The h Bar

Balarka Sen

5:00 PM

hell of a name

Obliv

This looks like a way to overcomplicate something.

Slereah

Metric of an ideal gas

0celo7

lol

Obliv

"The states of thermodynamic equilibrium are considered as points of an abstract equilibrium space in which a Riemannian metric can be introduced in several ways."

how does someone think of this .-.

0celo7

how does someone think of 0

Obliv

5:02 PM

did you see that post too? @0celo7 lol

0celo7

what?

no, it's a legitimate question

how does someone think of anything not in the night sky

Slereah

Originally 0 mostly came up in accounting books

It indicated that no more debt was owed

0celo7

If you can owe no more debt your lender is bad at his job

Secret

Confinite topology is soooooooo weird, but I kinda like it

Obliv

@0celo7 math.stackexchange.com/questions/1942112/… thought you were talking about this

Secret

5:04 PM

Slereah

All your pictures are wrong pictures

0celo7

What is that

Obliv

Maybe you should invest in a drawing tablet @secret

Would make your drawings much neater .. probably

Secret

0celo7: Trying to understand the proof of T1 does not imply hausedoff

Slereah

You can do the proof with just a counterexample

Secret

5:07 PM

@Obliv I sometimes use that, but it is not quick enough

Slereah: The cofinite topology on an infinte set is a counterexample. What I am trying to understand is why it is a counterexample

The issue is that I soemtimes get lost easily when reading the explanation of the proof itself

because each word has too many descriptions packed into it in layers

That is:

Slereah

Well here's a tip

Learn topology first

Secret

That's what I am doing currently, I use these set of notes to learn topology (and possibly reading more books afterwards

Slereah

Then why are you learning about Hausdorf properties before you know what a cofinite set is

Secret

Because the note laid out like this

Slereah

That's a wikipedia page

user218912

5:12 PM

@Obliv @0celo7 whoah you know stat mech?

user218912

help me.

user218912

because I'm dying.

Secret

I cap that from that ntes link I gave above, so perhaps they are plugging in wikipedia stuff?

Slereah

Obliv

@secret any reason why you're using these lecture notes instead of a textbook?

Secret

5:14 PM

Because I don't know any good ones and I tried to find notes by googling?

Obliv

@iceL nope but maybe 0celo7 knows some

Slereah

Isn't Spivak the standard topology book

Ahahah

user218912

@Obliv you're not allowed to post links like that.

Obliv

oh my bad

Slereah

What a square

Obliv

5:16 PM

@secret why not try bourbaki? A quick google search should yield you a link..

Secret

Doing it now

user218912

I hate my icelandic history class now. it's 3 hours long and the prof sucks.

Slereah

@Obliv you mischievous little imp

Obliv

^^ @slereah I'm sure bourbaki doesn't mind. Knowledge shouldn't have a price tag in an ideal world anyway.

Slereah

You don't recommend Bourbaki to learn topology

Obliv

5:20 PM

Why not?

Slereah

That's like saying to someone who needs a computer to fashion one himself out of a block of raw ore

2

Obliv

But that way you'll be able to understand how your computer works

ACuriousMind

@Slereah ...how do you prduce your computers? :P

Secret

Well, although I have no background on topology, I do want to self learn to the level that I can handle all the deep and nitty gritty stuff, because of 3 reasons:

Johnny Rockex

hello

Secret

5:24 PM

1. Most of 0celo7, Danu and ACM's conversation about bundles are incomprehensible to me and that annoys me
2. I need topology to go further in QFT and GR

3. (I will leave this for now)

Obliv

Hi @johnny

Secret

anyway just have borburbaki downloaded, what is the name of Spivak's book?

NB: My way of handing things that annoys me is to understand why it annoys me. This is one reason I have a drive to learn various things, e.g. I paid attention in thermodyanmics class because it annoys me

This Spivak book?

Slereah

You need basic physics for QFT and GR

user3183724

I have a rather elementary question but somehow I'm not sure how to proceed. Say we have some coupled spin 1/2 Hamiltonian $$H = - \frac{ \omega_a}{2} \sigma_{z,1} - \frac{ \omega_a}{2} \sigma_{z,2} + J_{12} (\sigma_{+,1} \sigma_{-,2} + \sigma_{+,2} \sigma_{-,1} )$$ then one can diagonalize this by defining $$\sigma_{S,A} = \sigma_{+,1} \pm \sigma_{+,2}$$ I am actually not sure how the corresponding $$\sigma_{z,i}$$ operators then change.

