The h Bar

Balarka Sen

10:01 AM

drag your family with yourself :p

user228700

No, I want to go on my own, you see!

Balarka Sen

okay

Sid

@Kaumudi.H then, don't tell your parents

I never understood why we would have to tell every damn thing to our parents..

user228700

@Sid Hehe, that makes sense to do! x'D Run away, you suggest?

Balarka Sen

you youngsters have a thing for runaways

Sid

10:08 AM

@Kaumudi.H Not really. I would do it in College time though if you have like 3-4 holidays. Say that you are in College but go wherever you want and then comeback

user228700

Ah! x'D Well, my parents aren't conservative in the slightest, nor are they overprotective, because of which I'm certain that they will allow me to go. When though, that is the question. I'd like to be able to go next summer!

Rana

@JohnRennie, my post......

Sid

@Kaumudi.H I am surprised when you say Indian Parents aren't conservative

user228700

@Sid No, I did not say that (all) Indian parents are not. Mine aren't :-)

Balarka Sen

I think that word is overused

Sid

10:12 AM

^exactly

Balarka Sen

Mostly popularized by overmodern kiddos of the upper middle class family.

user228700

Overmodern? x'D Oh, I certainly do not belong in that class, then.

Sid

People tend to relate conservatism to choice of clothes and hour of time till which they are allowed to move out or similar stuff

@BalarkaSen what is "overmodern"? :o

user228700

@Sid I have only been subjected to uses of this word in this particular context. I don't even know what it really means.

Prathyush Poduval

I didn't know shantiniketan still exists

Though it became some ruins or something like that

Balarka Sen

10:16 AM

@Sid When you're so modern and open-minded that your brain starts falling out of your half-open skull

And dangle in front of your face like a sack of slime

Sid

Lol

Prathyush Poduval

@BalarkaSen I've seen that in a movie......

user228700

@Balarka: What do you really mean?

Anonymous

@PrathyushPoduval Ah, it does. Nice place in terms of natural scenery.

Sid

No, seriously, what is "overmodernism?"

Prathyush Poduval

10:17 AM

@BalarkaSen youtube.com/watch?v=_nb-jtcLXzY

#HollyShit || Episode 17 || WTF Medical Miracles

►

Anonymous

@Sid I doubt such word even exists

Anonymous

Probably some meme

Prathyush Poduval

@Blue do they have classes still?

user228700

@PrathyushPoduval Ooh, what classes are you talking about? (Also, hi! :-)

Slereah

"Let Y be a Cohen-Macaulay variety."

>:|

you can't start a paragraph like that

the hell is this

Prathyush Poduval

10:19 AM

@Kaumudi.H Well, shantiniketan was a university right? How are you're classes going?

John Rennie

@Rana Hi Rana

user228700

@PrathyushPoduval Ahhh, right!

Balarka Sen

@Sid It's a made up word by me, intended as a pejorative towards the kids of the economically stable families who think any kind of restriction on their daily life is opposition against freedom of thought or action or speech or whatever.

user228700

@BalarkaSen Nicely put. I think I understand what you mean.

Anonymous

@PrathyushPoduval What classes ? It's a whole town! I think you're talking about Visva Bharati

user228700

10:20 AM

@PrathyushPoduval My semester ended two weeks ago and my finals are ongoing! :-) And for you?

Sid

@BalarkaSen hmm. I almost fit your definition but I don't

Prathyush Poduval

@Blue okay. My history is all messed up then :P

@Kaumudi.H College is going to get over this month

otherwise horrible as usual

user228700

Lolol, I see.

Prathyush Poduval

the only thing that makes it nice are my friends

Balarka Sen

There are thousands of families in India who oppose education for their child and drown the girls in familial troubles because of blindly cultural and religious reasons. That's what conservatism is.

Most people use the word without knowing what it means

But no matter, BJP is going to popularize it so we'll all get a taste of it soon enough

Prathyush Poduval

10:23 AM

ah yes, they already have

user228700

@BalarkaSen Hmm, right, I agree.

user228700

Sid

@BalarkaSen I don't think that is conservatism. I call that stupidity. Conservatism to me, is following age-old traditions and customs and to be completely averse to change

Prathyush Poduval

@Kaumudi.H Go in sleeper

it'll be wonderful, especially in long distance ones

user228700

Not bad at all! Only around Rs. 2000.

