So, once you have that last equation from wolframalpha you've got it, right? Log[Cot[u]+Csc[u]]=Log[(Cos[u]+1)/Sin[u]]. Use the half angle formula on (Cos[u]+1)/2 and factor out the sqrt as a constant.

shit I forgot about that formula

And then... do the same on the bottom? I didn't plan that out...

do something to fix the bottom.

well that's trivial then

use properties of logs to break it up

thanks

The half-angle formula is an easy one to forget :(

err

I'm bad at algebra, gimme a moment

all the trig identities are easy to do if you switch to exponentials

oh yeah that's how you fix the bottom. You use the sin[2(u/2)] identity on the bottom and the cos[2(u/2)] identity on the top.

@Qmechanic @DavidZ @dmckee: Sorry, I'm still confused about the res. rec. questions. I thought they weren't made CW anymore, so I've started to VTC them as primarily opinion-based or too broad on sight because I don't think people should derive rep from those questions. But Qmechanic keeps making them CW, while DavidZ doesn't, and dmckee seems to abstain from acting on those questions. Should we have a new discussion on meta about how to treat these questions?

@NeuroFuzzy err, I end up with extra factors of $2$ inside of the logs

@0celo7 but that's fine b/c of the +c

ahhh

thanks

actually it's not even that

it cancels when I put the logs back together again

derp

done, finally

@FenderLesPaul You could have prevented this...

All you had to do was sing a simple song...

@ACuriousMind : Let me note for later that e.g. MO.SE does still create CW posts.

@ACuriousMind yeah, a meta post might be a good idea. It will get us to decide on a consistent course of action quicker.

Interesting that the link provided by Qmechanic to MO asks me if I'm a robot...

@0celo7 prevented what?

One controversial meta post, coming up...

FWIW my position is that, since suggested edits were implemented, there is almost no valid use case for CW mode anymore.

@FenderLesPaul A library donation.

All you had to do was sing a song.

@0celo7 I don't believe you

I'll sing

and so you see

I have come to doubt

all that I once held as true

I stand alone without beliefs

the only truth I know is GR

bam

do GR

Is GR even science

yes

well according to Bajoran I'm not a scientist, so...

idk who that is

can't be doing science

@0celo7 Do you doubt Einstein and the Evidence™?

I do, in fact

I think spacetime is made out of bunny rabbits; Kip Thorne said so

@FenderLesPaul Bajorans are a race of aliens in Star Trek (particularly DS9). I have no idea why 0celo7 is talking about them, though.

Because no one can pronounce your name!

@FenderLesPaul See specifically this.

@yuggib No no no no no, it's rather the converse: The theory is a model of the world.

@Rigor lol

> Being in its infancy, QFT is unlike SRT, GRT, and QED

Implying QED$\not\subset$QFT

@0celo7 No, $\tan x = (\cot x)^{-1}$

The inverse is not in the argument. Basically, all those trig functions that start with co- can be completely forgotten/ignored, because they are just (normal trig function)^{-1}

(...except cosine, haha)

@DavidZ I think there is, for the sake of having useful things that people shouldn't be getting rep for

@Danu Actually I think @0celo7 is referring to inverse trig functions, in which case his stated identity is correct

i.e. arctan(x) = arccot(1/x)

strange but true

@0celo7 His name is very common in Europe

@MarkMitchison Hah okay

Not very strange, I guess: $\tan x = y=1/(\cot x)$

@Danu that's precisely the reason I don't think there's a valid use for CW. There's no such thing as a useful question that its author shouldn't be getting rep for.

@DavidZ Hmm, I disagree, I think. Haven't thought about it very deeply.

...so $1/y=\cot x$ and hence $\operatorname{arccot}(1/y)=x=\arctan y$

But thanks for pointing out that he was talking about that (and sorry @0celo7 for misunderstanding what you were saying)

Also hey @DavidZ, how are you?

tired, at the moment... it's 7 AM here :-P

I haven't been able to sleep

Ah, okay. Why not?

I recently had a similar experience (and complained about it here, of course)

Personal stuff, I wouldn't want to bother the room with it

I just have a lot on my mind

@DavidZ Oh, damn :( I'm definitely up for hearing you out if you'd like to get it off your chest or something, but I understand if you don't wanna talk about it.

I've never had something so bad that I really couldn't sleep at all. I hope you're okay.

