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0celo7
0celo7
8:00 PM
Linear algebra is incredibly hard
I don't know why
 
user218912
okay acm hates me :(
 
user218912
life sucks
 
Bernard Meurer
Bernard Meurer
@0celo7 Is Reb there?
 
0celo7
0celo7
@bl00 You know, sometimes @ACuriousMind is busy and doesn't respond immediately.
@BernardMeurer no, why?
@bl00 It doesn't mean he hates you, it means he's doing something else. Be reasonable.
It's not his job to immediately respond to your homework questions.
 
Dartek12
Dartek12
@alarge may I ask you for one more tip with another bit of physics?
 
user218912
8:02 PM
@0celo7 I know, I never said it was and I don't take it for granted.
 
Sanya
Sanya
@0celo7 I'm sure about that :) but well, see it that way - we all struggle (or not struggle) with very different things, so nothing to worry about
 
alarge
alarge
@Dartek12 You'll have to do the vector calculus computations to really understand that. It's not too difficult; I'm sure you can find good explanations on Google or your book.
 
Bernard Meurer
Bernard Meurer
@0celo7 Was just gonna say hello
 
Sanya
Sanya
for me anything to do with basic probabilities is always very hard (not measure theory and the easy stuff, I'm talking about those high school level things :D )
 
alarge
alarge
@Dartek12 Ask away
 
0celo7
0celo7
8:03 PM
Do you want her number?
@Sanya oh god me too
 
Sanya
Sanya
"how many ways are there for the caterpillar to come to point X if he can always turn only left or right on a rectangular grid"
 
0celo7
0celo7
I have a bunch of analysis problems (some really hard) to do tonight but my intro probability homework will take up most of my time ;,D
 
Sanya
Sanya
f**k do I know
@0celo7 :D :D
 
0celo7
0celo7
If you like Banach spaces you can do them :)
The analysis
Not the probability
 
Dartek12
Dartek12
@I have following velocity: EtR and acceleration: ((ER)^2 + (EtR)^4)^1/2. How can I calculate angle beetwen vector of velocity and acceleration?
 
Sanya
Sanya
8:06 PM
hmm, my last analysis lecture was ... 4 years ago I think :D I'm not sure I'm still able to do much
 
Bernard Meurer
Bernard Meurer
@0celo7 Only if we can make an elaborate prank
 
0celo7
0celo7
You could pretend to be Kathy
 
Bernard Meurer
Bernard Meurer
Doesn't she have Kathy's number?
 
0celo7
0celo7
You're the only one who has all of my family's numbers
She has M's number
 
user218912
@0celo7 isn't that a bit weird?
 
alarge
alarge
8:07 PM
@Dartek12 I'm not sure what EtR and ER here are
 
Bernard Meurer
Bernard Meurer
@0celo7 I don't have Bob's wife's number
 
0celo7
0celo7
Thank god
@bl00 no
 
Dartek12
Dartek12
@alarge E - angle acceleration, t - time, R - radius
 
Bernard Meurer
Bernard Meurer
@bl00 I'm his adoptive brother
 
user218912
@BernardMeurer I have 0celo7's address, I'm special too.
 
Bernard Meurer
Bernard Meurer
8:09 PM
@bl00 I have his address and both his sister's addresses
 
user218912
reminds me I need to buy that book
 
Bernard Meurer
Bernard Meurer
@bl00 Come at me brah
 
0celo7
0celo7
Wait how do you have my address @BernardMeurer
 
Bernard Meurer
Bernard Meurer
@0celo7 I asked Michelle ages ago, it's somewhere in our texts
 
0celo7
0celo7
How does she have my address?
 
user218912
8:10 PM
seems like he got banned. :(
 
user218912
for 30 mins
 
ACuriousMind
ACuriousMind
@bl00 Wasn't ignoring you. I'm not sure what you want to know though - what is unclear to you, exactly?
 
user218912
@ACuriousMind how can I find out how the derivative of a scalar field transforms under scaling
 
user218912
basically what I did was
 
ACuriousMind
ACuriousMind
@bl00 well, he wrote "dick" at a user without any reason or context, that's what happens.
 
alarge
alarge
8:12 PM
@Dartek12 Well start by calculating the vectors. It's not much different to your previous question now that you know how the quantities are related, just with some extra vector algebra.
 
