Mathematics - 2012-08-11 (page 1 of 6)

Jonas Teuwen

00:00

@JasperLoy I no has books.

BenjaLim

@HenryT.Horton Hey, I am just wondering what does $\textrm{GL}(V^\ast)$ look like?

Henning Makholm

@JonasTeuwen Not sure what that would mean, but he's been there since 1998. My understanding is he's basically the masthead of Microsoft Research Cambridge.

BenjaLim

that's V dual

well I know that $V^\ast$ consists of row matrices

but how does a linear transformation act on a linear functional in $\textrm{GL}(V^\ast)$?

user19161

@JonasTeuwen After I finish my three books I will send you a copy.

BenjaLim

@HenningMakholm Do you know how this happens?

Jonas Teuwen

00:01

@HenningMakholm I hope to see Windows 9 written in Haskell in that case.

user19161

@ben Did you check out Bredon for AT?

BenjaLim

@JasperLoy I am now using elements of AT

Peter Tamaroff

OK, everybody stop.

user19161

@BenjaLim OK. Use whatever you like.

Peter Tamaroff

Fractals time

Henning Makholm

00:03

@BenjaLim How what happens? Do you mean why Microsoft would employ programming language researchers?

BenjaLim

@HenningMakholm No, I mean how does a matrix in $GL(V^\ast)$ act on a linear functional in $V^\ast$

because the dimensions don't match up

a matrix is $n \times n$

an element in $V^\ast$ is a row matrix of dimension $1 \times n$

I can't exactly multiply them together unless the vector is multiplied on the left

which is what I am guessing...

Henry T. Horton

If $V$ is finite dimensional, then they act via the transpose

Jonas Teuwen

I would know why I would work for Microsoft if possible - they appear to pay well.

BenjaLim

it is now finite dimensional

@HenryT.Horton meaning?

Henning Makholm

@BenjaLim Yes, but GL(V*) is the space of linear mappings V*->V*.

BenjaLim

00:05

yes

invertible

user19161

@JonasTeuwen I used to work in a job that paid like shit, made me work like shit and made me do shit I did not like. I shan't say the details.

Henry T. Horton

If $T: V \to V$ is linear, its transpose is a map $T^\ast: V^\ast \to V^\ast$ defined by $(T^\ast \varphi)(v) = \varphi(Tv)$ for all $v \in V$

BenjaLim

@HenningMakholm so now what henry is saying is that

@HenryT.Horton ah so now I have the row vector on the left

Henning Makholm

@JonasTeuwen I think I would have some moral reservations, though.

BenjaLim

which is your $\varphi$

Jonas Teuwen

00:07

@HenningMakholm But perhaps they call you back with: "Is money the problem?" - I had that once.

Henry T. Horton

In finite dimensions $T \mapsto T^\ast$ is a isomorphism between $\mathrm{End}(V)$ and $\mathrm{End}(V^\ast)$

BenjaLim

ok

@HenryT.Horton So in that case any element in $GL(V^\ast)$

arises as the dual of some invertible linear transformation in $GL(V)$

Henry T. Horton

And $T \in \mathrm{GL}(V) \iff T^\ast \in \mathrm{GL}(V^\ast)$ unless something is horribly wrong

user19161

The worst thing is to do a job that requires you to go against your own moral conscience.

BenjaLim

we are in finite dimensions?

Henry T. Horton

00:08

Yes

BenjaLim

but I think what you wrote above makes sense

Henry T. Horton

Things do go horribly wrong in infinite dimensions

BenjaLim

If you have a linear functional $\varphi$

and $T^\ast \in \textrm{GL}(V^\ast)$

Then $T^\ast(\varphi)$ becomes the linear functional

such that when you act on a vector $v$ it acts as follows:

Henning Makholm

@JonasTeuwen I've had employers ask me that. But no, I don't think money would be the problem there. (Since I work for a startup angling for market leadership in our niche, I have contemplated how I would react if we were bought out by MS).

BenjaLim

$(T^\ast\varphi)(v) = \varphi(T(v))$ @HenryT.Horton

That is what I understand from what you wrote above.

