The h Bar

Manish Kumar Singh

1:01 PM

What does it mean when someone say to find the total emissive power R(v) of a BB, is it the kT^4 relation or something

Danu

@Huy Heh, nice right?

Huy

@Danu: I've browsed through most top questions on MO/MSE at some point during my studies, and it's funny how every time I check the answers again, I can appreciate some more answers.

Danu

@Huy Yes!! This!!!

Huy

@Danu: Before oral exams, it's nice to check this one: mathoverflow.net/questions/23478/… :>

ACuriousMind

1:23 PM

lol, I saw that

0celo7

@ACuriousMind Do you have two monitors?

ACuriousMind

@0celo7 Yes

0celo7

@ACuriousMind That explains it.

Why is Metro so hard...conversely, why am I so bad at stealth shooters?

Huy

Practice.

0celo7

Practice? I've done this section about ten times now.

I know I can just plow through everyone, but I'd like to do it properly.

Huy

1:27 PM

Practice more.

0celo7

:(

Huy

Practice with joy.

0celo7

It's this guy on a turret. He has a spotlight so I can't see his head. Shooting at him is a gamble.

Huy

Try with a Ray-Ban.

0celo7

@Huy It's post-apocalyptic Russia, not LA.

Huy

1:29 PM

Which one is it anyways?

I've only played one some time ago when I got it at a Steam sale.

0celo7

2033 Redux.

I got both on a sale last week.

Huy

Yeah, that's the one I have.

Played it a year ago or so.

0celo7

Yeah, I'll eat breakfast and then try again.

user54412

@ManishKumarSingh That's somewhat strange wording. And I've never seen R, v, or k used in this context (k is presumably sigma, the Stefan-Boltzmann constant?).

Danu

I don't get this: Let $Z$ be the center of $G$ (assume $Z\neq G$). If $|G|=p^2$ where $p$ is prime, then $|Z|=p$ and $|G/Z|=p$ so the latter is cyclic.

That last part weirds me out!

ACuriousMind

1:41 PM

@Danu There are no non-cyclic groups of prime order

Danu

@ACuriousMind Oh, lel thanks. I guess taking a 5 months long break between two parts of this book was not the greatest of ideas.

user54412

@Danu No offense, but your mathematical physics curriculum seems to have an astonishing lack of basic algebra.

user54412

Or maybe my school had an unusual fixation with algebra?

ACuriousMind

They seem to be geometry fetishists at LMU, indeed :P

Danu

No, I didn't do a bachelor's in mathematical physics (such a thing does not exist)

I just started my MSc. and one does not need to do any pure mathematics apart from some functional analysis courses.

My undergraduate education was extremely lacking in terms of mathematics... in Amsterdam nobody really cares to prove anything for the physicists.

user54412

1:45 PM

still, you seem to know far more advanced math than me, and where I'm from the sequence is algebra -> analysis -> geometry/topology -> branch out into everything else

Danu

I had no idea what I was getting myself into with this MSc haha

@ChrisWhite Luckily, in mathematics, one can typically get away with only knowing basic terminology from other fields.

So, basically, I'm self-studying algebra

I don't know any analysis

user54412

what book?

Danu

And topology is coming up this year.

Vinberg - A course in algebra (I find it to be quite good)

Russian-style mathematics books are great

user54412

lol

Huy

@ChrisWhite: I thought the sequence analysis -> algebra -> topology etc -> branch out would make more sense, since analysis is less abstract and has more direct applications in both lower-level maths and physics, plus most of it was done in high school already, no?

Kyle Kanos

1:47 PM

Well I now feel I lost out in mathematics, given that my courses went Lin Alg, Calc I -> III & Diff Eq (all that was required for BS in physics)

Danu

@KyleKanos Dude I had that too (add in complex analysis at the end)

0celo7

@Huy Jesus what high school did you go to...

Danu

@Huy Calculus $\neq$ analysis :P

user54412

we used Dummit & Foote for undergrad algebra (seemed the right level, though I'm told some places use it for beginning grads) -- it's actually one of my all-time favorite textbooks for its clarity

Danu

I know calculus quite well... Analysis? Nopenopenope

Huy

1:48 PM

@Danu: We don't distinguish calculus and analysis at my uni.

@Danu: Since it is assumed high schoolers know calculus well enough, so we start with analysis in the first semester.