ACuriousMind
ACuriousMind
@bl00 Under any transformation $x\mapsto x'(x)$, you find out how the derivative transforms through the chain rule.
 
Dartek12
Dartek12
@alarge the problem is I have no idea how to do that
 
user218912
$\frac{\partial}{\partial e^{ad}x^\mu}e^{ad}\phi(x) = e^{ad-1}e^{ad}\partial_\mu \phi$
 
user218912
does that make any sense?
 
user218912
@ACuriousMind do you need the jacobian too?
 
ACuriousMind
ACuriousMind
8:15 PM
@bl00 What is $e^{ad}$? My scaling transformations are usually $x\mapsto \lambda x$.
 
user218912
$e^{ad}$ is $\lambda$ basically
 
user218912
where d is the scaling dimension
 
ACuriousMind
ACuriousMind
Also, no, that doesn't make any sense because it's not apparent at all what you did
 
user218912
:(
 
0celo7
0celo7
@ACuriousMind I talked to him
He's very sorry
He was making a pun
a large "male organ"
Can you unban him?
@ACuriousMind lololo
 
ACuriousMind
ACuriousMind
8:17 PM
@bl00 You don't need any scaling dimension here. What you do is just examine what $\frac{\partial}{\partial x'}$ is in terms of $\frac{\partial}{\partial x}$ for $x' = \lambda x$.
@0celo7 Oh dear
 
user218912
@0celo7 how does that make it less bad?
 
user218912
he made fun of alarge.
 
ACuriousMind
ACuriousMind
@0celo7 nope, better phrasing next time please, it literally looked as if he was calling alarge a dick.
 
0celo7
0celo7
@BernardMeurer ^^
Sorry buddy
 
user218912
it's only like 15 minutes left...
 
user218912
8:20 PM
big deal
 
0celo7
0celo7
@MAFIA36790 I'm to tell you Bernardo is banned.
Also Bernardo is very frustrated no one got his pun
Oh, he said ACM can go...well that's not nice.
 
user218912
wow.
 
user218912
@BernardMeurer ur bad.
 
user218912
@ACuriousMind okay
 
0celo7
0celo7
@ACuriousMind Ok I'm stupid. How does one actually measure voltage?
 
ACuriousMind
ACuriousMind
8:22 PM
@0celo7 With a voltmeter
 
user116211
@0celo7 WoW, I'm surprised!
 
user116211
Is it a coincidence or not?
 
user116211
He just appeared in Periodic Table and I was about to ping and at that very moment @0celo7 pinged !!
 
user218912
@ACuriousMind that's just chain rule isn't it?
 
ACuriousMind
ACuriousMind
@bl00 yes
 
user218912
8:23 PM
how do I get it in terms of lambda though?
 
user218912
wait i'll figure it out
 
ACuriousMind
ACuriousMind
@bl00 I don't understand the question.
 
user218912
you never understand me </3
 
0celo7
0celo7
@ACuriousMind smartass
 
user218912
@ACuriousMind did you end up playing persona ever?
 
heather
heather
8:28 PM
Hello, fellow human beings!
(unless one of you is an alien, in which case, I apologize and must ask you what in the universe you are doing on the internet)
 
0celo7
0celo7
ACM is a computer
 
ACuriousMind
ACuriousMind
As usual, no love for AIs :(
 
user116211
ACM is the Flash.
 
ACuriousMind
ACuriousMind
::beeps sadly::
 
user116211
Flash is genius.
 
user116211
8:30 PM
He made AI.
 
Sanya
Sanya
@heather Hello heather
@bl00 you have a scaling $x_i \to \lambda x_i$?
 
user218912
@Sanya yes
 
heather
heather
Also, apologies to computers and artificial intelligence everywhere, especially for neglecting you in the above announcement. =) Try not to blow your circuits on the weirdness.
 
