what'd i miss?

A ruckus. An uninteresting algebra problem that requires more than high school non-cleverness.

Don’t you dare complain about geometry ever again!

i clicked through to the paper. yeah, this stuff is subtle. not surprising that you need a second operation.

there is a subworld of C* algebra people who do jordan algebras, and they're all weird.

I can’t get to the paper, but it fails with just a binary operation, so duh high school symbols won’t ever get it.

Funny how hypotheses might be essential.

not the same jordan as jordan canonical form or gauss-jordan elimination (which are also different jordans). the one who became a member of the nazi party in 1933.

I never knew …

Michael

We put history stuff in our linear algebra book chapters, so maybe different Jordans do appear.

apparently he wasn't really into it. joining the party in '33 for someone like him would have been relatively normal, i think? you have to watch out for the ones who joined in like 1931, or heaven help us, the 1920s.

@copper.hat The legend

per wikipedia: Jordan seemed to hope that he could influence the new regime; one of his projects was attempting to convince the Nazis that modern physics developed as represented by Einstein and especially the new Copenhagen brand of quantum theory could be the antidote to the "materialism of the Bolsheviks".

talk about knowing which way the wind was blowing.

We do discuss Wilhelm and Camille.

also i don't think he had a lot of luck with that. kind of weird to praise him for wanting nazis to get better at physics.

sorry, i was confusion jackson with jordan, how could i

haha.

Ms Jackson, if you're nasty.

i'm reminded of the character in office space who was named michael bolton.

"why should i change my name? he's the one who sucks"

I wonder if students ever read historical notes.

i love them

One of my students years ago had a brother named Michael Boulton.

many things make so much more sense when viewed in context.

peter lax's functional analysis is a depressing read. there's a lot of "so-and-so from theorem 6.1 killed himself to escape the nazis." lax is one of the last of that generation.

they used banach as a human incubator, to breed lice

jesus

i gather dive tables were constructed from data from said human experiments

they were doing their ignorant savage best at trying to understand the spread of typhus, i think.

no, it was something to do with survival in cold water,

from first principles, i presume, having thrown out any books by someone who might have a brain cell.

irishtimes.com/news/science/…

apparently when you confine a lot of people in bad conditions you get a lot of typhus. i can think of at least one way to prevent that.

And Leray invented sheaf cohomology in the concentration camps.

it is beyond my comprehension.

Mandela studied law in prison.

i can only dream that i would have the appropriate cohones to behave in an acceptable way should i ever be in such a situation

i was in robben island prison

copper: DUI?

i nearly killed another irish guy there, but that's a different story

its capetown's alcatraz

alcatraz is pretty cool. it's one of those tourists-only stops that would actually work as a destination if it weren't so full of tourists.

i love it, have been there 6+ times

ok, i should get some exercise

Did you request a private room for a weekend?

in the dotcom era they were thinking of allowing overnighters

i have a friend who worked on alcatraz

one of my daughter's friends.

i hope they did something. the last time i visited (early 90s) a lot of stuff was in bad shape and they'd recently shut off access to stuff that used to be part of the tour because they couldn't maintain it.

she was on my winning team at lockheed martin :-)

if that means dot com bros overnighting, i say, let 'em

i would have done it.

i am not up to it anymore, but at some stage i considered kayaking there at night and overnighting outside. illegal of course.

matheducators.stackexchange.com/questions/25041/… is an interesting question.

do people find these kinds of diagrams helpful? i generally don't, although i remember my first group theory book had a few of them.

mostly some variation of that genre of diagram depicting fibers 'over' a base. i don't think it helps at all, but maybe i'm just not seeing the right ones.

i see this kind of stuff on wikipedia from time to time and always wonder what it's teaching other people that it isn't teaching me.

Yes. My algebra book has lots of “fiber bundle” pictures. I also used explicit color-coding in lectures.

You’re anti-visual. The average math-learner is way more visual.

OK. i figured this was something specific to me, akin to color blindness.

one genre that i think just doesn't help, and maybe some of you visual folks will agree with me on this one, are those rainbow plots of complex functions that seem to appear by law in any wikipedia page involving a complex function.

it doesn't inline that image but if you click through you'll see an example.

those help nobody. i don't know what anybody is expected to do with them.

@leslietownes I find those pictures incredibly helpful, but I have also put a fair amount of effort into writing code which produces those kinds of images. They are a nice way of representing a four dimensional space in two dimensions.

Or the Riemann surface picture on the cover of my multivariable book.

we now all understand the gamma function.

