The h Bar

Cows

12:00 AM

I think i know the anal of functions tricks. They pretend functions are vectors and then derive a bunch of stuff

the idea of orthogonality falls out

triangle inequality etc

Norms etc

L1 . . . Lp and such

cool deal

I had seen something like this at a finite element workshop

@0celou7 you there?

I am going to start reading the text today

ACuriousMind

@Cows They don't "pretend". They are vectors - you can add them and you can multiply them by real numbers and there's a zero function, which is really all you need to have vectors.

Cows

@ACuriousMind it is pretty cool stuff. It turned on a light in my head.

woohooo! I think I get this stuff, at least the fundamental concepts :~)

Now I just need to make sure my vector background is strong

hehehe,

Functions are vectors!

@ACuriousMind are you aware of master integral technique?

I am learning about it (self -study as usual hehe).

ACuriousMind

@Cows I dimly remember that as a way to compute Feynman integrals but if I never have to compute a Feynman diagram ever again it'll be too soon.

Cows

@ACuriousMind yes, I have been learning how to compute qft stuff and have been looking at modern techniques too. I have been doing something like this in 0+0 dims hehehe

I want to be able to compute tough things

ACuriousMind

What's so funny about that? :P

Cows

12:13 AM

well it means I can't compute the real stuff yet. Well I will get there

hehe

i hope lol

@ACuriousMind what sort of techniques do you use in your work? What are the most ubiquitous modern techniques?

0celou7

@Cows that's what physicists do and it's mostly wrong if you think that way

There's no way to talk about such spaces without topology

Cows

@0celou7 which methods are better suited. I want to learn

dmckee

@JohnRennie One of my grad-school buddies came from an upper-middle class family in some part of northern India. He arrived in this country in his mid twenties not knowing how to run a microwave or even prepare hotdogs (he boiled then in the bag first time).

They'd had a cook until he went to school and then he lived in apartments without kitchens and always ate out (which is apparently easy in many Indian cities).

ACuriousMind

@Cows I'm afraid I don't know what you're asking for. There's a lot of differential and algebraic geometry, but I wouldn't rightly say I use "techniques", I don't "compute" much in the narrow sense of the word.

dmckee

Anyway, he shared an place with me and another grad student the summer we were sent to Fermilab so we got him basically squared away.

At least when the student is a physicist they can both follow instructions and deal with a little ambiguity in them.

Cows

12:21 AM

@ACuriousMind let me see if i can narrow it down a bit. Which text, or mathematical tool kit, or references drive the type of research you do? hehe this is the best re-framing of the question I could do in such short notice :P

this chat is much better that actually asking questions on the site

Real time responses :)

ACuriousMind

@Cows As I said, there's a lot of differential and algebraic geometry, as well as group theory. The main references currently are M-theory stuff done by Acharya, Witten and others, and the necessary mathematical tool kit depends a lot on the specific situation. It's the physics that requires certain math, not the other way around, so I'm a bit confused why you'd think a mathematical toolkit can drive research

Cows

@ACuriousMind by differential and algebraic geometry do you mean mostly surgery and sewing coupled with some study of geodesics?

and say non-trivial isomorphisms

like ads/cft

0celou7

12:36 AM

When you guys turn on your computer from sleep, does the chat load, then wait a few seconds, then reload?

ACuriousMind

@Cows Not at all. More stuff like holonomies, spinor bundles, Calabi-Yau manifolds, sheaves, cohomology

0celou7

It keeps doing that and deleting chat essays I'm typing

ACuriousMind

@0celou7 I never turn my computer to sleep, so I couldn't tell

0celou7

@Cows See if you can do exercise 5.2

Sir Cumference

@0celou7 That sometimes happens if the chat disconnects

0celou7

12:38 AM

I'm not sure if that Hint actually helps at all

Cows

@0celou7 I will try to do it.

