The h Bar

So anyway, how come most differential topology books don't have the proof that vector fields as curve tangents and vector fields as derivatives are equivalent

0celouvskyopoulo7

Ok I guess it works now

Slereah

I had to move heaven and earth to find it

0celouvskyopoulo7

@Slereah It's in Lee

user228700

Right. So, anybody?

0celouvskyopoulo7

1:05 PM

It's in Straumann

Slereah

could be

Is it?

0celouvskyopoulo7

It's in do Carmo

It's in other Lee

Slereah

I should check out Straumann more

0celouvskyopoulo7

It's in Kobayashi

It's in Wald

It's in Hawking

Slereah

whaaat

0celouvskyopoulo7

1:06 PM

What do you think $\gamma'(t)=\gamma(t)'^i\partial_i$ is doing?

user228700

IF ANYBODY KNOWS ANYTHING (other than that it exists) about the field of cognitive neuroscience, PLEASE PING ME!

0celouvskyopoulo7

It's kind of exactly what you want

@Kaumudi.H obe knows

user228700

@0celouvskyopoulo7 But he's gone, isn't he?

0celouvskyopoulo7

Yes, well you would know about that.

user228700

That, um, doesn't make much sense but listen, exactly how does he know? Is he in the field himself?

ACuriousMind

1:08 PM

@Kaumudi.H It might help if you specified what sort of information/knowledge you are looking for

user228700

@ACuriousMind I'm looking to understand the Bachelors degree one must get to get a Masters (and then a PhD after that) in the field.

user228700

(Also, if it was you who starred that, thanks very much! :-)

Slereah

@0celouvskyopoulo7 is it a proof or a "proof", though

John Rennie

@Kaumudi.H You're thinking of becoming ... a biologist???

ACuriousMind

@Kaumudi.H Given my experiences thus far, that will depend on where you want to study it much more than on the field itself.

0celouvskyopoulo7

1:09 PM

@Slereah HE might have a "proof"

But Lee has an explanation of all the various definitions of vectors

I don't know where you're looking

user228700

@ACuriousMind Ah, yes, see, this is probably why I've gotten pretty much nothing by Googling the crap out of this.

Slereah

user228700

@JohnRennie Erm, gimme a few to properly process this epiphany I've had :-P

Slereah

The fancy proof

user228700

Dang it, I don't yet know where I'll be able to get in for my Masters :-/ This is proving to be a bit problematic...

John Rennie

1:11 PM

@Kaumudi.H you probably ought to eat less of those funny looking red mushrooms with the white spots :-)

user228700

@JohnRennie I dunno what you're talking about :-P

ACuriousMind

@Kaumudi.H Yep. The structure of academia is culture-/country dependent - e.g. if you want to study in India, a Western European neuroscientist probably couldn't really help you at all with that.

user228700

Nah, I'm definitely not looking to study in India. This particular field has next to no scope over here. There aren't very many places doing the kind of research I'm interested in.

0celouvskyopoulo7

How does one get out of india

user228700

I've been Googling to find out how potential universities to which I'd want to apply accept students for this program but information is...scarce :-/

0celouvskyopoulo7

1:13 PM

@Kaumudi.H Does your family have money to send you abroad?

ACuriousMind

Sure, but it goes on - if you want to study in Europe, the account of a North American scientist is probably also not very useful.

@0celouvskyopoulo7 By plane, I imagine :P

user228700

@0celouvskyopoulo7 Some universities offer scholarships, y'know. We have some money, yes. Suffice it to say that money is not that big a concern if I'm being offered some sort of scholarship.

Slereah

@ACuriousMind follow the silver road

0celouvskyopoulo7

@Kaumudi.H I have a few scholarships

It's going to cost you at least $45,000 per year as a foreign student

Slereah

lol

ACuriousMind

1:14 PM

@Slereah You mean the silk road?

