4:02 PM
I have forgotten how to go from P^2 # T^2 to P^2 # K using cut-and-pastes, actually. I like to see it using blowups.

what's a blowup?
Got it!
$efeggf^{-1}$ is $P^2\# K$, right?
ugh, not quite
but I should be able to get $f^{-1}efe$ into a $P^2\#P^2$
woot

@0celouvsky I see eggs

4:18 PM
@0celouvsky Yes, right? $efef^{-1}$ is a Klein bottle, and the $gg$ is the $\Bbb P^2$ you're summing with.
Blowup is literally connected summing with bar{P^2} in dimension 2; it just has a more visual meaning in algebraic geometry. Don't worry about it

@JohnR: Are u busy?

@BalarkaSen yeah, it works

@Kaumudi.H No, I'm sitting digesting lunch (risotto with chestnuts and brussel sprouts) and staring idly at the screen :-)

5 cuts in all, not too bad

@JohnRennie I see :-) Would u mind reading and maybe consider responding to something, then?

4:20 PM
@BalarkaSen Hmm. I would like to learn algebraic geometry but it's not close to my main interests

@JohnRennie No, erm. Hang on...

Argh, I'm in algebraic geometry hell. What does it mean to take the cube of a divisor?

@ACuriousMind why does algebraic geometry show up in string theory?

@ACuriousMind $\alpha \cup \alpha \cup \alpha$?
$\alpha$ representing the cohomology class of the divisor.
Dunno.

4:26 PM
I don't even have Hartshorne in my PDF folder

@JohnR: You have mail...

@0celouvsky In this case because the relevant building blocks to construct asymptotically cylindrical Calabi-Yau 3-manifolds apparently are semi-Fano 3-manifolds and "semi-Fano" is an algebro-geometric concept. The Calabi-Yau cylinders in turn are the essential building block to construct compact $G_2$-manifolds through twisted connected sums.

christ

@Kaumudi.H Got it. I'll reply by mail.

@BalarkaSen Hm, yes, that makes sense

4:30 PM
@JohnRennie OK. Thank you :-)

@BalarkaSen is that supposed to be $\smile$

@Kaumudi.H YHM

@JohnRennie YHM means?

Young Hairy Mammoth

4:45 PM
OK, folks, here's a quiz: identify this wildly cited researcher

Ed Witten?

700k citations since 2012!
I doubt even Ed Witten could amass those numbers in a span of 5 years, isn't it?

@JohnRennie cooooold

i cannot think of anyone in physics who could amass that

@JohnR: I'm sorry, I'll respond in a bit...

4:49 PM
sigmund freud, maybe

Bill Nye the Science Commie
@EmilioPisanty well, who is it??

> The academic superstar everybody wants to be co-author with
of course

Groan :-)

That's an unfortunate name
He sounds like the thing you put when there are multiple authors

finally caught on camera, too
@0celouvsky she

4:54 PM
@JohnRennie I will stop with the sheep comments if you stop the nose
@EmilioPisanty what?

@EmilioPisanty I thought for a moment you were going to say Erdős, but his citation score is relatively low.

@0celouvsky Prof. Et al is female
see the homepage

That's some PC bullshit.
I'll default to female when they're the majority in science.

@0celouvsky Dr. A. Author is male, though
> Enter dr. A. Author. Ranking second in the field of citation analysis, his h-index is 30 and he has over 3500 citations. Among his most influential papers are “Title of article” with 159 citations and “Title of paper” with 128 citations to date. It is a matter of some regret to him that his 1990 “Instructions to authors” has been less influential, but perhaps its time is yet to come.

4:57 PM
I can't actually find the gender

@BernardoMeurer That's a working method, and for the size of a 2048 will never too long.
But there is a method that guarantees to choose a random empty cell in O(n) time and O(1) space, which you might prefer if the board was very large (when the stochastic method you are using has the possibility of a long running time).

@dmckee Oh, sweet, do tell!

Set a counter to c=1. Walk the cells in some definite order. Every time you encounter a empty cell you (a) set the selected cell to the current cell with probability 1/c, and (b) increment c. When you have exhausted the cells simply use the selected cell.

This use case is a little more complicated than usual because some cells are empty and some are not, but this is also the algorithm used to chose elements of a list (or other data structure with sequential rather than random access) randomly with equal probability.
So I had to jigger it a little to ensure that you select some cell (the first empty one you encounter).

