Mathematics - 2017-08-03 (page 4 of 4)

Balarka Sen

21:01

i use a single t-shirt and a pair of pants for a month

Eric Silva

Pls love yourself

3

Danu

Man, seriously, folding is the fucking worst. I cannot emphasize this enough

Semiclassical

It's a sign of how long it's been since I've done a proper question on the main site that I'm impatient about this one.

Eric Silva

It's not as bad as when you're forced to do your roommates dishes because they won't

Mike Miller

iu dont mind dishes

Eric Silva

21:03

I don't mind them if they're mine

Semiclassical

ugh, dishes.

Mike Miller

just put their dishes on the table

lol

Eric Silva

I'll just leave them outside their doors

Go from passive aggressiveness to straight aggressive

Mike Miller

no that's still passive

aggressive is throwing them at them

Eric Silva

Their doors open into the hallway so if I did this it would probably lead to broken porcelain everywhere

Balarka Sen

21:07

@EricSilva i have come to the conclusion that love is a primal and self centered concept at any level or any form. i do hate myself, passionately

Mike Miller

@BalarkaSen primal yes, self-centered not always

Balarka Sen

maybe i shouldn't spew more golden trash at this point of the hour

Eric Silva

It's ok to be a little self centered if it helps you take care of yourself

Mike Miller

you are the golden trash of my heart, balarka

anon

who took over all of your accounts

4

Balarka Sen

21:09

pure gold, anon

observation of a true algebraist

heeere comes johnny

hi @Daminark

Daminark

I promise it wasn't me

Also how'd you know my name is Johnny? :O

skullpatrol

Wasn't me.

Daminark

@skullpatrol lies

skullpatrol

Tell me lies.

Astyx

Djohnnyark

Daminark

21:13

Kek

skullpatrol

lol

Balarka Sen

Death Grips - Trash

►

applies to most of the convo

Astyx

applies to most*

Daminark

*applies

Astyx

*

Balarka Sen

21:18

Daminark brings a new level of trash to the chat

3

i can't do better than him even if i try

Keavon

I'm having trouble understanding why my suggested edit was rejected with the reason "This edit was intended to address the author of the post and makes no sense as an edit. It should have been written as a comment or an answer."

The answer I was editing was incomplete, and is wrong and nonfunctional in its current state without the information I added. The information was definitely not that of a comment to the author.

anon

if an answer has a conceptual error that makes it "wrong and nonfunctional," then tell the answerer in a comment.

Eric Silva

@Balarka now imagine going to school with him

Balarka Sen

I know right???

Eric Silva

It's constant highest quality trash

Balarka Sen

21:21

it must be so frustrating to have a schoolmate who's better than you no matter what

at trashing

Semiclassical

There's already a comment to that effect @anon

anon

oh

Semiclassical

For context: math.stackexchange.com/a/538472/137524

Daminark

Honestly I might just be the form of trash itself

Keavon

@anon Is there a reason that it shouldn't be simply added in an edit? I don't know that the author will return and make the edit since it was answered in 2013.

anon

21:22

then no.

Eric Silva

The platonic ideal @Daminark

skullpatrol

"Trash talk" is usually constructivist.

Jasper Loy

I really like the Platonic solids.

Eric Silva

@Daminark I asked today about the papers we have to write at the end of bootcamp stuff and André's postdoc was just like "tbh you can probably just do whatever you want"

Gg

skullpatrol

cya

Daminark

21:28

@Eric if a sequence of curves divides the area of a closed surface in two, their limit will as well, yeah?

Also kek

Eric Silva

What do you mean divided in 2

Like half?

Daminark

Yeah

Connected, closed curve btw

SteamyRoot

@Keavon Edits should always strive to uphold the "intentions of the author". It's mostly etiquette, but the general rule of thumb is: correcting typos/mathjax you can do right away, but adding anything that "changes the math" is a no-no.

Balarka Sen

so you know the curves are converging to some definite limit curve in some sense

?

Daminark

So the real point is that there's a lower bound on the length of closed curves that can do this

Balarka Sen

21:32

right

this is the shape of the drum talk isn't it

SteamyRoot

@Keavon I know it's annoying to leave a faulty/incomplete answer, but that's just how it is I'm afraid. If it's any consolation, most users also read the comments when figuring out an answer. And finally, you can check the profile of the author and see that he was "last seen 1 hour ago" - so there's a good chance he'll reply if you comment! :)

Daminark

Nope, the talk on closed geodesics and minimal surfaces

Balarka Sen

oh huh

SteamyRoot

ooh, shape of a drum

my office buddy does research on that

Daminark

We also had the shape of a drum talk which was nifty

SteamyRoot

21:33

kuleuven-kulak.be/posterwall/poster/2017/u0111239/…

Eric Silva

Ah yeah I've seen this

I gtg kitchen on fire

SteamyRoot

If I were you, I'd just run and not notify us that the kitchen is on fire first :P

Balarka Sen

some people just want to watch the kitchen burn

SteamyRoot

I sure do, except if it's my kitchen.