Danu

@ChrisWhite I think this is very similar in terms of content.

0celo7

@Huy What? Every high school is assumed to have taught calculus?

Huy

@0celo7: Just a public high school with focus on mathematics and natural sciences.

Danu

D&F is a bit longer, so it covers more.

Huy

@0celo7: Yes.

Danu

1:49 PM

@0celo7 EUROPE MOFO! :P

user54412

@Huy I guess we did have such a beginning analysis course, but all the profs hated teaching it and they tried shoving it onto applied math and physics to teach.

Danu

Yeah, gotta love high school education in Europe :)

Anyways, to give you an indication of how little I knew about mathematics: I didn't know what a "topology" was until about 2 months before I started my current degree.

0celo7

@Huy We don't have enough competent teachers to come even close to that here.

Danu

@Huy Well, here the physicists don't get any analysis at all, just more calculus :P

Huy

@0celo7: Here = USA?

0celo7

1:51 PM

@Huy Yes.

Huy

@Danu: As you probably know, the first undergrad year at ETH is almost identical for physicists and mathematicians.

skill patrol

Gamers beware

Danu

@ChrisWhite in any case, I find the algebra stuff not that interesting in its own right and so I think it didn't really pose any major obstacle being unaware of it in any of the geometry courses.

Huy

@0celo7: I heard other US students say that before. They are always very impressed to hear that in Switzerland, in order to become high school teacher, you must have a Master's degree in whatever you want to teach.

0celo7

The only competent math teachers I've had were my physics teacher and my calc teacher at the local community college.

Huy

1:52 PM

@0celo7: While that doesn't guarantee you to be a good teacher, I think it helps a lot.

Danu

Good joke my friend just told me:

Q: "What's an anagram of Banach-Tarski?"
A: "Banach-Tarski Banach-Tarski."

0celo7

@Huy Quote from my precalculus teacher: "I don't know what they teach you in calculus."

@Danu Nice.

skill patrol

badum tsss

Danu

I just want to know the algebra in order to, in the end, learn algebraic geometry.

Also, I will be self-studying algebraic topology this summer :P

Huy

@Danu: I know a better one: What does the B. in Benoit B. Mandelbrot stand for? Benoit B. Mandelbrot.

4

Danu

1:54 PM

(mostly getting through the first chapters of my book though, so one can probably ignore the "algebraic" for now...)

0celo7

@Huy Overused.

Danu

@Huy Ahh, nice! I think it's a good one

My reading list for now is: Vinberg & Bredon, and I wanna brush up my diffgeo again from last semester as well.

Huy

@0celo7: Just out of curiosity: What DO they teach you in maths in high school? In the last few years?

Kyle Kanos

Stats is the only math one needs

skill patrol

algebra, trig, geometry and precalc

Danu

1:57 PM

@ChrisWhite occasionally, I stop and think to my self: "What I'm doing is so irresponsible!" But then I look at my friends doing string theory without the slightest knowledge of geometry and I'm like... "Naaaaaaaaaaaaaaaaaaaaah"

0celo7

@Huy Euclidean geometry, Algebra 2 (quadratics, complex numbers, logarithms, conics), Trig, Probability, Calculus.

user54412

@Huy A typical "accelerated" student would do something like proof-based geometry -> "algebra II"/trig -> "precalculus" (aka logs and exponents and maybe series) -> calculus. Average students would be a year behind. And most states don't require 4 years of math.

0celo7

@Huy Now you can combine algebra 2 and trig.

@Huy There are usually two choices of calc, roughly corresponding to one or two semesters of college calculus.

Danu

@ChrisWhite Don't require 4? Wow! In the Netherlands we require 6, even for those who don't want to study anything scientific (to be fair, their last 3 years are just random statistics or whatever "calculator-science")

0celo7

I also took a year of statistics.

Kyle Kanos

2:00 PM

@Danu NJ (where I grew up) required only 3 years. Most students took Algebra I & II, then did statistics or something like that.

0celo7

What really irked me was that I had to take Alg2/Trig and then take precalculus, which was really Alg2/Trig with probability and limits.

user54412

@Danu Well, 6 starting when? We have required math up through grade 10, 11, or 12, where college is 13. But yeah, it's not a big focus. Physical education (gym class) and maybe English were all that NJ required every year for us.

