The h Bar

@0celo7 okay I'm going to derive the lagrange multiplier eq. without looking into the notes logically and concisely. maximize $f(x,y)$ with a constraint $g(x,y)$. We know $\nabla f(u)$ is orthogonal to the level curve $f(u) = c$ where $c$ is a constant. Thus, if we can find the largest level curve $f(x_m,y_m) = M$ (m denotes maximal) that the constraint allows, it is a solution. We need $\nabla f(x_m,y_m) = n\nabla g(x_m,y_m)$ because at this maximum level curve (a point of intersection b/t f,g)

heather

Wait, timeout: what is a parametrization? And it is indeed an interesting rant.

0celo7

@Obliv wtf is this

@DanielSank Proof :P

Obliv

Their normal line must be the same. It need not be exactly the same (can vary with a scale factor) in the equation of a plane i.e $\nabla f(x) \cdot (x-u) = 0$ and $\nabla g(x) \cdot (x-u) = 0$

DanielSank

Now @heather note the following:
I) It is easy to check whether a given pair (x,y) is in this manifold because you just plug into the equation and see if it works.
II) It is hard to just randomly find a point in this manifold. To do so, you'd have to solve for x in terms of y.

0celo7

1:07 AM

Reb is studying this right how for a test tomorrow

Obliv

for some point $x$.

0celo7

you two should form a study group

DanielSank

Ok, now here's the other way to specify the circle, using a parametrization:

Obliv

@SirCumference are you referring to something specifically

Sir Cumference

@Obliv Nah

DanielSank

1:08 AM

$$x = r \cos(\theta) \quad y = r \sin(\theta) \quad \text{for }\theta \in [0, 2\pi)$$

0celo7

Honestly calling me hypersensitive triggers me

flagging

Sir Cumference

I never called you that...

heather

@DanielSank, wait, I'm not sure I follow this part.

Obliv

@0celo7 my test isn't soon I don't think. We'll be going over multiple integrals before it

Sir Cumference

@0celo7 *Hyperflagging

DanielSank

1:08 AM

@heather ok, I'll pause.

What's up?

0celo7

Sir Cumference

That should be a term

"Hyperflagging"

Flagging oversensitively

heather

So, you have those two equations, but I'm not sure about the last part, for $\theta \in [0,2\pi)$

DanielSank

@heather Oh, I'm saying that you should think of $\theta$ as going from zero to two pi.

That's one trip around the circle.

0celo7

don't think she has had trig

Sir Cumference

1:09 AM

@0celo7 You're showing her chain rule?

heather

Oh, okay, and then, hmm, okay, I think I get it now.

Sir Cumference

She doesn't know calc

0celo7

@SirCumference I'm showing @Obliv

Sir Cumference

Oh, nvm

DanielSank

@heather Oh wait, do you know $\sin$ and $\cos$?

user218912

1:10 AM

hello!

Sir Cumference

Hey @bl00

heather

@DanielSank, yeah. With the unit circle and the x and y coordinates and everything. I do have a general idea of basic trigonometry.

Obliv

@0celo7 wow. that is such an easy explanation my textbook sucks

what book is that

Sir Cumference

@bl00 The notes you gave me are actually pretty neat

Gotten over 25% through so far

user218912

awesome.

0celo7

1:12 AM

@Obliv Rogawski, it's what reb is using

user218912

@0celo7 I heard your eye was fucked up, did you see a doctor?

NO

@bl00 Wait what

STOP ASKING

@0celo7 You okay?

user218912

1:12 AM

first time I asked...

0celo7

NO I'M GOING BLIND

@bl00 flagging.

user218912

...

Sir Cumference

@0celo7 Flagged you for flagging

0celo7

I call BS

Obliv

if it's only in one eye it's probably not a big deal. You can trust me I'm a PhD

Sir Cumference

1:13 AM

How is that BS?

Flagging is very offensive to me

I take it quite personally

0celo7

Prove it.

user218912

@Obliv right......

Sir Cumference

@Obliv I don't think that's how it works...

0celo7

Show the flag

DanielSank

@Obliv He lost acuity in one eye suddenly. It could be something rather grave and frankly I think you shouldn't joke about it.

Obliv

1:14 AM

Just get a high powered laser from your lab and shine it in your eye. I think that was one of the treatment options I read on webmd

Sir Cumference

@0celo7 Here

0celo7

@DanielSank It's only distance vision.

Sir Cumference

There's your flag

DanielSank

Particularly because he has been living with in for several days without going to the doctor, which is a very bad idea.

0celo7

No time

Sir Cumference

1:14 AM

Or here

2

0celo7

Why isn't everything open 24/7???

Sir Cumference

That enough flags for you?

Obliv

@daniel What is the worst that could happen (joking aside)?

DanielSank

@SirCumference Hahahahaha

user218912

dude aren't u smart or something... just skip ur classes @0celo7

user218912

1:15 AM

no big deal

DanielSank

@Obliv The worst? He could go blind in that eye.

0celo7

@bl00 No, I'm stupid, so I go to class to appear less stupid.