Slereah

US university costs

@ACuriousMind yes

ACuriousMind

@0celouvskyopoulo7 She didn't say she wanted to go to the US yet :P

user228700

@0celouvskyopoulo7 ...which is why I've mostly been looking up universities in Canada :-P

0celouvskyopoulo7

Ok

Slereah

My university was 400€ per year

user228700

1:15 PM

But Europe as well. Trouble is that I dunno many universities in Europe :-/

Slereah

How does the US even still exist

0celouvskyopoulo7

@Slereah Greatest country on Earth

ACuriousMind

@Slereah Historical inertia and nuclear weapons :P

Slereah

@0celouvskyopoulo7 except on the scale of math literacy

0celouvskyopoulo7

Ban @ACuriousMind

Slereah

1:16 PM

Life expectancy

etc etc

0celouvskyopoulo7

Do we have the best GDP/capita ratio?

ACuriousMind

@Kaumudi.H Well, there are many. I have no idea which might be good to look at in neuroscience, though

Slereah

Per capita, probably. Median, probably not

0celouvskyopoulo7

@ACuriousMind "there are many"

sage advice

Slereah

Let's see the US median income

not too bad, actually

#5

0celouvskyopoulo7

1:18 PM

@JohnDuffield greetins

user228700

@ACuriousMind Right. Hmm, OK, I think the best thing for me to do will be to look up that and then figure out what kind of bachelors degree I might need.

Slereah

The US isn't quite Chile yet

user228700

Gah, this epiphany could've done me a big favor and come to me when I WAS NOT TWO WEEKS AWAY FROM APPLYING TO UNIVERSITY!

0celouvskyopoulo7

@ACuriousMind Can you show me how to draw $\mathfrak P$?

@Kaumudi.H maybe you shouldn't be making such huge life decisions on a whim

user228700

@0celouvskyopoulo7 Oh, there's a difference between a whim and an epiphany.

ACuriousMind

1:20 PM

Oh, we have a chat session coming up...does anyone have topic suggestions?

0celouvskyopoulo7

@ACuriousMind drawing competition

ACuriousMind

@0celouvskyopoulo7 No, I can't actually write Fraktur by hand

user228700

@ACuriousMind Awesome! Chances of someone seeing that starred request are even greater now!

0celouvskyopoulo7

I doubt we have any neuroscientists

your best bet is to go to reddit

r/science maybe

they might close the post though

not sure

Slereah

Chile is the country with the worst income inequality

0celouvskyopoulo7

1:22 PM

what does little o notation mean again

ACuriousMind

Stan Shunpike was a neuro student iirc but he's not been here recently

0celouvskyopoulo7

Stan was very confusing to me

user228700

@ACuriousMind Stan Shunpike?!

ACuriousMind

lol

0celouvskyopoulo7

He studied neurology, econ, and GR

user228700

1:23 PM

vignette2.wikia.nocookie.net/harrypotter/images/4/49/…

user228700

^ This guy?! (:-P)

0celouvskyopoulo7

clearly not

ACuriousMind

clearly yes

0celouvskyopoulo7

@ACuriousMind Ugh

Elven lord is pretty lazy

We're supposed to have a take-home final for alg top

He hasn't given it to us yet, so I emailed him

he completely forgot about it

ACuriousMind

Sigh...why would you tag a question about a circuit with feynman-diagram and nothing else? Sometimes I don't understand people.

0celouvskyopoulo7

1:27 PM

Feynman circuit, clearly.

ACuriousMind

As an aside, I've noticed that the noise level at physics.SE has risen immensely as of late. It's almost as bad as is the noise level at stackoverflow.com. Perhaps almost all of the key questions that don't require a book as an answer have been asked. — David Hammen 17 hours ago

Slereah

he wants to know how this circuit works from a QED perspective

0celouvskyopoulo7

@ACuriousMind interesting

@blue how do I pronounce "Minakshisundaram"?

As on the tin?

is $\mathscr E$ to curly?

Slereah

it's quite curly

$\mathcal E$ is better

orthocresol

@JohnRennie Don't give me ideas. :)

0celouvskyopoulo7

1:41 PM

$H_k=\eta\mathsf{H}_k$

using mathsf unironically for a function should be illegal

Koolman

Why we cannot conserve angular momentum at centre @JohnRennie @Yashas

Yashas

@Koolman Your question is unclear.

Koolman

Slereah

"Manifolds are a bit like pornography: hard to define, but you know one when you see one."
- S. Weinberger

0celouvskyopoulo7

he actually said that?

