The h Bar

0celo7

12:18 AM

@BernardoMeurer what?

@skullpatrol that too

loocsieulb

12:36 AM

yeah i could listen to that deep voice for days so i'm not surprised @0celo7

Cows

1:24 AM

At the at&t hackathon. Let's see what happens hehe. I don't have a team. It's just me.

2

Akerai

1:51 AM

Hey guys, I am curious, when discussing vorticity in fluid dynamics, why is the diffusion of vorticity only dependent on the density? I would've imagined that it would be dependent on some sort of moment of inertia of the particles

i.e. what exactly is the vorticity

and if I have an infinite system with constant vorticity, i.e. vorticity(x,y,z) = 5 khat

is it equivalent to a system with no vorticity at all?

Cows

2:11 AM

Going over constest specs

Cows

2:29 AM

Just pitched my idea at the att havkathon in front of 300+ like a boss.

loocsieulb

2:47 AM

@Cows lone wolf

u show em

representing the h bar

Bernardo Meurer

@Cows Over in LA?

I might be going to Cal Hacks

2

Secret

7:01 AM

[Random thought]

Replace agent A and B with a pair of entangled particles. Perhaps quantum computing + blockchain will do something interesting

Fawad

7:37 AM

Negative magnification(for a concave mirror) means image is diminished or inverted?

Dec 18 '17 at 22:59, by Balarka Sen

no like a boss memes in 2017 pls

Oh it’s 2018

Physics Meta

9:26 AM

0

Q: What does the red circle mean next to a review queue?

Seems like it should imply this queue is important right now/needs help or attention yet it tells me the queue has been cleared. This is contrary to the grey circles, which go away after I have cleared a queue. What does the red dot mean?

John Rennie

11:01 AM

@BernardoMeurer Probably the cryptography API and in particular BCryptGenRandom

user55789

1:04 PM

Dumb question:

$n^\mu = h(x) \nabla^\mu S(x) \leftrightarrow n_\mu = h(x) \nabla_\mu S(x)$

True or false?

Slereah

1:35 PM

true

just apply $g^{\mu\nu}$

user55789

No way

Too easy

Can't be correct

:D

0celo7

@user55789 ...

Balarka Sen

1:53 PM

@0celo7 The proof of Darboux's theorem makes no sense

There's no content to the proof, only symbol pushing.

0celo7

@BalarkaSen the one in symplectic geometry?

Balarka Sen

@0celo7 Yeah

0celo7

@BalarkaSen do you have a specific reference?

I learned this from Arnold

@BalarkaSen Lee has an "elegant" proof

it's quite long, however

Balarka Sen

2:09 PM

It's in Eliashberg-Mishachev

Also in Canas da Silva

Someone once set me these set of notes by Auroux: ocw.mit.edu/courses/mathematics/…

These are nice and compact

0celo7

oh jeez if you can understand the Arnold proof I applaud you

Balarka Sen

How does he do it? Moser trick? That's the usual proof

0celo7

Moser's trick must be something else in topology

i.e. I don't know what it is

Balarka Sen

Moser trick sucks bro

0celo7

I know a moser trick but I doubt it's useful here

skullpatrol

2:12 PM

\o @Semiclassical

Semiclassical

@BalarkaSen I think I’m out of patience in the math room

Balarka Sen

Same

2

skullpatrol

lame

2

Semiclassical

lime

2

0celo7

@BalarkaSen the proof in EM is unintelligible

Balarka Sen

2:15 PM

@0celo7 The Moser trick I have in mind is that if $\omega_t$ is a family of symplectic forms on $M$ staying in the same cohomology class, then there is an isotopy $f_t : M \to M$ starting at the identity such that $f_t^* \omega_t = \omega_0$

0celo7

huh, that's remarkably like the moser trick I know

Balarka Sen

Oh what does yours say?

0celo7

any two metrics that define the same volume form are equivalent up to diffeomorphism

Balarka Sen

Hmm!