Obliv

Yeah that is pretty bad. Modern medicine is pretty good though so I feel like he'll be okay.

that's just my feeling

user218912

@0celo7 you have low self esteem.

Sir Cumference

0celo, what's up with your eye?

0celo7

1:16 AM

I can't see past 4 feet

everything is totally blurry

Sir Cumference

In one eye or both?

0celo7

the whiteboard looks blank it's so blurry

@SirCumference one eye

also the eye hurts from time to time

Sir Cumference

@0celo7 You need to get that checked out

user218912

and it occurred suddenly?

Sir Cumference

Sounds like an infection

Obliv

1:17 AM

I remember on the old forum I used to use (for videogames) someone posted about how his brother got a blood clot in his leg and whether he'd be okay. They brought him to the hospital and people were really supportive about it and saying he'll be fine. Later that day he came back to post that his brother had died.

0celo7

yes I have a fucking appointment with an ophthalmologist

Obliv

That was a bummer.

heather

@DanielSank, I think I get the first part of the parametrization thing.

DanielSank

@Obliv I want you to remember I said this for the rest of your life: If you have a sudden change in health in any way, you do not just hope it's ok. You get your ass to a doctor as soon as possible.

user218912

@0celo7 sounds like an emergency to me.

user218912

1:18 AM

go to the ER

DanielSank

My father is recovering at home right now from a detached retina. Do you know what that means? It means his retina was coming off of the inside of his eyeball. If that gets too bad, you're blind in that eye. Modern medicine cannot save you.

This also happened to my brother.

In both cases, they caught it quickly and are ok.

0celo7

I can live with one eye

DanielSank

Because they went to the doctor.

heather

@0celo7, wrong response.

user218912

I feel like 0celo7 is trolling us now.

Sir Cumference

1:18 AM

@0celo7 That is not the attitude you should have...

0celo7

It's the only reasonable one

heather

Seriously! That reduces video-game playing efficiency!

user218912

"I can live with one eye?" seriously???

2

DanielSank

@bl00 Going around telling people they'll be ok because modern medicine is good is a terrible idea and you should stop doing that.

0celo7

I don't need to be playing video games

Obliv

1:19 AM

@daniel wow how common is it? Sorry about that :(

user218912

@DanielSank you mean Obliv?

heather

math and physics efficiency as well!

0celo7

@Obliv one of my parents has had itt

Obliv

is it genetic or smthn?

0celo7

@bl00 you two are the same color

DanielSank

1:19 AM

@bl00 Maybe. You're both blue. It's confusing.

user218912

lol

DanielSank

@Obliv Sort of. If you're myopic you're more likely to get it.

Sir Cumference

@0celo7 That's racist

user218912

we should all be blue

Sir Cumference

Flagging

Obliv

1:20 AM

Oh no.. I am near sighted..

0celo7

@SirCumference I hate blue people

user218912

@0celo7 wow

Sir Cumference

@0celo7 We'll build a wall between us and the blue people

0celo7

@DanielSank I'm probably just extreme near-sighted and just noticed it.

user218912

blue master race.

Sir Cumference

1:20 AM

And we'll make @bl00 and @Obliv pay for it!

0celo7

@SirCumference And make them pay for it

Obliv

@0celo7 that wouldn't be very surprising honestly.

0celo7

I mean

DanielSank

@0celo7 In one eye?

0celo7

I do have glasses

user218912

1:20 AM

I'd gladly pay for the wall if it was blue.

user218912

@0celo7 nerd :D

0celo7

But they basically don't work any more

@bl00 I never use them

Sir Cumference

@0celo7 They run out of battery?

@0celo7 Same

user218912

lol

0celo7

I'm 20/15 in one eye and like 20/30 in the other

It's a tiny correction

Sir Cumference

1:21 AM

I'm 20/60 or something

0celo7

But now I really cannot see at all

Sir Cumference

See a doctor

Obliv

I can't read 1 feet away from me.

Sir Cumference

No pun intended

0celo7

oh my god I am seeing a doctor tomorrow

can everybody just calm down

Obliv

1:22 AM

@0celo7 people care about you young ocelot.

heather

SEE A DOCTOR NOW BECAUSE THIS IS A BIG DEAL!!!!!! (sorry, but, you know, it is a big deal.)

Sir Cumference

@0celo7 AAAHHHHHHAAHAHHA

0celo7

unless of course I can't get there, which is a definite possibility

user218912

I am 20/20 and can read the lowest line of letters. I'm so cool.

user218912

B)

Sir Cumference

1:22 AM

@bl00 Privileged bastard

(jk)

user218912

and I stare at a screen for several hours a day in the dark so no your vision won't get worse by doing that.

user218912

I am proof.

Sir Cumference

@0celo7 Dude, go to the ER at this point

That sounds like a blood clot in your eye

0celo7

I hope it's cancer

Sir Cumference

Wtf dude

user218912

1:23 AM

wtf?

lol...

no seriously

no seriously, wtf?

people pity you so much if you have cancer

user218912

you want attention?