Evident!

Slereah

1:47 PM

He is quoted as saying it, anyway

0celouvskyopoulo7

@Slereah let's see...

why $\mathcal C$?

That proof seems straighforward

Not too fancy

Slereah

I know, it's written right on it!

0celouvskyopoulo7

Did you check Straumann?

Slereah

Nah

0celouvskyopoulo7

@Slereah what?

Slereah

1:49 PM

I have to go to my sister's house to check on the cat

@0celouvskyopoulo7 "évident"

The proof is trivial, obviously

0celouvskyopoulo7

what does meme in French mean, anyway

even

Slereah

même means "same"

0celouvskyopoulo7

or same or actual

Ugh they call manifold points $m$

Slereah

the french translation of meme is "mème"

0celouvskyopoulo7

$T_mM$

Slereah

1:51 PM

Since it's a calque on gene, and that's "gène" in French

0celouvskyopoulo7

0

Q: Decomposing a tensor into symmetric and anti-symmetric components

I was looking at one of my textbooks and saw terms like $X_{(\alpha\beta)[\dot{\alpha}\dot{\beta}]}$ when I suddenly realised I dont actually know how to write this out. My first guess was $$X_{(\alpha\beta)[\dot{\alpha}\dot{\beta}]}=\frac{1}{2}(X_{\alpha\beta\dot{\alpha}\dot{\beta}}+X_{\beta\al...

tensor-calculus

oh god

Slereah

How do you write the contraction operator

Do you go like O'neill with $\downarrow$

0celouvskyopoulo7

2:06 PM

wot

Slereah

Oh wait, he uses $C$

What did he use $\downarrow$ for

I forget

0celouvskyopoulo7

@BalarkaSen Interesting result of Minakshisundaram-Pleijel: Let $M$ be a compact surface, and $\lambda_j$ be the eigenvalues of the Laplacian. Then $$\sum_{j\ge 0}e^{-\lambda_jt}\sim \frac{\mathrm{vol}(M)}{4\pi t}+\frac{\chi(M)}{6}$$ as $t\downarrow 0$.

So knowledge of the spectrum determines the topology of the surface!

Phase

Idek whether to flag this physics.stackexchange.com/questions/330440/…

Slereah

Ah, he uses up and down arrows for raising and lowering operators

0celouvskyopoulo7

One can indeed hear the shape of a compact 2-drum without boundary :)

Slereah

2:11 PM

Generalization of the musical isomorphisms, I guess

0celouvskyopoulo7

@ACuriousMind I'm thinking that hear the hypersphere guy wasn't all that crazy

One can hear the shape of a compact 2-manifold

Slereah

Is that the harmonics on a manifold thing

0celouvskyopoulo7

@Slereah what?

the $\lambda_j$ are defined by $\Delta u=-\lambda_ju$

AccidentalFourierTransform

and $\Delta$ is defined by $\Delta=-\Delta$

0celouvskyopoulo7

no, it's $\Delta=(d+d^*)^2$

AccidentalFourierTransform

2:20 PM

no, its $dd^*+d^*d$

John Rennie

@orthocresol :-) You wouldn't. Would you? :-)

Secret

In a few days, I might plan to do something crazy: Doing classical mechanics using cardinal numbers

0celouvskyopoulo7

don't.

loltospoon

What approximation method would I use for an electron illuminated by visible light?

Secret

The idea is first inspired from the following, which is inspired from a game called powder toy:

in Mathematics, 13 mins ago, by Secret

[Random] Consider a finite bag containing infinite number of gas molecules such that the concentration of gas in the bag is given by $\Bbb{Z}/n$ where $n\in \Bbb{Z}$. Initially, the concentration of gas in the bag is $\Bbb{Z}$. Now make a hole to leak out the gas, then as the gas fill in in the surrounding space, its concentration will go down indefinitely as $n$ increase without bound, but always less than $\aleph_0$

user228700

2:31 PM

@JohnR: No, not Biology. Well, not in the crudest form anyway; Cognitive Neuroscience is different from Neurology.

user228700

Dang it, is there no official chatroom for Biology?