0celo7

the EM proof has Darboux before Moser, however

Balarka Sen

2:18 PM

Oh I think they do it from the same general principle

ocw.mit.edu/courses/mathematics/…

just look here

0celo7

I see

well, so the proof is just symbol pushing? it's a proof that certain coordinates exist, those are never deep

Balarka Sen

I do think it should be something deep. Here's the idea: Take a chart $U$ around $p \in M$. You can pick a frame $(e_1, \cdots, e_{2n})$ on $T_x M$ for each $x \in U$ such that $\omega_x$ is the standard $dx_1 \wedge dx_2 + \cdots + dx_{2n-1} \wedge dx_{2n}$ on that frame. This defines a section of the frame bundle $F(TM)/M$ over $U$ such that $\omega$ is the standard form along that section

0celo7

@BalarkaSen oi, consider the embedding of $\Bbb R^n$ into $S^n$ via stereographic projection. Problem is, that's not really an embedding, is it? Just an injective immersion

Balarka Sen

$d\omega = 0$ should say that that local section of the frame bundle should be holonomic

It's an integrability condition

0celo7

@BalarkaSen what's an example of a non-open immersion?

Balarka Sen

2:25 PM

@0celo7 Um, it is an embedding in the topological sense. It's a homeomorphism onto image

0celo7

but the image comes arbitrarily close to self-intersection

Balarka Sen

You're thinking of the figure 8 picture, in which case the image of the map from R is homeomorphic to the figure 8

There's an actual self-intersection in the image

The topology of the image is different.

In this case there's no such thing

Proper injective immersions are embedding, but the converse is not necessarily true

0celo7

so the subspace topology on the image is the same as the original topology?

Balarka Sen

Mhm

0celo7

@BalarkaSen Oh wait, an immersion between equidimensional manifolds is always open

and an open immersion is an embedding

Balarka Sen

2:29 PM

That is correct, it's a local diffeomorphism

why is Britney Spear's kid drawing fucking DBZ fanarts jesus christ

this is 2018

normie ass people

skullpatrol

Ignore Political Posts. Upvote Abacus Raccoon!

Slereah

Help there is too much physics

Let's burn all the books

Abhas Kumar Sinha

burn?

books to burn?

Slereah

All of them

Let's just restart everything from the beginning

skullpatrol

451

Abhas Kumar Sinha

2:41 PM

we don't need to teachers to teach, we need learners to learn

-einstein

lol

Slereah

Sounds like the usual bitter teacher

Abhas Kumar Sinha

yep

Slereah

With students who don't give a shit

Abhas Kumar Sinha

my teacher is able to make interesting things shit

totally shit

i don't like that

previous teacher was amazing!

now physics seems boring...

0celo7

time to get out federer again

3:00 PM

This is music

I should be jobless again

You have plenty of times to do physics when you're on the dole

0celo7

$\mathscr p$

hm

$\mathcal p$

since when is there no mathscr p

Slereah

$\mathfrak p$

0celo7

$\mathscr{Op}$

Balarka Sen

@0celo7 I suggest using $\mathcal{O}$.

send p to gulag

Slereah

3:04 PM

$\wp$

Hell yeah

I swear mathscr had little letters

$\mathscr a$

AnxiousObject

Ok guys, I need a lot of help with spinors

I am an undergrad, and we were introduced to spinors in the second half of our first QM course, but besides that they're the analogue to the wavefunction for the spin; I didn't really understand how to use them and what they're for. Our textbook is Weinberg's lectures on quantum mechanics, but it doesn't speak about spinors at all

Do you know a good source to learn about spinors properly?