Henry T. Horton

00:10

Yeah matey

BenjaLim

@HenryT.Horton

@HenryT.Horton all right no probs

just helping some friends understand the contragradient representation

Jonas Teuwen

@HenningMakholm Hmm... Well, then probably you mean "within reasonably boundaries which they could offer", right? What would you say, if I may ask (and get response)?

BenjaLim

@HenryT.Horton Yeah I was just curious about $GL(V^\ast)$

Henry T. Horton

@BenjaLim Oh, what's a friend?

BenjaLim

I wanna apply a matrix to a linear functional, aka row matrix

but the dimensions don't match up :D

I was like

@HenryT.Horton Well they're learning representation theory of finite groups

something I've dabbled in before

Henning Makholm

00:13

@JonasTeuwen I'm not sure, actually. But there comes a point where more money is not that powerful a motivator. If I'm reasonably sure I can go find a job elsewhere that will pay my bills and allow me to sleep soundly at night, then what comparative difference would more digits on my bank statement mean?

Jonas Teuwen

Sure, not much. And I would not be "wanted" by software companies, it were more engineering firms...

And they seem to pay less.

BenjaLim

@JonasTeuwen have you sorted out your accomodation?

Jonas Teuwen

Except Shell, but that has some moral implications as well.

BenjaLim

I can ask pierre this wednesday

Jonas Teuwen

@BenjaLim Not yet, I am waiting for Pierre.

@BenjaLim No need, will be fine!

If he does not respond timely enough I will call him :P.

BenjaLim

00:15

oh wow

skype

Jonas Teuwen

Wow?

No, just plain old phone.

BenjaLim

EVEN BIGGER WOW

Jonas Teuwen

You know, with a hardware number pad and such.

user19161

@jonas I have been thinking of what to tell you after that email, but I still don't know.

Jonas Teuwen

What... wait... what?

@JasperLoy No worries.

@BenjaLim I just call him in his office - don't want to disturb him in private. But I prefer e-mail.

BenjaLim

00:17

I am drinking coffee now :D

Jonas Teuwen

I am so not drinking the coffee you are drinking.

Son of a crack, already past 2 AM again.

Why does time go so fast when I am sleeping through the day?

BenjaLim

god

user19161

@JonasTeuwen Go to sleep bro!

BenjaLim

ok bye guys

going to work!

user19161

@BenjaLim Bye.

Jonas Teuwen

00:19

Need to work man.

I need Haskell on my iPad.

user19161

@JonasTeuwen Can't work without sleep, think.

Jonas Teuwen

Can't sleep without Haskell on my iPad either.

user19161

Why do you need the iPad? Just throw it away!

Jonas Teuwen

@JasperLoy For portable Haskell for one.

user19161

@JonasTeuwen I know exactly zero programming languages.

user19161

00:21

But if I were to learn one, I would do Python.

Jonas Teuwen

Depends on your definition of "knowing" I know between 0 and about... 500?

Ah, Python, I love Python like my brother.

user19161

Python seems to be commended everywhere.

Jonas Teuwen

What? Why?

user19161

I don't know. People like it? I think a lot of Debian software is written in Python as well.

Jonas Teuwen

It is easy and it somehow forces good programming practices.

So no Perl/PHP shitty.

user19161

00:26

Well perl-tk is used for GUIs.

Jonas Teuwen

GUIs are for homos.

user19161

TL installer and manager GUI use perl-tk.

Jonas Teuwen

Also, I know a perl guru which is homo. QED.

user19161

latexmk uses perl.

Jonas Teuwen

Yes, I know. I am rewriting it. In Haskell.

user19161

00:27

I am hetero, in case you forgot.

Jonas Teuwen

Is it my idea or is pdflatex really bad with pipes? Probably my idea.

user19161

I can still use pstricks with pdflatex.

Henning Makholm

@JonasTeuwen What do you want to pipe where?

Jonas Teuwen

Everything -- including the .log to my program.

I want to add some signing to the .pdf and such.

user19161

Don't waste your time. Just do math Jonas.

Jonas Teuwen

00:30

And be better at determining enough runs.