Oh, not that! That’s going crazy using Mathematica to shade by function value.

yes. OK. thank you.

i do appreciate in abstract how cartoons of riemann surfaces can help. my question above was limited to variations on the above image.

which appear everywhere in complex analysis wikipedia, just because mathematica has some preset function to allow you to do that.

i will allow one use of such images - when you graph |f(z)| vs. z - and for the limited purpose of explaining why 'poles' might be called 'poles.'

but we don't need to see one for each complex function we meet.

surely the world needs more fractals as well

speaking of smartphones, i may need a new phone soon. i hate this.

i have a galaxy s5 that would probably crash if i tried to zoom in on that image.

looks a bit like some cheese i have in the fridge.

my daughter's taste in visual art goes in this direction lately.

lots of abstraction.

@leslie Munchkin needs to get back to the ducks.

she drew a parrot yesterday. i told her it looked more like a toucan. we agreed to disagree.

Close enough. She should draw our green parrots!

she should. we've collected a few feathers from those parrots at a park. she could use them as a color reference.

The best parrots ever. Damn, they’re squawky!

at our old house we had a magnolia tree. they loved that tree.

a dozen of them would land it in it and they'd shell the magnolia seeds, leaving an enormous amount of plant matter over the sidewalk.

When i view the torus as $\mathbb{R}^{2}/\langle(x+1,y),(x,y+1)\rangle$ can i just say that it is compact using that the restriction of the projection to $[0,1]\times[0,1]$ is surjective and continuous? The morale of this is that it is a fundamental domain but I don't really need it for a "weak" argument related to just compacteness, do I?

(Of course I could prove that the torus is compact as closed and limited, product of compact... but I'm interested if I'm doing something missleading when dealing with equivalence class)

what happened? my chat room suddenly changed into something more usenet like from the last century

no starred messages, etc

what is usenet? what is usenet?

I asked it earlier also but no one told me about it.

@Koro Hi !

Hi @copper!

Did the format of the room change a short while ago? I don't like it now.

usenet was a sort of bulletin board

copper, I see no change in the room format. I can see the starred messages as usual.

Oh, I thought usenet was like a room which could be accessed using only special browsers.

koro usenet is/was a set of mailing lists. roughly speaking. it was accessed via something similar to an email client.

people could post whatever to the 'newsgroups' (roughly speaking, message boards, or chat channels) of interest to them.

My chat window on my laptop has changed significantly in the last hour

there were concepts of sender and recipient and replies.

I don't recall changing anything

copper, you seem to be having some kind of technological seizure localized to you. everything looks fine down here.

oh, so something like reddit.

very similar.

Very wierd

sci.math and sci.math.research were the main groups for math. roughly analogous to math.SE and mathoverflow.

I have to hit the send button now as opposed to just enter

rot13

@leslietownes I see. So they were available on usenet?

I thought sci.math was a website.

yeah, it wasn't. it was a usenet newsgroup.

def having a tech hiccup here

there are fairly strong parallels between some of the better newsgroups and stackexchange sites of today.

some of the same participants, even.

copper, it may be due to internet issue. It happens a lot on my iphone.

I suspect it is the mobile version but I definitely selected the classic

Sometimes the area for typing gets so huge that send button disappears.

this is an utter disaster

if you select 'request desktop website', it should work.

yeah, it looks exactly like my phone.

this option comes somewhere in browser settings.

i participated on sci.math way back when. this is where i acquired the habit of not doing inline tex. chatjax was not available back then.

@leslietownes I wasn't probably even born when usenet was around :(.

@leslietownes I see. So \langle \rangle was simply <> back then :)

yes indeed.

nice

google bought an archive of usenet from somewhere and tried to reboot it unsuccessfully as 'google groups'. this was about 20 years ago.

hmm, i can't escape.

someone just downvoted an answer of mine from 2012

are things umop apisdn?

the accepted answer (from andre nicholas) was exactly the same but did not get downvoted.

not quuite, like barrel roll on google

@copper.hat compensated :)

:-) Thanks @Koro, appreciated but no need. I just like to whine

I see google has removed the Chuck Norris easter egg

@Koro How did you know what question it was???

Strange that they singled out my answer to downvote.

I did have a serial downvoter a few years ago.

@copper.hat Users-> search for name -> activity -> reputation

Got it back. I had to select "full site". I don't remember selecting "partial site"

:-) @Koro

That was wierd.

Time for a glass of wine.

i miss using an application called DC++ at college.

it ran on intranet and people could share their files through that. It could download very fast.

Where did you go to college?

I studied at IIT Guwahati.

Nice. Have you ever been to Bhutan?

sadly no.

I went to Meghalaya though once. :)

A wealthy (Indian) friend (who worked for me once) once said that he would bring me there for a hoilday, but I never took him up on it.

I'll visit all of east part of India one day :).

