@Danu Thanks for that suggestion. I am a little rusty on my point set topology, but as far as I can tell, that's how a textbook should be presented. Actually, theorem-definition-proof isn't so bad if it is preceded by motivation, preferably examples, and discourse about the applicability of the following definition to the greater theory.

@0celo7 Uh...I'm pretty sure that the existence/uniqueness for such linear second-order ODEs is not purely local, but I hate DE theory, so I can't help you.

@ACuriousMind I'm having an epistemological crisis, don't mind me

@Danu do you know happen to know of a textbook like that for group theory?

$\hbar$ is given in units $J \cdot s = kg \cdot m^2 \cdot s^2 \cdot s$ correct? @0celo7 then $\frac{\hbar}{Mc} = s^4$? Zee says this is a length..

$Mc$ is a momentum

what

what are the units of energy

energy is work, which is force x distance

force is mass x acceleration

or is he doing natural units

@0celo7 I need you

why

Is Michelle trying to get you to go to Michigan

In fact I need anyone in here who currently runs OSX or any Unix based OS

@0celo7 No, why?

I don't have money to go there

@BernardMeurer not relevant

@0celo7 Yes, relevant

oh my bad it was $s^{-2}$ not $s^2$

you need some lengths in there, dude

@0celo7 I'm working on face detection software, and I'm trying to make a guess of nose location based only on the rectangle detected as face area

@0celo7 It works for my face

just look up Joule on wiki

but I need someone else to try it and see if it'll work

so $\frac{kg\cdot m^2}{s} \cdot \frac{s}{kg\cdot m} = m$

ya checks out. i still dont understand uncertainty principle though. something about if two variables don't commute then they can't be determined simultaneously or something

why do you need that for Zee?

it's a GR book

@BernardMeurer I would ask "why are you doing that?", but I'm a bit afraid of the answer

You're probably trying to train your Linux potatos to latch onto human faces and then interface with their brains through the nose

oh god

I didn't think of that

@ACuriousMind Will you help me? :D

I have no clue if it'll run on Windows, probably not

it should work on OSX

@0celo7 he uses it in defining natural units. i dislike the idea of taking things for granted but you're right it's primarily a GR book so i don't need to learn it

@BernardMeurer Can only offer you Windows, I'm afraid

> To see how, note that Heisenberg’s uncertainty principle tells us that $\hbar$ 􏳊 divided by the momentum Mc is a length.

Uhhh

@ACuriousMind Let's try that then, gimme a sec

That has nothing to do with Heisenberg

@0celo7 I'm fine with it but it does introduce a constant that wasn't in newtonian mechanics that we use in determining a natural unit for length.

@ACuriousMind Do you know how to run something from the command line in Windows?

@ACuriousMind What the heck is $\Bbb R^\infty$

@BernardMeurer Does it involve more than navigating to the directory the exe is in and typing its name?

I remember I did that once for a Python script @ChrisWhite created that took command line arguments

@0celo7 Either $\prod_{i\in\mathbb{N}}\mathbb{R}$ or $\bigoplus_{i\in\mathbb{N}}\mathbb{R}$.

please explain both?

One is the product, the other the coproduct/direct sum.

Here you go drive.google.com/open?id=0B53os7BTst5lMU85ZzBOaGhVS28

@ACuriousMind I can read, too

@0celo7 Can you test it too?

It requires a webcam btw

@0celo7 Well, what is there to explain? If you know the definition of product/direct sum, you know what these objects are.

No, I have a Jew nose. I'll throw off your measurement.

@0celo7 Plox halp

@BernardMeurer ::sad trombone:: I don't have one of those

If the potatoes can't target jews I'll be called racist

@ACuriousMind Ok, I don't know what they mean then

What product

@ACuriousMind Balls, thanks though!

@0celo7 Product of vector spaces

@BernardMeurer I'm not a Jew, I just have a Jewish nose.

@ACuriousMind Huh, never heard of that.

@0celo7 I can't tell whether you're serious

I've always thought $V\times W$ and $V\oplus W$ are the same

Ah, they are, for finitely many spaces

@0celo7 That doesn't make my point any less valid

aw dang they're closing already

@ACuriousMind Ok, well, my definition of $\times$ is that of $\oplus$.

