Mathematics - 2011-10-21 (page 2 of 3)

robjohn

10:00

@Gortaur Buddha doesn't answer math questions?

Gortaur

@anon sorry, I didn't get what did surprise you

robjohn

I should stop with this line of convo, I don't want to offend anyone (if I haven't already)

anon

I don't know, I just never think of that many questions to ask

Asaf Karagila

Well you can't offend me.

Firstly, I'm not part of this conversation :P

Gortaur

the ghost again, heh

anon

10:02

I really don't care /atheist

Asaf Karagila

Atheist or agnostic?

robjohn

@AsafKaragila especially at lunch time

anon

@Asaf: semantics

Asaf Karagila

@anon: Not at all.

Atheists have an answer. Agnostics don't.

robjohn

@Gortaur that reminds me, I should refresh my chat window

there, no ghosts.

Asaf Karagila

10:04

Also, the use of "semantics" is ridiculous. To say "it is a semantical difference" is to say it is the same word with a different meaning. Also in this case it is also syntactic as the word is different.

Rajesh D

hello @Asaf

Asaf Karagila

Hi Rajesh.

anon

Otherworldly affairs wouldn't surprise me, but religions appear very artificial and man-made to me upon inspection. But - these days especially - the word "atheist" is more and more being taken to simply mean nonbeliever (i.e. atheist and agnostic are orthogonal qualifiers)

Rajesh D

@Asaf : What is your current stand on my question about a picture ? Do you still stand by the closing decision ?

t.b.

I'm a convinced agnostic. I'm also agnostic towards agnosticism...

Asaf Karagila

10:06

@Rajesh: I do. I don't think it has a mathematical sense to it. I don't think it is similar to the music theory or the cloth questions either. These questions were immediately transported into a purely mathematical realm, while yours do not leave the physical realm.

@tb Sounds a lot like me. I am agnostic towards my very own existence.

Rajesh D

ok

Asaf Karagila

I see that the question is now open again.

robjohn

@RajeshD: what about pictures?

Asaf Karagila

I do not intend to vote on its closing again, though.

robjohn

@Asaf what question?

Asaf Karagila

10:09

As I am not that adamant about it.

@rob: If I tell you, I will have to link you.

There you go: math.stackexchange.com/questions/71734

Oh, also, @rob, I was wondering... under what license does that logic software of yours is distributed and who owns the copyrights?

robjohn

@Asaf: the copyright is held by The Regents of the University of California, since I wrote it while working at UCLA.

t.b.

@Asaf: I think you can't vote to close again, anyway

Rajesh D

@rob : this one math.stackexchange.com/q/71734/2987 @Asaf : I agree with you to some extent, but not able to kill my curiosity to know an answer for it in mathematical terms.

anon

I think it was transported into the mathematical realm well enough

t.b.

It's an excellent answer by Willie, probably one of his best after his take on relativity

Asaf Karagila

10:13

@rob: Is it free, more than free (BSD/GPL/etc.) or does it cost money?

robjohn

@Asaf: I think the license is GPL or a derivative of it.

Asaf Karagila

Oh good.

robjohn

@Asaf: it is free.

Asaf Karagila

Well, I have to go and buy some groceries now.

robjohn

It should be specified on one of its webpages.

t.b.

10:14

Oh, I forgot about his answer on the classification of nonlinear pde

robjohn

@Asaf: shop well ;-)

Gortaur

:D

Asaf Karagila

The important thing is that we have established a real difference between agnostic and atheist, and this is indeed a semantical difference, but also syntactical.

I have to decide what crazy marinade I am making for tonight's chicken :P

robjohn

I don't know and I don't care. :-)

Apatheism

Apatheism (a portmanteau of apathy and theism/atheism), also known as pragmatic atheism or (critically) as practical atheism, is acting with apathy, disregard, or lack of interest towards belief or lack of belief in a deity. Apatheism describes the manner of acting towards a belief or lack of a belief in a deity; so applies to both theism and atheism. An apatheist is also someone who is not interested in accepting or denying any claims that gods exist or do not exist. In other words, an apatheist is someone who considers the question of the existence of gods as neither meaningful nor rel...

This is not neccessarily the view of the poster

t.b.

Didn't know about that term. Good to have yet another label ready :)

J. M.

10:18

Nope, he doesn't care about apathy at all...

