The h Bar

Also, it's funny that the irony escaped you, but I meant that it's rather typical for you not to have heard of Dylan. Not that it's a typical state for others :P

0celo7

6:12 PM

Oh the irony did not escape me.

I don't understand why it would be typical for me is all.

Danu

Well played, then :)

0celo7

Sure I might not have watched the Simpsons or whatever, but at least I've heard of them and seen it a few times

When you mentioned Bob Dylan the other day that was the absolute first time I'd ever heard of him.

Danu

'tis a sad life, some of us must lead

0celo7

Where was I supposed to learn about Bob Dylan?

Danu

Childhood

0celo7

6:17 PM

that was in Germany

Danu

Anyways, just get over your losses, and learn about him now

I didn't really get into Bob Dylan until about six months ago.

Now I listen to him like... 50% of the time :P

0celo7

It's not a loss

And the wikipedia page does not make me look forward to it

Counterculture is so boring.

Danu

Hahaha

0celo7

I missed the joke

@Danu My childhood music consisted of Eminem and Slipknot

Danu

@0celo7 That's very little music to fill an entire childhood.

I listened to Eminem, too. But tons more.

0celo7

6:25 PM

@Danu Correct

I didn't like music

My parents don't listen to music

Danu

Anyways, let's stop talking about this. I'm sure it's not inspiring anyone.

I listened to a talk today that made me think of you

0celo7

99% of conversations don't inspire anyone

Danu

Riemannian geometry of the analytic kind

0celo7

Oh?

on analytic manifolds or in the more general sense

Danu

Riemannian geometry involving lots of analysis

0celo7

6:26 PM

What kinds of stuff?

ACuriousMind

@Danu The new math thriller: "Close encounters of the analytic kind"?

0celo7

lol

Danu

Heh

I'm in one hell of a horror story then

0celo7

For the record, I watched that movie.

Danu

(interpreting analytic as in holomorphic, here)

0celo7

6:27 PM

@Danu So, what were they talking about?

Danu

@0celo7 Tricky stuff. So the level-0 idea is the following:

Consider an immersion of a a $n-1$ disk into $\Bbb R^n$. For ease, let's talk about $2$-disk inside $\Bbb R^3$

At a point where the principal curvatures' signs agree, the image is (at least locally) contained in a half-space

Now, there are some conditions that forbid this from happening. For instance, if the map is harmonic.

But you can very widely generalize this sorta set up

0celo7

@Danu Seems reasonable? They're curving away from the part of the space you don't want them to be in

So it's in the half space?

Danu

Yeah, pretty easy if you just draw it

As a first generalization:

0celo7

Was this a talk about minimal submanifolds?

Danu

Closely related

So for instance if $\gamma:S^1\to \Bbb R^n$ is a loop and if $u$ is a least-area filling for $\gamma$. Then $u$ is smooth and an immersion away from finitely many points, and if you pull back the Euclidean metric and then complete the space (calling the result $Z$) you get a triangle diagram between the disk, the space $Z$ and $\Bbb R^n$

with the arrow from $Z$ to $\Bbb R^n$ being a map that preserves length of every curve

0celo7

6:34 PM

Complete the space?

Danu

Geodesically or whatever it's called

0celo7

@Danu Hmm. What's $u$?

Danu

A least-area filling for $\gamma$

0celo7

Ok that's not a typo. What does that mean?

Danu

I don't know a definition. But the idea is pretty clear. Just consider a loop, and fill it out as efficiently as you can.

It's a map from a disk

And it must have nice properties to be minimal area

0celo7

6:36 PM

Dude I'm just confused as to what $u$ is.

Danu

That map ^^

0celo7

Is it a map, a space, ...?

Danu

38 secs ago, by Danu

It's a map from a disk

0celo7

@Danu Fill it out?

I feel like I'm being really dumb here

Danu

Draw a loop in $\Bbb R^3$.

