The h Bar - 2017-11-27 (page 3 of 7)

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3:06 PM

@0celo7 Butterflies don't go into comas. It was a dead butterfly. Posting that question showed only that the OP and reality are less related than is normally considered desirable.

boooo

Anonymous

@Joe No

@JohnRennie proof?

So I'm having a tad bit of an issue diagonalising this matrix... It has $\lambda_{1,2,3}=1$ and has an eigenvector $(1,0,0)$ along with generalized eigenvectors $(0,1,0)$ and $(0,-1,1)$ I tried to use these to make a matrix of change of bases $$\mathcal S=\begin{pmatrix}1&0&0\\0&1&-1\\0&0&1\end{pmatrix}$$ However doing $S^{-1}AS$ doesn't work?? :c Can I not use generalized eigenvectors to create a matrix of change of basis?

Captain Bohemian

@BalarkaSen actually I asked about homeomorphism and diffeomorphism groups because last time you said ``you can also study homeomorphism and diffeomorphism groups besides the isometry group of the geometries of a manifold."

3:13 PM

$$\mathcal A=\begin{pmatrix}1&1&1\\0&1&1\\0&0&1\end{pmatrix}$$

@Blue: Can you please explain in detail why not if I offer 50 bounties to that question?

Captain Bohemian

I am not good at reading these LaTeX codes, but I can't tansform them into figures.

Anonymous

@Joe It's simple. Just that $\phi\propto i$. The constant of proportionality turns out to be $1$ for only a particular choice of unit.

@JohnRennie look at mister butterfly doctor

Tell us all about butterfly biology plz

ncatlab.org/nlab/show/Einstein-Yang-Mills+theory

nlab isn't very big on physics notation

“compact smooth manifold underlying spacetime”

3:17 PM

$$L = R(e) vol(e) + \langle F_\nabla \wedge \star_e F_\nabla\rangle + (\psi , D_{(e,\nabla)} \psi) vol(e) + \nabla \bar H \wedge \star_e \nabla H + \left(\lambda {\vert H\vert}^4 - \mu^2 {\vert H\vert}^2 \right) vol(e)$$

@ACuriousMind are nlab people trolling?

@CaptainBohemian I did indeed say that

Anonymous

@JohnRennie My broadband is fixed now! Could you re-upload the Windows file on the server?

I think they just mean that you have to integrate over a compact region

But

if that's true

Where's the York boundary term

Exactly

3:18 PM

You blew it nlab

Nlab confirmed stupid

Why $\wedge {\star_e} $

Nlab is incapable of doing things like actual humans

I guess because it's $F^{ab}$ and $F_{ab}$

That’s the Hodge star of the metric, but they wrote it using the polytrad

3:21 PM

is "polytrad" a real word

I thought you just said "frame field" if there's $n$ dimensions

or vielbein

if you're a damn kraut

Anonymous

@0celo7 What have you done to your face, again? :P

I like the Greek word

Anonymous

It looks like an equation now

@Blue I changed it in honor of ACM. He is now a part of it.

Also

Anonymous

3:23 PM

@0celo7 lol...what does "He is now a part of it." mean ?

Why does the gauge term have no volume form???

Or

is it implied by the hodge star

I guess they don’t teach Indians economics

@Blue It's the formula of GDP

I think it involves a volume form

@Slereah you’re integrating an n-form

3:24 PM

yeah I figured

@0celo7 tfw Modi tries to show off his knowledge of economics

Anonymous

@BalarkaSen Ah. Interesting face :D

@BalarkaSen 2indian5me

do u not know what happened the last time he did that

Anonymous

@0celo7 economics is broring

3:25 PM

false

Anonymous

@BalarkaSen lolol

@BalarkaSen no. I don’t pay attention to Indian politics

Anonymous

@BalarkaSen I mean basic economics. There's some nice math in it (higher economics)

@0celo7 we got demonetized

the GDP fell by 2%

gg

Lmao

Anonymous

3:27 PM

@BalarkaSen Yeah, but it's long term effect is debatable

i assure you its well-established

Captain Bohemian

@BalarkaSen in the past I often heard people mention to symmetry groups, when I wondered which symmetry they are refering to. It turns out symmetry group can refer to 3 kinds of symmetries, isometry, diffeomorphism and homeomorphism. But I have only studied the exact definition of isometry. Based on the above discussion, it's like actually only isometry group is accurate or interesting for physics.

the only people who debate about it are BJP-endorsed [redacted for non christian word]