Prathyush Poduval

10:26 AM

no it's not the cost i'm talking about

user228700

I realise that :-)

Prathyush Poduval

it's the experience you'll get. (moreover, it's winter now and its going to be cold enough)

user228700

@PrathyushPoduval Yes, yes! If I can plan my trip well in advance, I might be able to book a flight back for cheap rates!

Balarka Sen

@Sid What I said are a consequence of the things you said

Prathyush Poduval

@Kaumudi.H When are you going?

Sid

10:28 AM

@PrathyushPoduval sleeper is not really very safe

Balarka Sen

Scanners (1981) US trailer

►

user228700

@Sid Yes, but A.C Sleeper is relatively safer.

Prathyush Poduval

@Sid Why not? If you're careful....

user228700

@PrathyushPoduval It is a risk for women to travel alone in non-AC sleeper compartments.

user228700

@PrathyushPoduval Hahaha, this is an idea I conceived in the past hour :-) I haven't even introduced it to my mum yet! We'll see :-) Hopefully, she will allow me to go next summer!

Prathyush Poduval

10:30 AM

I don't see why not

@Kaumudi.H if you get some outspoken partners, then it would be safer too

Sid

@BalarkaSen Not completely. The things that you mention are hard conservatism. I am talking about soft conservatism where maintaining your identity is more important than finding happiness

user228700

@PrathyushPoduval Outspoken partners? x'D

user228700

@JohnR: I see you're lurking :-)

John Rennie

@Kaumudi.H like a spider in the shadows ...

Prathyush Poduval

@Kaumudi.H the kind of guys\girls who'll kill any harasser with shame

user228700

10:32 AM

@JohnRennie :-) What do you think about this idea?

user228700

@PrathyushPoduval Hahaha, right. Well, I want to go on my own!

Prathyush Poduval

@BalarkaSen What the fuck is that movie about? o_O

John Rennie

@Kaumudi.H where are you panning to go?

Prathyush Poduval

@Kaumudi.H then it's a risk you have to take. If you want to experience the travel, take sleeper class. Otherwise flights the best option

user228700

@PrathyushPoduval Like I said, the A.C compartments are safer.

Prathyush Poduval

10:33 AM

@BalarkaSen did you watch Scanners

John Rennie

@PrathyushPoduval Scanners is a good film.

I saw it when it was released.

Exploding heads!

Balarka Sen

@Sid I see. That's a thing, sure. There are subtle issues I have with your motivation, "finding happiness"

Prathyush Poduval

@Kaumudi.H yeah. But train travels are lengthy (it takes around 2-3 days right?)

Balarka Sen

@PrathyushPoduval I love Scanners

Great cult sci-fi

user228700

@JohnRennie Shantiniketan.

Prathyush Poduval

10:34 AM

@JohnRennie The trailer escalated quite quickly

I'll watch it tomorrow then

Balarka Sen

Cronenberg made it on-spot because he didn't have time to finish his script so there's a lot of loopholes but it's a massive cult film

user228700

@PrathyushPoduval Yepp! I'd like to know what's like! If I book my ticket in advance, I will be able to choose my seat, in which case, I'd choose a side window seat without second thoughts!

Balarka Sen

Better than all the loose science fiction films out there

John Rennie

@Kaumudi.H isn't West Bengal one of the erm less enlightened areas of India?

Prathyush Poduval

I don't have a problem with not-serious loopholes

Balarka Sen

10:36 AM

Scanners was an instant hit on release I think @JohnRennie

user228700

@JohnRennie Less enlightened? Hmm?

Anonymous

@Kaumudi.H You won't like santinketan in the summer. Quite hot

Prathyush Poduval

@Kaumudi.H Yeah you can. I prefer flights for all travel because its more convenient and the fact that I can't sleep properly in trains

John Rennie

@BalarkaSen Exploding heads! :-)

Balarka Sen

Fantastic effects

Slereah

10:36 AM

@BalarkaSen what's the difference between the jet manifold and the jet bundle

Balarka Sen

@slere

user228700

@Blue Bruh, I hail from Chennai; don't talk to me about my ability to endure heat! x'P

Prathyush Poduval

I thought you hailed from kerala?