0celo7

6:37 PM

Ok

Danu

You can "see" the disk inside it (it might look like a twisted disk with singular points n shit)

ACuriousMind

@0celo7 It's a map $u : D^2\to \mathbb{R}^n$ such that $u\rvert_{\partial D^2} = \gamma$.

0celo7

@ACuriousMind Oh

Why not say that lol

ACuriousMind

Least area means that the volume of the image is minimal among all such $u$, presumably

Danu

Because it's clear from what I did say, or so I thought.

ACM got it :P

ACuriousMind

6:38 PM

@0celo7 Well, I got that from what Danu said - some mathematicians like to talk in formulae, others in words, it's something to get used to

0celo7

It's a minimal submanifold with boundary that loop $\gamma$

Danu

In any case, it's not like the guy giving a research talk was writing all this shit out anyways, so I didn't either. But it's all pretty intuitive so far

0celo7

Ok

Danu

@0celo7 Not a submanifold, because $\gamma$ is not an embedding per se

And the $u$ is the map, not the image

0celo7

@Danu Abuse of terminology/notation.

Ok I see what's going on now

Is $u$ a proper map?

Else I'm not sure what the "completion" is, unless you mean the completion as a metric space.

@Danu Also I don't think we can pull back a metric unless we have an immersion.

Danu

6:43 PM

It's an immersion away from finitely many points apparently and then somethingsomething you can control the singularities

0celo7

@Danu Ah, so there were technical details regarding the pull back?

@Danu Such things are interesting! Now I want to continue on the Journey of Riemannian geometry again :)

But first...a lab report

Danu

So he wanted to massively generalize this

0celo7

Oh there's more

Danu

Yeah, this was the this-has-already-been-done part

I didn't quite get the idea of the generalization though lel

But I learned a little bit about what a CAT(0) space is.

Still pretty interesting

0celo7

Well, we have maps $S^n\to\Bbb R^k$ like in higher homotopy maybe?

Danu

6:46 PM

No, totally different direction of generalization

0celo7

And then we have a similar map $u$

@Danu Oh

Danu

Anyways, I can tell you what a CAT(0) space is

which is already nice

0celo7

What is a CAT(0) space

I am a fan of cats

Danu

So let $(X,|\cdot|)$ be a metric space. You know what a length space is?

0celo7

No, should I?

Danu

6:47 PM

no

Anyways

0celo7

It it one in which one can define arc length?

Danu

Length space if for every $x,y$, $|x,y|=\operatorname{inf}L(c)$ where $L(c)$ is the length of a curve $c$ from $x$ to $y$

0celo7

So Riemannian manifolds

Danu

Geodesic space if $|x,y|=L(c)$ for some $c$

0celo7

Compact Riemannian manifolds

Danu

6:48 PM

(are all examples, yes)

Now, a CAT(0) space is a geodesic space for which*

Given any triple of points, and any triangle $ x,y,z$ given by geodesics between these points, there should be a "comparison" triangle $\bar x,\bar y,\bar z$ in $\Bbb R^n$ with sides of the same length such that, for any two points $p,q$ on the geodesics between the three points, $|p,q|\leq |\bar p,\bar q|$

where the second metric is the standard one

So basically what it says is that the sides of the triangle should be squeezed together

(draw it)

Examples therefore include all negatively curved Riemannian manifolds

0celo7

So a negative curvature space?

Danu

But another nice example is a tree

which corresponds to a $-\infty$ curvature space, in the sense of squeezed sides

0celo7

Hmm, ok

Danu

Nice properties of CAT(0) spaces: They are contractible and in them the Euclidean isoperic inequality (i.e. the isop. ineq. with the coefficient that holds in Euclidean space) holds in them

That's all I had to say :P

0celo7

They are contractible?