Daminark

Though I'm prob gonna focus more for now on the homology stuff, I'll still need to think about that talk carefully

Balarka Sen

21:37

@Daminark Compute $\pi_{368}(S^{78})$

Quickly!

Astyx

It's 4

Balarka Sen

well, 42, but yeah

what am i doing with my lif

i should be asleep

Daminark

Actually it's 7

SteamyRoot

@BalarkaSen If you really want to feel like you're wasting your life, go 100% cookie clicker or so

Daminark

Also, two questions

Mike Miller

21:44

fun fact: there is a left order on $\widetilde{SL_2 \Bbb R}$

meaning a total order so that $A < B$ implies $MA < MB$ for any other element $M$

Daminark

1) Is there some reason why we think that separation of variables should work?

Mike Miller

to figure out $\pi_{368} S^{78}$? yeah, it follows from the bousfield-kan spectral sequence

Balarka Sen

so whats the answer

@MikeMiller This is interesting.

Daminark

2) Similarly, why do we have all these weirdly specific dimension-dependent results?

Bonus question 3) Why is the Laplacian important?

Balarka Sen

I can go for 3. Laplacian = 0 means harmonic

in 2 dimension those are precisely real part of complex functions

Daminark

21:53

Do people not care about them in higher dimensions?

Balarka Sen

for higher dimensions you do still retain (IIRC) the various nice properties, like maximum principle, mean value property etc

yes they do

harmonic functions are a natural object of study

I have the notebook from the workshop beside me, let me quote you a big theorem

Daminark

Well I mean so, I imagine that there's just stuff to be analyzed about the heat/wave equations, but those seem very specific

Oh nifty

Balarka Sen

Big theorem: If M, N are compact Riemannian manifolds and N is negatively curved

Then any $C^\infty$ map $f : M \to N$ is homotopic to a harmonic map

Well, I didn't define a harmonic map to you.

But it's an energy-minimizer IIRC. similar ideas playing around

Mike Miller

@BalarkaSen Wow, really? $M$ whatever

?

How unique is the harmonic map in the htpy class?

Balarka Sen

Yeah apparently. Let's see if I have references

Mike Miller

21:58

I won't read them.

I just wanted to know.

Balarka Sen

Me too. :D

I want to know if I wrote correctly.

Eells-Sampson. Let's see...

Mike Miller

arxiv.org/pdf/1607.06388.pdf

pretty cool

Balarka Sen

Yup, that's it

nonpositively curved suffices btw

For genus >= 2 Riemann surfaces/negatively curved Riemannian surfaces (same objects) it's true that if $f$ is a diffeo I can give you a harmonic diffeo in the homotopy class

Sorta like a homotopy version of Hodge theorem, all this.

Mike Miller

What's npc? The codomain?

Akiva Weinberger

@Adeek Congrats

Mike Miller

22:02

I mostly care about $M = S^1$

Balarka Sen

The codomain, yeah

Mike Miller

@Daminark They are not very specific. The heat equation is the canonical example of a parabolic equation (for which there exists a general theory but often you need to work out the detailed analysis of specific cases). The wave equation, the same for dispersive.

Clement C.

is there any admin or moderator around?

Mike Miller

I guess it's hyperbolic, not dispersive. I don't know anything about dispersive PDE but it's all people do at UCLA.

Clement C.

I am not sure how to report this, or if I should (is the behavior mentioned below a violation of the rules?). Basically, an user downvoted an answer of mine because they had misunderstood the question. Since they couldn't apparently undo their downvote, to make up for it (I guess?) they have been through many of my older answers to different questions, and upvoted them.

Daminark

22:06

@MikeMiller What makes them canonical?

Mike Miller

People were doing them in like the 1800s.

They actually describe things in the world.

You can solve them (or at least they could).

Balarka Sen

@Daminark SemiC can tell you why the Laplace equation is relevant to physics

Solution to specific Laplace equation with specific boundary values give rise to potentials of various electrostatic systems

so there's that

Mike Miller

Sounds dumb. Solution to the Laplace eqn with specific boundary values are heat distributions on a disc / manifold that are stable over time :P

Balarka Sen

What does stable over time mean?

Mike Miller

Doesn't change when left alone to do its own thing.