ACuriousMind

@Danu Doing stuff like string theory or even advanced QFT without geometry and group theory seems like flying blind into a storm to me, and yet so many people seem to do it without the slightest concern.

Huy

@ChrisWhite: 4 years of math? How long is your high school?

@Danu: Same, we have 6 years of high school and everyone has to do all 6 of them with maths.

user54412

@Huy high school is generally grades 9-12

0celo7

2:01 PM

@Huy 4 years.

Huy

@ChrisWhite: High school starts at 7-12.

(over here)

Danu

@ChrisWhite Ages 12-18

user54412

6-8: middle school, 7-8: junior high school

Danu

@ACuriousMind Yeah, and it's fine :P Just not something I'd ever want to do.

Huy

Usually, you'd do precalc stuff, geometry, trig and algebra in 9,10 and then the last two years are for calculus and complex numbers.

Danu

2:03 PM

I hate how the system of "grades" for children is different in every country lol

user54412

6

Q: Diagram of education in the Netherlands

How would the dutch educational system be represented in a diagram? Or put differently, what are the different roads that lead to the academic world in the Netherlands? PS. This question ("What are the different roads to get into academics in the Netherlands?") came up in chat awhile ago, so I d...

netherlands

Danu

Complex numbers were not touched in the main curriculum in the Netherlands. Only people who to took "mathematics D" (a new type that was only introduced one year before I chose it) get to complex numbers. We also did differential equations, a tiny bit of graph theory and combinatorics there.

We also learned what induction was, which blew my mind at the time.

(I didn't get it)

0celo7

@Danu We did that too.

Graph theory?

I guarantee no one in my school has ever heard of that.

Huy

@Danu: We did that too and it became more important in grades 11, 12, since usually you start with differential calculus in grade 11 and you need induction for the binomial theorem, and you need the binomial theorem to show that $(x^n)' = nx^{n-1}$.

Danu

It was cool because there was no centralized final exam (on the national level) for this, so teachers got to do cool stuff.

0celo7

2:06 PM

@Huy Show? You actually proved things?

Danu

@Huy We didn't prove that haha

Huy

@0celo7: Of course.

Danu

Also, what does that even mean? AFAIK one defines a derivation pretty much by this

0celo7

@Huy I haven't proved a thing in high school.

Huy

Not to the extend as a real analysis course in university.

Danu

2:06 PM

@ChrisWhite Yup, that's correct!

Huy

@Danu: I mean that we got the slope of the tangent at a point of a function as a a limit of a quotient and tried to find rules to work with.

Danu

@Huy Ah, the limit definition of course

0celo7

@Danu is too geometric

Danu

(see, my lack of analysis showing again!)

@0celo7 That's literally impossible :D

0celo7

@Danu You forgot the limit definition :P

ACuriousMind

2:09 PM

:2323062 1. You define the derivative as the limit of the difference quotient. 2. The minimalist algebraist indeed defines the derivative of $x$ to be $1$ and then "extends by linearity", but this only defines the derivative of analytic functions, as you might notice.

0celo7

@ACuriousMind Extends by linearity?

Danu

@ACuriousMind Analytic functions are the only real functions ;D

ACuriousMind

@0celo7 Meaning you can extend this definition to all power series by imposing the axioms for a derivation (product rule, linearity)

0celo7

@Huy When did you learn multivariable calculus?

Huy

@0celo7: That's not compulsory for every maths teacher, but can be done in the last year usually, if time allows.

user54412

2:11 PM

On a completely random topic -- relativistic fluid dynamics -- I just came across this gem: "The time scales for these instabilities are very short; for example, water at room temperature and pressure has an instability with a growth time scale of about $10^{-34}$ seconds in these theories."

ACuriousMind

@Danu Amen to that.

Danu

@ChrisWhite Sounds... bad?

Huy

@0celo7: We did very little on it since our teacher preferred vector geometry and complex numbers/sequences, so I properly learned it at uni.

Danu

Ah, but that's what they wanted to argue.

0celo7

@Huy I once got into an argument with my calculus teacher -- she claimed I was inventing this "line integral" to confuse her.

user54412

2:12 PM

Apparently even once people realized parabolic operators made no sense in relativity, they still didn't immediately realize some strictly hyperbolic formulations had pretty serious problems too.