I never have to take the infinite product of vector spaces

i'll continue at home.

@0celo7 Plox halp

@0celo7 $\prod_{i\in I} V_i$ is the space where an element is given by a list of elements $v_i)_{i\in I}$ of the $V_i$. $\bigoplus$ is the same, except that all but finitely many of the $v_i$ are required to be zero.

@ACuriousMind I know that.

Oh, that probably pisses you off

I mean I know that, but don't know why it's true

It's...a definition

Who came up with that

Well, this is the "right" definition because these objects fulfill the universal property of the product resp. the coproduct

No category pls

What property would that be

@0celo7 How you get maps on the $\prod$ resp. $\bigoplus$ from maps on the $V_i$. The product comes with projections $\pi_i$ onto the $V_i$, the coproduct with inclusions $\iota_i : V_i\to\bigoplus_i V_i$. the universal property of the product is now that given maps $f_i : W\to V_i$ there is a unique map $f:W\to \prod_i V_i$ such that $\pi_i\circ f = f_i$. The u.p. of the coproduct is that for $g_i : V_i\to W$ there is $g: \bigoplus_i V_i\to W$ with $g\circ \iota_i = g_i$.

@WilliamBulmer No, Thurston is quite unique (and hyper-famous in mathematical circles).

@ACuriousMind O.O

Is that supposed to make sense?

@Danu That's disappointing. Maybe more people would get into theoretical math if more textbooks were written that way.

Instead of the Gavage Method (TM) of teaching mathematics

Why is more people into pure math a good thing?

@ACuriousMind Hmm

I see

@0celo7 Yes. Maybe it makes more sense in words: The product is a thing where you can project out the factors, and where giving maps into the factors determines a map into the product. The direct sum is a thing where you know how the summands embed into it, and where giving maps from the summands determines a map from the sum.

@ACuriousMind Yes, that's how I interpret that mess, too.

It's a good thing for all those who would love to study theoretical math, but can't stomach the way its presented

Good to know.

@WilliamBulmer How many people like that are there?

I mean, I learned more about Galois theory by just studying polynomial roots myself than I ever did attempting to read Garling

You were probably not ready for that book

@Ocelo that's a good question. How would we know unless we all stopped teaching mathematical concepts as if they emerged fully formed from the forheads of mathematical gods?

Oh, I am ready. I just don't like reading it

And so, I stop doing it

@ACuriousMind Is there a way to massage a connection out of a symplectic form?

@Ocelo7 snark aside, I don't think this is a matter of opinion. There is research that supports certain forms of pedagogy over others (on average)

@0celo7 Only if the cohomology class of $\omega$ is integral, then the symplectic form becomes the curvature of a U(1)-connection on a complex line bundle.

(That's essentially due to the integral of the curvature being the first Chern class and the Chern class being a class in integral cohomology, I think)

@ACuriousMind I don't know what that means, but I meant a connection on $TM$.

@0celo7 That I don't know anything about

Why is the integral of the Chern class an integer, anyway

But the connection I just described is in fact one of the steps in geometric quantization

What IS an opinion of mine (well, more like a hypothesis), is that the math community has inadvertently set up a filter that self-selects. More often than not, people who study pure math can learn with the definition-theorem-proof method of pedagogy. Then, those same people become mathematicians, and continue to perpetuate that pedagogy. People who fall by the wayside are considered "bad at math" but in reality, they just can't learn very well using the theorem-definition-proof method.

So?

@WilliamBulmer I still think your sense of... capability of speaking for everyone else when it comes to learning mathematics is... well, just plain wrong.

@Danu Read the literature on education

@WilliamBulmer Okay, if you really claim this then produce me some research that says this (I'm pretty sure nothing has been done to show something as specific as you claim)

@WilliamBulmer You give me a paper that proves what you say, then.

(I don't think it exists)

Burden of proof is on you, clearly

I don't see what's wrong with that format

What other format is there that isn't complete ass when you have to go back and look for a theorem/proof

I like the format, too. I find dry texts not... amazing but they can be great.

Are we talking about books that have no commentary?

@Danu Let's be specific. What are you asking me to prove? That students, on average, learn better when provided with examples and motivation, rather than just being force fed definitions and rules?

