Mathematics - 2015-07-02 (page 1 of 3)

12:44 AM

@robjohn As I expected, the votes appeared on my activity page at about 12:30 AM UTC, 6 hours after I cast the first vote. I cast another vote 10 minutes ago. It has yet to appear.

robjohn

@RandomVariable Yeah, I see the two votes this week, but nothing today

Random Variable

1:21 AM

@robjohn This time it only took 45 minutes.

Stan Shunpike

2:05 AM

@TedShifrin okay if I remove that comment about the constraint (which seems nonsensical now that i read it) does that improve the argument?

Semiclassical

evening chat

Fargle

Hi @Semi

Stan Shunpike

@Semiclassical is "semiclasical" a reference to physics?

Jeff

So, is my vision going bad or is the math in questions difficult to read on this site?

Vincent Williams

2:21 AM

Hi guys I have a programming problem but I think it can be solved with just math

but im bad at math

Ted Shifrin

No, @Stan: You still need to define $F$ correctly so that it maps to the right number of dimensions!

@Fargle !

Fargle

@TedShifrin !!

Vincent Williams

can i post a link to a question here?

Mike Miller

Why are we adding a space between names and exclamation points?

Vincent Williams

oh nvm it says dont ask to ask lol

2

Q: generate box2d bodies from isometric tiled map

I followed the tutorial here to generate box2d bodies from a tiled map and that worked fine.... for orthogonal tiled maps. Unfortunately isometric maps use their own coordinate system where (0, 0) is at the leftmost corner of the map, and this causes the bodies to be in the wrong place. I tried ...

Ted Shifrin

2:23 AM

Because I like to rile you, @MikeM !! :)

Vincent Williams

please read the question. it is math related

Fargle

@MikeM, I just did it because he did.

Mike Miller

Disgusting.

Ted Shifrin

Don't worry: That's the only way in which @Fargle intends to imitate me.

Vincent Williams

anyone? :/

Mike Miller

2:25 AM

So I shouldn't ask Fargle my complex geometry questions?

@VincentWilliams: I can't help, but in any case, you should wait a bit in case somebody sees before getting upset that nobody has.

Fargle

You probably would be better off asking me no questions, @MikeM

Ted Shifrin

So why is it a problem that $(0,0)$ is at the upper left corner, @Vincent?

Vincent Williams

@MikeMiller
ok thank you. I have been stuck on this problem for days haha

Mike Miller

@Fargle: Are there complex surfaces that are diffeomorphic but not deformation equivalent?

Ted Shifrin

I cannot tell what the real mathematics question in your question is, @Vincent.

WTF is "deformation equivalent," @MikeM?

Vincent Williams

2:27 AM

@TedShifrin
the problem is that (0, 0) is at the left most tile instead of the upper left corner

Mike Miller

@TedShifrin: Their almost complex structures are homotopic through integrable almost complex structures.

Fargle

@MikeMiller Probably? I don't know. Define "complex surfaces", "diffeomorphic", and "deformation equivalent". >_>

Ted Shifrin

So this seems a programming issue, @Vincent.

Vincent Williams

Do you know what an isometric map looks like? It can be solved with an equation I think

Mike Miller

At least, probably. I'm just going off a question asked in a Donaldson paper from twenty years ago.

Ted Shifrin

2:28 AM

But deformation theory of complex manifolds gives you a submersion where the fibers are different complex structures (all integrable). @MikeM

Vincent Williams

the screen measures 0, 0 from the top left corner, but the isometric map measures from the leftmost tile. I need an equation to convert from isometric to screen

Mike Miller

I have no idea what that means.

Ted Shifrin

Yes, @Vincent: It's of the form $f(x) = Ax+b$, where $b$ is a vector and $A$ is an orthogonal matrix.

Mike Miller

A submersion from what?

Ted Shifrin

From the family to the parameter space ...

Vincent Williams

2:29 AM

uhhh ya im not good at math lol

Ted Shifrin

This is classic Kodaira-Kuranishi deformation theory ... See, I can throw names around, too :P

Mike Miller

OK, clearly I'm out of my zone here. Nevermind.