Huy

@0celo7: Well, did you? :P

0celo7

@Huy Vector geometry? We only did vectors in physics.

Huy

@0celo7: Mostly intersection problems in $\mathbb{R}^3$, lines, planes, spheres, etc.

0celo7

@Huy We did nothing beyond $\mathbb{R}^2$.

It was in the book.

We just used a third of the book for a year-long course.

(This was in precalc.)

Danu

Okay, gotta go! byeee all

Huy

2:15 PM

@0celo7: I still have an exam I did with my students (11th) grade on vector geometry if you're interested.

skill patrol

later pal

0celo7

Funny thing: I had to teach my precalc teacher how to write an integral. (He did not know you needed a $\mathrm{d}x$.)

@Huy That would just make me sad.

ACuriousMind

@0celo7 We had this discussion before, but I'm shocked how little qualification one apparently needs to become a teacher where you are.

0celo7

My highlight in the 11th grade was a combinatorics test where we had to multiply 5 digit numbers.

@ACuriousMind I know. @Huy is new to our group of misfits.

@ACuriousMind I should remind you my school is in the top 600 schools.

ACuriousMind

@0celo7 Not sure whether laughter or tears are the appropriate response to that.

Huy

2:18 PM

@0celo7: i.imgur.com/PAybhoC.png

0celo7

@ACuriousMind It's the math department that sucks, tbh.

Huy

BRB, kitchen.

0celo7

Everything else is fine.

skill patrol

@ACuriousMind did you do any vector calculus in high school?

ACuriousMind

@skillpatrol Not "calculus", but what Huy said above, it's called "analytic geometry" here - find intersections of lines and planes in $\mathbb{R}^3$, find normal vectors, find the distance of points to lines and planes, that sort of thing.

0celo7

2:19 PM

@Huy Shit, I couldn't do that.

HDE 226868

@0celo7 It's not that bad.

0celo7

@ACuriousMind My precalc was called "analytic geometry". Didn't do any fucking analytic geometry.

@HDE226868 I've been complaining for the past hour. You need to specify.

HDE 226868

@0celo7 What @ACuriousMind's talking about.

It all stems from a few basic concepts.

0celo7

@HDE226868 I dare say I have the mathematical maturity to do it, I just haven't learned it.

HDE 226868

@0celo7 I think you could easily do it.

0celo7

2:23 PM

Doesn't change the fact that my high school math education was terrible.

I was actually a C (3 @ACuriousMind) student in German math.

ACuriousMind

@0celo7 What were the topics when you were here? Quadratic equations or something like that?

I'm a bit hazy on the order in the lower years

0celo7

@ACuriousMind I have my book, mom.

What kinda freaks me out is this: Has my brain developed and now I'm capable of being at the top of my class or are Americans and their schools so fucking shit that I'd still be a C student in Germany :/

ACuriousMind

@0celo7 I assure you that the average German student does not read string theory books ;)

0celo7

@ACuriousMind schroedel.de/artikel/…

@ACuriousMind Maybe, but I've definitely gone way too fast. I need to learn QFT again from the ground up. I took time with GR, so that's not a problem.

f.sbzo.de/onlineanhaenge/files/… Table of Contents.

ACuriousMind

@0celo7 Well, they don't read Gr books, either :D

@0celo7 I see

that's the year before quadratic equations then, I think

0celo7

2:31 PM

Quadratics are done in year 10 in America.

(Alg2)

HDE 226868

@0celo7 Depends. Some courses cover it earlier.

0celo7

@ACuriousMind But if they did, they'd be better equipped.

It was really good ol Prof. Nong at Northern Virginia Community College who saved me.

Huy

@0celo7: Actually, most maths teachers are tending towards less vector geometry and more linear algebra. Geometers are afraid that it will reduce spatial sense of students, but then again linear algebra has so many applications even in high school that somehow it must be taught more, imo.

0celo7

"Linear algebra? What's that?" -- my math teachers, very probably

Huy

You don't seem to be very fond of your math teacher. :D

0celo7

2:39 PM

Like I said, the only math teacher I ever had that I liked was the one at NVCC. He was a PhD student at GMU, so he actually knew his shit.

Huy

@0celo7: Having a PhD as a maths teacher isn't too uncommon here, actually.

0celo7

Having an MS as a math teacher is very uncommon here.