Not so surprising in light of the Cartan-Hadamard theorem, ok

Danu

6:55 PM

I think he said somehting about that it's clear because there are unique geodesics between points (contract along them, I figure)

0celo7

Hmm, that is actually surprising

Cartan-Hadamard states that the universal cover of a negatively curved manifold is diffeo to $\Bbb R^n$

But you're saying that any negatively curved manifold has trivial fundamental group?

@Danu Unless I'm missing something that's clearly false

Danu

Perhaps locally contractible

:D

0celo7

lol

what's a non-locally contractible space

surely all manifolds are

Danu

Yeah, I don't like this. Idk.

0celo7

@Danu Don't like what?

@Danu Oh, did you ever finish those GP notes?

Danu

7:02 PM

Clearly he wrote something wrong.

Yeah, a long time ago.

0celo7

Would you mind sending them to me?

Or uploading them to dropbox/whatever

user218912

@ACuriousMind can you help me out with scaling transformations? I need to know it for the homework but the prof never taught what it is.

0celo7

@bl00 I'm shocked you didn't ask me

user218912

please?

user218912

do you know as well?

Danu

7:03 PM

@0celo7 email?

0celo7

$x\mapsto \lambda x$?

user218912

yes

0celo7

^^ I know you can see deleted messages.

@bl00 what about them?

Danu

Sent.

0celo7

Thanks.

@Danu Did Ted tell you to do Stack of Records?

It can be used to prove the fundamental theorem of algebra, but maybe you knew that

Danu

7:07 PM

@0celo7 No,

It's used several times in the book.

user218912

@0celo7 I need to find the scaling dimension for the lagrangian that is a symmetry of $\partial_\mu \phi \partial^\mu \phi$.

Danu

I proved exercises that I needed, mostly. I started slacking at the very end.

user218912

he never taught this

0celo7

@Danu Ok, thanks for this!

Danu

@0celo7 I'm not sure exactly what you're referring to. Are you talking about the proof G&P give in the main text, because I clearly know that one :P

0celo7

7:09 PM

@Danu No, Milnor has a different proof.

It's on like page 8 of his diff top book.

Bernard Meurer

Okay guys

My Chemistry exam is this Saturday

for those who haven't been briefed the class is taught in Klingon and is just insane. We don't even know the maths the guy uses

0celo7

It's just basic calculus, right :P

user218912

@0celo7 can you give me a hint please?

user218912

is it trivial or obvious?

Bernard Meurer

@0celo7 Idk, are integrals over spherical coordinates basic calculus?

0celo7

7:11 PM

@bl00 what is a scaling dimension?

@BernardMeurer yes

high school in Germany, afaik

Bernard Meurer

Why does hybridization happen? I mean, why do 2S and 2P interfere in that way?

0celo7

@JohnRennie ^^^^^^^

call him a few times

Bernard Meurer

Also, why are P type orbitals divided into Px Py and Pz?

0celo7

I don't want to remember chemistry

ask @ACuriousMind

Danu

@BernardMeurer try the chemistry SE site/chat?

Bernard Meurer

7:13 PM

@Danu I don't like chemists

My professor is one

They're all insane

ACuriousMind

@BernardMeurer P means the orbital angular momentum is not zero, so we distinguish the orbitals where it lies in the x,y,z-directions, respectively

0celo7

@bl00 don't skype me

ACuriousMind

I'm afraid I can't help with hybridization

user218912

that's purely chemistry

user218912

@0celo7 k

0celo7

7:14 PM

oh yeah

it is Trivial

user218912

good to know.

Bernard Meurer

@ACuriousMind Hm, I see

0celo7

find the way that $\partial_\mu$ transforms

then find the way $\phi$ transforms

then you know the way that whole thing transforms

Bernard Meurer

@0celo7 Everytime you say something is trivial to me I add a counter to the number of pictures I'll take of you drunk on the floor

Secret

hybridisation is a simplified way to think about bonding. What actually happens require molecular orbital theory

user218912

7:15 PM

@0celo7 thanks.