@JasperLoy I am not always able to do math, then I do programming! Like put R on the iPad. I did it and then figured out somebody else did it... but I did it better!

user19161

@JonasTeuwen So how did you do it?

Jonas Teuwen

@JasperLoy Just -- beter, it works together with the GUI (Springboard whatever it is called). Opens the pdf in the viewer etc.

BenjaLim

@HenryT.Horton what you wrote above is not correct

Henning Makholm

@JonasTeuwen YOu can try making a named pipe called whatever.log, but it's not unlikely that pdftex will just unlink it and create a regular file in its stead.

user19161

@JonasTeuwen Just use TeXworks with latexmk. End of story.

BenjaLim

00:32

@HenryT.Horton You should have $(T^\ast\varphi)(v) = \varphi(T^{-1}v)$

Jonas Teuwen

@HenningMakholm Yes, but named pipes are already a bit... well erm, not how I would like it.

I've tried it (very briefly) and it gets unlinked, I can do ugly stuff like pretend it was able to unlink it and it was actually not.

Peter Tamaroff

Has anyone not watched this??

Jonas Teuwen

Or... I sandbox it and fix it through that. Must think about that. First Haskell!

Henning Makholm

@JonasTeuwen Pretend you were able to unlink it? Are you doing userspace file systems or something like that? Or hacking the source code.

Jayesh Badwaik

@JonasTeuwen Signing has in PGP signing?

user19161

00:33

@PeterTamaroff Watching.

user19161

@JayeshBadwaik GPG

Jayesh Badwaik

@JasperLoy Same Thing.

Almost (tm)

Jonas Teuwen

@HenningMakholm For example - or use pdftk on it.

@HenningMakholm No, I would not hack the source code, but use FUSE.

Jayesh Badwaik

@JonasTeuwen Pipe is such a bad thing for pdftex, it has so many output streams.

Jonas Teuwen

So actually pdftex is bad.

Henning Makholm

00:35

@JonasTeuwen Yes, that was my middle assumption. Hacking the source would probably be at least an order of magnitude easier.

user19161

@PeterTamaroff Beautiful. There is a lot of geometry in algebra and complex analysis that is not taught in courses.

Jonas Teuwen

Well... I would prefer a wrapper so I don't have to go back hacking if I need a new version or if I want to install it elsewhere.

Jayesh Badwaik

@JonasTeuwen To quote robert pike, (thought I myself won't believe it that much), the era of a program that could do one thing well was destroyed with the birth of perl :P

Henning Makholm

How is pdftex written, anyway? Does it have a PDF engine written in Web, or is it bolted onto the TeX kernel as a cweb extension thing?

Jonas Teuwen

@HenningMakholm I am really not sure about that, it never occurred to me to go that route as I would prefer to leave it like it is. It works fine and if I write a wrapper I at least totally understand how it works - or that is the idea.

@JayeshBadwaik :P. After Perl it could do many things... nongood?

So perhaps the FUSE thing is the easiest in that case. Or see why it exactly unlinks them.

Henning Makholm

00:40

@JonasTeuwen Yeah. Would it be so bad to let it drop the .log in the file system and then just clean up afterwards, though?

Anyway, going to bed. TTFN.

Jonas Teuwen

No. It is not, but other people have done that already.

Jayesh Badwaik

@JonasTeuwen Not saying anything, talking about how multiple streams / single stream is something we can see.
BTW, what do you exactly want to do?

Jonas Teuwen

@HenningMakholm Good night!

@JayeshBadwaik Wrapper. To ljonastex file.tex. Gives me .pdf and no other shit (no intermediate). Also, do some signing or whatever on the .pdf.

Do enough runs of pdflatex so it gets out fine.

Jayesh Badwaik

@JonasTeuwen OIC, and why is a bash/sh/zsh script not an option?

3 runs are enough for everybody, you can add a 4th for safety

and by the way, you would want to remove all the aux and outs only after the final version, else you will have to generate them everytime, slowing down your compilations

Jonas Teuwen

@JayeshBadwaik But you might need biber in between.

@JayeshBadwaik I am fine with some precompiled stuff. But not 9 files.

And it would be nice if I could put it in some subfolder called .auxillary-files.