Vincent Williams

can you give me an equation haha

Ted Shifrin

Whew :)

Vincent Williams

like with actual numbers :)

Ted Shifrin

2:30 AM

How 'bout something like $X = x-5$, $Y = y+3$ ?

Vincent Williams

what do the $ mean?

Ted Shifrin

That just translates, no rotation.

Oh, we type math in LaTeX in here.

Fargle

@MikeMiller Can you just ask me something easy? Ask me about the infinitude of primes or the irrationality of the square root of two or something.

Ted Shifrin

Ignore the $. I just am used to doing it.

Vincent Williams

what is LaTeX?

oh ok

Mike Miller

2:31 AM

@Fargle: It was a joke, since I had a complex geometry question for Ted.

Ted Shifrin

Oh, @Fargle, on Facebook I just learned the most fabulous proof of irrationality of $\sqrt2$, and it generalizes completely.

Fargle

@TedShifrin Do share.

Ted Shifrin

Suppose $\sqrt2$ were rational, and let $k$ be the smallest positive integer so that $k\sqrt2\in\Bbb N$.

4

Fargle

@MikeMiller Oh, I know. I was joking back. I would hope I know at least a little more math than that ;O

Mike Miller

Fair point. I don't know what you know :)

Vincent Williams

2:32 AM

the equation you gave me would just move it a constant value. I sorta need to "rotate" the isometric coordinates

Ted Shifrin

OK, now I have to try to remember how to do it, @Fargle. Half a minute.

Vincent Williams

maybe I can use a matrix to rotate?

but i have no idea how

Ted Shifrin

OK, @Vincent: $X=-y$, $Y=x$ rotates 90 degrees.

That's what my A was in my equation, an orthogonal matrix.

Vincent Williams

ok but what if i want to rotate 45 degrees?

Fargle

@TedShifrin Haha, you're fine. I hate it when I do this with cool proofs because I feel like a goober.

Ted Shifrin

2:35 AM

@Fargle: So let's look at $k(\sqrt2-1)\sqrt2$. Is it a positive integer?

Fargle

It would have to be--ah, I see. That's clever.

Ted Shifrin

Then you need $X=(1/\sqrt2)x-(1/\sqrt2)y$, $Y=(1/\sqrt2)x+(1/\sqrt2)y$, @Vincent.

Fargle

It's literally just $2k - k\sqrt{2}$, but we assumed $k$ was minimal, and $\sqrt{2}-1 < 1$.

That's preeeeetty clever.

Ted Shifrin

Yeah, pretty amazing :)

Vincent Williams

ok thank you

Fargle

2:37 AM

@TedShifrin That's only like two lines, basically!

Ted Shifrin

One of my math FB friends posted it and then another friend posted a link to a blog entry he'd written generalizing it somewhere.

So you can show that off to all your friends learning basic proofs in math, @Fargle.

Stan Shunpike

@TedShifrin hey Ted! If I have $\nabla f + \nabla(cg)$, that is $n+1$ isnt it?

Ted Shifrin

No, that's just $n$.

$c$ doesn't belong in there. You mean $\lambda$.

Stan Shunpike

Sorry typed to quickly

Fargle

All you'd have to do, for a given non-square $n$, is consider the minimal $k$ such that $k\sqrt{n} \in \Bbb N$, and then consider $k(\sqrt{n} - \lfloor \sqrt{n} \rfloor)\sqrt{n}$, right @Ted?

Ted Shifrin

2:40 AM

Hmm, maybe so, @Fargle. :)

robjohn

@RandomVariable That's better

Ted Shifrin

Wouldn't subtracting $1$ work, @Fargle?

Stan Shunpike

@TedShifrin $\nabla f + \nabla (\lambda g)$ how is this $n$? What is the rank of the gradient operator?

Ted Shifrin

$f$ and $g$ are maps on $\Bbb R^n$, right, @Stan?

Fargle

@TedShifrin Not for $n \geq 4$

$\sqrt{n} - 1 > 1$ for such non-square $n$, which doesn't contradict $k$ minimal.

Stan Shunpike

2:42 AM

@TedShifrin yeah....

