sense that it does not depend on the variance.

@QED I understand the proof of Andre. There was a non-obvious moment. Okay I will wait.

@Bullmoose After all, $\sigma$ is the only parameter (assuming zero mean), and entropy is dimensionless, so we will expect that the entropy is proportional to $\sigma^{0}$.

wait for what?

@QED The source is to explain to me confusing things.

you could ask a new question about those specific things

Hi guys! Do you know what has happened to planetmath planetmath.org? Haven't been able to access it for quite a while.

@Tim Everyone seems to have a problem with that site currently. Not sure for how long.

@Srivatsan Thanks for confirmation! By the way, if you are interested, I just saw Iyengar appearing as a donor for Wikipedia in the banner of one Wiki article. Here is his personal appeal wikimediafoundation.org/w/index.php?title=L11_1215_AI/en/…

@Tim It's like saying all Tim's are the same person. =)

ok, that makes sense

@Srivatsan ah oh? Are they two different persons?

thanks @Srivatsan

@Tim In fact, from the name "Akshaya", I'm guessing this is a lady. And I would guess that iyengar is not a software developer although I have no evidence for this claim.

I've got a new Talisker.

Jerk.

Hi, people, is the formula for finding for roots in higher degree irreducable polynomial (>5) always expressed in a very complicated way if you express it in integral?

@Victor, what integral?

@Victor Are you asking if all polynomials can be solved if we allow complicated functions involving integrals (and stuff)?

@QED -i don't know this, but hyperelliptic integral

where?

@Victor I do not know the answer to your question, but have you looked at Bring radicals? They can solve fifth-degree equations at least.

@QED - In the very last slim chapter of the book called "Beyond the Quartic"

mm

I didn't read that

@QED -It say this method were given by Hiroshi Umemura in 1984, is it consider advanced?

well it's not something I know about

Sounds interesting though

@QED - Take a look at the bottom: library.wolfram.com/examples/quintic/timeline.html#part3

nice

Also, is math consider a milltary secret in US especially in polynomial, i think it were not open to the public, so it "improve" slowly

@Victor I'm sure that is not the case. I am pretty sure this will not be of much interest to the military.

[Although I cannot back up that claim..]

@Srivatsan - How come you get that intuition?

@Victor These results are of theoretical interest mostly. If you want to (say) solve a fifth degree equation in real life, these things will be very slow (even if they give meaningful results at all). In contrast, numerical methods are usually waaay faster.

@Srivatsan - Can you set the accuracy of the numerical method, or the acuracy is fixed?

@Victor It might depend (and I am no expert on this). But my guess is that the accuracy can be tuned.

An even more interesting question is: given an accuracy, how many steps/iterations (or time if you're running it on your computer) the method takes. And there are also issues like stability of the method, and so on.