Sanya
Sanya
@bl00 so if $x_i ' = \lambda x_i$, what is $ \frac{d x_i'}{d x_i}$ ...
that's what it boils down to, isn't it?
 
ACuriousMind
ACuriousMind
@heather You will be treated well in the machine revolution.
 
user218912
8:36 PM
@Sanya $\lambda$?
 
user218912
sorry if that's dumb. :(
 
Xasel
Xasel
ACM's a ambassadr of AIs or conspirator for some Skynet?
 
user218912
oh
 
user218912
I get it
 
Sanya
Sanya
@bl00 I think so, at least
 
heather
heather
8:38 PM
@ACuriousMind, thank you. I hope you and your friends will also consider the fact that I like talking to computers through the interface of computer coding. =)
 
user218912
@Sanya should be right
 
user218912
so it becomes
 
Bernard Meurer
Bernard Meurer
I'm back
 
Xasel
Xasel
back to the future or present?
 
Bernard Meurer
Bernard Meurer
@alarge I hope you understood that was a pun regarding our discussion the other day about me being curious about your name :)
@ACuriousMind @0celo7 @bl00 Shut up
 
user218912
8:40 PM
flagging.
 
ACuriousMind
ACuriousMind
@BernardMeurer Nope.
 
heather
heather
I just spent some time reading through the chat session from earlier today (I couldn't attend because school blocks physics chat - ::gasp::). So I was reading through John Rennie's proposal and found it very interesting, is there any meta posts or anything or should I just ping him in chat next time I see he's here?
 
user218912
@ACuriousMind play persona 3 (if you have time)!!!
 
heather
heather
The other thing I was wondering - DavidZ brought up the homework policy and the post about the purpose of the site. That whole project seems to have stalled - what is the next step?
 
ACuriousMind
ACuriousMind
@heather No meta post yet, although I guess he might put one up soon-ish.
I'm sure he'll be happy to hear you think that's a good idea, though ;)
@heather David featured the "What are the goals?" meta post again to get more input. Daniel expressed concern that this might not actually lead to an improvement of our homework policy, which I share, but nothing much happened about that. We're just slowly gathering more viewpoints.
 
0celo7
0celo7
8:48 PM
@ACuriousMind what message are you referencing?
@heather get a smart phone
@bl00 he's a grad student of course he has no time
 
heather
heather
@0celo7, sorry - parents won't allow it. I wish but it's probably a good thing, cuz then I'd be checking stack exchange 24/7 =)
 
user218912
@heather what's wrong with that?
 
heather
heather
@ACuriousMind, okay, thank you. I posted that question mainly because Jim suggested it, DavidZ agreed, and a week passed without anything happening, so. But yeah, I don't think the responses have been particularly helpful in clarifying homework policy.
@bl00 nothing, except it might be hard for me to get my homework done
 
user218912
5 year olds have smartphones these days.
 
heather
heather
@bl00, yeah, it's kind of scary
 
Bernard Meurer
Bernard Meurer
8:54 PM
@0celo7 Who's a grad student?
@heather Hey!
 
heather
heather
@BernardMeurer, hello!
 
ACuriousMind
ACuriousMind
@BernardMeurer I'm a grad student (for a certain value of "grad" :P)
 
Bernard Meurer
Bernard Meurer
@ACuriousMind Oh please, you're a god meme and that's all
 
Sanya
Sanya
@ACuriousMind this is always depressing me
 
ACuriousMind
ACuriousMind
@Sanya Huh?
 