In essence I am doing a basis transformation, so I should be able to formulate some unitary right? Just a note, the two frequencies of the spins are equal, that's not a mistake.

What is a mistake (that is too late to edit now) is that it is more natural to write $$\sigma_{S,A}^\dagger = \sigma_{+,1} \pm \sigma_{+,2}$$

DanielSank

5:59 PM

What's going on in here?

Party?

0celo7

Topology test was really easy :D

Balarka Sen

Congrats

Secret

DS: me trying to study topology, other h barers talking about alcohol, strings and ranodm stuff, and then user 3183724 asking a diagonalisation question of two interacting spins

0celo7

It was some definitions, proving $\Delta\subset X\times X$ closed $\Leftrightarrow $ X Hausdorff, continuity in terms of nets, and box vs. product topology

Balarka Sen

sounds simple enough

0celo7

6:05 PM

Yes, now time to freak out about the analysis test

@BalarkaSen There's something called the Bochner theorem in geometric analysis which states that under certain curvature conditions, a compact $n$-manifold has first Betti number at most $n$.

DanielSank

@Secret What about alcohol?

0celo7

What's the intuition for the first Betti number?

DanielSank

Not seeing that as I scroll up...

0celo7

@BalarkaSen And under a slightly stronger condition, the first Betti number is zero.

Secret

For starters: 0celo7, slereah and Johnrennie chat about drinking antifreeze, methanol, ethanol and how they screw the body (and not screw the body). We then talked abotu various way to prepare alcohol such as onion volka garlic volka etc.

DanielSank

6:09 PM

@Secret gross

ACuriousMind

volka?

l is nowhere near d

0celo7

@BalarkaSen ACM said something about "holes"

Balarka Sen

@0celo7 It's the rank of H_1. And you know the intuition for H_1...

I don't like the hole business but yeah. The surface of genus g has b_1 = 2g.

Secret

@0celo7 What is the name for the standard spivak topology text called?

0celo7

@BalarkaSen From my perspective (Hodge theory), the Betti number is the cohomology rank.

Obliv

6:11 PM

I think @slereah said there was a standard spivak top. text @secret

0celo7

I don't have a feeling for those at all, even after reading half of Bott & Tu

Obliv

Not 0celo7.

0celo7

I don't know of a topology book by Spivak.

I have the first two books in his geometry series.

They're very good.

Balarka Sen

@0celo7 It's not. It's the rank of the k-th homology group, not the k-th cohomology group. That's the n-k th betti number.

Secret

I know, but since slereah was afking, I figure I will ask the other topology guys such as bala and 0celo7

0celo7: Ok. I planned to deal wiht diff geom after I get my head around topology

0celo7

6:13 PM

@BalarkaSen Poincare duality on compact manifolds gives isomorphisms between $H^{n-k}$ and $H^k$.

Balarka Sen

You have coefficients in R. Not everyone does.

But then, yeah.

0celo7

@BalarkaSen Yeah. Hodge theory.

ACuriousMind

@BalarkaSen I already had that conversation with him :P

0celo7

Real coefficients

Balarka Sen

@ACuriousMind I wonder how that turned out...

@0celo7 Do you know anything about the fundamental group?

0celo7

6:17 PM

Yes

Secret

filters, really? "head explode and have to go to sleep cannot handle the overloading of confusion"

Balarka Sen

Pick a bunch of non-homotopic loops in your compact manifold which generates the fundamental group. The cardinality of that set is b_1.

Slereah

What if it's infinite :O

Obliv

Aw man does anyone know how I can extract the values stored in excel boxes to c/p ? I have them set as equations and when I copy them, all I get are the equations.

Balarka Sen

Compact manifold. Can't happen.

Slereah

6:19 PM

Errr

What about...

Horned sphere?

Balarka Sen

That's homeomorphic to S^2

0celo7

@BalarkaSen Yeah, first homology is the abelianization of the fundamental group.

Balarka Sen

Which has pi_1 = well, 0.

Slereah

Is it?

Balarka Sen

Yes.

Slereah

6:19 PM

odd

Balarka Sen

That's the whole point of the horned sphere.

Slereah

Can you do a compact version of the loch ness manifold?

0celo7

what is that?