Huy

@0celo7: Our temporary physics/maths teacher had a PhD from Princeton, but to be honest he wasn't very good at teaching. :P

@0celo7: Do you think requiring it, or at least a BSc would result in a lot less maths teachers?

0celo7

My physics teacher had an MS from Princeton. She never let us forget that.

@Huy They all have BSs (I think/hope).

Huy

Ah, ok, and then they don't know linear algebra? O_o

Or line integrals? o_O

0celo7

2:42 PM

Math teachers aren't the good students.

ACuriousMind

@Huy The quality of American undergraduate education :P

Huy

@0celo7: But even not being a good student, you'd surely know basic linear algebra?

@0celo7: I would never consider myself a good student, but without very basic stuff, how on earth would you get a BSc?

HDE 226868

@ACuriousMind Think about the quality of American high school math education.

ACuriousMind

@HDE226868 There surely is a causal relation here, somewhere.

0celo7

@Huy They might have known it then, but 5, 10 years down the line? Forget it.

Huy

2:44 PM

I hope I won't end up the same way.

HDE 226868

@ACuriousMind Absolutely. Education obeys causality, at least.

Huy

@0celo7: I find something I love in most that I learned at uni and I tend to be passionate about it and want to teach it to others.

0celo7

My precalculus teacher pretty much told us he was shit at high level math so he became a math teacher.

Huy

=(

@ACuriousMind Can you explain this? Do they just let everyone pass anyways or what?

0celo7

I'm gonna stream Metro. I've been trying for about 30 minutes and keep failing. It's probably funny.

twitch.tv/revolver_0celo7

Huy

2:47 PM

@ACuriousMind: I guess at MSE I mostly meet students who are very passionate , talented and ambitious, so I tend to believe all US students are like that.

ACuriousMind

@Huy I don't know, but my general impression is that their studies are a lot more like school - you can cram for the exam with the exercises in your textbook, you'll pass, and you didn't actually learn anything, but I have no idea how accurate this impression is. (It's mainly based on the weird emphasis on textbook they seem to have in general)

Huy

I see.

skill patrol

as opposed to "lecture"?

ACuriousMind

@skillpatrol I...guess. As I said, I really can't compare the systems because I don't really know anything about the American one, it's just a completely unfounded impression

skill patrol

or the Socratic method?

0celo7

2:53 PM

We do that in non-STEM classes

@ACuriousMind holy fuck please tell me how to beat this @Huy

Huy

@0celo7: Sorry, I closed your stream as soon as I read "physics lesson".

0celo7

huh?

ACuriousMind

@0celo7 I haven't played the game very far, can't help you, sorry

skill patrol

@ACuriousMind did you get time to watch Moore?

0celo7

@Huy Renamed

HDE 226868

2:56 PM

@ACuriousMind I'm probably not the best person to respond to that (I go to a STEM school), but I've always had the format of math classes where the teacher lectures in some form, puts up some problems and does an example or two, then assigns homework from the textbook.

ACuriousMind

@skillpatrol Ooh, damn, I would've had, but I simply forgot

skill patrol

@ACuriousMind np

ACuriousMind

@HDE226868 Yeah, that's mathematics in school alright.

skill patrol

perhaps later

Huy

@0celo7: I don't want to start regularly watching streams again. Makes me even less motivated to study.

HDE 226868

2:57 PM

I've never known anyone who's crammed using only the textbook and successfully gotten anything higher than a C on a test.

0celo7

@HDE226868 That's how we did it for all but calculus.

HDE 226868

@0celo7 Did it work?

0celo7

@HDE226868 I guess.

HDE 226868

@0celo7 I stand corrected, then.

0celo7

High school math is trivial though.

HDE 226868

3:01 PM

Depends on the type of math.

And the student.

0celo7

@ACuriousMind I pretty much just said "fuck it" and killed everyone

ACuriousMind

@0celo7 Sounds like a working solution to me.

DanielSank

3:29 PM

@ChrisWhite How on Earth did you dig up that old comment? Google?

ACuriousMind

@DanielSank You can also search the transcript in the upper right corner of this room.

DanielSank

@DavidZ That's what I'm trying to understand :-) One of the categories is "not constructive". If someone said $F=ma^2$ in a comment, I'd flag it as not constructive. Does this not apply to non-physics statements?

@ACuriousMind Would you look at that! A tiny search box.