0celo7

the other parts are more interesting

and are related to e.g. conformal transformations in QFTCS

Bernard Meurer

@Secret not simplified enough

user218912

@0celo7 QFTCS?

0celo7

curved space

user218912

oh

user218912

7:16 PM

right

user218912

ahhh there is so much to learn

0celo7

@BernardMeurer Ask anyone: I'm as sober as a baby

user218912

I'll just be an experimentalist xP

0celo7

You'll never get me drunk on the floor because I don't drink

Danu

Don't worry. You'll get to QFTCS in 3 or so years if you keep studying.

Bernard Meurer

7:17 PM

@0celo7 Babies are drunk all the time

Danu

Physics is not so deep ;D

0celo7

@ACuriousMind When are you changing your avatar?

@BernardMeurer I don't drink OK

I don't like the way it tastes, I think it's immoral

Bernard Meurer

@0celo7 Rebecca get out of this chat and call Ryan

Secret

in the context of hybridisation, orbitals can be superimposed just like wavefunctions. This is employed to explain the bonding geometry of the molecule (as long you are not going into metal complex territory or hypervalent moelcules)

hybridisation occurs when two orbitals have similar energy

user218912

@0celo7 are you being serious? because I remember you drinking a few months ago.

0celo7

7:18 PM

@bl00 wtf

Bernard Meurer

@Secret I see, I see

0celo7

@BernardMeurer you're creepy

Dartek12

hello everyone

ACuriousMind

@0celo7 dunno

Dartek12

I am in physics chat, arent I?

ACuriousMind

7:22 PM

What passes for it here, yes, welcome

user218912

@0celo7 the questions tells you how $\phi$ transforms already right?

Dartek12

may I ask sth about dynamics

?

Bernard Meurer

@Dartek12 I think you have the wrong address, this is the horse-breeding chat, try physics.gov/chat

Secret

In other news, I just spent nearly half of my whole day fixing and organising my abstract algebra blog article. However the abstract algebra people are currently asleep in Maths chat, thus I am going to search for them later

0celo7

@bl00 right

@ACuriousMind lol

Dartek12

7:23 PM

@BernardMeurer one like me is always doubtful

0celo7

> youtube.com/watch?v=OhY6zuGaAjc

user218912

wut

Bernard Meurer

@0celo7 Very interesting, what do you think their offspring will look like?

Dartek12

well, I must to calculate tangential acceleration

ACuriousMind

@Dartek12 just ask, if someone wants to answr, they will

Bernard Meurer

7:25 PM

@Dartek12 Of the horses?

Dartek12

yes

0celo7

@Dartek12 the acceleration of the thrust?

@ACuriousMind @Danu :(

Bernard Meurer

@0celo7 I think so, the horse-thrust ratio

ACuriousMind

@0celo7 Oh, sorry, did you want to wait till someone flagged that? :P

0celo7

@ACuriousMind Why would someone flag Science?

user218912

7:26 PM

lol

ACuriousMind

@0celo7 Your quickly-deleted comment shows you know that well

0celo7

Oh I forgot I have a lab today

Crap

Dartek12

Angle of rotation is as f(t) = At + Bt^2 where A = 3 rad/s and B = 2 rad/s^2. Find tangential acceleration at the moment of t = 0.5s if linear velocity is 2.5 m/s at that moment.

I hope it's clear

user218912

@0celo7 does the derivative transform as $\partial_\mu \phi ' \to e^{ad +1}\partial_\mu\phi $

0celo7

beats me

Dartek12

7:29 PM

(if sth is incomprehensible please give me feedback, beacuse the content is translated)

user218912

sorry fixed

user218912

is that right?

0celo7

beats me

user218912

:(

0celo7

it looks wrong

Dartek12

7:30 PM

@0celo7 what does beat you

user218912

@0celo7 which part exactly?

0celo7

the thing in the exponential.

