The h Bar

Yashas Samaga

16:00

messages were sent an hour ago

but I want to have a title message inserted before those msgs

so that it can be pinned

ACuriousMind

Uh, no, I can edit old messages but not insert new ones.

Yashas Samaga

ok ty

Anonymous

@YashasSamaga You can bookmark a series of messages I guess and give them a title.

Anonymous

There is such a feature

Yashas Samaga

@Mystic or ACM could simply edit one of your previous messages and change the text

Ben Niehoff

16:05

@0celo7 Oh no! All the effort! Why didn't you get the bounty, did he just wait until the bounty expired?

Yashas Samaga

@Mystic "So Nitrogen Family:" to "Nitrogen Family Revision"?

0celo7

@BenNiehoff he's got two days left :(

But he accepted my answer so idk what happened

Anonymous

@YashasSamaga Okay sure! I'll do it everyday to complete the syllabus then =)

Anonymous

I will finish N family by today

Yashas Samaga

@ACuriousMind Can you do it? chat.stackexchange.com/transcript/message/35899591#35899591

0celo7

16:07

@ACuriousMind did you see my Riemann tensor uniqueness proof?

Anonymous

Typing is a great way to memorize!

Ben Niehoff

@0celo7 maybe it went into bounty-limbo :(

I think I answered some other ones where the bounty expired...I'm not sure, because I don't think it tells you if a question used to have a bounty, but no longer does

ACuriousMind

@0celo7 Yes, and I was suitably horrified by the objects with 10 indices :P

Ben Niehoff

10dices, we call them

ACuriousMind

The user still has 2 days to award the bounty, maybe they just want to give the question and its answers maximum exposure

0celo7

16:08

@ACuriousMind :)

ACuriousMind

I don't award bounties right after I got the answer I wanted, either. (Granted, I rarely get the answers I want even after bounties :/)

Ben Niehoff

when you offer a bounty, does it come out of your own rep, or is it newly-created rep?

Curious about the economics of pretend Internet points :)

0celo7

::ahem:: Gerard 't' Hof't' ::ahem::

@BenNiehoff own rep

Ben Niehoff

there's a huge photo of him on the wall in one of the conference rooms in Utrecht :P

a painting, rather

0celo7

physics has a lot of figure worship

ACuriousMind

16:10

@BenNiehoff It is substracted from your own rep. If no answer is given, it vanishes into limbo. If answers are given, and are scored above +2, and you choose to not award it manually, the highest scored answer gets half of it. If you choose to award it, that answer you award it to gets all of it

Ben Niehoff

he wasn't there when I was visiting, though, so I didn't get to meet him :(

0celo7

@ACuriousMind I think Kato has the most complicated proof of the spectral theorem in finite dimensions in the world: via holomorphic functional calculus.

ACuriousMind

I'm willing to believe that

0celo7

He doesn't have a single characteristic polynomial anywhere

It's wonderful

Ben Niehoff

so, new rep is created by upvotes and accepted answers, whereas bounties do not create new rep

ACuriousMind

16:12

Yes, exactly

@0celo7 ::shudders::

0celo7

@ACuriousMind I think the idea is that this method extends to bounded operators on Hilbert spaces.

ACuriousMind

Yes, I get it. It's still complete and utter overkill and obscures many of the niceties of linear algebra

0celo7

@ACuriousMind It's a graduate text on functional analysis, I don't think he's doing an intro to linear algebra here.

Although if you asked me to prove the spectral theorem without functional calculus I'd be pretty screwed :)

@ACuriousMind I'm thinking about how to prove the spectral theorem algebraically. How do you know that you have $n$ linearly independent eigenvectors?

Ben Niehoff

So I saw some neat talks on gravitational waves today

0celo7

That is, how do you know that the geometric and algebraic multiplicities agree?

Ben Niehoff

16:18

Actually they put me to sleep because I'm not an experimentalist

but it was nice to hear a bit

0celo7

I know it's true for normal operators, but how do you see that elementarily?

(Kato proves it using functional calculus.)

Ben Niehoff

They included a talk by Bruce Allen, if anyone knows who that is

ACuriousMind

@0celo7 You can find various proofs of the spectral theorem everywhere

0celo7

@ACuriousMind I want a purely algebraic proof though

Ben Niehoff

this guy: en.wikipedia.org/wiki/Bruce_Allen_(physicist)

ACuriousMind

16:20

@0celo7 I don't want to bother with that right now, sorry

0celo7

@ACuriousMind It's in Shankar, don't worry

skill patrol

@BenNiehoff impressive

Ben Niehoff

His talk was the most interesting, by far...but the other ones definitely put me right to sleep

skill patrol

@BenNiehoff have you worked with Witten?