Slereah

I like this as an introduction

physics-quest.org

Chapter 17 to 20

0celo7

$$\mathrm{cap}_q(K)=\inf\{\int_{\Bbb R^n}|\nabla\phi|^q:\phi\in\mathscr D(\Bbb R^n) \text{ and } \phi\equiv 1 \text{ on }\mathfrak{Op}(K)\}$$

Slereah

3:10 PM

wot

0celo7

that doesn't look right either

AnxiousObject

our QM course is entirely nonrelativistic, and that stuff is relativistic QM

Slereah

Then try Landau "Non relativistic quantum mechanics"

It has a chapter on spinors and the Pauli equation

AnxiousObject

How understandable is that for an undergrad? Also, we were never introduced to tensor algebra, will be this a limit?

user55789

From the QFT stuff I read from Weinberg, anything is more understandable

:-)

Slereah

3:15 PM

Landau's pretty understandable

It only uses wavefunctions

No hilbert spaces at all

AnxiousObject

Weinberg is really complete, but you really need someone who explains stuff beforehand

0celo7

hilbert spaces are the best though

Abhas Kumar Sinha

4:11 PM

hiii

joke - "What was the need to get the discovery of Gravity. If there was no Issac Newton, then also, things would fall down." hehehe XD

Bonsay

Hello to everyone! I was looking for the rotation matrices for spin 1 systems but I didn't manage to find them, can anyone help me out on this one?

Slereah

4:26 PM

Those are the rotation matrices

Since spin 1 systems are vector fields

Abcd

4:45 PM

How to find the degree of freedom of a mixture of gases? Average? Or weighted average?

skullpatrol

nice blog @ACuriousMind

Abcd

(nvm, I got it.)

ACuriousMind

@skullpatrol Hm? I haven't written anything on there

skullpatrol

@ACuriousMind I was commenting on how professional it looks :-)

I found this interesting.

Slereah

5:11 PM

Is the notation $\times_G$ defined by $A \times_G B = A \times B / G$?

0celo7

yes, but you need to define what the action is before $/G$ makes sense

Yashas

I was looking at some examples of sample spaces (probability theory). I came across this: (Uncountable) speed of a vehicle measured with infinite precision => sample space = R

what's the significance of "infinite" in the example?

skullpatrol

infinitely divisible

0celo7

@Slereah I'm going heathen and writing $\mathcal E$ for $\delta_{ij}dx^idx^j$

Yashas

why would it be wrong to say just speed of a vehicle

0celo7

5:15 PM

the $\mathcal E$uclidean metric

Slereah

Is that the euclidian metric

Odd choice

Why not $d$

If you're going with something other than $g$

0celo7

why would you use $d$??

Yashas

Ugh, I think I got it. I had confused countability with integerness.

skullpatrol

right

think fractions

Slereah

that weird paper on QM has the Hilbert bundle as the associated bundle $FM \times_G \mathcal H$

Anonymous

5:18 PM

@Yashas Infinite precision just means arbitrary precision. So surely the sample space is $\Bbb R$. Are you studying probability measures or something?

Yashas

@Blue Machine Learning

I thought you were taking that course too

Anonymous

Ah, one of most hand-wavy cs topics ;) Yeah, I did the first few lectures....but now learning statistics properly before doing that

Yashas

There are only revision tutorials of probability and linear algebra atm.

and one assignment which is due on 22nd :(

Anonymous

It formally begins on 22nd isn't it?

Yashas

yes

Anonymous

5:22 PM

Cool, I'll resume then

Anonymous

:)

Anonymous

How's college going?

Yashas

I have Advanced Graph Theory too. I might choke on academic load.

skullpatrol

(removed)

Anonymous

Ah, awesome. My CGPA will drop because of carpentry and engineering drawing I think

Anonymous

5:23 PM

I purposely suck at those

Anonymous

By choice :P

Yashas

what's the first 3 characters of your name?

skullpatrol

carpentry?

Yashas

Luckily, I don't have carpentry and engineering drawing lol

skullpatrol

they make you hammer nails?

Yashas

5:24 PM

I have Intro to Biology, General & Structural Chemistry and a ton of CS courses

Anonymous

@skullpatrol Yup, in the first semester we had to cut and shape wood. The teacher said that if we don't get jobs we can at least keep carpentry as back-up. XD

Anonymous

@skullpatrol Yup

Yashas

@Blue I hope that isn't the actual purpose of the course lol

Anonymous

lol

Anonymous

maybe...who knows

Anonymous

5:26 PM

I don't know any other purpose that could possibly have

Rick

Don't Take Capacitors for Granted

►

Yashas

I have Group Theory Basics, Linear Algebra Basics, IT Workshop, Data Structures, Computer Systems Organisation + Biology & Chemistry

Rick

What exactly went wrong here?