Slereah

Jet manifold is already the jet at every point

Prathyush Poduval

@BalarkaSen do you watch doctor who?

Balarka Sen

10:37 AM

@Slereah Jet manifold is the total space of the jet bundle

user228700

@PrathyushPoduval Ah, that's a bummer :-/ I find that I am able to sleep quite comfortably in A.C compartments.

Anonymous

@Kaumudi.H Lolol.

Balarka Sen

@PrathyushPoduval Nope

Prathyush Poduval

@Kaumudi.H It's too constricted and i'm also a bit tall

Slereah

@BalarkaSen Isn't the jet bundle already the total space?

Anonymous

10:38 AM

I'd suggest cold places like Shillong for summers though

Prathyush Poduval

@BalarkaSen Watch it it's quite a good show. What 'bout star trek?

Slereah

@PrathyushPoduval which one

there are many star tracks

Balarka Sen

@Slereah A bundle is a projection $p : E \to B$.

$E$ is usually the total space

Slereah

oh

user228700

@Blue The only reason I am hopeful about being allowed to go is that Shantiniketan sounds like a relatively safe place. Shillong? Are you kidding me? x'D

Sid

10:40 AM

@Kaumudi.H J&K! That is like the safest place possible.

Prathyush Poduval

@Slereah Any of them. I very much liked TNG, not yet watched DS9 and enterprise. TOS is very boring compared to TNG

user228700

@PrathyushPoduval Hmm, right, right.

user228700

@Sid x'D

Balarka Sen

@PrathyushPoduval Nope I don't watch TV series

Sid

@Kaumudi.H Shillong is actually relatively safer than say Delhi or Bombay..

Slereah

10:40 AM

@PrathyushPoduval I'd rather watch the holocaust than Enterprise

Prathyush Poduval

That bad?

Slereah

It is very bad

Prathyush Poduval

what makes it very bad? how does it compare to other star treks?

Slereah

Hell I'd rather watch Discovery than Enterprise

Enterprise is fairly boring

The captain isn't charismatic

Prathyush Poduval

I liked discovery

Slereah

10:42 AM

most characters aren't memorable

Prathyush Poduval

what 'bout DS9?

Slereah

During the later half they tried to pivot to some gritty storyline that I barely remember and it was stupid

DS9 is mostly good

Balarka Sen

@JohnRennie I am surprised to know you liked Scanners. Do you in general like movies with less cinematic artisery?

You dislike pretty much anything I consider to be artistically flavored :P

Maybe you're a cult person

Prathyush Poduval

@Slereah I haven't watched the movies yet. Where do you suggest I start from?

user228700

"Cult person" is a curiously amusing term :-P

John Rennie

10:43 AM

@BalarkaSen Scanners had a strong SF link i.e. the community of people with powers, and the struggle between them. And of course exploding heads :-)

I like Videodrome for the same reason i.e. the sci fi links. Or I suppose that's more speculative fiction in Videodrome.

Balarka Sen

@JohnRennie Have you seen They Live?

John Rennie

@BalarkaSen no

They Live

They Live is a 1988 American science fiction horror film written and directed by John Carpenter. The film stars Roddy Piper, Keith David, and Meg Foster. It follows an unnamed drifter (referred to as "John Nada" in the film's credits) who discovers that the ruling class are in fact aliens concealing their appearance and manipulating people to spend money, breed, and accept the status quo with subliminal messages in mass media. It is based on the 1963 short story, "Eight O'Clock in the Morning" by Ray Nelson. At release it was number one in the box office, but sales soon suffered, though the film...

Slereah

@PrathyushPoduval 1 is fairly boring, 2-3-4 is good, 5 isn't generally liked but I kinda like it, 6 is often considered the best, 7 isn't good, 8 is alright, 9 is terrible and 10 also pretty bad

John Rennie

That film?

Balarka Sen

Yeah

Slereah

10:45 AM

The JJ Abrams Star Trek are nothing to write home about

Balarka Sen

It's more politically flavored than sci-fi flavored but I have a feeling you might like it

John Rennie

It doesn't seem that weird ...

Balarka Sen

Oh believe me it's weird lol

John Rennie

What I really like in SF is when the author comes up with a really weird idea and makes it work.

Slereah

@BalarkaSen is the target projection of the jet bundle just the Taylor expansion of the appropriate order?