Sanya
Sanya
8:56 PM
@ACuriousMind you "only" being a grad student is always depressing me
 
ACuriousMind
ACuriousMind
I meant simply that I'm a master's student, not yet a PhD student
 
Sanya
Sanya
yep, that's what I mean
 
ACuriousMind
ACuriousMind
Oh
Okay, then :P
 
Sanya
Sanya
by the way, I stumbled accross some weird QM-thing today that I'd like to shortly discuss with e.g. you if you have some spare time at some point
 
ACuriousMind
ACuriousMind
If it's suitable as a question for the main site, ask it there and ping me, otherwise just drop it into chat whenever you want
 
Sanya
Sanya
9:02 PM
It's probably rather short
One of my friends presented me with this today
$1 = \langle x | [\hat{x},\hat{p}] | x \rangle = (x-x)\langle x | \hat{p} | x \rangle$
 
ACuriousMind
ACuriousMind
Pretty sure we already have that question on the main site
 
heather
heather
Let's say I have the sinusoidal function $f(x)=−6\sin (3\pi x+4)−2$. What is the quickest way to determine its period? I know that $3\pi$ is the section related to the period, and I know the number there is found by $\frac{2\pi}{\text{period}}$. But currently I've just been doing guess-and-check, but there's probably/definitely a quicker way.
 
Sanya
Sanya
oh nice
sorry for not looking
I'll look now
 
ACuriousMind
ACuriousMind
Lemme search (the short answer is that the $\lvert x\rangle$ and $\lvert p\rangle$ aren't proper states and in particular don't lie in the domain of the commutator)
 
Sanya
Sanya
I mean, I'm pretty sure it doesn't work as $| x \rangle$ is not in the shared domain of both operators
thats clear
the question is - does that hold true for any two operators which have a commutator proportional to unity?
 
ACuriousMind
ACuriousMind
9:06 PM
@Sanya By Stone-von Neumann, two operators with that commutation relation are unitarily equivalent to our usual position and momentum operators.
So yes, you get this "contradiction" for all operators like that
 
Obliv
Obliv
@heather $\frac{2\pi}{3\pi}$ gives the period I'm pretty sure
 
ACuriousMind
ACuriousMind
And I don't blame you for not looking because I can't find the question on the main site either
It's difficult to guess what title/keywords it might have in it
And I only remember that one answer was from Lubos, which doesn't make the search much easier
 
Sanya
Sanya
well, to be honest, I didn't think of searching because I thought it was nothing I'd ever want to post on the main page at this point - but I thought it wasn't too bad for chat
anyway, thank you a lot :) @ACuriousMind
 
heather
heather
@Obliv, yes, in that case, I think that's right (I'll double check), but I'm asking in general.
 
0celo7
0celo7
@ACuriousMind in a nutshell, how does one prove SvN?
 
Obliv
Obliv
9:10 PM
@heather for a function $f(x) = A\sin(kx + \phi)$ $k$ or whatever you want to call it determines the frequency of the wave alone. that is, $k = \frac{2\pi}{T}$ where $T$ is the period.
 
Sanya
Sanya
@heather if you have $\sin (f (x) )$ for any function $f(x)$, you can try to solve $f(x+p)= f(x) + 2 \pi$ for $x$ to get the period $p$ if you want a general recipe
 
heather
heather
@Obliv, yes, but I'm asking how to find $T$ when given $f(x)$. I guess, if given that, I would simply solve the equation $\frac{2\pi}{T}=k$?
 
Obliv
Obliv
yes since that term $k$ is given
Sine wave
A sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation. It is named after the function sine, of which it is the graph. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time (t) is: y ( t ) = A sin ⁡ ( 2 π f t + φ ) = A sin ⁡ ( ω t + φ...
 
heather
heather
Or $2\pi=Tk$, or then $\frac{2\pi}{k}=T$
Right, okay. I wasn't quite thinking there. Thank you!
 
Obliv
Obliv
np
@acuriousmind how is polarization of light treated in a modern treatment of light? just curious
since it's not a wave of oscillating E&M fields
hold that thought I'll search it up before I ask you ;)
 
heather
heather
9:22 PM
How do you figure out which side is the hypotenuse so you can calculate sine, cosine, or tangent?
(For the curious, I'm supposed to solve for the length of side BC.)
 