@ChrisWhite Oh my goodness. This was such an... issue when we were setting up our lab at Google.

As you can imagine, at Google whiteboards are standard issue. Several of us were not pleased by this. We lost the battle against the architects but rebellion is brewing even yet.

user54412

@ACuriousMind or just memorize it...

user54412

Jul 30 at 22:50, by ACuriousMind

(Yes, my memory for this chat transcript almost rivals my webcomic memory)

ACuriousMind

@ChrisWhite Touchè

0celo7

3:43 PM

@ACuriousMind has forgotten some things

DanielSank

@ChrisWhite But did you find that from memory?

user54412

not gonna answer that...

skill patrol

Of course he did :-)

0celo7

@Huy I did indeed have a PhD math teacher in Germany. I never liked him because I once had to explain in front of the class why dividing by zero is bad and he broke out laughing because I had no clue.

user54412

Speaking of chalk, is anyone here a Hagoromo user?

Huy

3:46 PM

@0celo7: I don't think teachers are supposed to do that, generally.

ACuriousMind

@ChrisWhite No idea what that is

0celo7

@Huy I was pretty shit at math. My dad got me a tutor so I wouldn't be like my sister.

user54412

@ACuriousMind Japanese chalk favored by mathematicians, now out of business

user54412

A number of math profs have bought up lifetime supplies -- the stuff is supposed to be quite good.

skill patrol

@0celo7 The important thing is that you now know why dividing by zero is "bad."

0celo7

3:49 PM

@skillpatrol Uh, not really. Rings or something?

DanielSank

@ChrisWhite The other important thing is the construction of the board.

David Z

@DanielSank you mean if the entire text of the comment is merely "$F = ma^2$"? Sure, that's not constructive, but so is a comment whose entire text is "$F = ma$" or "$E = mc^2$" or the like. The constructiveness is roughly orthogonal to the correctness. Or such is my understanding, anyway.

DanielSank

Pained wood -> sadness.

@ChrisWhite Slate is dreamy but really expensive.

@DavidZ "The constructiveness is roughly orthogonal to the correctness." Got it.

user54412

Apparently no one wants to take up the man's dedication to good chalk. I'm half inclined to go to Japan, climb some mountain, and find him seated in a relaxed pose, where I will request the tutelage of the sensei himself.

skill patrol

@0celo7 because zero has no reciprocal

0celo7

3:50 PM

@skillpatrol 1/0 :P

ACuriousMind

@skillpatrol That's saying "You can't divide by zero because you can't divide by zero", only in disguise

skill patrol

@0celo7 but 0 times any number is zero, not 1.

user54412

@DanielSank There was one lecture hall in my undergrad with perfect slate blackboards. 9 large ones, all visible simultaneously and controlled by silent motors. I would sneak in at night and do calculations on them.

ACuriousMind

The proper way to do this is to assume that zero has an inverse, and then derive a contradiction.

skill patrol

"Proper" in what way?

DanielSank

3:52 PM

@skillpatrol As in "actually a proof".

ACuriousMind

@skillpatrol Proper in the sense that you are not just saying "it is not defined", you are proving that it can't be defined.

DanielSank

@ChrisWhite Heheh, illicit physics. I like it.

0celo7

@ACuriousMind For the record, I do know this is what you do.

skill patrol

Proving 0 times any number is 0 will suffice @ACuriousMind @DanielSank

0celo7

very helpful, Google

DanielSank

3:55 PM

@0celo7 'murica.

user54412

you typed too much -- type less for both sides of the issue :P

user54412

0celo7

haha

Is this enough?

ACuriousMind

Hm, the first actual math proof in the suggestions is "proof you can't trisect an angle"

skill patrol

geometers :P

ACuriousMind

3:58 PM

@0celo7 Yes, after you've shown the assumptions from the fact that zero is the additive identity. ;)

0celo7

@ACuriousMind I define my 0 by that property

you can keep your ring shit

Why is Wiki's TeX so low res?

skill patrol

@0celo7 Exactly, it is called the multiplicative property of 0

Huy

@0celo7: Because you need a 5k monitor to properly view it.

skill patrol

0*(any number) = 0

ACuriousMind

@0celo7 But ring shit is awesome shit :(

@skillpatrol And it directly follows from the definition of the zero, i.e. $x+ 0 = x$. No need to add it to the axioms.

user54412

4:01 PM

@0celo7 It's poorly-rendered images rather than vector fonts. I have no idea why they do it this way -- really rather inexcusable to be honest.