Which is not possible with TeX Live I thought because it also puts the .pdf there.

@JasperLoy Fuq dis. I go to bed, good night Bro!

@JayeshBadwaik Thanks for the advice. I need to sleep. It is 3 AM.

Jayesh Badwaik

00:57

@JasperLoy Good night

J. M.

01:18

@HenryT.Horton I have only one chin, and I keep it to a goatee since I can't grow a decent beard.

user19161

@JonasTeuwen Good night bro!

user19161

@JayeshBadwaik Good night. I am going to bed soon.

Jayesh Badwaik

@JasperLoy Good night.

user19161

@J.M. I shave my goatees when they become goatees, so no goatees.

robjohn

@J.M. You got me editing and commenting on the new answers to this question.

I remember working on that problem while at Big Bear.

J. M.

01:26

@robjohn "I will refrain from using Euler-Maclaurin..." - feels a bit like swimming while wearing a wool coat, I thought. :)

robjohn

@J.M. I guess I should probably just remove that part. I had been doing a lot of stuff with EM and so I included that where it really didn't belong.

@J.M. However, I think part of the reason was to emphasize that the question was tagged as algebra-precalculus

J. M.

No, I meant you could do it without EM, but it's somewhat slower... :)

...and yes, you wanted it to be at the level the OP can parse.

Jayesh Badwaik

@robjohn Let it be. The OP will probably look up the thing if it interest him. It is always good exposure I will say.

J. M.

(On a more serious note, swimming while wearing a shirt was one of the ways I got trained to build endurance. It's surprisingly grueling.)

robjohn

@J.M. However, the Riemann sum proof that I added to a comment is pretty nice, too.

Jeff

01:31

@J.M. @JM Next time, try swimming with sneakers! :D

robjohn

@J.M. I usually do that so that I don't get sunburned.

J. M.

@robjohn Oh, certainly.

@Jeff No, that's just nuts. :P

Jeff

@JM Yeah, I know. I jumped in a lake once with my sneaks on. They now reside at the bottom of it. :D

robjohn

@Jeff does that allow you to swim up on someone and catch them at unawares?

Tiptoe through the seaweed...

Jeff

@robjohn no, it allows you to not swim at all. you basically have to kick them off if you want to have any control of yourself at all.

robjohn

01:34

@Jeff I know; I was just joking.

Jeff

@rob oh :D

robjohn

Remember, I am twisted and mean >8(

Jeff

@rob well, you're not the mean square today (i can't make out what your new icon is, though)

J. M.

@Jeff you've heard of Möbius and his strip?

Jeff

i have - but i don't really know anything about it

robjohn

01:36

@Jeff You can see the full size here

Jeff

:D the mean square on a mobius strip! :D

J. M.

So basically, he's twisted, one-sided, and mean. :D

3

robjohn

@J.M. two-faced fits in there somewhere :-)

Jeff

lol

J. M.

"I'm not two-faced! If I were two-faced, I definitely wouldn't be using this one."

Jeff

01:38

mobius strips are the "one-sided" strips. do they really exist in life? Or just in graphical form?

@jm ha! :D

robjohn

@Jeff You can make one with a piece of paper, scissors, and tape

Jeff

oh yeah? but a piece of paper has two sides. i'm gonna google instructions on that

robjohn

@Jeff Give it a half twist before taping

Jeff

i'll have to try that out and look at it.

robjohn

@Jeff Try coloring just one side of it :-)

Jeff

01:41

i will. (I'll have my niece and nephew do it).

robjohn

@Jeff Cool... outreach :-)

Jeff

yeah. start 'em young! :D

J. M.

@Jeff See this.

Jeff

what plugin do you need for that?

it tells me 'no plug in available'

J. M.

Whoops, let me look for an alternative...

@Jeff Try this.

Jeff

01:47

A patent for a Conveyor Belt for Hot Material?

J. M.

The conveyor is in the form of a Möbius strip, if you'll notice the drawing. :)

See this as well.

robjohn

@J.M. They don't mention Möbius at all in that patent

J. M.

@robjohn Yes, I'm not sure why. But the drawing shows that their conveyor is one-sided.