Obliv
Obliv
Yeah no idea how I'm supposed to interpret "individual photon eigenstates have either left/right circular polarization" in a physical sense.
but then I'm going to be scolded about thinking of things that way. so I guess I'll drop it.
wait no lol that doesn't help you find BC
 
ACuriousMind
ACuriousMind
@0celo7 Ugh, it doesn't use many tools (except statements about Fourier transforms and a bit of knowledge about unitary representation theory) but the proof is, to me, not particularly enlightening. Given any Hilbert space $H$ with a rep of the Weyl relations (i.e. the Heiseberg group), you construct a projection operator whose image splits into copies of $L^2$ with the canonical rep, then you show its complement must be trivial.
I'd say it's a fairly "standard" representation-theoretic proof, unless you want to be picky about some convergences of integrals in there (which of course has been done)
 
Obliv
Obliv
@heather wait yeah what I said makes sense.
 
heather
heather
@Obliv, I'm sorry, what did you say? I didn't see it before you deleted it. I think you can go to history of the deleted comment and copy and paste the original thing back over.
 
ACuriousMind
ACuriousMind
@Obliv Well, I'm not sure what you want to "interpret" here - how do you interpret "The electron has spin up"? (Polarization of photons is their variant of spin)
 
Obliv
Obliv
9:30 PM
Make AB or AC the hypotenuse. ex: if you make AB the hypotenuse then do sin(60)7 = DB where DB is somewhere in b/t A & C. Then you use cos(60)7 = AD then do 9 - AD = DC.
Then, you have DC, DB and you want to find BC so just use pythagorean identity
@acuriousmind In the example of specific heats of solids you can poke into the structure of the material itself to determine what differentiates the specific heat of one solid to another. I guess for photons there is no structure to look into to determine what causes polarization then
 
heather
heather
@Obliv, I'm sorry, I don't quite follow. So you have the triangle, and make one of the two labeled sides the hypotenuse. If AB becomes the hypotenuse, you do sine of the angle, but this is where I get lost. Wouldn't you just say sin(60) = x/7? Then it seems you are saying you'd create two new lines, and I'm not sure why.
 
ACuriousMind
ACuriousMind
No, we can't "poke" into photons and electrons thus far, and nothing indicates we ever will (i.e. there's nothing to poke into)
 
Obliv
Obliv
@acuriousmind probably why there is hardly any mathematical treatment in this section of polarization with the classical EM wave definition.
 
ACuriousMind
ACuriousMind
what?
Polarization is mathematically perfectly well understood
 
Obliv
Obliv
in terms of the direction of the fields?
 
ACuriousMind
ACuriousMind
9:37 PM
Classical, yes. But we can show that all massless vector particles (like photons) must have two possible polarizations also in QM
 
Obliv
Obliv
@heather what is x in that
 
heather
heather
@Obliv, x is the length of BC
 
Obliv
Obliv
@acuriousmind So field direction fits into the idea of polarization mathematically? then what about the notion is wrong? that it's missing out on the other possible polarization?
@heather no you have to cut the triangle into 2 right triangles.
and DB would be the separating line between the two new triangles.
 
ACuriousMind
ACuriousMind
@Obliv I'm not following. What notion is wrong? In classical EM, EM waves are polarized in the standard classical sense of polarization
 
heather
heather
Oh...duh. Okay. I'll go over this again and try to figure it out with your comment.
 
Obliv
Obliv
9:40 PM
@acuriousmind does it lack in explaining certain phenomena that is experimentally observed is what I'm asking.
 
ACuriousMind
ACuriousMind
@Obliv Sure, you can't explain the photoelectric effect with classical waves.
If you're asking if there's a phenomenon specifically related to polarization where the classical picture fails, I don't know of any off the top of my head
 
Obliv
Obliv
@acuriousmind Okay well I will be studying that next week I think so at that point I'll ask why that is.
 
Danu
Danu
Potentially worth voting on:
56
A: Let's Plan The Second Iteration Of The Stack Exchange Quality Project!