In common parlance, only isometries count as "symmetries" in physics

@CaptainBohemian There are many many notion of symmetry, depending on your object of interest

If your objects are pseudo Riemannian manifolds as in GR, isometries are the relevant symmetries

but you could study complex manifolds and then your symmetry group changes to conformal symmetries, eg

Captain Bohemian

3:31 PM

actually I have only studied books or literature about geometry for physics. I don't know too mathematical stuffs.

sure, i mean, symmetry literally means various configurations of a given object

there is absolutely no reason to think all the symmetries of various objects out there are X, Y, Z

you could study symmetries of object which have nothing to do with manifolds. symmetries of objects which are not even the least geometric

"symmetry" means nothing beyond the literal English meaning of the word

Captain Bohemian

is Kahler manifold a complex manifold?

A special kind of complex manifold, yes

The worst kind

It has three very different structures imposed upon it

3:35 PM

Of no use really

Captain Bohemian

i don't exactly know what the definition of a Kahlier manifold is. But I see this term often. It's talked in papers about twistors and Cauchy-Riemann structure. Thus I guess it's a complex manifold.

I don't know much about them. It has a complex structure, a metric and a symplectic structure upon it

is there a link between Kahler manifolds and spin manifolds?

Doubtful

shrugshrughshrug

3:44 PM

Okay can I form a matrix of change of basis with a generalized eigenvector

At this point I'm going with no

3

Q: Which Kahler Manifolds Are Spin?

As is well-known (see here for a M.O. question) all Kahler manifolds are $spin^c$. I would like to ask which are in fact $spin$. Taking my motivation from the case of complex projective space, I make the following (naive) conjecture: Conjecture: A compact $2n$-dimensional Kahler manifold $M...

dg.differential-geometry complex-geometry kahler-manifolds spin-geometry

Eww wiki page says some weird stuff

I'm staying farrr away from that for now

@CooperCape Well, no.

Algebraic topology is the worst. Ugh.

Okay cool.

3:46 PM

But considering generalizes eigenvectors gives you a certain change of basis indeed

Look up Jordan normal form

what is $\text{spin}^c$

Yeah wiki started talking about some Jordan stuffs and I was like I'm not good enough for this

@Slereah like spin with an EM field for free

I can’t remember definitions that involve commutative diagrams.

wot

Buy one spin get any EM field free only at $\text{spin}^c$

3:48 PM

The classifying map M --> BSO(n) of the tangent bundle lifts to M --> BSpin^C(n) prolly

Spin^C(n) is an extension of SO(n) by S^1

The hell os $BSO$

Bournemouth Symphony Orchestra

i love that

@Slereah It's the classifying space of SO(n). Also known as the infinite Grassmannian of n-planes

Is it just fancy talk for the frame bundle and the $U(1)$ bundle together, or is it like

more connected

3:49 PM

Any bundle on M is classified by a map to an infinite Grassmannian

I still don’t know what a classifying space is

There is no actual definition as far as I know

lol

kinda true

there are ten million defn

none of them are useful, tbh

That’s what people say, and then ramble on about them regardless

I just ignore topologists

@0celo7 is it like

Fortunately, the charging one has been solved now that we've all standardized on mini-USB. Or is it micro-USB? Shit.

Apparently I am in the top 2% of PSE

Which means PSE is a barren desert

user image

Captain Bohemian

3:56 PM

@0celo7 I got a friend who studies PhD in algebraic topology from Facebook. He doesn't know much about physics but seems quite good at some math used in physics.

do you mean that he is a facebook friend, or that he studies algebraic topology on facebook

Anonymous

The latter would be fun

social networked ph.d

@0celo7 One concrete thing to do is the following. Construct the space (EG)_n of step functions [0, 1] --> G with at most n singularities. Choose a metric on G, and give this fellow the metric $\int_{[0, 1]} d_G(f, g)$ for any two f, g in (EG)_n. Take the direct limit as n --> infty to get a space we call EG.

This admits a free proper G-action. BG is EG/G

I learnt this from Somnath Basu, a student of Sullivan

Anonymous

@BalarkaSen What is Sullivan?

4:00 PM

user image

Captain Bohemian

@Slereah he added me as his Facebook friend, but before he added me I didn't know him at all. After some discussion, he told me he got admission for a PhD in algebraic topology and he is so nice in helping me clarifying some maths used in physics. His math concepts are quite clear though he doesn't know their association in physics. He did join much related Facebook groups about algebraic topology.