John Rennie

10:46 AM

In Videodrome you had the idea of a TV broadcast that would distort your reality - very Philip K. Dick esque!

Balarka Sen

@JohnRennie Right, I liked that idea very much

John Rennie

Kind of like the Ring

I can't remember what date The Ring was written

Balarka Sen

Cronenberg is full of weird ideas. His first movie, They Came From Within, is about an apartment full of people which goes haywire once a scientist discovers a disease that amplifies sexual libido

It's a great idea

Almost like J G Ballard's novel "High Rise"

John Rennie

1991 so a decade after Videodrome

Balarka Sen

Hah

John Rennie

10:49 AM

@BalarkaSen there was a film about a parasite that did that ... Damn, I can't remember the name.

Slereah

"Let $(E, \pi, M)$ be a bundle and let $(U,u)$ be an adapted coordinate system on $E$, where $u = (x^i, u^\alpha)$"

Wait what

What is $U$

there's already coordinates for the base manifold and the fiber

Balarka Sen

You know how Ridley Scott's "Alien" is considered to be one of the first movies which has those visual effects, of chestbursters gnawing out of the chests of the victims?

John Rennie

@BalarkaSen aha! The film I'm remembering is Shivers, which is the same film released under a different name!

Balarka Sen

It's taken from They Came From Within, where similar effects are used

@JohnRennie Ah yes they were released with different names in US and Canada

@Slereah Well, the jet bundle itself is the space of Taylor expansions of the appropriate order

John Rennie

@BalarkaSen I can take or leave J G Ballard. I like scifi that is tech oriented while Ballard is more interested in the psychological side.

Balarka Sen

10:53 AM

You have to have a map f : M --> N first to take it's jet bundle

@JohnRennie That's true.

John Rennie

Hmm, it looks as if that nice Mr. BitTorrent can supply a copy of They Live ...

Balarka Sen

lol

Carpenter's idea of horror is sharply different from Cronenberg's in my view. It's what he likes to call "right wing horror vs left wing horror", where left wing = horror from the inside, and right wing = horror from the outside onto a group of people.

It's a nice analogy

John Rennie

I think Carpenter's version of The Thing is the finest horror film I've ever seen.

Balarka Sen

In most movies of Carpenter the chaos comes from the outside

I love The Thing!

user228700

@Balarka: Ah, a ~~major~~ minor detail has just occurred to me; Hindi is widely spoke in WB, no?

Balarka Sen

10:59 AM

Also the effects of that movie, damn.

How did they even make them

The transformation of the dog, for example

@Kaumudi.H Hm, I think most people understand it, yes.

You shouldn't have trouble with that in Shantiniketan

user228700

Right, thanks.

Balarka Sen

A lot of Indians and foreigners visit that place

user228700

Right, of course.

John Rennie

@BalarkaSen for me the film was the perfect blend of suspense, plot, jump scares and humour (rather dark humour :-)

Balarka Sen

Exactly

It was a great balance

I thought the idea of having the evil undercovered among the group of people stranded in an isolation is fantastic

Story-wise it was quite original

John Rennie

11:03 AM

@Kaumudi.H there might be a club or group at the college for people interested in travelling ...

user228700

@JohnRennie I checked to find that no, there isn't.

Balarka Sen

I haven't read the original novella

John Rennie

@Kaumudi.H maybe you could start a group ...

user228700

@JohnRennie Only technical clubs are sanctioned by the Principal, I think.

John Rennie

@Kaumudi.H Do all groups have to be official?

user228700

11:05 AM

Ah, hmm, you make a good point.

John Rennie

@BalarkaSen I've got it somewhere if you want a copy.