Rajesh D

@t.b. : I am not fully convinced with Willie's answer with the use of Fourier space (spatial frequency)....i have given a example image which is a bit nonstationary..having stripes only on the upper half of it.....anyway waiting for Willie's comments......

FT it doesn't have the localization capability

J. M.

@robjohn If you can remember only two theorems for differential geometry, that'd be TE and Gauss-Bonnet...

Rajesh D

@rob thanks for the link to Theorema Egregium, seems like truly inspiring

Asaf Karagila

Well. I have a few more minutes.

robjohn

@JM Those are two of my favorites from DG

J. M.

10:26

@Asaf: Why not have your lady pick the marinade, if you can't decide?

t.b.

I'd throw in the Sphere Theorem and Cartan-Hadamard

robjohn

@JM sort of the 2 and 3 dimensional versions of the same thing, and the fact that TE is intrinsic points out that there is something interesting going on.

J. M.

Yep yep.

t.b.

Mostow Rigidity is pretty amazing, too.

I'll stop now.

J. M.

@t.b. I gotta confess, I don't know where differential geometry ends and Riemannian geometry begins... but I suppose there's no point in drawing a line. :D

robjohn

10:32

@JM It stops at the boundary of the Klein bottle.

Asaf Karagila

@JM We'll go to the store and see what's available, then we'll see who decides what. I usually do these things as a spur of the moment.

J. M.

@Asaf: Impulse buying... I approve!

Asaf Karagila

:P

robjohn

I keep all my important ideas inside a Klein bottle.

Asaf Karagila

I wrote them on a Moebius strip.

robjohn

10:34

@Asaf: on the back?

Asaf Karagila

Where else?

J. M.

@Asaf, I said "I approve"! It's what I do when I don't know what to cook for dinner...

Rajesh D

@rob : what is a Klein bottle ?

Asaf Karagila

It's a 3-D Moebius strip, so to speak.

robjohn

@J.M.: when you don't know what to cook, read some of my answers :-D

t.b.

10:35

@rajesh: kleinbottle.com

robjohn

Klein bottle

In mathematics, the Klein bottle () is a non-orientable surface, informally, a surface (a two-dimensional manifold) in which notions of left and right cannot be consistently defined. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a Klein bottle has no boundary. (For comparison, a sphere is an orientable surface with no boundary.) The Klein bottle was first described in 1882 by the German mathematician Felix Klein. It is sometimes claimed that it was originally named the Kleinsche Fläche "Klei...

Asaf Karagila

@rob: He doesn't cook, he makes dessert. :P

Well, now it's time to go.

J. M.

Okay, this time t.b. beat me to it... :D

t.b.

Ha! Once in a lifetime achievement, I presume :)

robjohn

@Asaf: if he approves when reading my answers, I don't care if he makes dinner or dessert :-)

J. M.

10:36

@Asaf, I can't just be eating dessert all day, man. :P

After looking at that Klein page again, I see they did the more difficult embedding...

robjohn

@t.b.: a friend actually gave me one of those klein bottles for my birthday from Acme.

I have it sitting in a display case in our entry hall.

t.b.

And I assume that you fill it with your ideas ?

robjohn

that's where I keep the best ones I have.

J. M.

Talk about "stuck knowledge"...

Gortaur

@JM: good evening

J. M.

10:46

(since I'm forgetful about times) Good day, Gortaur!

Gortaur

Have you guys seen the picture about how people in science see each other?

just for the case labspaces.net/blog/1444/How_people_in_science_see_each_other_

J. M.

I love the diagonal elements...

t.b.

the last two lines are pretty nice, too. Thanks @Gortaur

J. M.

...and I sympathize with the technician's viewpoint.

robjohn

That is really funny. I tried to upvote, but it didn't work.

J. M.

10:51

@rob: Oh no... :D

Gortaur

what?

robjohn

Perhaps I've been here too long. My wife didn't understand when I upvoted dinner.

Gortaur

I think she should be happy about it, no?

robjohn

If she understood, perhaps.

Gortaur

@tb you're welcome. some guy put it on the whiteboard in our control room - I've found it funny and of course I liked how postdocs see professor

robjohn

10:53

She doesn't hang out on SE.