Ted Shifrin

Oh, right. You win, @Fargle :)

Stan Shunpike

Wow, how come that never happens to me @TedShifrin lolol

?

Ted Shifrin

My brain isn't functioning. I've been spending the day on a liquid diet getting ready for a colonoscopy tomorrow morning. Not a happy camper.

Fargle

@StanShunpike I had to bring him down to my level to beat him.

Ted Shifrin

I dunno, @Stan. Up to you to fix that :P

Stan Shunpike

2:43 AM

Hahahhahaha

Both very funny

Ted Shifrin

I'm still waiting to drag Fargle up to my level in diff geo. It'll happen.

Stan Shunpike

@TedShifrin my grandfather had one and it sounded horrible. Even worse for you because you have a memory

Ted Shifrin

When you get old, @Stan ($\ge 50$) you have 'em regularly. This is my third ... somewhat earlier than I'd hoped.

robjohn

@TedShifrin spending time in one room ;-)

Stan Shunpike

@TedShifrin yeah i thought it was on a 10 year basis.

Fargle

2:45 AM

@TedShifrin I've had a lot of distractions this past week. Draconian institutions that shall go unnamed, and school transfer. I've barely had time for ring theory, even.

Mike Miller

Draconian institutions, school transfer, colonoscopies

Ted Shifrin

I understand, Fargle. I was not criticizing you in the least. Did things get resolved with the cops?

Why would you want ring theory when you could have diff geo, anyhow? :D

Stan Shunpike

Differential geometry is my jam

Ted Shifrin

BTW, @Stan, it's presumptuous of you to suggest I have a memory.

Fargle

@TedShifrin Not fully. And I don't know. I just really, really like algebra. It feels like a really complex, really symmetrical and beautiful symbol game, and I like all of those things.

Ted Shifrin

2:48 AM

Yeah, I don't like symbolic manipulation for the sake of symbolic manipulation. Of course, some people think (particularly advanced) diff geo is that, but it really isn't if it's learned/taught right.

Stan Shunpike

@TedShifrin :P

@TedShifrin so what is the rank of the gradient operator? I thought it was $n+1$....

Ted Shifrin

Huh? How do you take the gradient of a function, @Stan?

Fargle

I like both kinds of math--the heavily symbolic and the kind that requires visual/geometric intuition. (Not that these are by any means either disjoint or all inclusive.)

Ted Shifrin

And you shouldn't say rank, really.

Stan Shunpike

Lolol

I didnt think i used that right

:/

How do u use the term properly?

Shivlov's book is a really nice blend of linear algebra and some manifold stuff by the way

Ted Shifrin

2:51 AM

although people do talk about rank of tensors (and it's not what you're meaning), let's reserve rank for linear maps here ... and it is not merely the dimension of the domain/range.

Only linear manifolds, @Stan, although he uses that word for an affine subspace. That's not current usage.

Stan Shunpike

Wait, so "linear manifolds" is outdated?

Mike Miller

@TedShifrin Very carefully...

Ted Shifrin

Without divulging too much, are things getting resolved, @Fargle, regarding yesterday's disaster?

mostly, @Stan, although mathematicians will know what you mean, of course ... It's an awfully fancy term for a subspace (or a translated one).

Fargle

@TedShifrin Slowly, yes. I should have it resolved within the week. I also won't be associated with them anymore within the week.

Ted Shifrin

Well, that's good. On both counts.

skill patrol

2:53 AM

Have you found a doctor in Cali yet professor@TedShifrin?

Mike Miller

I'm not much of a mathematician but I would have no idea what he means

Ted Shifrin

hell no, @skill ... I'm still in GA ... And I have to find about 4 or 5, I suppose.

Stan Shunpike

@TedShifrin but, correct me if i am wrong, by definition the gradient operator is a linear map so it is appropriate to talk about its rank right?

Ted Shifrin

Nonsense @MikeM

Fix a point. Then you have a linear map $\Bbb R\to\Bbb R^n$. Rank is at most $1$.