Dartek12

?

user218912

1 sec

user218912

@Dartek12 he's talking to me

Dartek12

7:33 PM

:<

user218912

@Dartek12 do you know how to find tangential acceleration?

0celo7

@bl00 try $e^{\alpha(d+1)}$

user218912

it should be the derivative of the tangential velocity.

Dartek12

its a derivative of linear velocity

user218912

yeah whatever

Dartek12

7:40 PM

hmm... exact problem is that my answer under the task is that tang. acc. -> 2m/s^2

and all I do is wrong

0celo7

so maybe $d=-1$?

not sure

best check with a physicist

it's probably wrong

because shouldn't it depend on the spacetime dimension?

I don't know any more

user218912

it should.

user218912

that's why it says to find it for general n+1

0celo7

@BernardMeurer Do you have a second account called "Carlos"

Bernard Meurer

@0celo7 Why?

user218912

7:44 PM

@ACuriousMind help please :(

user218912

how does the derivative of the fields transform under scaling?

user218912

or could you link a pdf or a book that I can learn scaling transformations from?

alarge

@Dartek12 First get the radius (from tangential velocity), then the acceleration.

Dartek12

@the radius comes as 5/8 rad/m and that's what confusing me

alarge

@Dartek12 Radius has units of rad/m?

Dartek12

7:46 PM

no, but it's how it comes using it

alarge

@Dartek12 What's the connection between tangential velocity and radial velocity? How do you get the latter?

Dartek12

v = wR; v(0.5s) = (4 rad/s + 2rad/s^2 * 0.5s) * R = 2.5m/s

rob

@DavidZ Heh. I happened to open my computer at the start of the group chat.

Dartek12

3 rad/s*

alarge

@Dartek12 f(t) is position, not velocity.

0celo7

7:49 PM

@BernardMeurer I think you do

Dartek12

f is an angle in my task, it depends from the time as following function f(t) = At + Bt^2

Bernard Meurer

@0celo7 Yeah, I could tell, but why do you think that?

0celo7

I've only seen two people ask about PhD level über complicated computer science

alarge

@Dartek12 Right, so from angle, or "radial position" if you will, how do you get the radial velocity?

user218912

@Dartek12 take the derivative of that?

Dartek12

7:50 PM

yeah: w(t) = f'(t) = A + 2Bt

0celo7

I wonder if ACM will take pity on you and help

user218912

me?

alarge

@Dartek12 Ok, so with that, maybe try attacking the problem again?

Dartek12

and with that thinking I get R = 5m/8rad

user218912

@ACuriousMind why are you ignoring me :(

Dartek12

7:52 PM

hmm

small calculating mistake

user218912

I'll die seriously

Dartek12

@alarge still R is not satisfactionary - 0.5 m / rad

user218912

@Sanya hi can you help me out? :(

user218912

how can I figure out how the derivative of the fields transforms under scaling?

alarge

@Dartek12 Radians are really dimensionless; 0.5m sounds fine.

Dartek12

7:56 PM

@but as long as it depends from R its kind of recurrent

Sanya

@bl00 I'm unsure I can ... you mean scaling of the coordinates?

Dartek12

@okay, now the answers are corresponding to each other, thank you :D

0celo7

@Sanya dude

I had to do Gaussian elimination avian

Again

Sanya

@0celo7 good evening to you :)

0celo7

I understand it now

@Sanya it's afternoon

Sanya

7:57 PM

I was positive you would

0celo7

But good afternoon

Sanya

@0celo7 good afternoon then, here it's 10pm :D

0celo7

@Sanya doing it a billion times in linear algebra didn't

alarge

@Dartek12 Good to hear.

0celo7

It was only with that damn scattering problem that it made sense

Sanya

7:59 PM

I think you are pretty unique in that that made it clear to you - but we all learn differently and it's the fact that it does make sense to you now that makes me happy :)

0celo7

I'm unique :)

Dartek12

@alarge but normal acceleration (v^2/R) seems a bit confusing :D

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