Ben Niehoff

no, I've met him, but we work on very different things

and I think anything I do is unlikely to be interesting to him :P

skill patrol

16:27

how about Susskind?

Ben Niehoff

I've also met Susskind

skill patrol

cool

Ben Niehoff

I've probably met most famous theorists at this point, it happens if you go to enough conferences :P

I'm decent friends with two of Susskind's former students, but again nothing I work on would be interesting to him

Susskind talks exactly like George Carlin, but I guess you know that since he makes videos

Anonymous

meta.stackexchange.com/a/117571 This might do the job!

Anonymous

@YashasSamaga

Emilio Pisanty

16:30

@BenNiehoff maybe you can help this guy

> Never mind the paper. I am trying to find Glogower. He was a high school chum. I can find no trace after stay at Brandeis

Ben Niehoff

I've never heard of this Glogower guy! Or this paper :\

Yashas Samaga

@Mystic I think I am stupid

@Mystic I could have written [Nitrogen Family Revision](the link to the transscript)

Anonymous

@YashasSamaga ? =P

Yashas Samaga

and pinned it

Ben Niehoff

but surely the best way to track someone down would be to email those institutions where you know they've been

Anonymous

16:31

Right

Yashas Samaga

my brain stops working few days before JEE

Anonymous

=D

Anonymous

LOL XD

Anonymous

Mine too

Anonymous

Exam phobia!

Ben Niehoff

16:32

is JEE that huge Indian exam that determines your entire future?

Anonymous

@BenNiehoff No.

Anonymous

Not entire future =P

Ben Niehoff

oh, what is it then?

haha

Yashas Samaga

It is an exam which is harder than USA olympiads lol

ACuriousMind

@EmilioPisanty Have you been searching for someone who can find Glogower since that answer was posted?

Yashas Samaga

16:33

The American students freak out when I tell that their AP syllabus is easier than our regular high school syllabus

Ben Niehoff

honestly, AP syllabi are a joke

Anonymous

Just a popular entrance test in which millions participate in @BenNiehoff =D It is basically like Olympiads

Anonymous

It is not that "you entire future depends on it" XD

Anonymous

That sounds too grim

Ben Niehoff

but your score determines what subjects you can choose to study in university, right?

Anonymous

16:35

@BenNiehoff Yeah, right. But not everybody studies in an IIT or NIT...95 percent of students don't get through. In other colleges you can select any subject of your choice..

Ben Niehoff

ah, ok

Yashas Samaga

@BenNiehoff that's the worst thing out there

rank determines subjects

top rankers take CS

and fail

and don't allow the talented CS students to get seats

Ben Niehoff

yeah, it sounds silly to me

Anonymous

Agreed ^

Anonymous

Anyway I don't care for CS

Anonymous

16:37

I am not gonna take CS

skill patrol

What part of String Theory do you work on? @BenNiehoff

Ben Niehoff

I mostly do supergravity and black hole microstates (or "fuzzballs")...have been branching out into some holography

skill patrol

cool

Ben Niehoff

and one CS paper: inspirehep.net/author/profile/B.E.Niehoff.1

skill patrol

16:52

29 mins ago, by skill patrol

@BenNiehoff impressive

:-)

Ben Niehoff

well, hopefully someone will hire me for a real job someday :P

Yashas Samaga

what kind of jobs do string theoriests do?

Ben Niehoff

by "real job" I mean hopefully a tenure-track job

right now I'm a postdoc, which is a fixed-term contract

people who don't stay in academia go to a variety of places...I have some friends who went into big data or finance

Anonymous

@BenNiehoff tenure-track job like ? Is there any job where you will need to apply your knowledge of string theory/physics (outside academia) ?

Anonymous

Or you need to completely change tracks?

Anonymous

17:07

I don't think finance or big data needs knowledge of string theory!

Ben Niehoff

a tenure-track job means a professorship; i.e. someone who can earn tenure

And no, you don't directly apply string theory, but you can apply a bunch of high-powered maths

Anonymous

Oh being a professor is a good idea. You can earn and do research at the same time =)

Ben Niehoff

actually, it's probably easier to do research as a postdoc

as a professor you also have to teach, and do administrative stuff

but you do get paid more :)

Anonymous

@BenNiehoff Yeah, but you won't get paid for it!