@ACuriousMind ah yes, complex mnflds, restrictions, ker/L = H_n type stuff etc not too familiar with spinor bundles though

So I guess the goal is describing and studying properties of objects? Not just computing stuff

bolbteppa

@0celou7 you need Riemann-Lebesgue for the proof of Fourier series

0celou7

@Cows What I was saying is that functions are indeed vectors, but that's not to say the study of such vector spaces is at all like linear algebra

in fact linear algebra plays a very small role

Cows

@ACuriousMind I have some competence with basic complex manifolds, some competence with basic homology (of triangular looking things) but need some work with my diff and alg geom knowledge

@0celou7 hehe this changes everything. I should infact read the book then hehehe

loltospoon

Hello all!

I have a question.

Cows

12:47 AM

hi@loltospoon

loltospoon

For the derivative, I think of integration as its opposite

(in fact, I think of the derivative as going down and integration going up. But anyways...)

What, then, is the opposite of the divergence, curl, and gradient??

ACuriousMind

@loltospoon Integration.

bolbteppa

They are covariant derivatives, hence derivatives

ACuriousMind

Go look at Stokes' theorem

loltospoon

Ah ok

@ACuriousMind I will do that now

0celou7

12:49 AM

@bolbteppa I'm not saying I don't understand the proof of RL, I'm saying don't understand the derivation via the translation operator.

Assuming such a thing is even possible, which I am skeptical of.

bolbteppa

My point is, how can you derive a theorem you needed in order to justify the thing you're using to prove the existence of the theorem you needed to get the thing you're using to prove the theorem which you needed to justify the existence of the thing...

0celou7

What on Earth are you talking about?

Fourier series and transforms have little to do with each other

bolbteppa

lolwut

Have you ever gone through the proof of Dirichlet's conditions or weaker for the existence of Fourier series?

0celou7

I know the proof for $C^1$

I still don't see what Fourier transforms has to do with this

but you can just ramble on as usual

bolbteppa

"The Fourier transform is an extension of the Fourier series that results when the period of the represented function is lengthened and allowed to approach infinity." en.wikipedia.org/wiki/Fourier_transform#Introduction

0celou7

12:56 AM

Everyone knows that

bolbteppa

Except you apparently

0celou7

Why do you talk to me?

At least try to be helpful

Cows

i don't know that

I just learned it

ACuriousMind

@0celou7 Hmmm? Fourier series and Fourier transforms are very closely linked - you can develop a general theory of Fourier transforms on locally compact topological groups, and the standardFourier transform is the transform on $\mathbb{R}$, while the series is the transform on $S^1$ (resp. $\mathbb{Z}$, see en.wikipedia.org/wiki/Pontryagin_duality)

0celou7

Oh please, not you too

bolbteppa

12:58 AM

You are trying to prove Riemann-Lebesgue using Fourier theory when Fourier theory depends on Riemann-Lebesgue if you've seen the most basic proof, turns out you haven't seen the proof and want to go in circles and insult people who try to help, enjoy

0celou7

you're getting blocked

Not you, ACM

bolbteppa

Incredible

0celou7

@ACuriousMind That still has nothing to do with the Riemann-Lebesgue lemma on $\Bbb R^n$

ACuriousMind

@0celou7 Never claimed that

I was just miffed by your statement that the series and the transform have little to do with each other

0celou7

Ok, then why did you bother writing a comment obviously meant to try and show me up

bolbteppa

1:00 AM

Why did you bother to ask a question if when someone answers you you insult them

0celou7

They don't when it comes to proving the Riemann-Lebesgue lemma

All I want to do is understand the rumor that one can prove it a certain way

But all you people do is assume I'm stupid

Whatever, bye

bolbteppa

I just pointed out RL is used to prove Dirichlet's conditions in some proofs, so you might be being circular

ACuriousMind

@0celou7 Your statement didn't sound like that to me. If that's all you meant I have no quarrel with that :P

bolbteppa

Pretty simple stuff

Nobody assumed you're being stupid, just trying to point out it might be circular, that's all

0celou7

@ACuriousMind If you're proving things about transforms on $\Bbb R^n$ I claim you will rarely need information about the series

that's the clarification

bolbteppa

1:04 AM

Wikipedia says they are the same thing

0celou7

@ACuriousMind Do you remember anything about polygonal presentations of surfaces?