user55789

Hi all! (homework question) I would like to show that the Majorana mass term $\mathcal M = i\left(\psi_L^\dagger \sigma_2 \psi^*_L - \psi^T_R \sigma_j \psi_R\right)$ is Lorentz invariant ($\psi_{L,R}$ are the left- and right-handed Weyl spinors). My approach was to consider the general variation of $\mathcal M_j$ with Pauli matrix $\sigma_j$ instead, but it's not going anywhere:

$$
\begin{align}
\delta \mathcal M_j &= i\left((\delta\psi_L^\dagger) \sigma_j \psi^*_L + \psi_L^\dagger \sigma_j (\delta\psi^*_L) - (\delta\psi^T_R) \sigma_j \psi_R- \psi^T_R \sigma_j (\delta\psi_R)\right)\\
&= i\left(\frac12\left(-i\theta_i - \beta_i\right)\sigma_i\psi_L^\dagger \sigma_j \psi^*_L + \psi_L^\dagger \sigma_j \frac12\left(-i\theta_i - \beta_i\right)\sigma_i\psi_L^* - \frac12\left(i\theta_i + \beta_i\right)\sigma_i\psi_R^T \sigma_j \psi_R- \psi^T_R \sigma_j \frac12\left(i\theta_i + \beta_i\right)\sigma_i\psi_R\right)\\

So my question is as follows:

Do I need the equations of motion to show this?

John Rennie

@BalarkaSen Though Campbell's style is a bit dated by modern standards.

Balarka Sen

@JohnRennie A soft one? I can probably libgen it.

user228700

Still, I am a little reluctant to do this sort of thing. What would the club do?

Balarka Sen

11:07 AM

Yeah it's on libgen

@JohnRennie I see.

John Rennie

@Kaumudi.H I haven't really thought this through, but you're interested in travelling and I'd guess there will be like minded students. Travelling as a group would give you the protection of numbers so it would be less scary.

user228700

Hmm, right, right.

user228700

Well, not until the 2nd year can I hope to do anything, so there is time, still, to think it through :-)

John Rennie

@BalarkaSen aha, I have it as an EPUB.

user228700

@Balarka: Is Shanitniketan essentially equivalent to the school, Viswa Bharathi?

Balarka Sen

11:10 AM

Ahh. I might ask for it if the libgen links are broken

I'll try downloading it later

@Kaumudi.H Viswa Bharati is located in Shantiniketan

John Rennie

@BalarkaSen it's not the greatest read ever. There is a tendency to revere the golden age authors like Campbell because they were so instrumental in getting modern SF going. But a lot of the old books aren't that great.

user228700

@BalarkaSen Ah, I see.

John Rennie

@Kaumudi.H I used to make all sorts of wild plans as an undergrad, few of which came to anything.

I had a plan to canoe round the Aegean Sea visiting all the islands.

Balarka Sen

Mmm, makes sense. I wish I was more familiar with the history of science fiction. It seems to be a really interesting and developed genre.

user228700

@JohnRennie Oh, wow!

user228700

11:14 AM

(This has reminded me of the book, "Three Men In A Boat")

John Rennie

Sadly it turns out there are really dangerous currents in the Aegean i.e. currents that flow faster than I could paddle a canoe.

Balarka Sen

It's strange when other people shrug and cringe at the mention of science fiction

John Rennie

So I took the wise decision to abandon that one :-)

Also I had a plan to motorcycle up the Norwegian coast to the Arctic circle.

user228700

Ah, dang, I see.

user228700

@JohnRennie My, my!

John Rennie

11:16 AM

But, that would basically be a thousand miles of nothing but fjords. And after the first few fjords I suspect the novelty would have worn off :-)

user228700

Ah, right, right.

Balarka Sen

maybe it'd be more interesting if you have some norwegian black metal playing on your radio

John Rennie

Motorcycling to Rome was the only big trip I ended up actually doing. That was really great fun though.

user228700

:-) Sure does sound like it!

John Rennie

Well ... you have a motorbike licence :-)

user228700

11:18 AM

@JohnR: You are going to be around in the evening, no?

user228700

(i.e: After you go out to get lunch)

John Rennie

@Kaumudi.H Yes. From around 16:00 UTC. 21:30 your time.

Though the level of maths you're doing is right at the edge of my skills if not beyond, so if it's maths I won't be able to help that much.

user228700

Ah, yes, OK :-) There is a particularly nasty chapter in Physics and I have many questions!

John Rennie

I bet it's electrodynamics?

user228700

Hehe, no :-) Photonics.

John Rennie

11:21 AM

Photonics?

user228700

LEDs, Photovoltaic Cells, etc.

John Rennie

@BalarkaSen burn down a few churches along the way :-)

Balarka Sen

aw yiss

John Rennie

@Kaumudi.H hmm, OK, I'll have to keep Google handy :-)

user228700

Alright, then, I will spend the hours between now and then reading, napping and eating ice cream. ::Sets alarm for 9:30:: See you then!