Balarka Sen

22:15

if I understand correctly, that should be what it is. Potentials (in electrostatics) don't change over time

Mike Miller

The setup I have is M is a manifold with boundary, and I have a machine making sure that the boundary always has heat function $f(x)$. And then I let... the temperatures move around, like they want to.

Harmonic fcts are the ones that don't move.

After all the heat eqn is $\partial_t f = - \Delta f$.

The easiest example to think about is where the function is on $[0,1]$

$f_t(x,t) = f_{xx}(x,t)$, $f(0,t) = 0, f(1,t) = 1$, say.

See how things evolve.

(Pick a Fourier expansion of $f$ on the interval and plug it into the eqn, where the coefficients are functions of t)

Balarka Sen

@MikeMiller Ah, OK

Ted Shifrin

Heya Nate!

Dodsy

Heya guys!

Ted Shifrin

@ClementC. As far as I know you can always undo a downvote.

Dodsy

22:20

I am not having a very good week, I will tell you all that much. :)

Ted Shifrin

Oh oh @Dodsy

Dodsy

Basically I was offered admission with no conditions and decided not to finish chemistry or english, and had an 82.5% average. I got a call a couple days ago from the person in charge who said I was supposed to have conditions and that I must have an 84% average, and that I need to get my courses done by the 15th.

Ted Shifrin

@MikeM @Balarka @PVAL Here is a question for you all.

Dodsy

so, I might not even be going to school next year.

even though I already own an appartment.

Ted Shifrin

I suppose you don't have the (original) terms in writing? This is risky stuff.

Balarka Sen

22:24

The way I think about harmonic functions is that if I have an isolated charge and I draw a sphere around it, then by Gauss' lemma $\text{div} E = \rho/\epsilon_0$ where $\rho$ is the volumetric density, which is 0. So $\text{div} E = 0$. As $E = -\text{grad} V$, that says $V$ is harmonic.

Dodsy

I do indeed.

but whenever I push on this lady she just pushes right back.

Ted Shifrin

Then they need to stand behind that or at least make some compromise. Someone screwed up, but it's not your fault.

I would say jump in there now and do your absolute best to get to the 84% mark.

Don't shrug it off.

Dodsy

yeah that's my plan

Ted Shifrin

OK, go for it, man.

Dodsy

I' hoping to meet that 84% but if I don't I'll definitely be causing a stink.

Ted Shifrin

22:25

But the head of admissions needs to know that they're messing up.

Document everything in writing.

Dodsy

For sure.

brb.

Ted Shifrin

I've been in a similar position with people saying that the transfer credit website said we'd give them credit for such and such a math course. I had to remind them that the website has a disclaimer on it and that ultimately I was the one responsible for such decisions, but the website with inaccurate info. But it still made for very unhappy people.

Mike Miller

@TedShifrin Tell them to look at Wall's old work.

Ted Shifrin

Hi DogAteMy

LOL, not for me to say. I don't think about this stuff.

Balarka Sen

I have forgotten electrostatics

Ted Shifrin

22:27

Are you still across the non-existent wall?

Balarka Sen

shit

Ted Shifrin

All the electrostatics you knew you've forgotten? Sounds like you need a meme.

Balarka Sen

lol

Mike Miller

lol

Ted Shifrin

Where's @Hippa when we need him?

Mike Miller

22:30

I left a comment.

Ted Shifrin

OK.

Tobi

are these waves or glitches?

Mike Miller

I dunno.

Ted Shifrin

I certainly don't see wave motion in a particular direction. They're sort of chaotic waves. Does that make them glitches?

Mike Miller

I think he's trying to make Brownian motion.

Things seem to cluster slightly more to the right and bottom.

Ted Shifrin

22:35

Well, the latter seems right.

Dodsy

The thing is, that I thought she'd cave after I sent this email:

Hello Tamarra,

I appreciated our conversation today, and will do my best to complete and send my final HS transcript by the date we decided upon. However, I did want to emphasize that I was not aware of these conditions as it was not outlined in my offer of admission. My offer of admission stated that the basis for my admission was my 2013 high school transcript, and I felt that anything I completed would only serve to act as a prerequisite to further learning.

edit my full name out of there real quick

:P

Ted Shifrin

The letter of offer should be the definitive statement. However, if there's any ambiguity in that, ...

Dodsy

here's my letter of admission

imgur.com/a/pgMrW

and she has admitted that it was a mistake on their end.

sorry, I know I seem to always complain here.

:P

Ted Shifrin

Well, I have no definitive word on such things, but I think that she doesn't get to admit it was a mistake. They have to stand by it. Some Dean of Admissions needs to rule on this.

Dodsy

I agree. So best idea is to give this test a shot, if I fall short then go a little deeper down the rabbit hole?