Yashas

+ Intro to ML and Advanced Graph Theory from NPTEL

Anonymous

I see, they focus a lot on CS in IIITH from the first year itself. That's nice

Anonymous

5:27 PM

I have been learning some extra physicsy and mathy stuff

Yashas

I haven't had a single physics course yet -_-

I don't know if Thermodynamics & SM counts as a physics topic

It's right in the intersection of Physics, Chemistry and what not

Anonymous

Are you working on any side projects under your profs?

Yashas

It's too early for that

Anonymous

That might be a good way to gain experience in physics

Anonymous

It helps a lot

Anonymous

5:29 PM

In motivating you to learn new stuff

Anonymous

@Yashas I don't think so. Just go and speak up with the ones whose work you like

Yashas

@Blue I like everyone's and my basic courses aren't over yet. I need to complete them so that I will be well-informed before I choose my research area.

Anonymous

Well, as you wish :)

Emilio Pisanty

is the German around?

@ACuriousMind

> Aufbau is a German noun that means construction or "building-up". The aufbau principle is sometimes called the building-up principle or the aufbau rule. Since the name originates from a common noun, it should not be capitalised in English

(second paragraph in en.wikipedia.org/wiki/Aufbau_principle)

that sounds like BS to me

is it right?

0celo7

@EmilioPisanty which part is BS?

Emilio Pisanty

5:36 PM

@0celo7 the "it should not be capitalised in English"

plus the entire rationale

0celo7

@EmilioPisanty it's not a proper noun, is it?

do we capitalize kindergarten in English?

Emilio Pisanty

it's still capitalized in German, no?

ACuriousMind

Well, whether it should be capitalized in English or not depends on whether you consider it a German word used in an English sentence or an English word

0celo7

@EmilioPisanty everything is capitalized in German...

ACuriousMind

And @0celo7's kindergarten would've been my example for the latter

Emilio Pisanty

5:37 PM

@ACuriousMind I mostly lean for the former

ACuriousMind

@EmilioPisanty Do you capitalize bremsstrahlung in English, too?

Emilio Pisanty

@ACuriousMind hmmmmm

good question

I don't

but I do capitalize Ansatz

ACuriousMind

That's weird :P

0celo7

you're not internally consistent, so we can't help

Emilio Pisanty

heck, I normally pluralize it to Ansätze

0celo7

5:39 PM

also how has no one commented on my pic :(

ACuriousMind

@0celo7 A cat with an abacus. Nice! ;)

Emilio Pisanty

@ACuriousMind whut

that's not a cat

if you think that's a cat

ACuriousMind

I know :P

Emilio Pisanty

I would recommend that you don't approach any cats while in the US

0celo7

it's a trash panda

@ACuriousMind is coming to the US?

ACuriousMind

5:41 PM

What? No!

Emilio Pisanty

huh

ACuriousMind

@EmilioPisanty racoons live in Europe, too, you know

Emilio Pisanty

apparently there's raccoons in Germany

skullpatrol

lol

ACuriousMind

Yeah, some cities have trouble with them raiding trash cans

Emilio Pisanty

5:42 PM

ok

so

please don't attempt to pet any cats before confirming with a biologist that they're not in fact a raccoon

ACuriousMind

So I have to catch any possible cats and get them to a biologist before petting them?

0celo7

ACM will get rabies

ACuriousMind

That doesn't seem like a good plan :P

skullpatrol

3 hours ago, by skullpatrol

Ignore Political Posts. Upvote Abacus Raccoon!