Mike Miller

I would interpret linear manifold to mean affine manifold

Ted Shifrin

2:55 AM

Oh ... You mean in the sense of an affine structure? I don't think it's used that way, even in modern days.

Mike Miller

I don't think anybody even says "linear structure" in modern days is all I mean

I'm drinking a blackberry porter and it's delightful

Ted Shifrin

No wonder you're prattling on ... :D

Stan Shunpike

@TedShifrin okay, what is the dimensionality of the vector space of the gradient operator in this case maps onto?

Mike Miller

Give me one or two more before I'm out of my gourd

Stan Shunpike

@MikeMiller what happens to your math skill at that point?

Are you still intelligible?

Mike Miller

2:58 AM

I can still work after a few beers. Too many and I can't. I'm at the sweet spot right now, and will be until I no longer intend to work.

Ted Shifrin

@StanShunpike You're making presumptuous assumptions again.

@StanShunpike Huh?

Mike Miller

That I was intelligble to start with?

Ted Shifrin

Precisely.

Stan Shunpike

LOL

Mike Miller

I didn't finish all my homework, which is a shame, but I did do about half of it.

Ted Shifrin

2:59 AM

It's still early on the left coast.

I have to get up at 5 AM to continue my "regimen." :(

Stan Shunpike

Eww

Ted Shifrin

That's if I sleep much at all, that is.

Mike Miller

Not sure what that means. I guess I have some time tomorrow to do more reading, but not all of it.

Ted Shifrin

@Stan: The point is that the gradient gives you a mapping $\Bbb R^{n+2}\to\Bbb R^n$.

Vincent Williams

@TedShifrin
I tried your equation and for some reason the coordinates didnt change at all

I must be doing something wrong haha

Ted Shifrin

3:01 AM

The equation I gave you is in fact a 45 degree rotation.

Try putting $x=1$, $y=0$ in there.

Vincent Williams

ya it must be an issue with my program then. Thanks any way

Ted Shifrin

Sure thing.

Stan Shunpike

@TedShifrin Okay then that is my error. I thought it wouls be like $\frac{\partial}{\partial x_1}\mathbf{e}_1+....+\frac{\partial}{\partial x_n}\mathbf{e}_n+\frac{\partial}{\partial c}\mathbf{e}_c$ and therefore n+1

Ted Shifrin

No, we're just doing the $\mathbf x$ gradient. Think back through LM.

I suppose that you may have been taught the Lagrangian with the $\lambda$ derivative in there as well to give you the constraint equation, but I never present it that way. It's too confusing.

Stan Shunpike

My prof didnt even use vector notation....

or gradients

Ted Shifrin

3:05 AM

Phooey.

Stan Shunpike

It was a bit pathetic

I was sad people were okay with that lolol

Ted Shifrin

What I detest about Buck's rather well-known Advanced Calculus book is that he avoids vectors and writes everything out in 2 and 3 dimensions in components. Totally obscures the mathematics.

Stan Shunpike

EXACTLY

Okay, I will rewrite it tonight and see if you think it is acceptable.

Ted Shifrin

You had some sloppy typos and other things, too.

Mike Miller

It turns out the relevant bit in this paper was a line at the very end, @TedS. Whoops.

Ted Shifrin

3:08 AM

At some point, though, @Mike, you should read a little bit about classic deformation theory. There's a bit of nice Cech cohomology in that, too.

Stan Shunpike

Yeah, does anyone know how to deal with typos with LaTex? My iPad latex editor has no spell check.

Mike Miller

@Ted: I have too many things on my reading list as is.

Ted Shifrin

Oh, I don't mess with LaTeX on my iPad. But on the desktop there is a utility that spell-checks nicely.

Well, fine, then, @MikeM.

Mike Miller

Sorry :)

Maybe it'll show up when I con people into doing my h-principle seminar.

Ted Shifrin

No, totally not.

It shows up in complex manifolds and algebraic geometry.

Mike Miller

3:10 AM

TYPO.

Ted Shifrin

oh, sorry

Mike Miller

Seriously bad typo.

Considering it's two completely different bits of mathematics I conflated...

Ted Shifrin

just so long as you're not over-inflated ...

skill patrol

Too much beer?