Ted Shifrin

22:41

Regardless, you should do your best to get it finished, but since they messed up they should make time allowances at this point. Stop wasting time and get work done.

Dodsy

good point.

thanks Ted.

Ted Shifrin

There usually are appeals processes, and especially if you have her admission that they messed up, some sort of official appeal should be granted.

Daminark

22:55

Hey @Ted!

Sorry @Dodsy, good luck!

Jasper Loy

Heya @Daminark and @TedShifrin and @Dodsy LOL

Daminark

Hey @Jasper!

Jasper Loy

I don't understand how Balarka can wear the same thing for a month, lol. I was reading the transcript.

I think maybe I tried it for three days at most long ago.

Balarka Sen

i lead a minimalist life

Jasper Loy

Oh I am trying to be vegetarian now @BalarkaSen.

Balarka Sen

23:01

I do want to buy a big commie Russian coat at some point

Tobi

@TedShifrin How about now?

Daminark

I dunno if it was for a month but I spent quite some time in life where I never woke up in time to change so I'd go to school in pajamas

Tobi

Daminark

@BalarkaSen Vodka for you, comr... Wait buying? KAPITALIST PIGDOG

Simply Beautiful Art

Does anyone know of any links concerning the series $\displaystyle\sum_{k=2}^\infty(-1)^k \frac{\lfloor\log_2(k)\rfloor}k$? I tried to ask Approach0 but came up with nothing

And what the heck are you guys up to? O.o

Balarka Sen

23:04

@Daminark No need to be afraid, komrad. I would merely lend it, and send the owner to GULAG

Jasper Loy

I am going to sleep, see you all in my dreams.

Daminark

I was worried that komrad Balarka Sensky bekom kapitalist pigdog

SteamyRoot

Just don't go full gopnik

Akiva Weinberger

Senislov

Balarka Sen

@Daminark Have faith in the RED FLAG

LegionMammal978

23:16

Hmm, trying to find a "simple" expression for the positive real solution of $7x^6-56x^4+112x^2-64=0$

The smallest garbage I can get from Mathematica is

$$-(-1)^{3/4} \sqrt{\frac{56 i \sqrt[3]{13+3 i \sqrt{3}}+\sqrt[3]{14} \left(\sqrt[3]{14} \left(13+3 i \sqrt{3}\right)^{2/3} \left(\sqrt{3}-i\right)-14 \left(\sqrt{3}+i\right)\right)}{21 \sqrt[3]{13+3 i \sqrt{3}}}}$$

I somehow suspect this is the best it will get

Daminark

has faith

Hey @PVAL!

LegionMammal978

Apparently, it's also equal to $\frac{2 \sqrt[14]{-1}}{1+\sqrt[7]{-1}}$

PVAL-inactive

Hey @Dami

LegionMammal978

The problem is, I don't really trust radicals with $-1$ in them

Daminark

How's it going?

PVAL-inactive

23:24

I just got like a $300 book recalled from the library, and I couldn't find it.

but I found it so all is well.

Daminark

Oh that's good, lol those recalls are sp00ky

PVAL-inactive

I'm pretty certain it was from my advisor

whose putting it on reserve for a class.

Daminark

iseewhatyoumean.winrar

Which is it?

Simply Beautiful Art

@LegionMammal978 lol

PVAL-inactive

Ozbagci-Stipsicz "Contact Surgery on 3-manifolds and Stein surfaces"

Akiva Weinberger

23:26

@LegionMammal978 Mathematica likes to use those to represent roots of unity

SteamyRoot

Hmm

Daminark

Nifty

SteamyRoot

Shouldn't be too hard to simplify that and end up as a real number

PVAL-inactive

@Legion What happens when you substitute y=x^2.

and at the end just take the square root of the postiive real root.

SteamyRoot

@LegionMammal978 $2\cos(\pi/14) / (1+\cos(\pi/7))$

or, in fact, just $\sec(\pi/14)$

Surprisingly "clean" solution o.O

Simply Beautiful Art

23:35

@SteamyRoot Darn it, I was just about to suggest a solution with trig functions...

Akiva Weinberger

Now plug it into the original thing and see if it checks out

SteamyRoot

It does.

Akiva Weinberger

I'm betting $\sec(n\pi/14)$ will work for $n$ less than and coprime to $14$, actually

$n=1,3,5,9,11,13$

SteamyRoot

Actually, it's not that surprising it's a clean solution, since that polynomial only had even powers... heh

Akiva Weinberger

That gives us six roots, and it's a six-degree equation

So hopefully that's all of them

SteamyRoot

23:40

Those are all solutions, yes.

Simply Beautiful Art

@AkivaWeinberger xD That was fast

Transcript for

$Mathematics$ Mathematics