John Rennie

11:23 AM

Bye, enjoy the ice cream!

user228700

:-) I most certainly will.

Balarka Sen

Rana

11:41 AM

@JohnRennie, hi

John Rennie

@Rana Morning

Rana

Same to you

@JohnRennie, did you see what is wrong with my......

John Rennie

@Rana what are you asking about?

Rana

The same old story, I posted yesterday nearly as now's time

John Rennie

Link?

The question about a magnet moving towards a solenoid?

Rana

11:47 AM

I am trying to dig it up

Anonymous

@Rana chat.stackexchange.com/users/323469/rana?tab=recent

Rana

That's awesome of you @blue, thanks

@JohnRennie yes that one, I gave certain views on that, blue has given the link

John Rennie

@Rana to see what it going on you'd need to do the calculation rigorously, which would be hard. If you consider just a single loop of wite then as the magnet approaches the loop the change in flux will induce a current in the loop.

Then the current in the loop will generate its own magnetic field. So some of the kinetic energy of the magnet is stored in the magnetic field generated by the loop.

If the magnet has a low mass, so a small kinetic energy, and a high field then I'd guess the induced field could be high enough to male the magnet bounce back again. But you'd have to do the calculation to be sure.

It's not a calculation I've ever done and I feel no great desire to do it because it's a hard calculation.

Rana

Heehee

Let's talk leaving calculations away (can we do so?)

John Rennie

I'm not sure how much more there is to say ...

Rana

11:59 AM

Yes yes it would be very hard to bounce back the magnet,, to convert whole of kinetic to potential

Thanks very much ;I didn't come up with this fact. I have been wrestling with this question since long time

John Rennie

If you make the mass of the magnet negligibly small the it's KE will be very small, and under those conditions I think it's entirely possible that the magnet would bounce back. But you'd have to do a proper calculation to be sure.

Rana

Yes I am trying

Problem is that I am in high school and that's why......... It may take time

I hope my being in high school wouldn't matter

@JohnRennie see you back, soon

John Rennie

12:17 PM

@Rana bye

nbro

12:29 PM

Is anyone here familiar with Fourier series?

Slereah

Yes

nbro

Ok, nice! I am really new to Fourier series and I get the idea of approximating a periodic function with basic periodic functions such as sines and consines.

However, I am unable to proceed with a proof for an exercise, because I am not so familiar with Fourier series and I would not know how to modify a Fourier series...

This is the exercise.

And here's what I've done so far.

But now that I have a Fourier series for $h$, which is a shifted version of $g$, I am not sure how to modify its Fourier series to get to the Fourier series of $g$.

Anonymous

That just looks like change of variables...

nbro

Well, I am not sure exactly how to perform the change of variables...

As you can see, I have $\frac{2\pi}{N}$ as part of the exponent of $e$, whereas I am multiplying $x + \pi$ by its reciprocal to perform the equivalence between $g$ and $h$

ACuriousMind

1:27 PM

T-8 days to Winterbash

2

Get ready for your hats, people!

Balarka Sen

Last year's hats were dumb

Hopefully there will be good hats this year

Anonymous

I'm looking forward to some popular meme hats this time. :D

nbro

"...French-vanilla, butter-pecan, chocolate-deluxe
Even caramel sundaes is gettin' touched..."

0celo7

Will there be a MAGA hat?

Balarka Sen

lol

0celo7

1:41 PM

@BalarkaSen Bernardo has seem my sister more than the rest of our family has seen her in recent memory

it's pretty strange

Balarka Sen

I see

0celo7

Well, not that strange. We all live on the east coast and she's an CA, and is working like a madwoman

So you have to go there to see her

Emilio Pisanty

this book looks nice

nbro

2:16 PM

@nbro So nobody here is able to help me with the problem?

Emilio Pisanty

@nbro so?

you've got $g(x)=h(\mathrm{transformation}(x))$ and you have a Fourier series for $h$.

all you need to do is plug stuff in

nbro

Yes, but how do I plug stuff in?