0celo7

@ACuriousMind give me until my Junior year and I take abstract algebra

then I might appreciate it

skill patrol

@ACuriousMind Good sir, I am suggesting to prove it from the properties of real numbers :-)

ACuriousMind

@skillpatrol Meh, boring special case

0celo7

@ACuriousMind I'm retarded, how does it follow from that

ACuriousMind

@0celo7 I eagerly await your enlightenment

skill patrol

4:03 PM

:(

ACuriousMind

@0celo7 $x y = (x + 0) y = xy +0y \implies 0y = 0$

0celo7

@ACuriousMind I see

user54412

One of the first benefits that comes from studying abstract algebra is getting out of the mindset of "everything is a field, and probably R at that"

skill patrol

@0celo7 so how does that forbid division by 0?

user54412

Turns out lots of results don't need all that baggage.

0celo7

4:05 PM

@skillpatrol what

skill patrol

0y = 0

0celo7

@skillpatrol cf. the wiki image above

dividing by 0 leads to the contradiction n=m even when n!=m

skill patrol

Again with the contradiction argument :(

I'm saying you don't need it

0celo7

does @ACuriousMind agree?

skill patrol

I want you to please think about it for yourself :-)

0celo7

4:10 PM

mmmm

what's the argument?

ACuriousMind

@skillpatrol 1. A contradiction argument is nothing one should avoid. 2. What alternative proof that zero can't be invertible do you propose?

@ChrisWhite Looking at it as "baggage" is already a decidedly algebraic stance ;)

0celo7

@ACuriousMind Hawking & Ellis is like one giant contradiction proof

Huy

@ACuriousMind: If there's a direct proof, that usually is more enlightening than a contradiction proof.

0celo7

I have to expand my crazy acronyms for @Huy

ACuriousMind

@Huy Depends highly on what is being shown, I'd say. For a statement "X cannot exist", I think a contradiction argument "If X existed, this wrong thing would hold" is quite enlightening.

Huy

4:12 PM

@ACuriousMind: mathoverflow.net/questions/12342/…

skill patrol

Have a look at this @0celo7

0celo7

@skillpatrol I'm stacking all my books right now, will read later

skill patrol

np pal

1 hour ago, by skill patrol

perhaps later

0celo7

oh man I have a lot of crap

I'm still missing three books and I can't lift the box

I have to decide which books to leave D:

ACuriousMind

The boxes with the books are always the heaviest at moves. Books are just too dense

0celo7

4:29 PM

Freaking BBS is like 20 lbs

Slereah

4:50 PM

When people say that a quantum field can be expanded into $\varphi = \sum a_j u_j + a^\dagger_j u^*_j $

Is it a general thing or does it only apply to linear theories

ACuriousMind

@Slereah What do you mean with "linear theory"?

I highly suspect people are talking about free fields there, though

Slereah

Well yes

Free fields, which give rise to a linear EOM

Since linear equations do allow such superpositions of solutions

ACuriousMind

Then, yes, this is for linear theories. The creation and annihilation operators are not really defined for the fully interaction field (since, again, the Hilbert space of interacting theories is essentially unknown)

0celo7

Ok, I can leave Shankar. I have a PDF and hardly reach for it anymore. ACM is my one-stop shop for heresy trivia nowadays :D

Slereah

Thx

So that is what people mean when they say that particles aren't well defined in an interacting theory?

0celo7

4:57 PM

@Slereah yes, and once again, Wald QFTCSBHT describes this in some detail

ACuriousMind

@Slereah Yes - you can't build a Fock space because you lack the creators/annihilators, so you have no clue how to define a particle state in the interacting space. This is why the LSZ formalism resorts to asymptotically free states.

Slereah

You can't build the Fock space at all?

Or does it take on a different meaning

Like I know that QFT in curved spacetime has also poorly defined particles

But it still has a Fock space

Its meaning is just dissociated from particle numbers, though

0celo7

I know I should leave Zee, I don't use it anymore...

ACuriousMind

@Slereah How would you, you've got not creators, and the Fock space is built by tensoring the 1-particle space with itself

Slereah

I suppose so!