ACuriousMind

@0celou7 I remember how to make the surface of genus $g$.

0celou7

@ACuriousMind I'm trying to show that a certain word gives $P^2\# P^2\# P^2$ and my current algorithm takes 20 cuttings and gluings lol

ACuriousMind

Well...sometimes it is like that

OBE

hey

i'm in the process of getting good

should take like 1 year

ACuriousMind

1:09 AM

There's no general recipe for how to do things with these presentations, it's a bit of an art to see the short/elegant ways

0celou7

@OBE what have you learned so far?

OBE

I'd rather not say lol

I do know some qft stuff from 1 and 2 that i've been doing

but it doesn't work that way because I need to learn better math in order to be good.

0celou7

@ACuriousMind These things are very strange. Why on Earth is $T^2\#P^2=P^2\#P^2\#P^2$? So random

DanielSank

Hi, everybody.

ACuriousMind

Damn, I just lost an hour to DST :P

DanielSank

1:15 AM

DST?

ACuriousMind

Isn't that (Daylight Saving Time) what the habit of changing our clocks twice per year is called in English?

0celou7

@ACuriousMind the least productive hour of your life

@ACuriousMind it is

DanielSank

@ACuriousMind Ah yes. Take that.

ACuriousMind

@0celou7 Yeah, the connected sum is not actually a very nice operation

DanielSank

wtf @0celou7 your name...

My brain asplode

0celou7

1:16 AM

@DanielSank Hmm?

DanielSank

Don't you "Hmm?" me, young man.

0celou7

You wanna fight?

DanielSank

@0celou7 Sure. How?

Wits?

0celou7

@DanielSank That would be a featherweight vs. heavyweight, not exactly fair.

DanielSank

@0celou7 Ok, let's pick something you're good at.

0celou7

1:19 AM

Pokemon trivia?

DanielSank

@0celou7 You'd destroy me.

Star Wars trivia?

0celou7

@ACuriousMind moderate pls

@DanielSank I think I'll lose, but I'm willing to be impressed here

No Google, on our honor.

ACuriousMind

@0celou7 ::moderates furiously::

DanielSank

@0celou7 I agree.

How shall we proceed?

0celou7

ACM is moderating!

DanielSank

1:22 AM

ACM, shall we hurl questions at each other, or will you provide them?

ACuriousMind

Uh

I'm afraid I don't know enough SW trivia to come up with decent questions

DanielSank

Ok then, @0celou7 I yield first attack to you.

0celou7

@DanielSank Name two of the Jedi that were present for the arrest of the Chancellor in EP. 3.

DanielSank

Windu

Skywalker

0celou7

I clearly meant the arresting party :P

DanielSank

1:26 AM

Technically, I believe I have defended successfully. However, I will admit I do not recall the names of the two who were killed immediately when Palpatine resisted.

ACM, a judgement, please.

0celou7

Kit Fisto is crying

DanielSank

@ACuriousMind?

@0celou7 Perhaps.

ACuriousMind

Your answer was technically correct, which is the best kind of correct. @0celou7 should have specified "the arresting party" in the question to begin with

DanielSank

Very well. We shall continue.

0celou7

Damn German precision.

DanielSank

1:28 AM

@0celou7, what is the name of the creatures, encountered inside the asteroid creature in episode V, that Han believes are likely chewing on the Millennium Falcon's power cables?

Hint: they look like large bats.

0celou7

I don't know! But I do know I got nightmares from them back in the day.

DanielSank

@0celou7 Would you like an easier question?