Emilio Pisanty

@nbro you take one expression and you substitute it with whatever it is equal to

we're happy to help, but if you're solution-shy then nobody is going to do your work for you

you have all the pieces already

nbro

Well, but, in this case, I have a Fourier series for $h$, which is an approximation for $h$

and

Emilio Pisanty

@nbro it's not an approximation

it's exact

(assuming a regular-enough $h$ and an infinite series. If either of those fails, then the exact result will degrade to an approximation, but you're only required to produce an equally-good approximation for $g$.)

and, in any case: you know $g(x) = h(\frac{2\pi}{N}x - \pi)$. You have an expression for $h(\tilde x)$. Just plug in values.

nbro

2:35 PM

@EmilioPisanty Well, I was not even realizing that since $h(x) = g(\frac{N}{2\pi}x + \pi)$, then $g(x) = h(\frac{2\pi}{N}x - \pi)$...

Emilio Pisanty

@nbro if you're doing Fourier series, then you're getting to the big-boys table ;-). This is the kind of connection that you need to be able to recognize and operate with, without second thoughts, and the exercises you're set will increasingly assume that that's the case.

so... sharpen up, is I guess what I'm saying. This is where math and physics really start to get interesting, but it's also the rough location of a kink in difficulty

nbro

But why don't you use parenthesis $h(\frac{2 \pi}{N}x - \pi)$ (i.e. $h(\frac{2 \pi}{N}(x - \pi))$? Indeed, I think we don't need parenthesis..

Emilio Pisanty

@nbro your second version is wrong

nbro

I mean, we want to scale x by $\frac{N}{2 \pi}$ and then add $\pi$

Emilio Pisanty

$x$ is a length and $N$ is a length

$x-\pi$ makes no sense

nbro

2:42 PM

You mean that $h(\frac{2 \pi}{N}(x - \pi))$ makes no sense?

Emilio Pisanty

@nbro well, you're using notation that explicitly makes things harder

but $\displaystyle \frac{x-\pi}{N}$ has zero chances of being right in this context

nbro

Well, the initial idea to write $h(x) = g(\frac{N}{2 \pi} (x + \pi))$ is that first we shift $x$ by $\pi$ and then scale by $\frac{N}{2 \pi}$ so that to map $N$ to $2\pi$...

Emilio Pisanty

Getting a bit more of the subtlety, in the spirit that all dimensional analysis is a scaling argument in disguise: from the set-up of the problem, you can scale up both $x$ (the argument of $g$) and $N$ via the same factor $\lambda$ and it doesn't change anything. You can't do that with $\pi$. Thus anything that combines $x-\pi$ (where $x$ is to be fed to $g$) will not be invariant under that transformation, which means that it can't be right

@nbro again, that's your notation making your job explicitly difficult

make $x=\frac{N}{2\pi}(y+\pi)$ so that $g(x) = h(y)$

and operate on those symbols

nbro

@EmilioPisanty Why can I scale up both x and N via the same factor? That is, x is a variable and N is the period. Well, x will also be N at some point... I understand that I shouldn't touch $\pi$, though

Emilio Pisanty

@nbro I don't have time for this kind of discussion. If you have actual questions about Fourier analysis, I can chip in, but if you're just confused about variable substitutions, I'll pass the baton to other people.

the math chat might be able to help you.

nbro

2:52 PM

@EmilioPisanty I asked this question first there, but so far no one has answered me... I am just not very familiar with variable substitution, so, as you can observe, I am a bit confused. I know that for you these are completely trivial things...

Emilio Pisanty

@nbro If you're not familiar with variable substitution, I would strongly recommend working on that until you have a solid understanding of that, and other pre-calculus techniques, before attempting anything as sophisticated as Fourier series.

I don't have any further time to contribute to this conversation, though. Good luck with your substitutions.

nbro

Well, I have some background in pre-calculus and calculus, but I've not practiced very much these variable substitutions and my head (in these days) is a bit (too much) fucked up...

apt45

Hello guys, do you have any idea of a possible answer to the following question?

1

Q: Two-point function of massless scalar theory in 2d CFT

Following the derivation of the massless free-boson two-point function given in Di Francesco, Mathieu and Sènèchal, I had an apparently stupid doubt. Look at the attached picture. Where does the contribution $\lim_{\rho \rightarrow 0} \rho K'(\rho)$to the integral in Eq. (2.100) go? Do they sup...

conformal-field-theory

ooolb

@nbro are you alright

we can talk about it

Transcript for