Also, I hate the word "prove." Let's say demonstrate

he wants you to prove any of your claims

He does not buy any of what you're saying

@WilliamBulmer what?

@WilliamBulmer No, that "broad perspective" in mathematics textbooks produces measurably more "learning" (how will you even measure this?) than pure Definition-Theorem-Proof style

Let him answer.

And yes, you're making claims this specific so I want a result this specific.

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ Can't wait to see how many dead flies there are now

@Danu Well, presumably "broad perspective" in mathematics is a corollary to "students learn more efficiently when presented with examples and motivation", no?

mhahaha

@WilliamBulmer No.

@Danu why not?

This conversation is not long for this world

Examples and motivations are not at all at odds with the Definition-Theorem-Proof style, and I don't see why you think it is.

@WilliamBulmer Ah, never mind it; I shouldn't engage in this anyways.

You win ;)

Called it

:D

@Danu No, I am perfectly willing to be proven wrong

I'm not willing to spend my time on this any longer

cya later

I'm sorry for trying to call you out

I have no ego in this.

I shouldn't have gotten involved again :P

@ACuriousMind Agreed, Defn.-Theorem-Proof is essential, but doesn't exclude examples&motivation which might help

@Danu What are you apologising for?

@WilliamBulmer Wasting both of our times

Now I will really stop---I'm not responding about this specific topic any more.

@Danu got it

By the way, @WilliamBulmer I found Vinberg's book on algebra pretty decent

@Danu Thanks

It's the definition-theorem-proof style you hate, but the Russian school of textbooks is a bit different from others

Maybe you prefer it

Eww, Russian

There are some "physical" examples

Maybe I should have been more specific

I probably should have used what I initially called it--Bourbaki style

Bourbaki is something very different from just def-thm-proof

How so @Danu

Have you read one of those books?

No

I have not had a reason

Then?

Bourbaki is well-known for strong preference for abstraction and generality

Yes, I know that.

cmat.edu.uy/~marclan/TM/Algebra%20i%20-%20Bourbaki.pdf

Well, there you go.

that's bourbaki style

I know nothing about algebra, so this will look horrible to me no matter what style

and rigor

All math books are about rigor :D

(hopefully haha)

Indeed.

Rigor is important

I think I'm losing hair

Also important

@BernardMeurer what is it that you need help with

@Danu, I know you don't want to talk about it, my wife and sister are teachers. I will ask them what the literature specifically says

Teachers?

I made those statements based off of conversations with them

@WilliamBulmer Your more generic claim is not very interesting. Applying it to something as specific as you claim to is wrong, in my mind. (damnit, I oughta stop replying)

(I know some teachers don't know what the scientific method is. My wife and sister do, so I trust their assessment)

@Danu Well, we can talk about it, if you want. As I said, I have no ego in this, and I don't mind being proven wrong. There is absolutely nothing wrong with calling me out

Just know that if you do want me to follow up (which it sounds like you don't), it likely won't be today

@0celo7 get this drive.google.com/open?id=0B53os7BTst5ld1BBUi1OdmtYeHc

unzip it anywhere

run from commandline

the face_detect file

what what what

> get virus

I don't know how to do any of that

@Danu Also this

You murder calculators for a living, you cannot be trusted

@Danu The code's on github

I just wanted to save myself (and him) from having to compile code again

did you get Michelle to do it

@0celo7 She's at work rn

Implying she actually works lol

why do you think she got a butt lift

@0celo7 Just help me out man

chill

I'm doing a proof

will help you when I'm done

@0celo7 Alrighty

I read "doing a prof" and was very proud for a moment there

@BernardMeurer I have not met any sexy profs yet

all the grad students are chinese dudes, so no luck there either

@0celo7 Lame

There's a cute grad student in maths there

Where

lol

Lemme check my history, i found her a while ago

There is a cute grad student from Stanford who collaborates with us

But she's convinced I'm my prof's cousin (???), so no luck there

@Danu From the little I have read of Vinberg, it seems like a pretty good textbook. Thanks. Maybe I AM wrong, and have simply sampled the wrong textbooks. Is this representative of the Russian School of Textbooks style?