Fortuon Paendrag

@robjohn : How did you create your current Icon? You probably have been asked this before, so you could just direct me to the archives instead.

robjohn

@J.M. yes, I see the mention of a 180° twist

Jeff

01:53

@what's the significance of it being a mobius strip to it being useful for conveying hot material? IOW, couldn't it just as easily have been a two sided escalator style strip?

...and still met the requirements?

robjohn

@FortuonPaendrag I used Mathemtica and its built-in Texture[] primitive.

J. M.

@Jeff The wear on the conveyor is distributed evenly.

Jeff

ok. so it's just for wear-and-tear.

Fortuon Paendrag

@ Ah, ok

Jeff

note, though, that each "tile" of the conveyor has two sides!

robjohn

01:55

@Jeff but they are not orientable. You can't say that one is on a given side of the belt.

Jeff

@rob yup. if you try "coloring one side" as you said, you will eventually color both sides of the tile.

robjohn

Just like the paper used to make a Möbius strip has two sides, but when connected to make the strip, both sides become one.

The non-orientability is a global feature.

Jeff

what do you mean by 'global feature'?

Fortuon Paendrag

The neighborhood of any point will look ordinary-flat. Only if you zoom out entirely, will you realize that this is not an ordinary strip.@jeff

robjohn

@Jeff well, as you say, locally the strip has two sides, and disconnected from the whole strip, it is orientable. But when put together to make the whole strip, it is non-orientable.

locally it is orientable, globally it is not

I have to go take my dog for a walk. BBL

Jeff

02:01

@rob ok.

see ya

user19161

Could not sleep so back here...

Peter Tamaroff

Why would a PhD candidate answer this?

Jeff

@Jas Did you try counting sheep?

user19161

@Jeff Well, it's OK. But that does not work.

user19161

@PeterTamaroff Hmm, why not? Isn't Alex an undergrad?

Jeff

02:08

you could try reading math papers. that always puts me to sleep! :D

user19161

@PeterTamaroff You can answer too if you want.

Peter Tamaroff

@JasperLoy I linked to "Paul" not "Alex".

Jeff

@jasper @peter wow, do you guys remember everyone's level?

Peter Tamaroff

@Jeff I don't remember much, I just "quoted".

user19161

@Jeff Well, only those I know about. Levels don't mean too much really. I know many idiots with PhDs, not in math though.

Peter Tamaroff

02:09

"Two years are fled. In the third year of PHD, my major is general topology and I'm facing with graduation from PHD. "

Maybe he was trolled?

user19161

@PeterTamaroff Oh you are saying he gave a bad answer? Well, it happens.

Peter Tamaroff

@JasperLoy Bleh. I think the more you know about math the more you realize some stuff simply hasn't a "easy" solution.

user19161

@PeterTamaroff Yes, though some hard stuff might have a solution that seems easy after you read it.

Jeff

@peter I think the more you know about math the more you realize you don't know (for me at least, so far)

user19161

@Jeff Perhaps the same is true for everything.

Peter Tamaroff

02:13

@Jeff Well, I would say the more you read. Knowing is a side effect.

user19161

I would say @peter is doing very well for his level. He might win the Fields medal.

Jeff

@JasperLoy !

@JasperLoy that is "pretty well for his level", i would say :D

user19161

@Jeff I mean he has not even begun first year and he is already studying such stuff!

Jeff

@peter what're you studying?

Peter Tamaroff

@Jeff Just introductory general topology.

Jeff

02:16

@peter we didn't have a single topology class even offered for my degree :(. i'm still not even sure what it is (I tried reading a Wikipedia page - but that is always so general).

user19161

@Jeff Not even point set topology?

Peter Tamaroff

@Jeff What is your degree?

Jeff

@JasperLoy nope (I don't think so). what is that?

user19161

@PeterTamaroff Mine is 36.5 degrees Celcius.

user19161

@Jeff OK, that answers it.

Jeff

02:17

@peter MS in Pure and Applied Math (I only finished the course work, still working on my thesis)

Peter Tamaroff

@JasperLoy You mean Celsius, mein Führer.

user19161

@PeterTamaroff Oh I am sorry. I am becoming retarded.