0celou7

maybe

DanielSank

Ok

Name four characters who have handled Anakin Skywalker's lightsaber.

(I can think of six)

0celou7

Anakin, Obi, Luke, R2

DanielSank

1:32 AM

Very well. R2 had slipped my mind.

For fun, additional characters are Han, Rey, Finn.

Sir Cumference

@KyleKanos Say...what's a computational astrophysicist?

DanielSank

The attack is yours.

0celou7

I'm going to throw in Maz because I'm not sure about R2

DanielSank

@SirCumference Oh, it's a tricky way to spell Python/C programmer.

0celou7

I think R2 only handled the reconstructed green one.

DanielSank

1:33 AM

@0celou7 Ah yes, also Maz. Very good.

Sir Cumference

@DanielSank Isn't that all astrophysicists?

0celou7

@DanielSank Who else were you thinking of?

Oh, Rey too.

DanielSank

@0celou7 That's a good point. Not Anakin's.

0celou7

And I guess Finn as well.

DanielSank

@0celou7 I said Rey. Look up.

0celou7

1:34 AM

@DanielSank Aha.

DanielSank

1 min ago, by DanielSank

For fun, additional characters are Han, Rey, Finn.

0celou7

When did Han handle it? Did he play with it on the Falcon?

DanielSank

@0celou7 He cut open a Taun-Taun with it and stuffed Luke inside in V.

That was Anakin's.

0celou7

Ahhh

@DanielSank Anakin Skywalker had limbs amputated X times. What is X and what were the limbs each time?

This might he harder than what you asked

DanielSank

@0celou7 He lost an arm in II.

He lost a bunch of stuff at the end of III.

Legs, arms, skin, etc.

0celou7

1:37 AM

Which limbs tho

DanielSank

Well, in III he lost most of both legs, and I think he lost his remaining biological arm, although I'm not 100% sure if that's correct.

AFAIK, in the films, that's it.

0celou7

Yeah, I'm not entirely sure if he lost both arms at some point

Final answer?

DanielSank

I do not think he lost any limbs in the Clone Wars series.

Assuming the EU books are no longer canon, I'll go with:

X = 2

First time: arm
Second time: two legs, and maybe an arm

0celou7

We're just talking about movies here, I hope

DanielSank

@0celou7 Sure.

0celou7

1:40 AM

@DanielSank Luke cuts off his hand in VI

DanielSank

@0celou7 Yes but that was mechanical so I wasn't counting it.

0celou7

...

@ACuriousMind

DanielSank

I didn't think we were double-counting limbs ;-)

Also, I'd hardly call that an amputation. It was not surgical.

The other cases involved traumatic damage/removal of most of the limbs, followed by surgical intervention.

0celou7

He did lose both arms IIRC. Because he lost an arm in 3 but that infamous scene where he claws at the dirt on Mustafar, he does so with a robotic hand

DanielSank

In VI, the hand is dismembered and Anakin dies shortly thereafter without any medical treatment.

ACuriousMind

1:41 AM

A "limb" seems to me to be a limb regardless of the material it's made of.

DanielSank

@ACuriousMind Yes, but see note on "amputation".

0celou7

Oh please

DanielSank

@0celou7 That's how I was thinking :-\

0celou7

Next question then

DanielSank

I will admit I was probably wrong not to count the second arm in III.

0celou7

1:43 AM

@DanielSank Do you know which arm was cut off in 2?

DanielSank

@0celou7 I am reasonably sure it was the left.

let me think

loltospoon

Question: If I'm trying to make a device that makes me jump higher, what quantity am I trying to increase here? Force? Work? Impulse? Acceleration?

I'm trying to reason this backwards and I've come to the conclusion that my takeoff velocity must be higher than the control velocity (without the device). But I can't just design a device that will just give me a faster takeoff velocity. The device doesn't know any parameters of my body yet. So I have a gut feeling that tells me that I should be looking for the amount of force that the device needs to exert to help propel me higher. Is this re…

ACuriousMind

@DanielSank I see the point about "amputation" implying some sort of medical procedure, but I'd say that if we're going by that he never had an amputation - none of the limbs was removed as part of a medical procedure.