0celo7

"We shall moreover
show that the new invariant plays the same role with respect to the spectral invariant
as the Cabibbo–Kobayashi–Maskawa (CKM) matrix in the Standard Model [5]
plays with respect to the list of masses of the quarks."

wot

skullpatrol

5:48 PM

I think they are using "aufbau" as a common synonym for "build-up"

0celo7

@BalarkaSen that Connes paper does not actually seem to contain the claim from the Wiki page

Balarka Sen

5:59 PM

@0celo7 Hm, strange

0celo7

@BalarkaSen I read the intro and there's nothing about Riemannian manifolds

he has a companion paper on R folds but it doesn't seem to be about that claim either

oh, it's in the other paper

that's an 80 page proof!

might be worth it, and I know an operator guy who's referenced in these papers

Semiclassical

hi chat

0celo7

hello

Balarka Sen

i see

there's a lot of appearance of the word "standard model" in these papers

whats with that

0celo7

you're just as clueless as me about this stuff

I should probably get his book first

600+ pages, mama mia

Balarka Sen

6:03 PM

lmao

get rekt

Slereah

6:24 PM

To be honest I'm not 100% sure of what the standard model is, in full

There's so much bits to it

lots of ad hoc matrices

It's like the $SU(3) \times SU(2) \times U(1)$ gauge + Higgs + fermions + the Higgs coupling matrix + the weak mixing matrix + the neutrino mixing matrix + all the ghosts and renormalization + whatever you do to select a vacuum

Yashas

"In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X that includes the empty subset, is closed under complement, and is closed under countable unions and countable intersections"

What does "closed under countable unions and countable intersections" mean?

0celo7

$A_1,A_2,\dotsc\in\Sigma\implies \cap A_k\in\Sigma, \cup A_k\in\Sigma$

Slereah

the union of countably many sets is in the sigma algebra too

Yashas

6:39 PM

is it for all combinations of subsets or for all subsets of the sigma algebra?

0celo7

what?

Yashas

Suppose A1, A2, A3, A4 belongs to S. Does that rule imply that A1 U A2 must belong to S (and other combinations) or does it imply that A1 U A2 U A3 U A4 belongs to S?

Anonymous

@Yashas Any combination

Balarka Sen

union of any countable family

vzn

@BernardoMeurer @Cows how about some more info/ links re hackathon(s)? :)

Balarka Sen

6:42 PM

fundamentals of measure theory is boring

Bernardo Meurer

calhacks.io

Yashas

What's the use of sigma algebra?

Bernardo Meurer

To show off

Balarka Sen

To define measures

0celo7

it's the appropriate thing to define measures on

Balarka Sen

6:43 PM

They are what measures are defined on, pretty much

Anonymous

You know that just $A_1 \cup A_2$ and $A_1 \cap A_2$ belonging to the same structure is sufficient. The rest, like A1 U A2 U A3 U A4, follows

Slereah

It's just so that you can perform a measure on $[a,b] \cup [c,d]$

Yashas

What's a measure? :3

Slereah

and then you can just say $\mu(A \cup B) = \mu(A) + \mu(B)$

Balarka Sen

A notion of "volume" on your space

Slereah

6:44 PM

A measure is a thing u use to measure

vzn

@BernardoMeurer thx! do you have an idea for it?

0celo7

It is very important that the operations can be taken with countably infinite families.

Slereah

hence the name

Yashas

"In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size."

Why are mathematical definitions awfully complicated?

0celo7

Indeed the failure of that is why Riemann integration is shit.

Anonymous

6:45 PM

@Yashas That's a pretty good definition

Anonymous

What's wrong?

0celo7

@Yashas If you think a measure is complicated, you shouldn't be learning measure theory.

Anonymous

There are some good youtube videos on measure theory

Balarka Sen

It's not complicated. It's boring.

Yashas

@0celo7 The sigma algebra stuff appeared in probability theory.