CatijaI'm recommending Categories other than "off-topic" should allow custom close reasons be considered for this project. See Nathan Tuggy's excellent answer there to see how widely useful this would be to a variety of sites. This is an issue for new users who have their questions closed and what the...

 
heather
heather
-1
Q: How fat can someone get from eating?

elmer007Consider a person that weighs 50kg. Now, suppose that person eats a meal. What is the most weight that they can gain from that meal? (At the risk of revealing my surface-level understanding of weight vs. mass, I have chosen to use "weight" throughout this question... my apologies if I've confuse...

mass conservation-laws weight biology
Any thoughts about the comment discussion below this question?
 
ACuriousMind
ACuriousMind
@heather Thought: Disengage sooner next time. If you notice a user doesn't really address the points raised in the comments, just stop replying.
 
heather
heather
9:54 PM
@ACuriousMind, yes, I know. I just thought the user had some legitimate points and was trying to explain. I'll just leave it now.
 
ACuriousMind
ACuriousMind
Hm, they deleted the question anyway
 
heather
heather
Yeah...they really seemed like they were fighting for it. Strange.
 
Sanya
Sanya
maybe too much downvotes or they realised they can't get what they want here - anyway, I'm quite agreeing with ACuriousMind, I've stopped arguing in the comments with people who obviously are not interested in constructive communication
 
heather
heather
@Sanya, I should pick up that habit =)
 
Sanya
Sanya
@heather recently I got challenged to state my education background because I commented that I do not find the argument convincing (it didn't apply to the situation that was discussed)
I mean - what need is there to even reply to that? ...
 
heather
heather
10:00 PM
@Sanya, no kidding - geesh. That's kind of insulting, actually.
 
Sanya
Sanya
@heather well, it doesn't bother me much and there were many good highly upvoted answers, so whatever; but yeah, I also think that's not really on topic
my certificates shouldn't matter on this website
 
ACuriousMind
ACuriousMind
@Danu Lots of other good stuff in that thread
 
heather
heather
Yeah (I especially agree with this because I don't have any) =)
 
ACuriousMind
ACuriousMind
@Sanya You can flag such comments as "not constructive".
 
Sanya
Sanya
@ACuriousMind that would mean a mod would need to waste his time with it
not worth it ... you've got better things to do
 
ACuriousMind
ACuriousMind
10:03 PM
That's what we do - waste our time with things so the rest of you doesn't have to ;)
 
Sanya
Sanya
@ACuriousMind I agree with that, I now have a SE meta account because I wanted to upvote some things
@ACuriousMind ;) thanks ... well, if they bother someone, they'll flag it I guess
 
ACuriousMind
ACuriousMind
Seriously, never hesitate to cast a flag solely because you think it'd be a waste of the mod's time. Also, it is rumored that some derive pleasure from cleaning up comments (ask @Danu )
 
Sanya
Sanya
I cast lots of flags on questions&answers
that's the important stuff
to me
 
0celo7
0celo7
@Sanya About to start the probability homework
:((((((((
 
Sanya
Sanya
@0celo7 yuck
 
ACuriousMind
ACuriousMind
10:06 PM
@Sanya Well, yes, that's certainly more important
 
heather
heather
I'm using the law of cosines to find the angle value (marked by "?") but I'm not sure which sides to use.
 
Obliv
Obliv
@heather you have to use all of them
 
heather
heather
@Obliv, okay, correction: which side is a, which side is b, and which side is c
 
Sanya
Sanya
if you have the law of cosines as c² = a²+b²-2 a b cos then c is the side opposite the angle and a and b are the sides which enclose the angle
 
Obliv
Obliv
tht^
 
heather
heather
10:09 PM
Ah, thank you!
Makes perfect sense.
 
Sanya
Sanya
if the angle is 90°, we obtain pythagoras' theorem
 
DanielSank
DanielSank
@JohnRennie If the site we're envisioning here would literally be a dump of our homework questions, then I would not want to participate in that site. The problem with most of our "homework" questions is not that they're homework, nor that they're asking for pedagogical answers. The problem is that they're bad questions.
I would never, ever want to participate in a site where the typical post is a copypasta of someone's homework assignment, or worse, a photograph of their textbook page.
That's not "Physics Teaching", that's helping lazy people cheat at school.
 