5:05 PM
void randCell(int _board[BOARD_SIZE][BOARD_SIZE]) {
int row;
int col;
int num_empty = 0;
int empty[BOARD_SIZE*BOARD_SIZE];

// Check if there's any empty spaces
for (int i = 0; i < BOARD_SIZE; ++i) {
for (int j = 0; j < BOARD_SIZE; ++j) {
if (_board[i][j] == EMPTY) empty[num_empty++] = i*BOARD_SIZE+j;
}
}

if (num_empty > 0) {
int random_cell = randRange(0, num_empty)
col = empty[random_cell]/BOARD_SIZE;
row = empty[random_cell] % BOARD_SIZE;

@EmilioPisanty Wow, Prof. Et al.'s Erdös number is 1! :P

You'll find it easier to prove to yourself without having to worry about the empty cells. Just write out the probability to select the nth item in a list of m using this method.
@John's code above is also O(n) in time as well, but is O(n) in space as well. However, it is clearer than the scheme I suggested and therefore easier to debug and maintain.

@dmckee Pretty interesting

I have to say David's idea is pretty slick :-)

@JohnRennie Nice solution too
I fixed the bug that crashed the program, and I have timer and score working

5:11 PM
@JohnRennie Like most of my best ideas I stole it.

Great programmers steal!
2

In fact, I think I first encountered it in a Stack Overflow post somewhere.

I will have to pause development for the weekend because I have VHDL stuff to do
sigh

@dmckee My VHDL cpu works now :)
RISC, and the pipeline works already

5:13 PM
@JohnRennie Indeed they do. NIH is the bane of getting stuff done.

Okay, gotta go buy food, be back in a bit folks

5:29 PM
@BernardoMeurer Get me food.
@JohnRennie C is terrible.
type-first declarations. Blerg.

@JohnR: I'm sorry that I've taken so long; I was a bit of a mess to respond properly but you have (what's probably an irritatingly small) mail :-)

Hi @EmilioPisanty.
Thanks for getting that driven oscillator problem.

Hey guys! I need some suggestions for a good book on QFT; the one which starts QFT from scratch, builds up concepts intuitively and with the right mathematical rigor

What math do you know?

@NaveenBalaji The "right" mathematical rigor depends entirely on what you already know, etc.

5:39 PM
Basically no QFT book has mathematical rigor

My math level is that of a 1st year graduate

@NaveenBalaji That means very little, actually.

That's because outside of free QFTs, there are pretty much no rigorous models of QFT

That doesn't meant anything.

Do you know how to handle functional integrals?

5:41 PM
yup

functional integrals are bullshit

@AccidentalFourierTransform ?

@DanielSank in QFT they're pretty much all divergent

they are. period.

are they

5:42 PM
@NaveenBalaji Maggiore's QFT is good, probably will end up looking in every book no matter which one you pick though

@NaveenBalaji read Schwartz "QFT and the Standard Model"

Schwartz is pretty good

its a shitty book but more or less decent if its the first book you read

@0celouvsky so?
All you normally care about are various logarithmic derivatives.

5:44 PM
ok, its not shitty, but there are many books that are way better

What does that even mean

Any book, apart from these which illustrates more about the physical significance? That would make a fun read

@0celouvsky everything in QFT is divergent. Path integrals are no exception

@DanielSank which are not defined if your function is infinite everywhere. How physicists make predictions with this crap is amazing

@0celouvsky It means you care about things like $$\frac{\partial Z}{\partial \beta} \frac{1}{Z} \, .$$

5:45 PM
@AccidentalFourierTransform My position that QFT in general is bullshit is well known.

@0celouvsky Ehhhhh.

@DanielSank that is still very divergent

Not if you regularize it correctly.

@DanielSank yeah, I found the hamiltonian there to be pretty funny

@0celouvsky it is one of the most consistent bullshits we know!
thats amazing imo

5:46 PM
Guys come on, there are all kinds of cases in physics where we write stuff that implicitly requires taking a particular limit.
@AccidentalFourierTransform lololol

I mean, its true

@DanielSank Sure, you can probably do that integral with fancy contour integration, but why forgo an opportunity to pull up the old Ei functions?

physicists dont care about rigour as much as mathematicians do, but we do care about consistency

@AccidentalFourierTransform wtf is "consistency"?

@EmilioPisanty Contour integration is not fancier than Ei functions, bro.
Especially that one where it's all nice simple poles.

5:48 PM
@DanielSank =P

you can calculate the same observable using many different tools. All the manipulations are meaningless, but the final results agree

I'll leave it as is

we love mathematically rigorous theories, but that's not always possible

@EmilioPisanty If I feel brave later I'll edit in the exact solution, maybe.

in those cases, consistency is the only thing we ask

5:49 PM
if OP chooses to calculate the integral with the more complicated method, when you've offered an alternative, it's on them

Guys, you realize you can work with path integrals by stipulating the value for a basic case and then relating more complicated cases to that basic one via self-consistent algebraic relations, right?

@AccidentalFourierTransform Just now a prof I know recommended this book by some
Zeidler dude, any good?

@DanielSank in QFT that doesnt work
you get divergences everywhere

@AccidentalFourierTransform Ok, I admit I do not know QFT.