Slereah

$\Bbb{R}^2 \#T^2 \#T^2 \#T^2 \#T^2 ...$

I guess you could do that to $S^2$

0celo7

what does that look like?

things like this always make me uneasy

Slereah

6:21 PM

The loch ness monster

Hence the name

It's a plane with infinitely many handles

Balarka Sen

That's by construction not compact

0celo7

I see

Slereah

What if you did it to a sphere, though

Balarka Sen

Still noncompact

Slereah

Why not

It's a connected sum of compact manifolds

Balarka Sen

6:23 PM

Infinite connected sum.

Slereah

Hm, although

ACuriousMind

And why should an infinite connected sum of compact manifolds be compact?

Slereah

Yeah

I guess since it's infinite there's no finite subcover

Balarka Sen

@0celo7 I said something wrong, I am sleepy; I meant which generates the nontorsion part of $\pi_1$. And even then I need to assume $\pi_1$ is abelian. Very sorry.

So I guess I don't have an entirely geometric explanation of the betti number for ya.

0celo7

It's annoying that dR cohomology has no real interpretation, AFAIK.

Slereah

6:26 PM

DRRR DRRR DRRR

0celo7

@ACuriousMind Got a 100 on that PhD level probability homework

Balarka Sen

What do you mean "real interpretation"?

ACuriousMind

@0celo7 The least you could do :P

Bernard Meurer

In the latest episode of insane chemistry class two thirds of the classroom have given up attending theoretical lessons

0celo7

@ACuriousMind I have another problem set due Friday lol

Tomorrow I'll despair over it

@BalarkaSen What """is""" it?

ACuriousMind

6:29 PM

@BernardMeurer Has anyone complained about the class to the professor?

Slereah

Oh no

I accidentally bought raspberry jam

Instead of strawberry

Bernard Meurer

@ACuriousMind Apparently he's been at it for years

ACuriousMind

I had a lecturer in my first semester who also went waaaaaay to fast, but it was a genuine mistake because he thought since no one was complaining everything was fine.

Bernard Meurer

@ACuriousMind My mentor (older student that guides the freshman) told me that everyone skips the lessons and learns by themselves from the appointments since the man is insane

ACuriousMind

After someone told him most people didn't understand a word he was saying, he slowed down considerably and did an amazing lecture

Bernard Meurer

6:30 PM

I'll keep attending though, but I shouldn't

0celo7

@ACuriousMind JACK QUEEN KING ACE ARE WORTH 10

haha

ACuriousMind

@0celo7 lol

0celo7

he's saying that most of the class got that wrong

ACuriousMind

@Slereah The horror!

Slereah

That is pretty subpar jam

ACuriousMind

6:31 PM

I agree, I don't like raspberries much either

0celo7

@BalarkaSen Interesting. My topology exam is printed in the same font as Hatcher.

Bernard Meurer

@ACuriousMind The man is crazy

and I'm literally freaking out

ACuriousMind

Many university professors can seem slightly insane :P

Doesn't mean they have to give bad lectures

Bernard Meurer

Also I don't think Boolean algebra forms a field

Balarka Sen

@0celo7 It all depends on how you want to interpret it. I don't know of any entirely topological way to think of it. It's like a completely different, new idea - a homotopy-invariant coming from obstruction to solving differential equations on your manifolds.

Bernard Meurer

6:33 PM

@ACuriousMind Look, I don't think I'm stupid. I'm not a genius, but I'm not stupid. It can't be expected for me to not understand anything is a class for freshman

Balarka Sen

That's why it's exciting, in my opinion.

0celo7

I know that's why it's exciting

But if I had to explain a dR group to a 5th grader, I could not.

ACuriousMind

@BernardMeurer I know, I'm not doubting the lecture is horrible. I'm doubting nothing can be done about it

Balarka Sen

I couldn't either, not in 2 lines.

Bernard Meurer

@ACuriousMind Well I've sent an email to my course's headmaster, waiting on a response

Balarka Sen

6:36 PM

I like Hatcher's font.

Bernard Meurer

@ACuriousMind We haven't been through Calc I yet and this guy wanted us to show something about the probability density of an electron on an s3 radius being iso-something by integrating over the volume of the sphere

or something like that, it was all chinese to me

0celo7

> the ultraproduct of the universe

set theory is meme math

Bernard Meurer

set theory is nice

ACuriousMind

@BernardMeurer Yeah, that's clearly inappropriate

0celo7

@BernardMeurer Isotropic?

Balarka Sen

6:39 PM

TIL there is a group called SU(1, 1)

0celo7

@BalarkaSen Meh, it makes it look like an intro calc book or something.

Bernard Meurer

@0celo7 Don't know, like, the probability density for a given radius is the same all around the atom or something

idk

0celo7

Yes, isotropic.