DanielSank

@ACuriousMind They were though. The limbs were mostly severed in battle, but then surgical intervention was needed as the entire limbs were replaced with bionic parts.

ACuriousMind

@DanielSank Yes, he had surgery - but the limbs were already gone at that point

DanielSank

1:44 AM

@0celou7 disappointingly, I do not remember which arm it was in II.

0celou7

@DanielSank Hint: it was the same one that Luke lost.

DanielSank

@ACuriousMind Most of them. Not all. ::shrugs::

@0celou7 That would be the right.

@0celou7 Shall we move on?

0celou7

Yes

DanielSank

I see the score as sort of even since we passed you on the mynok question and I sort of failed this one.

0celou7

I don't think we're actually counting, but ok

DanielSank

1:46 AM

Oh, I'm counting.

0celou7

Yikes, ok

let's do "name the theorem" next time

DanielSank

heheh

0celou7

Although that would be a stale mate, we could just name random things from our areas of expertise...

DanielSank

What is the name of the rebel leader who runs/introduces the briefing at which the attack on the Death Star is planned in VI?

(The first speaker)

0celou7

:( Was it the woman who was also in Rogue One?

heather

1:48 AM

Jyn?

0celou7

With the short hair

DanielSank

@0celou7 Perhaps

heather

or wait, is that with two "n"s?

DanielSank

@heather No way, dude. She dies in Rogue One.

0celou7

Senator something is the best I can do

DanielSank

1:49 AM

@0celou7 Final answer?

0celou7

Yeah

heather

@DanielSank i know, i was wondering of that was what 0celo was thinking of

DanielSank

@0celou7 You are incorrect. It is not "Senator Something". It is Mon Mothma.

heather

wait @0celou7 what did you do to your name!?

the "u" is terrible

DanielSank

The attack is yours, @0celou7.

0celou7

1:50 AM

@DanielSank She was a senator tho

DanielSank

@0celou7 Correct.

0celou7

And I should have remembered that name

DanielSank

Until IV.

@0celou7 Correct.

0celou7

@DanielSank Such titles are kept, no?

Like President Obama

DanielSank

@0celou7 The senate was dissolved in IV.

@0celou7 Oh, perhaps. I don't know. But in any case her name was Mon Mothma, not Something.

0celou7

1:51 AM

@heather wrong

heather

@0celou7 ::shivers:: it is

0celou7

your whole name is terrible

@DanielSank What is the name of Ackbar's homeland?

DanielSank

@0celou7 Mon Calamari. Give me a hard one.

0celou7

Stupidly hard or just obscure?

DanielSank

@0celou7 Harder than Mon Calamari.

0celou7

1:56 AM

What was the name of the creature that Obi rode during the fight again Griveous

I'm afraid I must leave

DanielSank

@0celou7 Damn, I have absolutely no idea.

0celou7

@DanielSank name of the planet?

loltospoon

2:09 AM

@0celou7 a Boga

(I'm assuming anyone can play this game)

The planet he rides the creature on is Utapau

TrY iS CheM

@0celou7 why it is banned

0celou7

@TrYiSCheM because it's invasive

TrY iS CheM

I don't think so

I think IIT is best exam

DanielSank

@0celou7 Planet what? Where Grievous and Obi fought?