@Blue the right question should be "Who is Sullivan"

he's a bigshot topologist

Anonymous

I thought it's an university's name :P

Anonymous

I see

Anonymous

Dennis Sullivan

Dennis Parnell Sullivan (born February 12, 1941) is an American mathematician. He is known for work in topology, both algebraic and geometric, and on dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center, and is a professor at Stony Brook University. == Work in topology == He received his B.A. in 1963 from Rice University and his doctorate in 1966 from Princeton University. His Ph.D. thesis, entitled Triangulating homotopy equivalences, was written under the supervision of William Browder, and was a contribution to surgery theory. He was ...

Anonymous

4:01 PM

@BalarkaSen So, where did you meet him?

here and there, somewhere

Anonymous

heh

apparently it's the cover for this book

amazon.fr/Quantum-Fields-Strings-Course-Mathematicians/dp/…

good cover

lolol

AMS is being memey

@blue: Win10 CD link here

Anonymous

4:04 PM

@JohnRennie Thanks..."742 KB/s - 41.8 MB of 3.6 GB, 1 hour left" :D

@Slereah apparently? no way

they look so different

Don't sass me boy

@Blue modern Internet connections are pretty flippin' fast! :-)

Let me know when the download has finished so I can take the file off my server.

@JohnRennie on the other hand, modern websites are pretty flippin' huge

Do you see the amount of bullshit you have to download to load a page

Anonymous

@JohnRennie Yeah, of course :)

4:09 PM

user image

here's all the garbage you download to load PSE

@BernardoMeurer ^

get triggered

4:28 PM

malware

Bernardo Meurer

This is proprietary malware

Use Firefox with Privacy Badger, uBlock, NoScript and httpseverywhere

Has someone else started downloading the Win10 install image from my server? I've suddenly seen the traffic double.

I misclicked on it a few minutes ago but immediately cancelled.

Someone in the UK is downloading it. The IP address is a BT Internet account.

Lmao

@BalarkaSen wtf?

why are you people on JR's server

@JohnRennie why don't I have your server info

4:37 PM

it's linked in the chat...

Anonymous

@0celo7 It's the Windows 10 installation files...

@0celo7 it's boring.

Anonymous

Scroll up

There's nothing exciting on there.

@Slereah Not so bad, check this. There are two tendencies: 1) every summer, there is a temporary setback 2) there is a long-term, linear, stable boost.

4:38 PM

@JohnRennie Oh, so you're downloading it yourself and trying to put the blame on somebody else?

Anonymous

1.2 GB has been downloaded on my end

@Slereah (1) happened this summar just as always. (2) seems to slow down, but there is still a raising tendency.

Nice try JR

Unless you count the World's second best collection of Hawkwind live recordings

@Slereah Btw, (2) is far better as most large sites of the SE.

Anonymous

4:38 PM

I can only see 2 Brits apart from JR in the chat room :P

@Blue it turns out it was a download on one of the other web sites hosted on my server. Not someone else grabbing the Win10 installer.

Anonymous

Hah. So Balarka was right...lol

Anonymous

:D

4:52 PM

Are you distributing pirated copies of W10?

What’s going on here?

Physics question. Anyone here know of a clear explanation reconciling the fact that "magnetic fields do no work" with the apparent physical phenomenon that if I put two magnets close to each other they certainly appear to attract/repel and do work?

Anonymous

@0celo7 If you already have original version of Windows, then you can upgrade for free

Is there a clear mathematical proof showing how the work in that scenario is actually done by an electric field or something?

Anonymous

So not really piracy

So what’s the point. Why do you need JR’s server?

4:54 PM

@0celo7 no, you can download the W10 install image from MS. They make it freely available since the image is of no use to you without an install key. But there are lots of different images available for various versions of W10, and I have an image that is just right for Blue. That's why I'm sharing it with him.

Perfect xi :) gyazo.com/d99af23b934bd73165ed283ab24969c9

@enumaris the Lorentz force does no work because it's always at right angles to the current.

I don't contest that

However the force between two magnetic dipoles is not a Lorentz force and does do work.

hmmm

4:56 PM

The work put in is stored in the magnetic field.

the electromagnetic field is really weird

Can you show the force between two magnetic dipoles?

The magnetic fields do no work statement is much repeated but essentially meaningless.

Is the force some function of the magnetic fields like F(B)? Cus that would imply the statement "magnetic fields do no work" is false

@enumaris you can Google that for yourself.

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