Ben Niehoff

and having a permanent job is kind of important

Anonymous

17:10

Taking up pure physics indeed needs passion and dedication =)

Ben Niehoff

I think it's a bit like becoming a monk

Anonymous

Hehe :-P You need to look beyond all worldly wealth and stuff. It is kinda sad that in my country research scientists are paid far lower than other professions (which don't require much skill- like IT)..

ACuriousMind

Interesting review on spectral geometry by Connes appeared yesterday. Now I want to learn more about non-commutative geometry, damn

@BenNiehoff That's...a surprisingly good analogy

Ben Niehoff

@ACuriousMind Hey, my salary is low and I've decided not to start a family...I'd say it's remarkably like monasticism :P

2

Anonymous

"Not start a family"....OMG...that's too much =D

ACuriousMind

17:16

@BenNiehoff Yeah, I went from "Heh, that's funny" to "Huh, it's funny 'cause it's true".

Yashas Samaga

@BenNiehoff What's your age? (if you don't mind answering)

Ben Niehoff

I'm 34

Yashas Samaga

isn't 34 already late to start a family?

Ben Niehoff

hence why I'm not doing so

Yashas Samaga

lol

do you ever want a family?

Ben Niehoff

17:20

I would have had to start while I was in grad school...there's no way I could have gotten any work done if I had

Anonymous

Actually it is not so funny once I ponder on it. This is one of the major evils/drawbacks of our present day society. I sincerely hope it changes in future so that more students are attracted to take up pure science.

Ben Niehoff

that's a depressing question

Yashas Samaga

aw I'm sorry

Anonymous

@YashasSamaga That's too personal!!

Anonymous

Hsssh!

Yashas Samaga

17:20

yea I am sorry

I think after I speak.

Anonymous

=P

Ben Niehoff

Well, when enough scientists die out from lack of reproduction, then the populists can have their way with the environment! It's win-win! :D

0celo7

@YashasSamaga what?

Anonymous

@BenNiehoff That's NOT funny =(

Ben Niehoff

haha

0celo7

17:22

Men can start families whenever they want, it's the women who go stale :P

Yashas Samaga

huh

ACuriousMind

@Mystic That's ~~monk~~ physicist humor for you :P

Anonymous

@0celo7 Stale? Are they vegetables or what?

ACuriousMind

@0celo7 I highly doubt the point here was biological possibility :P

Ben Niehoff

@0celo7 depends on whether those men want to tolerate raising kids into their 50s, but hey

0celo7

17:24

@BenNiehoff fertilize then split. That's my motto

Ben Niehoff

I'm pretty sure they have a name for people like you

0celo7

@Mystic no, meat

Anonymous

I don't think starting a family means producing children.

Anonymous

Actually it doesn't.

ACuriousMind

My parents were in their mid-thirties when they had me, it's not that rare, actually

Ben Niehoff

17:25

oh, I definitely can't afford adoption

0celo7

@ACuriousMind my parents were older

@BenNiehoff get more money

Bootstrap your salary

Ben Niehoff

from where?

ACuriousMind

@0celo7 ::stern look::

2

Balarka Sen

@BenNiehoff i already gave my valuable opinion about this

0celo7

@ACuriousMind humans are meat, not vegetables

Yashas Samaga

17:26

meat huh

we could have humanoids in the future

they are quantum computers :P

ACuriousMind

@BalarkaSen You mean rob a bank?

Balarka Sen

Yes

skill patrol

^

Anonymous

LOL

Anonymous

That's the best way

Anonymous

17:27

I'll help =D

Anonymous

Let's rob the World Bank =P

Yashas Samaga

and the cops will rob your world =)

Anonymous

Let us all (members of PSE) chalk out a plan =D

0celo7

@ACuriousMind To clarify, I can't answer stupid questions with stupid answers?

Ben Niehoff

I have a feeling robbing a bank would not look good to the adoption agency

@0celo7 No, that's for SnarkExchange

4

Anonymous

17:29

Use quantum teleportation or some hi tech physics to rob it

Anonymous

XD

0celo7

@BenNiehoff I don't think I'm snarky

Ben Niehoff

I'm really snarky, I have to try hard to avoid it

Anonymous

@0celo7 The stupid question was a rhetoric to your stupid comment =D

skill patrol

@0celo7 tell it to your gf

ACuriousMind

17:30

@0celo7 What? I didn't say anything about what you can or cannot do, I just found that particular reply...not tasteful and expressed my disapproval.