Gortaur

@robjohn your luck )

robjohn

@Gortaur: and how the profs see the grads

J. M.

Speaking of upvoting things you can't upvote... xkcd.com/77

(not exactly the same issue, but similar)

Gortaur

let me find one...

yayu

i am sort of stuck on part of a derivation for a while..

would any of you guys want to have a look?

(matrices, algebra)

t.b.

10:55

I'm all ears

Gigili

Anyone knows about Galois theory here?

Hello.

yayu

I have three marices... J1, J2, J3... '

Gortaur

@JM yeah, there is one in English: xkcd.com/386

J. M.

Let's make a queue. yayu came first, so Gigili, can you wait?

Gigili

I read this but I didn't understand it well ...

@JM Of course. thanks.

robjohn

10:57

@Gortaur That is why I never sleep :-)

yayu

Gortaur

@robjohn pity yourself, it's 3-57 now in CA

J. M.

(I hope you understand, it'll be messy to talk about linear algebra and Galois theory all at once... ;) )

yayu

ok.. i think i can do this without tex.

J. M.

@yayu: you did bookmark the CodeCogs LaTeX renderer, no?

Gigili

10:59

@JM I understand, you're right, it's okay.

yayu

yeah.. but i am in my opffice

although its am right now.. so i can enjoying being in the cabin but not actually working

robjohn

http://latex.codecogs.com/gif.latex?

yayu

(for what im paid, ie)

t.b.

@JM I'm always a bit puzzled when I see Akito ask a question, thinking: "why on earth, didn't Jeff say he didn't like maths"

yayu

so we have three matrices with these commutation relations, and we construct two new ones...

Asaf Karagila

11:01

Okay. Pomegranates.

yayu

Asaf Karagila

Tonight we're going with chicken marinated in pomegranates and whatnot.

yayu

Everything is fine... except that in one of the intermediate steps... they use

J. M.

@t.b. Quite peculiar. I can't see why they like that icon so much.

Gortaur

@AsafKaragila they're focused on application of Galois theory in linear algebra, so our offtopic may be a bit confusing I guess :-x

yayu

11:02

which appears wrong to me

but is crucial to the derivation

Asaf Karagila

@Gortaur I am Koenig, my word is the fine either way.

t.b.

Let's check: start by expanding the left hand side

Gortaur

@AsafKaragila at the time of Bismark, Koenig didn't mean so much )

yayu

Ill try to post my working here... a couple of secs

that might be easier to point out mustakes

Asaf Karagila

Well, good thing this is not the time of Bismark.

Gortaur

11:04

@AsafKaragila it is. He united Germany so his time will never finish

Asaf Karagila

Yeah, and Stalin and FDR split it again after Hitler.

J. M.

"Follow the Moskva\Down to Gorky Park..."

Asaf Karagila

Screw The Scorpions!

Gortaur

@AsafKaragila and it was united again

J. M.

@Asaf: Why did I know you'll say that... :D

robjohn

11:07

@yayu: that would seem to imply that J_- J_+ = 0

Asaf Karagila

@JM Because you quoted them? :P

@Gortaur Doesn't count.

Gortaur

* facepalm *. Somebody is wrong in the Internet )

Asaf Karagila

Yeah, you are.

anon

gets out the popcorn

J. M.

There's a certain picture of Bruce Lee that comes to mind...

yayu

11:09

@robjohn yes, but the derivation crucially relies on it

Gortaur

I remember when we were kids, the arguing meant only yes it is, no it's not, yes it is, no it's not, yes it is, no it's not,

robjohn

oops, negate that

yayu

i am typing up the working..

Asaf Karagila

I remember when Monty Python used that in the argument clinic sketch.

►

Gortaur

and I was quite surprised when I gone to school that arguing can be different from it.

J. M.

11:10

@yayu: if it's very long... I think it's better on the main site than the chatroom.

robjohn

That's contradiction.

yayu

and taking the commutation suggest that the relation is probably wrong

J. M.

Okay, so the imaginary parts are the commutators...

yayu

I did not take the commutation, just did the expansion... so [J+,J-]=J3 according to this

robjohn

@yayu where do the 1/2 factors enter?

yayu

11:15

ill state the relevant page in the book too

ahh forget about those, sorry... they were rovided in the definition which i omitted while writing here

as they wouldnt change anything much, sorry

Asaf Karagila

Monty Python are awesome.

robjohn

So J_+ is 1/sqrt(2) times what you gave?

yayu

yes

robjohn

@Asaf: I agree!