Secret

NB due to the existence of bounded countable sequence, it is possible to pack infinite number of things into a finite sized space

The Biosphere

General discussion for biology.stackexchange.com

1

user228700

Ooh, thanks! :-)

loltospoon

Anyone have any ideas?

Slereah

Take an eletron under a plane wave EM field

Good first approximation

Phase

3:18 PM

As someone who's in the early stages of learning basic topology, what use do Equivalence and order relations have later on?

Slereah

A fair bit

Especially for quotients

Phase

Quotients?

What's a quotient in the context of topology?

Slereah

A quotient is when you take a topological space and define equivalence classes with respect to some equivalence relation

en.m.wikipedia.org/wiki/Quotient_space_(topology)

Ahah

The PDG people answered me

They open the email with "Dear Colleague"

They are not imagining a crazy man is ordering that book for his house

Sir Cumference

@ACuriousMind I dunno, it's kind of like why you'd strongly recommend a book if you like it

ChatJax gave me plenty of headaches

ACuriousMind

@SirCumference I'd recommend the book once and then drop it if they'd show no interest :P

@Slereah You are truly unimaginable.

Sir Cumference

3:29 PM

@ACuriousMind Ok, better analogy: kind of like why you'd tell a family member to get an android instead of an iphone (or vice versa)

ACuriousMind

Does anyone else have issues where the question tabs are empty and the questions only show up after several reloads?

Emilio Pisanty

@ACuriousMind nope

I do have issues where I'm redirected from physics.stackexchange.com to com.com on my mobile

thankfully now my browser stops at the Something Fishy Is Going On ssl error screen

I don't think it's related to your issue though

Phase

@Slereah thanks

loltospoon

What type of approximation method might I use for the Ahronov-Bohm experiment?

ACuriousMind

3:45 PM

Why do you want to use an approximation method? What quantity do you want to approximate?

Secret

Hey guys, are there any experimental set up that can allow you to watch the formation of an entangled state from a product state in real time?

Slereah

Was general relativity ever sergeant relativity?

6

Did it have to move through the ranks

Emilio Pisanty

@Slereah sargeant

David Z

hey y'all, I think I can make it to this chat session after all :-)

Emilio Pisanty

scratch that, it's actually sergeant

loltospoon

3:52 PM

@ACuriousMind I'm doing a practice exercise made up by my professor and it is extremely vague. We learned about approximation methods in my QM class, such as Perturbation theory, adiabatic theorem, variational principle, etc...

It only says "Identify the approximation methods you would use for each type of quantum system"

Emilio Pisanty

@loltospoon if your professor sets vague questions, what he deserves is vague answers

loltospoon

So for the Ahronov-Bohm experiment, we see that the vector potential affects the phase of a beam of particles

@EmilioPisanty I wish I could tell him off, but he controls my grade so.....

ACuriousMind

@loltospoon I'm voting to close this question as unclear what you're asking. ;P

loltospoon

Aaaaaand I have a final exam tomorrow morning. This sucks :(

Emilio Pisanty

@loltospoon just write whatever is vaguely appropriate from the methods you've covered and move on

loltospoon

3:54 PM

@EmilioPisanty I don't need to write anything, this is just practice/studying for my final tomorrow. I just need to understand things

My guess would be something that helps me notice a phase difference

Emilio Pisanty

@loltospoon there is nothing to 'understand' there

it's just a poorly phrased question

if you're doing this to study, there's a gazillion better ways to brush up on QM than that

loltospoon

@EmilioPisanty I'd love to think that, but my professor would just say something like "Oh, you couldn't figure that out? It was CLEARLY [BLANK]"

What a wonderful world.

Emilio Pisanty

@loltospoon Do you know for sure that that exact question will show up in the exam?

loltospoon

@EmilioPisanty possibly. He is a sly goose, so he might take some questions from this practice set.

I need to understand each question here as if every single one of them will be on the final though. And with some other questions from my book. I know it sounds like a bit much, but my professor made us a nice deal

He said that if we get an A on the final, we get an A on the class.

So......

I'm studying like my life depends on it!!1

David Z

@ACuriousMind you running the chat session today?

The Biosphere

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