Yashas Samaga

I thought @0celo7 was married o0

Anonymous

@skillpatrol he doesn't have =P

Anonymous

He is married

Anonymous

He has a wife

0celo7

Lol, when did I say that?

Yashas Samaga

17:31

who said married men shouldn't have girl friends? :P

skill patrol

^

Ben Niehoff

or boyfriends

Yashas Samaga

@0celo7 is your wife a physicist?

0celo7

I'm not married, but not single either

Yashas Samaga

o0

ACuriousMind

17:32

You're Schrödinger's husband?

6

Yashas Samaga

I remember @0celo7 talking about his wife

Anonymous

Even I remember ^

Anonymous

I think he forgot

Anonymous

Ahhhhhh!

Yashas Samaga

loool

skill patrol

17:33

:D

Anonymous

Such a bad husband ='D

0celo7

This is bad

Yashas Samaga

aw

0celo7

my wife AND gf are going to kill me

and I don't even know who one of them is!!

it could be anyone

DanielSank

w00t I passed 13k rep

2

Where's my prize?

Ben Niehoff

17:35

your prize is...13k rep

DanielSank

dang

skill patrol

congrats

Emilio Pisanty

@ACuriousMind oh, hell no

Anonymous

@0celo7 Don't worry. We won't tell your wife about your gf and vice versa. =D

Anonymous

This is too funny :'D

0celo7

17:40

@DanielSank The real advantage of Kato's linear algebra is that it doesn't involve determinants, so is suitable for general Hilbert/Banach spaces.

I doubt there will be any finite-dimensional examples because it's pretty overkill in that case.

Anonymous

Feb 27 at 16:48, by DanielSank

@0celo7 Who's Bernice?

Anonymous

Now I remember the name!

0celo7

Lol.

Anonymous

Feb 27 at 16:48, by 0celo7

My wife

0celo7

That was my phone doing stupid autocorrect on "be nice."

Anonymous

17:42

Your lies can't save your now ='D

Anonymous

We know your secret!

Ben Niehoff

bleh, I'm waiting for Mathematica to invert a 5x5 matrix and it's taking forever

Anonymous

Do it by hand ^ =P

0celo7

@ACuriousMind please modhammer physics.stackexchange.com/questions/317311/…

Ben Niehoff

haha

I've been trying all week to find a better basis to do this in

both by hand and in Mathematica

skill patrol

17:44

ask a mathematician :P

0celo7

mathematicians don't know how to invert matrices

@BenNiehoff is the matrix Hermitian?

Ben Niehoff

it's real and symmetric, so yes!

0celo7

Diagonalize, flip all the diagonals, rotate back.

Doesn't that work?

Ben Niehoff

hahaha, "diagonalize"

the entries are a bunch of nasty algebraic expressions

0celo7

Ah, well. I tried :P

Ben Niehoff

17:46

the last thing I want to do is to introduce a bunch of roots of 5th order polynomials on top of that

0celo7

Good point, the characteristic equation won't be solvable

Anonymous

Ask on Math SE how to simplify it

Anonymous

=P

Emilio Pisanty

@0celo7 surely that's a duplicate

Anonymous

Something could be done using row and column transform

0celo7

17:48

@BenNiehoff show us the matrix

Anonymous

Yeah ^

Ben Niehoff

can't do that unfortunately

0celo7

why not?

is it proprietary?

Ben Niehoff

it's part of a project I'm still working on

but the thing is like a few pages long in Mathematica

Emilio Pisanty

@BenNiehoff Would Kramer's rule be acceptable there?

Ben Niehoff

17:50

the matrix, I mean

Anonymous

@EmilioPisanty Cramer's rule to invert matrices? :O

0celo7

what's wrong with Cramer's rule?

it's awful, but works

Emilio Pisanty

^ that

Ben Niehoff

I mean, I assume that's basically what MMA is doing anyway

Anonymous

I mean that is used to solve for the variables...I don't use it for inversion..

Ben Niehoff

17:52

taking 1/det times the adjugate matrix, or whatever

0celo7

@Mystic there is more to linear algebra than JEE

Anonymous

The best way would be to trying simplifying the determinant

Anonymous

@0celo7 I was trying to learn something more than JEE I suppose when I asked the question.

Emilio Pisanty

@BenNiehoff possibly? who knows

0celo7

the determinant of a 5x5 is always horrible

Emilio Pisanty

17:53

MM symbolics are mysterious as hell

0celo7

@Mystic do you know what a cofactor matrix is?