Asaf Karagila

Not like you have a choice... you're married.

Gortaur

11:17

)))))))))))))))))))

yayu

Does anyone else finds Monty Python's humour hard to get because of the thick accent...

Asaf Karagila

Nope.

J. M.

Not really. It's not Cockney or anything...

If yayu's done... @Gigili?

yayu

On page 58 here: mural.uv.es/rusanra/…

i think he uses this in 3.11

and 3.13

unless i am mistaken and confused otherwise

J. M.

Oh, not yet done... so yayu, you have all that, and you want the commutator of J_+ and J_- in terms of J_1 and J_2? Did I understand you correctly?

yayu

11:21

no...

somehow, J+J- = [J+,J-]

robjohn

It seems to me

yayu

yes, thats what i got too

Asaf Karagila

@JM: The bread I bake is quite heavy to digest, how do I make it somewhat lighter?

J. M.

@Asaf: I presume it didn't rise much?

robjohn

@AsafKaragila Slice it thinner?

Asaf Karagila

11:23

No. :\

Gigili

@JM I'd appreciate if you could explain the "The permutation group approach to Galois theory" part of the link to me

Asaf Karagila

@robjohn When you bake a small loaf for just one meal the thickness of the slices plays no actual role :P

robjohn

just a thought :-p

showering chickens, now role-playing with bread

J. M.

So far as I can tell you either killed the yeast too quick or didn't leave it long enough to rise... I'm not there so it's a bit hard to diagnose.

@Gigili: Yeesh. Permutations are one of the things I'm unskilled at. Sorry... :(

Asaf Karagila

@robjohn I am not showering the chicken. Just bathing :P

@JM I'm guess perhaps both. It did rise during the baking though.

robjohn

11:25

oh, sorry, my mistake.

Asaf Karagila

It was quite dense though.

Gigili

@JM Oops.

ks0830

I'm hungry

J. M.

Well sure, not enough gas from the yeast and/or the baking powder.

ks0830

Can anyone help me?

I need help

J. M.

11:27

@ks: is it quick, or would you need a lecture?

ks0830

I'll link you

0

Q: How Can I Reform This Sequence?

One of my friend asked me for help with this floorly sequence, but I also can't figured out for the solution what he wants. There is the sequence formed with four floor function which looks very unusual. I asked him for the sequence's meaning but he'll divulge it later when I found the solution. ...

Asaf Karagila

@JM I should feed them cabbage or something.

J. M.

@Asaf: which "them"?

ks0830

chicks

J. M.

@ks: what exactly was not helpful about Brian's and Phira's?

ks0830

11:29

no

they were helped

but, what I need is to find $\Phi$

J. M.

Okay, what then is your worry?

ks0830

Phi's general term

I think

J. M.

I'm sure they're looking at it. Give them time.

ks0830

Phi would be log increasing

Asaf Karagila

@JM These amoebas that need to give more gas :P

ks0830

11:31

Ok

J. M.

@Asaf: Yeast won't live on cabbage. Mold does.

Asaf Karagila

@JM Can I use mold to bake bread?

J. M.

Anyway, lengthen the kneading time to help with adding more air into the dough.

@Asaf: No, but you presented the cabbage idea... :P

Asaf Karagila

@JM I don't like cabbage. I am not a rabbit or a turtle.

yayu

must i come to the conclusion that 3.11 and 3.13 steps are wrong?

Gortaur

11:33

@AsafKaragila who do you drink vodka then?

Asaf Karagila

@Gortaur I don't drink vodka either.

J. M.

He's loyal to arak... :D

Asaf Karagila

And scotch.

Gortaur

@AsafKaragila that explains

Asaf Karagila

Yeah. I guess vodka wrecks enough of your body so cabbage doesn't matter anymore.

robjohn

11:36

@yayu just a minute...

ks0830

@robjohn hi

robjohn

@yayu: 3.6 is what I posted above.

yayu

yes..

robjohn

I don't see it. Unless J_3 acts the same as J_1 J_2

yayu

that cannot be... because J_3 was chosen to be diagonalized

and since it doesnt commute with J1 and J2,

they cannot be diagonal

this is stated in 2nd last sentence of page 56

Asaf Karagila

12:03

►

I wonder if modern fish can run IBM software.