Bernardo Meurer

3:01 AM

@JaimeGallego You have sinned son

To be forgiven you must repeat our prayer 50 times

"There is no system but GNU and Linux is one of it's kernels"

Free yourself from this proprietary malware

Secret

3:49 AM

Last night dream is food related: A 5 year old girl stole half of my cheese pizza and the whole family made for a run up the escalator

Slereah

4:10 AM

"In the case of singularities constructed by changing the periodic coordinate identifications, the b-boundary coincides with the set of the fixed points of the periodic coordinate before the identification is changed. For example, for the two-dimensional cone with the metric $ds^2 = dr^2 + r^2d\phi^2$, where $0 \leq \phi ≤ \Phi < 2\pi$, $r = 0$ is its singular b-boundary, due to the deficit angle resulting in the violation of the regularity condition (6)."

"In an interesting recent paper, Ozsvath and Schucking describe Godel’s excitement in 1949 upon learning that in his new cosmological solution of the Einstein equations, one has the ability to “travel into the past”. They report on his lecturing at the IAS in Princeton on the subject with the attendance of such luminaries as Einstein, Oppenheimer and Chandrasekhar. The Godel solution was followed in 1956 by Kundt’s calculation of its geodesics. Evidently, Chandrasekhar was influenced by the Godel

What a bunch of tools

"Unwrapping does not change the metric at any of the regular points, so the unwrapping singularities are always quasi-regular. Provided the original spacetime is asymptotically flat and has no event horizon, neither does the unwrapped one, so the resulting quasi-regular singularity is naked, i.e. there are future directed null curves originating arbitrarily close to the singularity that reach the future null infinity."

Secret

4:28 AM

Black hole kicked out from its galaxy

Nick

4:58 AM

Should this question be migrated to bio SE?

1

A: Is near point defined for a myopic eye and far point defined for a hypermetropic eye?

You're overthinking the theory. Think practically and the answer is obvious. The standard eyeball has a crystalline lense whose focal length is varied by the ciliary muscles. The maximum and minimum accommodation of focal length is what determines far point and near point respectively. The near...

Also, while you're there. Give me some upvote love.

@Secret hope it doesn't visit us.

Secret

that will be something we worry about at least 1 billion years later, I suppose if we as a species have not destroyed ourselves, we might have mastered gravity and developed black hole countermeasures at that time

Slereah

5:18 AM

this paper is fairly informal, though

It doesn't define timelike homotopy groups or anything

it's all just "let's just make the cyclical coordinate uncyclical and see what happens"

which I guess for a timelike curve is probably always doable?

If they're not contractible just use the covering space, if they are just define some coordinate system where the CTC is along a cyclical coordinate

but then you get a quasi-regular singularity

user228700

@JohnR: Morning :-)

John Rennie

Morning. How did the meal go?

user228700

It was excellent :-)

John Rennie

Good :-)

user228700

What about ur lunch?

John Rennie

5:23 AM

I love eating with friends. In our family eating has always been a social occasion.

user228700

@JohnRennie That's nice :-) Not so much in my own family.

John Rennie

@Kaumudi.H I wasn't feeling too lively yesterday, so I just bought some burgers.

user228700

Oh, I see :-| Do u feel better today?

John Rennie

And some very sweet and sticky cakes for dessert. Nice, but not the most original meal.

I feel much better today, so I'll have to come up with something special for lunch to make up for yesterday :-)

user228700

Eh, do u really care about originality? I bet it tasted great anyway(?)

user228700

5:25 AM

@JohnRennie Hmm, OK :-) Let me know what u decide.

John Rennie

Although we switched to British Summer Time last night, so I was up an hour earlier than usual.

so I'm a bit tired, but for reasons unrelated to health.

user228700

Ah, I see...

user228700

The news on this side is that I am racing against time to finish lots of stuff before my exam next Sunday.

John Rennie

Wow, only a week away.

Those exams come round awfully fast!

user228700

Yes. I'm terrified but also trying my best to work without freaking out every 2 seconds.

user228700

5:27 AM

@JohnRennie And before we even know it, it's all going to be over!

John Rennie

At least once they're over, no matter how they go, normal life can be resumed. That has got to be a huge relief.

user228700

...well, yes but I am so out of touch with whatever "normal life" is that I don't even know how to be excited about that.