I mean, it kinda works

5:50 PM
Yeah even the free QFT path integral is divergent, technically

@Slereah Right but my point is that you stipulate the result for the free case and relate everything else to that.

you have to renormalize it

but not really, because everything is divergent. It would work if things were convergent though+
@Slereah that depends on how you define
technically speaking, one can define free partition functions rigorously, and everything is well defined
no need to regularise stuff if you define things properly

I know it's divergent if you define it as a limit of oscillators

@AccidentalFourierTransform I know!
@NaveenBalaji that's very mathematical
Probably not a good introduction at all

5:53 PM
@NaveenBalaji I never read that one

I'm surprised and physicist would seriously recommend that as an introduction

my favourite QFT books are Weinberg, Itzykson&Zuber and Zinn-Justin
those are great, but they don't really work as introductions
you have to have read some other book first

Weinberg is pretty bad for an intro

Just a prof I know, never specified that I'm looking for an 'introduction', that might be the reason for that recommendation

Schwartz is fine for an intro

5:55 PM
^

Or Peskin-Schroeder

meh
I never liked that one

it's not that great but it's fine as an intro

they introduce a lot of crap that I dont find useful
who cares about creation and annihilation operators anyway
they are useless

again, any book that solely talks about the physical significance without math, just to supplement what I'll be doing in class.

5:58 PM
sorry, I dont really care about physical significance
Im not sure what that even means!
just learn the math, thats the important part
the physical significance is irrelevant

lol! Really?

yeah lol

Well then I guess QFT ain't all that famous like GR for fiction to be based upon it...

@AccidentalFourierTransform whaaat

@Slereah I bet it works better if you use a limit of lossy oscillators.
And then put the limit of the loss to zero after the infinite space limit.

6:02 PM
But that is renormalization :O

@Slereah Are you serious?

Well, regularization, anyway

^ that

oh no
no no no

It's the whatchamacallit regularization

6:03 PM
Yes, this is a standard trick in my field. I wasn't sure it applied to QFT, but I suspect it does.

and he writes $\mathrm i$ for the imaginary unit
disgusting

@AccidentalFourierTransform instead of $i$?

What a bastard.

indeed
just because of the $\mathrm i$

6:04 PM
Ah, I think it's the heat kernel regularization

lets see what metric convention they use
if its the bad one, Ill buy the book and burn it

lel
IIRC most QFT books use $(+---)$

Zeidler is a 3 volume discussion of QFT, absolutely no intro course would use that, few intro courses would ignore creation and annihilation operators, should use a standard book like Peskin, or Maggiore, or Ryder or Mandl or Zee, or all of them and more, books like Zeidler and Weinberg later
haha that's the good metric

How do you Wick rotate $(+---)$

you dont
we have been over this already!

6:07 PM

wick rotations are idiotic

At the end of the day, just banging your head off the wall with Peskin is the safe choice, Maggiore can help with it

Feb 16 at 16:04, by AccidentalFourierTransform

Ban @AccidentalFourierTransform

haha
Peskin even has a nice cover

6:09 PM
Schwartz has a cover that looks like "I painted it myself"
Except not as good an artist as Spivak

@Naveen you mentioned while back you were looking into CERN/ LIGO internships, wondering did you have any luck with that?

what a terrible book
$m_0$ for the mass

(bare mass)

no, rest mass
they write $\Delta E\Delta t\sim \hbar$ and call it a "magic formula"

that is quite an odd choice

6:12 PM
more than two hundred pages of history and basic facts about particle physics

@vzn Oh yeah, LIGO, I didn't apply cause I was not at all hopeful. CERN, on the other hand, I might just get the theoretical physics internship for June-July-August, as I got a mail of confirmation.

they dont even set $\hbar=1$
why LIGO? who cares about gravitational waves?

@AccidentalFourierTransform has quite an attitude

Lol, I thought GW was the shit.

no, they're crap
GR is crap

6:19 PM
Yeah, I had a look at it, immediately deleted the soft copy
If GR is crap, then what is 'good', just asking

Yo 10k'ers, look at this bizarre shit
20 questions with bounties that later got deleted

@NaveenBalaji Our lord and saviour Jesus Christ is Good.
@EmilioPisanty well, some of them are crappy questions anyway
not all of them though, some are good

Zeidler looks like a pop-sci book for people who know qft, maybe that's bad but that's my impression

vote to undelete

@AccidentalFourierTransform haven't actually looked at them

6:26 PM
@bolbteppa at least they use the correct metric, -+++

Please don't tell me you are one of those creationists...Hopefully that was a joke

@NaveenBalaji very cool, congratulations. any idea what area of CERN? are you studying QM? what areas? are you in india? btw we have a guest spkr series, plz let me know if you have any interest :) physics.meta.stackexchange.com/questions/7783/…

I NEVER JOKE ABOUT THE SON OF GOD AND NEITHER SHOULD YOU

Cartoons don't lie, especially about metrics

@vzn theoretical physics, of what I was informed. Yup Indian