I would love to visit the Assam region sometime. The closes I have been was Siliguri

You know Guwahati is in Assam, right?

Yup

Among many other things, I want to drink tea there :-)

It is so completely different from where I grew up. Food, people, weather, countryside,

Copper, if you know Siliguri then you may have heard of New Jalpaiguri (NJP) also. Pineapples are very cheap at NJP railway station.

if you are taking pineapples with you over long distances, do not remove the leaves at the head of the pineapples else they'll spoil :).

I believe we passed through there on the way to Darjeeling

But a long time ago :-(

I like pinapple

yeah, it is almost at the border of Assam and West Bengal. I suppose it's about 8 hrs journey from NJP to Guwahati.

I don't know how to open them

I loved the trains back then, I suppose they have changed

they used to serve tea in little earthenware cones

I love pineapples too. They have many health benefits. To open them, I just cut them till I see the eatable part :).

@copper.hat I suppose it's still there at some stations but many have replaced those cups with paper cups now a days.

Have you been to Bangladesh?

sadly no. One of my friends has. Some of my friends kept visiting places and asked me also to join them but at that time I hesitated in travelling.

I would love to visit.

So sad, so many places, so little time.

copper, in order to go from my college (located at outskirts of Guwahati) to city, there were too ways -1) take ferry, 2) take college bus.

Taking bicycle with you on ferry and then going to city, was so amazing :).

Sounds lovely.

the ferry would take about 10 to 15 mins or even more iirc, to cross Brahamputra river to take you to the other side of the river -that is to the city.

Did it flood in monsoon season?

i think it did. but whenever there was any such warning, the ferry services were shut.

Some day...

I'm off to bed! Good night, nice chatting.

good night, copper.

@MatíasMatteini Yes, you can just say that.

@TedShifrin Actually I want to correct this. I didn't show that if $M$ is a commutative magma (or groupoid if you prefer) with $x^3x = x^2x^2$ holds for all $x\in M$ then $M$ must be power associative. I only showed that if it holds for one specific $x$ then it doesn't imply that the magma generated by $x$ is power-associative.

Hi guys I am new to Math stack exhcange a guy answered my question and was very helpful, however I am having trouble accepting his answer, is there a guide for it? I could not find suitable help from googling

I have a PDE question someone please help math.stackexchange.com/q/4401548/854335

@AleeEmran are you saying that you don't know how to accept the answer or you don't know whether you should accept the answer?

@AleeEmran Welcome 😁

I am not really following the jump to 3 dimensions. what is 's'?

I get that $r=\sqrt{x^2+y^2}$

or is $r=\frac{x}{\sqrt{x^2+y^2}}$?

is $s=\frac{y}{\sqrt{x^2+y^2}}$?

@robjohn I'm following web.stanford.edu/class/math220a/handouts/firstorder.pdf basically.

@robjohn $r$ is a parametrization of curve $x^2+y^2 =1$.

@robjohn $s$ is a parametrization of characteristic curve $(x(s),y(s),z(s))$.

I don't follow that totally, but it gets the right answer, so it gets there.

@barista: it is hard to follow without some explanation. Also, you've written total derivatives where there should probably be partial derivatives. It makes it hard to decipher.

@robjohn Right I should write partial derivative. But if I specified $r$ is a parametrization of the initial curve, $(r,\sqrt{1-r^2},r)$ and $s$ is a parametrization of characteristic curve, then isn't it clear?

@PM2Ring Thank you! If the function f(x) has positive-sign only (e.g. $x^​2+​16*​x+​2789$) or negative-sign only for all real x, then it has no real roots, then in this case, we cannot apply Bisection method, right? If so, then we can say that biseciton method doesn't work if roots are not reals.

@user777 Right. And if we want to search for complex roots, we need a different strategy, since asking if w=f(z) is less than or greater than zero doesn't make sense when w is complex. Bisection is ok when you're searching along a line. It's not so helpful when you need to search a 4 dimensional space. ;) However, if you can somehow find a line in the complex space that contains a root of w=f(z), then you may be able to use bisection on that line.

mse is down for maintenance.

@barista it's fine

@Koro are you having a panic attack about it @Koro?

@dc3rd the website is up and running now :-)

I had written an answer to a post and saved it awaiting some clarification from the OP, and not my saved answer is gone.

Goood to hear. How's your Groups class going?

the coaching centre where I was taking classes had completed groups few months ago.

what are you taking now? WHat's a coaching centre?

They organise test series also, which one can take up for practice.

During lockdown, I had joined one. I wanted to have a classroom environment. They charged some fee for the coaching centre though.

Ah. I get you. In the meantime you are sharpening your mathematical skills so when time comes for the masters you will be as skillful as Leslie, Ted, and Copper..... :-)

yeah, that and my personal interest too :-).