Fargle

Geez, @MikeM, the porter getting to you? >_>

Ted Shifrin

3:11 AM

soon he'll be transportered, @Fargle.

Stan Shunpike

@TedShifrin whats the best book you have ever reas on writing?

Fargle

Boooooooo

Semiclassical

@StanShunpike yep, namely to semiclassical methods in quantum mechanics (Bohr-Sommerfeld quantization, WKB, etc)

Ted Shifrin

Yikes, I dunno, @Stan. Do you know about Karen Elizabeth Gordon? She has some wonderfully humorous books on style, punctuation, etc.

Mike Miller

Just read good papers and books and pay attention to what they do and you'll learn how to write well.

Ted Shifrin

3:12 AM

But so many aren't good, @MikeM.

As with everything else, one has to practice.

Fargle

I dread writing papers in my future. I always feel weird overusing the same phrases, I feel like it'll be stale to read.

Ted Shifrin

Good editing/revising. I also search for "which" and "that," because I usually mess up a few inadvertently.

Fargle

"Let". "Note that". "Since". "We define". "If [this], [these] are exactly [those]."

Stan Shunpike

@TedShifrin no! I will have to look that up

Ted Shifrin

I actually kept those books and am moving them with me, @Stan.

The New Well-Tempered Sentence, The Ravenous Muse, The Deluxe Transitive Vampire :D

Stan Shunpike

3:15 AM

@TedShifrin wow, thats quite a statement. You gave away a bunch right?

Ted Shifrin

Many hundreds ....

Mike Miller

And none to me.

Ted Shifrin

I also kept French and German dictionaries and grammar books. Just my old obsessions :P

Not true, @Mike. I don't remember what I put aside for you, but I agreed to something.

Mike Miller

Oh, you're right.

Ted Shifrin

One of our grad students actually wanted several Gunnings, and other grad students took other ones.

Where has @AlexW been?!

Mike Miller

3:17 AM

Hmm... it seems a bit weird to say that "____ has beautiful applications to _____" where ____ is a previous paper by the first author...

Ted Shifrin

Reminds you of the self-congratulatory style of one of our comrades?

Fargle

I don't know who you could possibly mean by that. /s

Ted Shifrin

Then you haven't paid attention, @Fargle :D

Semiclassical

the tricky thing with things like 'beautiful' in a paper is: are you making an objective claim, or a subjective one? if you're doing the first one and referring to your own work, well...

and if you're doing the second, maybe it shouldn't be in the paper :/

Ted Shifrin

I cringe enough when other people say they like my lectures or books.

Fargle

3:20 AM

@TedShifrin I haven't had to. Hard to miss. <_<

skill patrol

:D

Fargle

@TedShifrin I'm that way with any creative or otherwise constructive endeavor I pursue.

Stan Shunpike

@TedShifrin old as in past passions or old as in you are old and you have developed obsessions with French and German. Not that you are old of course.

Mike Miller

I've avoided telling people this week that something they wrote has influenced me. Seems weird.

Stan Shunpike

@MikeMiller why?

What do you mean "influence"?

Ted Shifrin

3:22 AM

I have always been fascinated by language and grammar, @Stan ... going back to high school. Old in that sense.

Stan Shunpike

Thats awesome. Me too.

I surveyed 17 languages to decide which ones i wanted to study

Ted Shifrin

I was not nearly so methodical.

Semiclassical

writing is something that comes with a lot of difficulty for me

Ted Shifrin

It usually gets better with practice/experience, @Semiclassic.

Semiclassical

though maybe the issue is really how hard it is for me to get something written

Ted Shifrin

3:24 AM

It still makes me irate that I had reviewers of my books get upset that I try to inject a sense of humor. They insisted that that has no place in a mathematics course/book. rolls all 20 eyes

Stan Shunpike

@TedShifrin Not always. My mother treats people with LDs.

Fargle

I've always found myself well-spoken in text, moreso than in voice. But maybe I overestimate my own ability to write. A sort of localized Dunning-Kruger, if you will.