J. M.

Has chat always supported YT embedding?

Asaf Karagila

Apparently, maybe.

robjohn

@yayu: is there any reason for that to be 0?

@JM it isn't really embedded, it is just linked with an image.

@yayu: good luck. I have to wake up the house and walk the dog in a while. I may be back before the walk, but check out the second image and see if it needs to be 0 for some reason.

J. M.

@robjohn So it is! I wonder how balpha and Marc pulled this off...

Holy everloving... Didier is up to 46? Too bad he couldn't have been a "Guru"...

J. M.

12:35

...but he is now a "Populist". Wow.

Asaf Karagila

I have decided to postpone the cooking for tomorrow.

We just hung laundry to dry, and frying stuff will get it all smoky and whatnot.

I just know you all care so much :D

J. M.

Good decision.

Explorer

@JM Drogba?

J. M.

All told, Didier's answer is the most profitable answer ever.

Asaf Karagila

Which answer?

J. M.

12:38

@Explorer: Yes? What were we conversing about?

@Asaf: "W".

Asaf Karagila

Hah.

Explorer

I thought you were talking about Didier Drogba!

J. M.

Oh, no. Didier is one of the members of math.SE, who just posted a most fabulous answer.

Asaf Karagila

I think that the most elusive badge is Reversal.

J. M.

which has caused him to cap yesterday and today.

@Asaf: That kalle-numbers bit was strange, but it did get Elliot a Reversal.

Asaf Karagila

12:40

Yeah.

J. M.

Methinks it might be easier to get a Reversal on meta... :D

Asaf Karagila

Haha, yeah.

J. M.

"Unsung Hero" would be acquirable on SO; here not so much...

Asaf Karagila

Yeah most gold badges are unfeasible here, but Reversal, apparently... :-)

J. M.

I'm surprised Chris got "Tenacious" myself...

Asaf Karagila

12:45

Yeah.

I wonder when I'll be a Copy Editor.

The data.SE queries are just inconsistent.

J. M.

I've forgotten how to count valid edits myself...

Asaf Karagila

Oh well.

Wanna place a friendly wager?

yayu

@robjohn i tried but couldnt see any reason. though that is the only way that step could be true... it is harder to see when he uses the same thing again in 3.13

J. M.

@Asaf: Sorry, was on the phone. Wager?

Asaf Karagila

@JM Yeah, what is gonna happen first? You hitting 20k or me getting Generalist? :-)

J. M.

12:57

I've been dry the past few days, so I'm not sure if I can end this month with 20k. On the other hand... :D

...I can't help but feel you have something up your sleeve to propose that. :P

robjohn

Asaf Karagila

Just bored :P

Also, I just realized something very awesome.

Olive oil is the blood of olives.

robjohn

OLIVE KILLERS!

J. M.

@Asaf: ...you can put it that way, yes. :D

Mmm, olives...

I like them on my pizza, my pasta, and my vodka...

Asaf Karagila

I like my vodka from a Klein bottle.

J. M.

13:10

I must step out for now. See you guys in a few.

Gortaur

13:56

Incredible. @robjohn, you've spent the whole night here

Asaf Karagila

Oh man, I can't wait for a day or two from now.

Gortaur

@AsafKaragila we say it simply 'weekend'

Asaf Karagila

Well, it's not that.

I just want to vote for deletion this question...

Gortaur

@AsafKaragila which one

Gortaur

14:18

@JackSchmidt: hi Jack

Jack Schmidt

hi

Gortaur

can you help me about a projective space P1?

Jack Schmidt

maybe, feel free to ask. I'm grading for midterms at the moment, so response might be slow

Gortaur

ok, so first - I imagine it like a half-circle without one boundary point

I hope that's nice imagination - but certainly e^{i pi x}:[0,1)->P1 is not a homeomorphism

and I would bet that [0,1) and P1 are not homeomorphic

because in P1 the 'end points' (in my thoughts of it like a half-circle) are 'glued' - so P1 should be homeomorphic to the circle S1, but I guess it's wrong and cannot find a intuitive explanation for this fact

@JackSchmidt: so I will be happy if you could help me with this question in the case you have time

Jack Schmidt

14:36

P1 is homeomorphic to S1, you are right. It is not homeomorphic to [0,1) because as you say 0 and 1 are glued. I think this is one of the early examples of a quotient map

Gortaur

yes, it is

Jack Schmidt

P2 is not homeomorphic to S2, but P1 and S1 are

Gortaur

ah, ok - nice. But why does in happen with P2 and S2?