@dc3rd: Did you finally get the contradiction in the problem you were solving the other day?

Yeah. Figured it out. Talked it over with copper as well. Hopefully I get a chance to work on more problems tonight.

:)

@robjohn Davide Cervone didn't have anything to say beyond what he already told you. I left a comment for a developer explaining where MathJax continues to be broken. It's unlikely this will get fixed unless it again spreads beyond the Activity page.

@RandomVariable I'm not surprised. There are so many bugs right now.

Things were pretty stable, then they tried to unify the desktop and mobile interfaces, much to the desktop users chagrin.

@robjohn I didn't mean to imply that the developer said that. That's just my own opinion.

@robjohn Some of us mobile users aren't too happy with the changes, either. (I mostly use mobile these days).

Are straight books, equations, application etc. without talking, are these useful?

direct books

Is there a known term for the quality of these books?

@PM2Ring, hello

Is the quality of these books will not help in deep understanding?

@M17 Hello. I'm sorry, I don't know what books you're talking about, or what you mean.

Question here for everyone if someone has any comments

What kind of books is this given a name? Because I feel like it's a good reference when it's something you want to go back to

it is with a creeping sense of dread that i finally find a context where Kato's book on perturbation theory is useful to me

Why dread?

there's lots of scary shit in that book

I actually don't know it.

Seems like main is down (still?) (again?).

formal perturbation theory

@TedShifrin It seems to be up right now.

Not to be confused with Cato from The Pink Panther.

Now it might be awake.

Just rewatched one of my favorite movies of all time. Mon Oncle, by Jacques Tati.

I can't imagine an American director being able to create the kind of atmosphere that Tati achieves.

here's an intimidating perturbation theory question that i don't know how to properly handle

first, a standard problem: given a linear operator $T(\lambda)=T_0+\lambda T_1$, compute to first-order in $\lambda$ the effect of $\lambda T_1$ on the eigenvalues of $T_0$

what Kato does is extend that to $T(\lambda)=\sum_{n=0}^\infty T_n \lambda^n$, with various provisos. (in particular I should have said that $T(\lambda)$ is not merely linear but Hermitian and has discrete spectrum.)

here's the problem that scares me: what if you have two perturbation parameters, i.e., $T(\lambda,\mu)=\sum_{n=0}^\infty\sum_{m=0}^\infty T_{n,m} \lambda^n \mu^m$?

how do you even begin to do a systematic theory for that?

like, if you assume that $\lambda\sim \mu$ then you can treat their ratio as some fixed parameter and use only one of them as a perturbation parameter

but that won't cover $\lambda \sim \mu^2$ and so forth

to put it differently, how tf do you do analytic perturbation theory in two variables?

(in principle you could just study specific special cases, along the same lines as I said for $\lambda\sim \mu$, but the general theory seems...yikes)

semi i don't know if there is a general theory. the example theory in kato was motivated by specific examples in whatever he and others were interested in (some kind of physics).

as you probably already know it can get subtle when eigenvalues/points in the spectrum split or merge in a continuous way. although with various assumptions on the points you are considering you can do slightly more than that. i think a lot of that bizarre decomposition of the spectrum into things beyond 'eigenvalue vs. not' is related to distinctions that matter in perturbations.

yeah

i'm pretty sure everything in my case is not bad enough to cause issues

the specific structure of my problem goes along these lines, and writing in more physics notation for my own brain: $H(\lambda,\mu)=H_0+\lambda U_1+\mu V_1+\lambda^2 U_2+\mu^2 V_2$

Specifically you start with a specific triply-degenerate eigenvalue of $H_0$ and consider $\lambda\sim \mu\ll 1$.

$V_1$ lifts the degeneracy of this eigenvalue but $U_1$ doesn't, so the limit with $\mu \to 0$ seems fishy

(the HW problem only asked for the leading correction to the eigenvalues, so you toss out the $U_2,V_2$ terms. some students kept those terms, and I wanted to explain why that's not kosher.)

I need a statistician...I'm completely befuddled by a statistical model....

@dc3rd The only one I know here is @Clarinetist, but he doesn't hang around much these days.

Yea...I've been hoping for him to pop up but he hasn't

I've asked the question on stat-exchange, hopefully someone answers. But even that I think my question is muddied....

semi: how rude, to give people that as homework.

i remember buying kato because it had some of the context for homework in a class i was taking. there's quite a lot of good general operator theory in there.

@robjohn, @TedShifrin, et al., Thanks to @Xander in the math mods' office: webcache.googleusercontent.com/…

It's down again. Amazing that chat rooms survive!

\o @Buraian

Excellent work

Russian hackers trying to prevent me from gaining reputation points