Anonymous

6:46 PM

If you want to just know the abcd of it

Slereah

A measure just assigns a number to a subset of your space

but not all of them

Because otherwise it would be bullshit

Bernardo Meurer

@vzn Not really, but hopefully I have some minions already

Slereah

so you have to restrict the type of subsets you can measure

Balarka Sen

Truly complicated stuff are when one uses measure to do something

Slereah

For instance if you take the basic measure on $\Bbb R$, that is, the one where $\mu[a,b] = b - a$

You can't define the measure $\mu(\Bbb R)$

Because that would be too large

Balarka Sen

6:48 PM

Yes, you can. It's $\infty$.

0celo7

@Slereah what are you on about

Slereah

$\infty \notin \Bbb R$

Balarka Sen

A measure takes values on $\Bbb R \cup \{\infty\}$

Slereah

Does it?

0celo7

@Slereah measures map into the extended line

Balarka Sen

6:48 PM

Yes.

Slereah

Oh well

Nevermind then

Balarka Sen

Nonmeasurable subsets of R are complicated

Slereah

is there a simple example of a bullshit set

That isn't like

0celo7

it requires axiom of choice

Anonymous

I can give an example of use of measure theory if you've had a course on signal processing @Yashas (Although my professor shooed me away when I tried to say that his notion of integrating the dirac delta function like Riemann integration is bullshit)

Slereah

6:49 PM

Vitali set

Balarka Sen

the simplest example I know is the Vitali set

vzn

@BernardoMeurer do you want to be a "director" or work on a prj? have some AI prj ideas lately :)

Slereah

Vitali set isn't very pleasant

Yashas

@Blue your message went above my head

I can't even see it

Bernardo Meurer

@vzn I want to work on a project, but as team lead. Let me cook breakfast and we can talk more, one second

Yashas

6:50 PM

it's in deep space

Anonymous

Well, I expect you guys will have a course on fourier stuff sometime soon. We can discuss then

Balarka Sen

I need to do chemistry

:(

Anonymous

Invert your lips then

0celo7

chemistry is worse than biology

and that's saying something

Anonymous

biology is THE best

Anonymous

6:54 PM

:P

0celo7

I think you need to see a doctor

Anonymous

Something that's actually useful

vzn

@BernardoMeurer strange cant find a lot on the prjs but did find this ~3yr old dailycal.org/2014/10/07/5-amazing-projects-cal-hacks

Yashas

Biology is awesome

Slereah

Biology has more ladies, certainly

Balarka Sen

6:55 PM

ihes.fr/~gromov/PDF/16[71].pdf

This is biology

Slereah

I remember that I had a biology class once

it had all the ladies

vs my physics class

Which had one lady

Yashas

"cell division" and "hyperbolic geometry" WTH?

they appear to be sooooo unrelated lol

Slereah

There's a paper somewhere that's like

"Cat righting reflex and gauge groups"

2

0celo7

@BalarkaSen I will be picking my PhD topic with the maximum likelihood of avoiding a Gromov paper

Balarka Sen

papa Gromov is the best

you're just a hater

0celo7

6:58 PM

I do hate him

Slereah

Falling cat problem

The falling cat problem is a problem that consists of explaining the underlying physics behind the observation of the cat righting reflex: that is, how a free-falling body (cat) can change its orientation such that it is able to right itself as it falls to land on its feet, irrespective of its initial orientation, and without violating the law of conservation of angular momentum. Although amusing and trivial to pose, the solution of the problem is not as straightforward as its statement would suggest. The apparent contradiction with the law of conservation of angular momentum is resolved because...

"In the language of physics, Montgomery's connection is a certain Yang-Mills field on the configuration space, and is a special case of a more general approach to the dynamics of deformable bodies as represented by gauge fields (Montgomery 1993; Batterman 2003), following the work of Shapere & Wilczek (1987)."

Cats were the Yang-Mill field all along

vzn

hey all you mathematicians (taking over) are you gonna write anything outside of a chat room? o_O

Anonymous

Tbh cell division and graph theory doesn't look that unrelated

Balarka Sen

@vzn i'll write my chemistry homework. 0celo7 will write his PhD

what will you write?

Anonymous

That gromov paper is basically graph theory

Anonymous

6:59 PM