Slereah

Well yes

Bernard Meurer

Also I didn't get something to do with penetration

Slereah

6:40 PM

There is a SU group for every (p,q)

Balarka Sen

What do they do

Slereah

They unitary

Balarka Sen

That's not very specific

ACuriousMind

@BalarkaSen They leave the pseudo-inner product with p pluses and q minuses invariant.

Bernard Meurer

Or something he called "bulletproofing" of the effects of the nucleus on one electron by another, innermost electron

something like that

Slereah

6:41 PM

They preserve the scalar product of signature (p,q)

Balarka Sen

@ACuriousMind I see.

Slereah

If $L \in SU(p,q)$ then $\langle LA, LB \rangle = \langle A, B \rangle$

Balarka Sen

Why are they interesting? (SU(1, 1) is because, I learnt, it acts on the unit disk and that action is "the same" as the action of SL2(R) on H^2, after identifying H^2 conformally with the disk)

0celo7

@Slereah that's SO, not SU

Slereah

What does SU(p,q) do

My copy of Robinson has shipped

0celo7

6:52 PM

Nerd.

Who reads books?

Slereah

You're right

I should throw that copy of Steenrod away

0celo7

Do it.

No one needs it.

Betcha won't do it!

Slereah

you're right

I'll never throw it away

keep it forever

0celo7

That's fine, nerd.

Balarka Sen

Nerd is good

Slereah

6:55 PM

I'm reading a signal processing book

They use $j$ for the imaginary unit

Filthy plebs

Balarka Sen

yeah, ugh

Physics Meta

1

Q: Note: why the migration close reasons are stronger as the others

This question is now closed as offtopic on 2 reasons: It is mainly math, although its markup and formulation clearly shows the described problem is a physical problem. The current review practice is that also this type of questions are closed as offtopic and sometimes migrated to the MathSE. It...

0celo7

Nerds don't get the grils @BalarkaSen

Balarka Sen

Who cares for em

0celo7

Most straight men

Slereah

6:58 PM

Hawking got 'em

0celo7

Hawking is famous, that's an exception.

Slereah

He wasn't famous when he got married

0celo7

Proof

Maybe he wasn't a nerd.

sure

Dear god

7:01 PM

Ok, set of measure zero get the grils

Oh she's a butter face

Slereah

Well Hawking's face is basically butter these days

0celo7

Heyooooo

Slereah

Why is he spewing bullshit about AI instead of rewriting the large scale structure of spacetime

0celo7

We need a second edition

Slereah

7:03 PM

yes

Things have changed since then

Also maybe write that Godel proof explicitely

0celo7

What has changed?

Slereah

The state of cosmology, for a start

HE is pretty old when it comes to cosmological data

Balarka Sen

@Slereah also about extraterrestrial life

Slereah

It's not like Hawking is Neil Degrasse Tyson

He is actually famous in physics circles

Obliv

Poor dude. At least his condition doesn't disable him from doing physics.

Slereah

7:20 PM

Hm, what was Hawking's last good paper

Let's see

0celo7

His thesis probably

Slereah

I liked his 1992 paper

arxiv.org/pdf/hep-th/0107088v2.pdf

good title

0celo7

ABSTRACT

Slereah

No

peterh

@Slereah People wants wizards. He is a wizard. At least he makes the sciences more popular, I think his effect is clearly positive for the governmental support.

peterh

8:40 PM

@ACuriousMind Please think to the prohibitve form of the Golden Rule: "One should not treat others in ways that one would not like to be treated."

ACuriousMind

8:50 PM

@peterh Uh, what kind of thought do you want to hear? That it's a simplistic rule that yields no useful directives for what to do when faced with people who don't follow it?

0celo7

Lol

ACM showing he never went to kindergarten

ACuriousMind

@0celo7 Hmmmm?

0celo7

> W. H. Woodin, A. R. D. Mathias, and K. Hauser
[∞] “The Axiom of Determinacy.” de Gruyter Series in Logic and its Ap- plications, Walter de Gruyter & Co.

what kind of date is [∞]

ACuriousMind

Written at the End of Time, obviously

0celo7

wtf

how can you cite it then :o

@ACuriousMind if you don't respect the rule there you get your ass beat

Wipqozn

9:33 PM

:32606187 Please don't flag 2 hour old messages to be deleted due to being "off-topic"

IT's a waste of moderator time.

0celo7

ooo, what message was flagged?