John Rennie

It will be like being released form prison :-)

user228700

I realise that that doesn't make much sense but you have to realise that my life has been this way for over 3 years.

John Rennie

Maybe you can ask a psychologist to rehabilitate you :-)

user228700

5:30 AM

@JohnRennie Hopefully it will awesome :-)

user228700

It's all going to go by so quickly after next week; exam after exam after exam.

user228700

After this one, I have another one 3 days later and then two more at the end of April, for which I'll be going to Kerala. And then, another one in the second week of May and hopefully two more at the end of May.

John Rennie

My finals were all done in a week, and I think that's a good way to do it. You get into an exam mood and you just sustain it for the week and collapse afterwards.

user228700

I agree. This two-month thing is brutal.

John Rennie

Are you going to rest for a few days after the first set of exams finish and before the end of April ones?

user228700

5:34 AM

If by "rest" you mean sleep for a reasonable number of hours then absolutely, yes.

user228700

What's your summer gonna be like?

John Rennie

I haven't really thought about it ...

Life is fairly routine these days - though routine in a good way

user228700

:-) I see. I remember u telling that u'll be visiting family again during easter. No other plans as of yet?

John Rennie

No, I don't have any plans farther ahead than Easter. I just take life as it comes.

user228700

Taking life as it comes sounds heavenly, actually :-) I too am a big fan of routine.

user228700

5:39 AM

...which is probably why I'm looking forward to old-age so much :-P

John Rennie

Aren't you looking forward to going to university?

user228700

Lol. Yes, very much.

Secret

Routine bores me. This is why I like science and research

John Rennie

Well that won't be routine! :-)

Secret

In fact, I measure effort by how many times I need to repeat something

and thus you have paradoxical results where you spend more time on making a large table simply because it is more tiring to make 4 smaller tables

user228700

5:43 AM

I know but it will be a welcome change from this stuck-in-a-single-room-for-10-months-situation :-P

John Rennie

Agreed! :-)

user228700

I better get back to revising...

John Rennie

OK. Take care.

user228700

:-) Thank you. Hope ur lunch turns out great! I'll still be kind of around so do post a picture later in the day :-P

Slereah

6:16 AM

Hm

I think I have a proof in mind that no CTC is contractible to the trivial curve

But I need some way to prove that for any contractible curve, all curves in $s \in (1-\varepsilon, 1)$ for $\gamma_s(\lambda)$ is within an arbitrarily small neighbourhood of $p$, the base point

I'm guessing the intermediate value theorem would help here but gotta show it

I guess I can just pick for every coordinate the max and min of $x(\lambda)$ since it's a compact set

then it will be within any neighbourhood larger than that

since $\gamma_s$ varies, for $s$, in between the coordinates of the base point and whatever else

(well, timelike contractible)

(obviously a fair amount are contractible)

Secret

6:32 AM

I wonder how micro CTCs (those that has a squared interval of less than a millisecond) behave compared to their largest cousins...?

Slereah

8:07 AM

Math people, are "quasiregular singularities" a thing in math

I seem to only find it for GR

user228700

8:21 AM

Crap. @JohnR: Halp!

John Rennie

8:42 AM

@Kaumudi.H What's up?

user228700

9:35 AM

@JohnRennie I have a quick question about the effect of a dielectric on the capacitance of a capacitor.

user228700

...which is that in every derivation of the expression for the new capacitance, I find that we are working under the assumption that the charge on the capacitor remains the same even after introducing a dielectric in b/w the plates of the capacitor.

John Rennie

@Kaumudi.H on the phone to my Mum ...

user228700

Wokay. I shall wait...

John Rennie

It's Mother's Day here in the UK!

user228700

Oh, wow, it is!

user228700

9:39 AM

Sheesh, when is it in India?! :-o

user228700

Phew. 14 May.

user228700

9:54 AM

@JohnR: Ping me when u come back...

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