Mike Miller

@Stan: There's only one common definition of 'influenced'

Ted Shifrin

I am an absolutely horrid creative writer, though, @Fargle. Horrrrrid.

Semiclassical

drafting is something i struggle with. i keep mentally editing/analyzing while i'm trying to write, so i have a hard time getting a draft out.

Ted Shifrin

3:26 AM

Don't try to write the final version as you write, @Semiclassic. Just get stuff down. This isn't the old typewriter age. It's easy to revise and rewrite, multiple times.

Semiclassical

that's one reason i started coming to MSE, actually: get more spontaneous about writing

Fargle

@TedShifrin I've been dabbling in poetry lately, and that's an example of something that I'm always uncomfortable showing others and getting praise (though both of those are infrequent). I'm not much count at creative writing myself, but at least when it comes to writing analyses of things, I have that down pat.

Semiclassical

yeah, that's the right way to look at it

Ted Shifrin

@Fargle: Any poetry I wrote in school was putrid. Same with short stories. But I, too, write analysis well, and I like to think my math writing is clear and slightly stylish.

Semiclassical

i liked the poetry i did in high school well enough, though that doesn't mean it was actually good :)

Ted Shifrin

3:29 AM

I've studied enough literature to have some sense of good poets. :)

Fargle

Poetry is one of those things that I do less to be good at it than to process existence and emotion in a way that means something to me.

Same with what little music I write.

Semiclassical

i'm not widely read on poetry, i'll be honest, with one big exception: i know waaaaay too much about TS Eliot's work

Ted Shifrin

Well, ultimately, you do it for yourself, @Fargle, so go for it.

Ah, J Alfred, @Semiclassic

Semiclassical

aye. though my interest tended towards his later work.

e.g. The Hollow Men, Ash Wednesday, Four Quartets, his plays

Fargle

It's partly why the "math is art" thought process bugs me a bit. Art is about expression. I mean, don't get me wrong. Math is beautiful, and I find the process of doing proofs and thinking critically and creatively very cathartic. But it doesn't serve the same purpose, both to the creator and to the consumer.

Mike Miller

3:34 AM

Why not?

Ted Shifrin

My dad wrote some songs with TS Eliot text, @Semiclassic. There's even a CD out of 'em.

Fargle

Shrug. Maybe I'm splitting hairs. I just don't think of math as a conduit for my emotions.

Semiclassical

interesting

sort of reminded now of a TS Eliot quote, actually :)

Mike Miller

That's fine. But it's an overgeneralization to claim that it isn't for anybody, which is how I read that paragraph.

Fargle

Yeah, I didn't mean to blanket it like that.

Semiclassical

3:36 AM

"Poetry is not a turning loose of emotion, but an escape from emotion; it is not the expression of personality, but an escape from personality. But, of course, only those who have personality and emotions know what it means to want to escape from these things."

Fargle

I don't know. It just seems like people want to justify math by associating it with other constructs, when to me math stands perfectly well on its own. But again, suum cuique.

Semiclassical

reminds me of an old math article i read. googling time

Fargle

Like, take the proof @Ted posted earlier about the square root of 2. Beautiful, even elegant in its simplicity. But I would hesitate to call that either a work of art or a scientific finding.

Mike Miller

"Meanwhile, I was doing well in mathematics. It was fun to solve mathematical problems, but in a deeper sense mathematics was boring and empty because for me it had no purpose.

"If I had worked on applied mathematics I would have contributed to the development of the technological society that I hated, so I worked only on pure mathematics. But pure mathematics was only a game. I did not understand then, and I still do not understand, why mathematicians are content to fritter away their whole lives in a mere game."

Semiclassical

ah, here we go. Commutative Diagrams in the Fine Arts

2

i mostly have in mind the last few paragraphs, and the reflection on math v. art therein

Fargle

3:52 AM

@Semiclassical "A scholar’s business is to add to what is known. That is all. But it is capable of giving the very greatest satisfaction, because knowledge is good. It does not have to look good or sound good or even do good. It is good just by being knowledge."

2

That's what I was trying to say, much less eloquently.