Peter Tamaroff

@Jeff What are you working on?

Jeff

can you describe point set topology? maybe i'll recognize it.

Peter Tamaroff

@Jeff That is General Topology.

Jeff

02:18

@peter something to do with something called the FPU Paradox (or maybe FPU Problem). Fermi-Pasta-Ulam (three well known mathematicians).

Peter Tamaroff

@Jeff Wha....?

Jeff

@peter: oh. :D I'm gonna have to read up on it one day. all this stuff is so fun.

user19161

@Jeff General topology was one of my fave topics! It's really fun!

Jeff

@peter Well, it's kinda hard to explain in chat, but the FPU problem comes from the first ever "math experiment" that FPU did on one of the earliest computers....

@JasperLoy i want to learn Game Theory and Probability (so I can play black jack and hold 'em and backgammon)

user19161

@Jeff Hmm, dunno any game theory.

Jeff

02:21

@peter they programmed a one-dimensional (or chain, or string) of masses and springs. But the springs were not linear (linear spring: F=-kx)....

@peter they ran the simulation and measured the energy in each normal mode of motion (do you know what that is? it has to do with Fourier analysis)....

Jayesh Badwaik

@Jeff I thought dynamical systems required topology of some kind?

user19161

@JayeshBadwaik Oh you like DS? The book by Teschl is awesome!

Jeff

@peter oh, they started the system with all the energy in the first mode. they expected the energy to "leak" into all the modes and spread among them equally. instead, the energy did that, but then almost all of it returned to the first mode...

Jayesh Badwaik

@JasperLoy you mean tedeschi?

Jeff

@jayesh got me? i think dynamical systems require differential equations, which I also never took (my advisor showed me how to do the diff eq necessary for this system).

user19161

02:23

@JayeshBadwaik No, Teschl's ODE and DS.

Peter Tamaroff

@Jeff You really need differential equations dude. SPIEGEL "Applied Differential Equations" is quite awesome.

Jeff

@peter and even now, nobody really agrees on why the energy returned to the first system. My thesis is to program a 2-dimensional FPU system and learn something about it.

user19161

@PeterTamaroff See my above recommendation. Online for free.

Jeff

@peter how is that book "Div, Grad, Curl"? I like the title

Peter Tamaroff

@JasperLoy You still need to pay for the internet. Duh.

Jeff

02:25

oh wait.. .i think that's vector calculus! :D

user19161

@PeterTamaroff OK OK.

Jeff

@jasper can you repeat your above recommendation?

Jayesh Badwaik

@JasperLoy Dude, never heard of it. I did my differential equations from krantz and then birkhoff rota then fourier series from brown churchill

user19161

@Jeff Gerald Teschl's "Ordinary Differential Equations and Dynamical Systems"

Jeff

@JasperLoy sounds like it's just what i need, too

@jas .... and now it's downloaded! :D

user19161

02:27

If you guys are into probability I recommend Oliver Knill's "Probability and Stochastic Processes"

Jayesh Badwaik

@JasperLoy Ohh, I should study it. My forays into dynamical system have been trying to get synchronized chua's circuit in a controllable frequency range

@JasperLoy I recommend Feller for probability.

@JasperLoy Teschl is nice :-) Kind of redundant to me though now though, will go through in detail it sometime though.

Jeff

03:10

good night everyone. try to get some sleep!

Gustavo Bandeira

I can't find the community wiki. =/

anon

community wiki is a mode that posts (answers and questions) can be in, it is not a separate forum

(I run the risk of failing to get a joke)

there is meta (meta.math.stackexchange) though

Mark Dominus

03:43

@Jeff I did not much care for Div, Grad, Curl; I thought it wasn't dense enough, and it still didn't really answer my questions. But I think a lot of other people like it.

BenjaLim

@anon I posted a comment to your answer and +1

anon

yup

BenjaLim

@anon I posted another comment

anon

03:59

I don't really understand what you're asking. When you look at the dual space as column vectors you apply linear maps as matrices multiplying from the left, and when you look at dual vectors as row vectors you right-multiply by the very same matrix's transpose.

Transcript for

$Mathematics$ Mathematics