Emilio Pisanty

but you can force it to do it by hand

Anonymous

@0celo7 I do.

Anonymous

Yes now I get it

Anonymous

Aha

Anonymous

17:54

But that's too bad

Anonymous

I never use that method

0celo7

I mean, the general idea is what when you're solving $Ax=b$, you're really finding $A^{-1}b$.

Anonymous

Of row multiplied by cofactors

Ben Niehoff

second-guessing Mathematica's Inverse[] function doesn't sound like the best route :)

Anonymous

@0celo7 Yeah, I see now.

Anonymous

17:55

That would be an indirect way!

0celo7

@ACuriousMind They're playing German Schlager in the student union. I think the world is ending.

Anonymous

Why do it when you can directly find the determinant ?

Anonymous

@0celo7

0celo7

@Mystic What does the determinant give you?

Anonymous

And use adj(A)/|A|

Emilio Pisanty

17:56

@BenNiehoff Is Inverse[] meant to handle symbolic expressions efficiently?

0celo7

adj is just the cofactor matrix modulo some signs or something.

Emilio Pisanty

for all you know it's doing gaussian elimination and then computing a crazy-expensive Simplify[] after each step

0celo7

mathematica.se

Ben Niehoff

@EmilioPisanty I assume it's meant to handle the mechanics of matrices efficiently; the symbolic simplification step is last, and is what takes the longest, because it now has 25 horrible expressions to simplify

Anonymous

@0celo7 are you asking for its physical significance?

0celo7

17:57

@ACuriousMind Elven lord was talking about me to one of his other classes. Now I have two awkward things to confront him about!

Emilio Pisanty

@BenNiehoff how much do you care about the simplicity of the resulting expressions?

Ben Niehoff

rather, 25 horrible expressions, of which only 15 are independent, because it is symmetric

I care very much

0celo7

@Mystic I mean why do you want to compute the determinant alone, you need the adjugate matrix.

And that's just more determinants.

Determinants all the way down, and determinants are horribly complicated.

Anonymous

@0celo7 Finding adjugate matrix is easy for 5*5 system...

Ben Niehoff

lol, what?

it's only easy on a 2x2 system, where it basically gives you the answer :P

0celo7

17:59

What's the big-O for computing adjugates?

Ben Niehoff

determinants are a sum of n! terms, each a product of n factors

Anonymous

You will get a bunch of 4*4

Ben Niehoff

but I think there's a more efficient way than just the dumb way

Anonymous

determinants

0celo7

$O(n!)$, haha

Anonymous

18:01

which will be easier to simplify than 5*5

Anonymous

anyway its dumb

Emilio Pisanty

@BenNiehoff What kind of entries does your matrix have and roughly how complicated are they?

0celo7

5!=120

Emilio Pisanty

120 = manageable

ish

0celo7

Gauss Jordan is $O(n^3)$, which would be worse for a 5x5

So I think straight-up GJ is better than Cramer's rule.

Because

You have to compute a bajillion determinants

The best inversion algorithm according to Wiki is $O(n^{2.373})$.

Anonymous

18:04

Now I really want to see the matrix=)

Ben Niehoff

well, I aborted it anyway, I need to leave

later

0celo7

@Mystic so yeah, doing adj/det is worse than O(n!)

Gauss-Jordan is better for a 5x5.

Anonymous

@0celo7 Agreed!

Anonymous

What is the complexity of Cramer's ?

Anonymous

It is $O(n.n!)$

Anonymous

18:11

That is worse!

Anonymous

@0celo7

Anonymous

That's why I said Cramer's isn't a good way of finding inverse

Anonymous

Gauss Jordan > adj > Cramer's

0celo7

I think cramers is just adj/det...

Cramer's rule

In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the vector of right hand sides of the equations. It is named after Gabriel Cramer (1704–1752), who published the rule for an arbitrary number of unknowns in 1750, although Colin Maclaurin also published special cases of the rule in 1748 (and possibly knew of it...

Anonymous

@0celo7 When you said Cramer's I thought something else

Anonymous

18:17

"In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution"

Anonymous

The method of adj/det isn't referred to as Cramer's rule AFAIK

0celo7

That's how I learned it and how you see it referenced in the literature.

So it might as well be called that :)

Anonymous

Okay semantics problem then!

0celo7

19:20

@ACuriousMind So the algebraic way is to inductively block diagonalize, with each block a 1x1 equal to the eigenvalue?

Using symmetry to set the rows equal to the columns

Seems pretty straightforward.

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