Semiclassical

it's a nice quotation, yeah. one thing i found thought-provoking was at the top of that page, when he asks what the effect of a 'mathematical typo' in one of these displays

Fargle

Yeah, that was pretty cool too.

Semiclassical

the average person wouldn't recognize the error, and so for them the artistic meaning would be the same. but someone equipped to see the error would interpret it differently, precisely because the math is no longer right

Fargle

Anyway, I'll certainly pass out soon, so I must bid you all a goodnight. :)

skill patrol

Later pal

Semiclassical

4:00 AM

"from a purely graphical point of view, it could still be enjoyed no less than a page of Chinese calligraphy might be enjoyed by a person who is unable to read it"

night fargle

which points to additional issues of language tying into that

Random Variable

4:17 AM

@r9m The answer you posted is really nice. I was debating whether I should edit my answer since there is a small error that might confuse someone. I probably should.

r9m

@RandomVariable Thank you! okay :-)

@RandomVariable I actually didn't know that $\displaystyle \int_0^{\infty} \frac{\cos ax}{b^2+x^2}\,dx = \frac{\pi e^{-ab}}{2b}$ was a well known thing .. so I used a double integral to deal with that .. today I found a really nice way of proving the integral in Apostol's Mathematical Analysis book :-)

Random Variable

@r9m There are several ways to show that, but using the residue theorem from complex analysis is by far the fastest. You can actually do it on one line. It's pretty crazy when you think about it.

r9m

@RandomVariable :) indeed! It's a one line lightning kill :-)

Random Variable

4:38 AM

@r9m The residue theorem is great, except for the many times when it's completely useless. For example, basically any Euler sum that can be expressed only in terms of zeta values can be evaluated using the residue theorem. That's great and everything, but there are a lot of Euler sums that can't be expressed just in terms of zeta values.

r9m

@RandomVariable agreed! But residue theorem often has the power to evaluate integrals that look completely hopeless to real-analysis ..

Mike Miller

4:52 AM

Hi @PaulPlummer. Just saw you there. How's things?

Paul Plummer

Going pretty good. Saw the discussion of art etc, so right now I am looking through my computer for some old poetry files from when I took a class @MikeMiller

How about you, I think I saw something about you going to canada...? @MikeMiller

Mike Miller

That's cool, @Paul. On writing poetry, or the study of poetry already written?

I'm in Vancouver for the next week and a half for a conference.

Paul Plummer

There was a bit of both in the class, I was looking for poetry that I wrote though.

Oh that sounds awesome

Mike Miller

It's too hot, but otherwise it's great.

skill patrol

At UBC?

Paul Plummer

5:01 AM

Found a paper where I wrote about how voting, at least how it is done, and that we really don't live in a democracy... and my recommendations. is BS. It is weird looking over old stuff

Mike Miller

Something like that is true, though, Arrow's theorem and all that

Of course Arrow's theorem is for at least 3 choices, but let it model the primaries or whatever instead

Paul Plummer

I think that was what inspired me to write on it,...and the Douche vs Turd episode of South Park

Mike Miller

lol

I hate that episode

dunno why that message didn't go through until now

Paul Plummer

haha

My first paragraph (I think this was a draft version because a later version has very different structure on the same topic)
In 2004, the television show South Park aired an episode called, “Douche and Turd,” which discussed apathy towards voting and some of the reasons citizens of the United States have become apathetic about the process of voting for elected officials. In this episode, Stan feels that it does not matter which candidate he were to vote for, the “giant douche” or the “turd sandwich,” and thinks his vote counts for nothing. In the end, he does vote because, “every election i…

Mike Miller

I think "The truth is in the middle!" garbage is toxic

Paul Plummer

5:14 AM

Is that why you hate the episode?

anon

@PaulPlummer but the question first is, which lawmakers want more voters voting?

Mike Miller

yes, essentially

there were some funny bits but it was mostly aforementioned garbage

Paul Plummer

True :D @anon

skill patrol

here

Mambo

5:40 AM

@MikeMiller Sorry to bother. Can you help me with something?

Mambo

5:58 AM

@Huy Sorry to bother. Are you here

Huy

Yeah, what's up?