Jack Schmidt

I'm not sure. I think it is very weird that if you "unwind" P1 (thought of as the two half-circles identified with each other) to S1, it actually is still homeomorphic. I think almost always, if you "unwind" a space (take a covering space), the unwound one is not the same as the wound one.

Gortaur

why are you talking about unwind argument?

to show me that P1~S1 is just one case of such logic?

Jack Schmidt

14:41

to show that P1 ~ S1 is one case of that logic, but that it is a very special case where two things are equal that should not be

Pn is Sn with opposite points identified. Pn is a very different space from Sn, except when n=1.

Gortaur

thanks a lot. that means that the logic I've applied is dangerous

may I ask one more question?

Jack Schmidt

sure

Gortaur

about the cone. CS^n~B^n or to closed B^n?

Jack Schmidt

(I don't mind questions; I am just busy and not very good at topology.)

Gortaur

I see

Jonathan Gleason

14:46

im pretty sure the cone of S^n is B^{n+1}

Jack Schmidt

If we took the center of the sphere as a cone point, then the (immersed) cone would definitely be B^n. However, we are supposed to take the cone point somewhere completely independent

Jonathan Gleason

or D^{n+1}

Jack Schmidt

sorry B^(n+1) thanks Jonathan :-)

Jonathan Gleason

np

Gortaur

sorry, sure

Jack Schmidt

14:46

definitely works for n=1

(both in topology and pde, i always annoyed my professors and failed to understand, because i always checked n=1 first)

Gortaur

but then the cone is (S1 x [0,1]) / (S1 x {0}), right?

Jonathan Gleason

hah well that's how i determiend it was n+1 and not n

i just thought of the cone of S^1

mhm

a cylinder, where you collapse the bottom circile to a point

Gortaur

right

but the interval [0,1] is closed

Jack Schmidt

@Gortaur yes. I think the second coordinate is "r" and the Sn coordinate is the "angle", and the cone is just "the ball in polar coordinates"

when r=0, all angles are the same, so we quotient by (S1 x {0})

Gortaur

so intuition tells that the S1 x {1} goes into the 'boundary' of closed B2

Jonathan Gleason

14:49

yup

Gortaur

yeah, but r may be equal to 1 then, right?

and the ball is closed rather then open

or am I missing something

t.b.

do it geometrically: embed your sphere into R^(n+1) and connect the point (0,...,0,1) of R^(n+2) to each point in the sphere. Then squish the whole thing flat down to R^(n+1)

@Gortaur it definitely is compact (it's a quotient of a compact space)

Jack Schmidt

oh

Gortaur

thank you, @tb

Jack Schmidt

@Gortaur: yes, by B^n we all mean the closed ball, also known as D^n

Gortaur

14:52

ah, ok

then there is a typo in the new version of Lee

robjohn

D^n whose boundary is S^{n -1}, right?

Jack Schmidt

@robjohn yes.

Gortaur

as I understand it, yes

because he denotes D as \bar{D}

robjohn

I have to find out from people asking questions what they mean by S^n. Sometimes they really mean S^{n-1}

@Gortaur and D is the open disk

Gortaur

D is the closed disk

stop

robjohn

14:55

but then why \bar{D}?

t.b.

Usually D denotes the open disk and \bar{D} the closed disk.

Gortaur

@JackSchmidt B is open, D is closed?

t.b.

I don't know about Lee's conventions, though

Gortaur

in his book: B is open, \bar{B} is closed

on the same page he states that if (x,y)~(-x,y) on d\bar{B}^2 then \bar{B}^2/~ is homeomorphic to S^2

so in his book dimension of sphere S2 is 2

on the next page he states that CS^n homeomorphic to B^n

first, n rather than n+1

Jack Schmidt

hehe, yes two typos then

Gortaur

14:59

second, B rather than \bar{B}

thank you guys for clarifying

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$Mathematics$ Mathematics