@0celo7 Is she blonde, with a slightly large nose and blue eyes?

Sure

I can't find a picture but that's how I remember the person

@0celo7 what

^

@BernardMeurer Asian

@0celo7 Not who I'm thinking about

Can't find this girl in my history goddamit

@ACuriousMind Her English isn't perfect, and something got lost in translation once

It's been a running joke

Only she doesn't know it's a joke

Why should that matter?

What?

@BernardMeurer You were creeping on a girl from my school?

Being your prof's cousin.

@0celo7 No, I was looking for something and I ended up there, and I saw her so I kept her in a tab to make fun of you later but eventually I closed that tab

and forgot to make fun of you

@skillpatrol It's an Asian thing

Explain

@BernardMeurer Why were you going to make fun of me?

@skillpatrol It brings dishonor.

@0celo7 AHA!

I'm stuck on a Riemannian geometry proof. I hate my life

Dude I'm good at this

What about her

She's not asian

She's a physics graduate student though

Oh, she's never at work then

Not very studious

Why?

why what

and how is that making fun of me

should I try to get her number or something

Why isn't she studious

she's not Asian, clearly

It's not, I no longer remember how I was going to use her to make fun of you

lol

@0celo7 If you didn't have a girlfriend who's as weird as you already I'd say go for it

but that being the case, stick to what you've got

Hey...

Shut up and listen

Hum?

Can't, in the library

@Danu Meh, not the best conductor

Specially for that piece

True, but it's not so easy to find shit on youtube

meh

(in Germany)

@Danu I have the complete symphonies conducted by Haitink in lossless if you want

@Danu It's pretty easy to find shit on YouTube. It's finding the good stuff that's hard :P

that sounds nice

@Danu Literally

are we talking about PIRACY

@0celo7 Nope, I'll sell him my USED CD for 0,01 BRL

Pretty sure that's piracy

which is 0.002 EUR

technically I am but reselling a product

I wonder if this is a typo.

@BernardMeurer Still stuck on this proof, hold up

@0celo7 Alrighty

Well, I am going home. I hope I didn't stir the pot too much. Have a good night, everyone.

cya later

@Danu interesting choice

@ACuriousMind I doubt you'll want to look at a Riemannian geometry proof, right?

@BernardMeurer still stuck holy crap

I don't see how that's relevant

Man, my google drive is sooo much slower than Dropbox

Perhaps it depends on the device?

This has got to be a bad joke. After intense searching I'm about six or seven reference levels deep into spinor papers and I finally find one that says that the existence of Majorana spinors can be deduced from general group theoretical arguments

It then gives the reference [5] and then says it will deduce their existence by explicit computation

I look into the references section, and there is no [5]

Also, two to four papers seem to have been grouped here under the same label anyway, and still there's [6] twice instead of [5], totalling four papers. Who the hell thought this would be a good way to label references?

Ouch!

@ACuriousMind That's physics

@ACuriousMind Please, Riemannian geometry, your favorite

No, not now

Can't you see he's busy?

I've already read two of the possible candidates for [5], this is not yet a dead end

Happy hunting :P

@skillpatrol He can take his mind off of it with this proof

Which, to be fair, I have been stuck on for months.

I have a feeling the proof is just wrong.

hi

I know about 7 Riemannian geometry books, and this is the only one which proves it like this.

Hmmm, the prof actually is here at my university. I could go and ask him whether he remembers what the correct reference for a paper he wrote 33 years ago is... :D

:O

What are the chances :P

I can follow Milnor's proof, which is the same as do Carmo

I can also follow the Lee-Lee-Petersen proof

And the Jost proof

Are there any more Riemannian geometry books?

Walschap

Kobayashi-Nomizu

What's so important about following this proof?

If this proof is correct, it's very elegant

But it makes zero sense to me, and seems quite wrong.

Yes, I drew a picture

:-)

proof without words

Aha...it appears the answer lies in Tits

lol

:D

Time to dust off the ol' Kobayashi

Don't let your dust allergies get in the way

oh god soldering forms

@ACuriousMind help

No, they use a proof similar to Lee, but it's harder to follow

Damn. The book by Tits has what I want, but it is just tables of facts, no proofs and no specific references -.-