Mambo

Can you help me with something?

Huy

Depends what it is.

Mambo

Consider the Torus

$T(x,y) = (xy,y)$

This is a continuous map on torus

Do you have any idea what topological entropy is?

Huy

No, sorry.

I'm not quite a topology expert.

Mambo

6:04 AM

It's fine

Do you know metric spaces

Huy

Yes.

Mambo

What metric do you know on a Torus?

Huy

Urm, the induced one by $\mathbb{R}^2$ and taking the product, is the first that comes to mind.

Paul Plummer

Why don't you just ask your question @Mambo If someone wants to help, and can help, they will help

Mambo

Say suppose d is that metric

For each n, define $d_n(x,y) = max d(T^i(x),T^i(y)) 0 \leq i \leq n-1$

With this metric, torus is compact

I want to find an \epsilon net

@PaulPlummer Do you have any idea?

@Huy you there?

Kartik Watwani

6:26 AM

Is any one intrested in solving this question :math.stackexchange.com/questions/1346693/…

Chris's sis the artist

6:59 AM

@r9m Cool! (+1) :-)

@r9m It would have been even nicer if you had shown a brilliant elementary (real) solution to $$\displaystyle \int_0^{\infty} \frac{\cos ax}{b^2+x^2}\,dx = \frac{\pi e^{-ab}}{2b}$$. :-)

@r9m I'll add to my book such a solution (one that I never saw anywhere).

(I mentioned that since out there are tons of solutions to it)

As a matter of fact $$\int_0^{\infty } \frac{\cos ^2(x)}{1+x^4} \, dx=\frac{1}{8} \pi \left(\sqrt{2}+2 e^{-\sqrt{2}} \sin \left(\sqrt{2}+\frac{\pi }{4}\right)\right)$$

Masacroso

a quick question about integrating and deriving series... if I derive or integrate some serie I move forward or backward the index that start the series, right?

I assume that going "backward" on the index when you are integrating a series is the same that adding a constant so you can take 0 everytime you do it

r9m

8:06 AM

@Chris'ssistheartist wait then please!! I'll add one nice real analytic proof :D

Chris's sis the artist

@r9m No need for other efforts. :-)

r9m

@Chris'ssistheartist oh! okay! many thanks :D

Chris's sis the artist

@r9m btw, about the series we discusses yesterday, did you got my solution form?

r9m

@Chris'ssistheartist complex, double integral, differential equation approach .. too many of those :)

Chris's sis the artist

@r9m Yes.

16

Q: Proving that $\int_0^1 \frac{\log \left(\frac{1}{t}\right) \log (t+2)}{t+1} \, dt=\frac{13}{24} \zeta (3)$

Are we aware of an elementary way of proving that? $$\int_0^1 \frac{\log \left(\frac{1}{t}\right) \log (t+2)}{t+1} \, dt=\frac{13}{24} \zeta (3)$$ Of course, with the help of Mathematica it can be done, but I wonder if there exists an elementary, simple, easy way of finishing it. $$\int \frac{...

calculus real-analysis integration definite-integrals

r9m

8:10 AM

@Chris'ssistheartist I was too lazy :P .. I guess we'd have to use the landen identities somehow

Chris's sis the artist

@r9m OK

r9m

@Chris'ssistheartist lemme try it now :-) I think the cannabis has left my system by now .. I feel relatively well :P

Chris's sis the artist

@r9m Do you consume cannabis for real? :-))

r9m

@Chris'ssistheartist ya! This was my 4th time :P lol

Chris's sis the artist

@r9m lolll :-) Take care of your health though.

r9m

8:14 AM

@Chris'ssistheartist I heard cannabis don't affect health on minor consumptions (unless one has heart conditions)

Chris's sis the artist

@r9m Better to be careful. ;)

r9m

@Chris'ssistheartist :) okay

Chris's sis the artist

@r9m this one $$\int_{-\infty }^{\infty } \frac{\cos (x)}{1+x^2 }\cdot\frac{\log \left((e^x+1)^2\right)+\log \left(e^{2 x}+1\right)-3 \log (2) }{x} \, dx$$