Wipqozn

The message I just deleted by mistake posted by @peterh

I was trying to reply to it, but deleted it by mistake

Interestingly enough it still shows his name on the ping, nifty

Figured it would just show the message id, aka :12342342340193

user218912

condensed matter is not bird after all, this problem set is hard.

peterh

@JohnDuffield The acceleration will be zero, I think this is what you interpret by F=ma that the force is zero. But the acceleration will be zero due to the time stop, I am not sure how can it be analogized to a Newtonian force.

Danu

10:48 PM

@0celo7 So... then nobody respects the rule, and everybody gets their asses beat?

ACuriousMind

I don't remember anyone getting their asses beat in kindergarten :P

Danu

ACM always punches to the face

Did Philippe ever return?

I've made loads of progress on complex geometry in the past 24 hours.

ACuriousMind

@Danu I'll not reveal my secret fighting techniques!

Danu

> punch to the balls

ACuriousMind

@Danu Not sure, but I don't think so

@Danu Good for you, although I hope you slept some of those hours ;)

Danu

10:57 PM

@ACuriousMind 3:30-9:30 :) it's alright

I understood both the Euler sequence and the blow-up constructions!

I really am curious if this will eventually help me understand mirror symmetry :P

0celo7

@ACuriousMind You went to a kindergarten for wusses.

ACuriousMind

@0celo7 It was a loving and nurturing environment.

user218912

11:14 PM

I can't do this integral... $$\int_0^\infty \frac{dt}{\tau} e^{-t/\tau}$$

user218912

it's supposed to be $= \tau$

user218912

but I get some weird thing.

ACuriousMind

Pretty sure that integral is equal to 1.

Danu

lol

SUBSTITUTE

user218912

@ACuriousMind you're right.

user218912

11:21 PM

I'm probably doing something wrong.

user218912

oops I forgot to multiply by $t$ in the integral.

0celo7

@ACuriousMind Wtf, why were strangers loving you

ACuriousMind

'cause I was adorable? :P

0celo7

grossly inappropriate

user218912

lol

0celo7

11:29 PM

@ACuriousMind If someone loved my kids, I'd pull them out of that "kindergarten." And sue them.

The kindergarten is exactly that, a garden. The kids must grow like carrots into strong men to fight for the country!

ACuriousMind

@0celo7 You might have an overly narrow and sexualized conception of "love", I think

@0celo7 If carrots are growing into strong men, you might be living too close to some toxic mutagenic waste :P

0celo7

@ACuriousMind Gross.

user218912

@0celo7 then how do you explain this

user218912

Sep 7 at 0:08, by 0celo7

I love rabbits.

user218912

weirdo

0celo7

11:32 PM

I don't remember kindergarten

I remember being smarter than the teachers

but that's about it

@IceLord I like rabbits. They're fluffy and adorable

user218912

@0celo7 then why is it gross if ACM was adorable and loved by random people?

0celo7

@ACuriousMind What was your avatar when we met?

ACuriousMind

I'm fluffy and adorable, too!

0celo7

@IceLord It's not. I just wouldn't want someone random loving my child.

ACuriousMind

@0celo7 I can't remember whether it was Edwin or Morte. (Sinister hooded bearded dude or skull with googly eyes)

0celo7

11:34 PM

@ACuriousMind I think of you as a skeli, so I have a hard time imagining you being adorable.

ACuriousMind

Well, I was adorable. Nowadays I'm fearsome

0celo7

Doubtful unless you've (a) bulked up since I last stalked you on facebook (b) carry around a knife and stab people

or both, I guess

ACuriousMind

Why would I carry a knife? I'm not living in 'Murica where I have to fear clown assassins

0celo7

@ACuriousMind You said you're fearsome

ACuriousMind

@0celo7 I've got a mighty roar

@0celo7 Also, wtf

0celo7

11:38 PM

My fears are (a) being the dumbest person in the room when at least three are present (b) being stabbed (c) losing a limb

@ACuriousMind What?

Stop smoking peyote pls

ACuriousMind

...does one actually smoke peyote?

0celo7

I don't know. I'm not a drug-using terrorist.

Analysis homework moved to monday >:((((((((((

@ACuriousMind You've told me before, but why do we define PG bundles with a right action?

ACuriousMind

So that it doesn't conflict with the left action from the transition functions.

0celo7

11:58 PM

@ACuriousMind And is there some special reason we can't rig those to act on the right?

ACuriousMind

No, you could switch the actions and have them act from the right and the bundle action from the left

0celo7

exactly

so your answer is, in JD terms, a "nonanswer"

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