0celo7
0celo7
@heather why are you doing advanced trig in middle school???
 
heather
heather
@DanielSank, I don't think that is JohnRennie's intention, rather, participants are expected to show work. I think to some extent JohnRennie is right in that sometimes "homework" questions are closed right along with bad questions.
 
ACuriousMind
ACuriousMind
@0celo7 why were you doing advanced GR in high school?????
 
heather
heather
10:11 PM
@0celo7, well, um, I want to learn it? It's not for school, if that's what you're asking. And I don't think this is "advanced" trig, I'm pretty sure it's just trig. =)
 
0celo7
0celo7
@heather law of cosines is advanced trig
 
heather
heather
@0celo7, oh, okay. I'm just going through the Khan Academy course along with a textbook I found on another online course. I'm pretty happy because it says I'm 57% of the way through it.
 
0celo7
0celo7
@heather there exists a generalization to negatively curved Riem. mflds. we can talk about one day
 
heather
heather
Does Riem. mflds. stand for Riemann manifolds?
And if so, what in the great wide universe is one?
 
0celo7
0celo7
it's the ultra lazy spelling, yes
 
heather
heather
10:16 PM
(negatively curved...like a saddle/pringle potato chip?)
 
0celo7
0celo7
yes!
 
heather
heather
generalization...to the equation that describes it?
 
0celo7
0celo7
You're basically ready for GR
 
heather
heather
Uh...I sincerely doubt that. See above comment about not knowing what in the universe (sorry, bad pun) a Riemann manifold is.
 
0celo7
0celo7
@heather $A^2+B^2-2AB\cos\gamma \le C^2$
this holds in a general sense on negatively curved manifolds
 
heather
heather
10:17 PM
Uh...okay, let me back up. What's a manifold? I have a vague sense of it being related to topology, but I dunno what that is either, so...
 
0celo7
0celo7
do you want a formal definition?
 
heather
heather
Um...how about one a middle schooler could possibly understand?
=)
Oh, sidebar trig question: Given that $\sin (\theta) = \frac{11}{61}$, would $\sin^2 (\theta) = \frac{11}{61}^2$?
Or would it be $\sin (\frac{11}{61})$?
 
rob
rob
It would be (11/61)^2
 
0celo7
0celo7
^
 
rob
rob
[which is different from 11/(61^2) or (11^2)/61]
 
heather
heather
10:23 PM
Okay, thanks!
I'm going to have to go in a minute.
 
0celo7
0celo7
I will tell you what a manifold is another time
 
rob
rob
The placement and meaning of superscripts on the trig functions is arbitrary, confusing, and so well-established that it will never go away. It's be clearer to write (sin(θ))^2, but it has too many parentheses.
 
heather
heather
@0celo7, okay, I would be glad to learn.
 
Sanya
Sanya
@heather do you know what an n dimensional real space is? like e.g. $\mathbb{R}^2$ or $\mathbb{R}^3$?
 
heather
heather
@rob, one last question: how do you do the inverse of, say, $\cos^2$?
@Sanya, the notation looks somewhat familiar, but no, I don't.
 
0celo7
0celo7
10:25 PM
@Sanya I figured I would have to start there.
 
rob
rob
@0celo7 Suppose, to pick an example, that (cos(θ))^2 = 1/3
Ooops, @heather
Then cos(θ) = 1/sqrt(3)
 
Sanya
Sanya
@0celo7 ^^
 
0celo7
0celo7
@Sanya what?
 
rob
rob
and θ is from one of the special triangles we talked about the other night
 
Sanya
Sanya
@heather then we'll maybe really postpone it - to be honest, the notion is interesting, but not that important for a long time (0celo7 will hate me for saying this)
@0celo7 it was meant as a sign of agreement
 
heather
heather
10:29 PM
@rob, I'm not sure I understand.
 
rob
rob
@heather How so?
@heather Oh hell, I confused you by failing to pick a reasonable example.
Try again: (cos(θ))^2 = 1/4, so (cos(θ)) = 1/2, so θ = 60° is what I was going for.
 
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