Really, never? Lucky you... it happens to me all the time

@DavidZ Seriously? Man, that sounds heavy :\ Or does it mean that maybe it ain't so terrible, you just don't sleep much?

@Danu well, at this point I would like to maintain a buffer between SE and my real life. Thanks for the thought though.

@DavidZ I understand

How is your professional life? Still "meh" about the work you're doing in China, or are you feeling better about it?

(this is one of the few distractions I have that hasn't been "infected" with personal stuff)

@Danu Probably some of both? I guess it always seemed fairly normal to me to have something on my mind that keeps me up until the wee hours of the morning a few times a week

@Danu not really better. Still planning not to continue in physics after this postdoc ends.

@DavidZ wow, a few times a week?!?!

And as much as China is interesting, I much prefer the US for the long run

@DavidZ I didn't know that. Not interested in trying out some different subfield?

I cannot imagine having anything that really keeps me up all night (except certain... good things)

@Danu yeah... well, FWIW my normal sleep schedule has me up until 4 AM, so staying up until 7 is not so much of a stretch. Going a full night without sleep is still exhausting of course.

@Danu yeah, lucky you :-P have fun with that

@DavidZ all of my wat

@Danu if you mean a different subfield of physics, that's not an option

Staying up beyond 2:30 is not nice

@DavidZ Why not?

I'm not really trained for anything too different - I couldn't switch into gravitational physics or something like that - and even within HEP they want people who have experience in the precise field topic they're going to work on as a postdoc/professor/whatever

@DavidZ I'm not saying something as drastic as gravitation, but surely you could have some interesting thoughts on QCD-related things

I dunno, I rather doubt it

Maybe gauge theories more generally, or even different aspects of QCD (I think there are many unresolved things)

I can't even come up with interesting thoughts on my own research :-P

@DavidZ Aw, don't be so harsh on yourself---it may be a matter of a bit more time or just a change of scenery (or even a holiday!)

...or reading some new book, article, whatever

I think many researchers can (and do) have less fruitful periods for a few years

Exhibit A: I was rejected from one postdoc in nuclear particle physics because my research interests weren't compatible with the position they were looking to fill. The postdoc was on something like parton distributions in mesons, whereas I work on small-x gluon distributions in baryons and nuclei.

@Danu when they have tenure, sure. Having a less fruitful period before then just means you get replaced with someone else who doesn't.

It doesn't have to be so drastic

@DavidZ I have a hard time judging what that means (or what any of those words mean :P)

Basically, they were looking for someone who studies nearly the same thing I do, just in different particles

Okay. Well, a single rejection should probably not be ascribed to something systematic

(although, of course, I imagine it is quite discouraging)

To be clear, I'm not inferring the reason for the rejection - I was actually told that my research interests weren't in the right area. It's one of the very few that I got feedback on.

@DavidZ Yes, but even then that doesn't mean that you won't be able to get a similar position somewhere else

(but yeah, that does suck :)

The odds are against it though

Do you have any ideas what you'd like to do outside of physics?

Probably data science, or maybe software development

@DavidZ Alright. Keep your head up, and your eyes open for unexpected opportunities, I guess.

yeah, I'll work on that ;-)

@DavidZ A positive attitude can really go a long way sometimes (as stupid as it sounds)

I don't think I'll be lacking for opportunities - that stuff is basically what I do at work anyway, and I've got friends who are willing to put in a good word for me at some major tech companies if the chance comes up

@DavidZ That's very good to hear

I often think about "what if I don't end up in academics"

Hopefully the reality turns out to match the expectation

Honestly, the advantage of being in academia is that you get to work on something you love (assuming you do love it, but I guess that's why you're here), you get a lot of flexibility in how you do that work, and you get that sense of moral superiority satisfaction that you "made it" through the pipeline. Other than that, non-academic jobs seem better in almost every way.

@DavidZ Sounds about right

The "love it" factor is pretty much all that matters in my (still naive) opinion---I guess we'll see how it turns out for me in about 5 years

Yeah, we'll see. Good luck!

It takes luck, too. A lot of totally qualified people don't get to go into academia simply because there are so few jobs.

Let's see if I can get some sleep now

@DavidZ Best of luck on that

I should too... but Federer is playing

@DavidZ take care brah

haha :-)

see y'all