Sir Cumference

1:24 AM

because you can die

0celo7

@SirCumference oh, never thought about it like that

Sir Cumference

The cons kind of outweigh the pros

0celo7

hmm, yeah

ok never mind

Sir Cumference

that was...weird

Anyways

user218912

if 0celo7 dies I will fail qft, and then kill myself so we'll both die.

user218912

1:24 AM

btw I finished that problem from yesterday :D

0celo7

wtf

Sir Cumference

@0celo7 XD

I remember the new Ghostbusters movie, one of the women could create a device to catch ghosts because "no one knows quantum physics better than her"

That is just so cringy...

0celo7

so ACM?

Sir Cumference

Almost as bad as this

Obliv

that's why I don't watch sci-fi films. @sirC

pop-culture sci-fi anyway

Sir Cumference

1:27 AM

@Obliv The fact that they relate QM with ghosts is just so...

Dunno the word for it

user218912

well there are ghosts in qft.

Sir Cumference

@bl00 virtual particles don't count as ghosts

heather

@SirCumference, sad? disturbing? upsetting?

Obliv

theres also spectral theory

Sir Cumference

@heather screwed up is better

heather

1:28 AM

@SirCumference, hmm, yes.

0celo7

@heather do you wanna know what a topological space is

heather

@0celo7, sure, yeah!

Sir Cumference

@0celo7 Dude, one step at a time

user218912

@heather ummm... learning that won't help your understanding in any way

0celo7

ok

user218912

1:29 AM

just sayin

0celo7

metric spaces first

heather

@SirCumference, ah, going in order. Who cares. =P

0celo7

good point

@bl00 will tell you what a metric space is

heather

@0celo7, okay, sure. Anything is cool.

Sir Cumference

@heather From experience I've learned going in order is really the best

It ensures you won't miss out on much information

user218912

1:29 AM

@0celo7 what's the point of that?

heather

@SirCumference, yeah, I know. But sometimes I enjoy jumping out of order.

0celo7

@bl00 practice!

good woman

the order is for chumps

user218912

well isn't a metric space just a space with a metric so distances are defined?

0celo7

Precise definition please.

Sir Cumference

@0celo7 Who needs order? Chaos is far cooler

user218912

1:30 AM

idk more than that... i'm an experimentalist now.

user218912

experimentalists don't know anything.

0celo7

oh crap

we didn't define functions

heather

@bl00...um. Well. I'm not quite sure what that metric bit is.

0celo7

@heather Ok we need functions first.

heather

@0celo7, functions. Okay. @SirCumference, see, I am going in order - functions are in Algebra II and precalc and everything in the universe. =)

0celo7

1:31 AM

@heather Ok, $X$ and $Y$ are two sets.

heather

ok

0celo7

Remember what $X\times Y$ is?

Ian Emnace

hi all

Sir Cumference

I've never seen 0celo so eager to teach

When I ask him questions he laughs at my ignorance...

Ian Emnace

does LateX really not work here?

heather

1:32 AM

yeah, the set of coordinates (x, y) where $x \in X$ and $y \in Y$.

user218912

wish he was like that with me too.

Obliv

@ian use chatjax

@bl00 I know right.

heather

well, I mean, the set of all coordinates. but yeah.

Obliv

Never teaches me topology..

Sir Cumference

@Obliv We're unloved...

user218912

1:32 AM

:(

0celo7

@heather coordinates?

heather

@0celo7, er, I mean ordered pairs. wow. that was bad.

0celo7

Oh, actually we need $Y\times X$

But same thing basically.

heather

yeah

Sir Cumference

@Obliv Watch what happens when I upvote three of your answers

0celo7

1:34 AM

A relation between $X$ and $Y$ is a subset $R\subset Y\times X$.

user218912

@SirCumference keep reading the notes. you'll be done in no time. then you can learn calc 3 and once you learn that you'll understand all your astrophysics papers.

user218912

or at least, know enough to learn the stuff required to understand them.

0celo7

For "$x\in X$ related to $y\in Y$" we write $yRx$.

heather

okay

0celo7

Now that probably makes zero sense.

We need an example.

heather

1:35 AM

what sort of relation might this be and yes^

0celo7

Let's consider the relation $\le$ on $\Bbb R$

user218912

@0celo7 you're being too rigorous :<

user218912

heather is a physicist.

0celo7

Heather is a mathematician but doesn't know it

heather

@bl00, I am nothing, currently, but a student

user218912

1:36 AM

aren't we all? xD

Sir Cumference

^

0celo7

Ok, so what is the $R$ associated to $\le$ in $\Bbb R\times\Bbb R$?

Sir Cumference

@0celo7 What'd you say the lower mass limit for a Kerr black hole was?

0celo7

$e^2+a^2$

heather

Um...I have no idea, honestly

0celo7

1:37 AM

@heather Ok let's go easier

user218912

@0celo7 what? even I'm lost.

0celo7

consider the relation $=$ on $\Bbb R$

heather

@0celo7, okay

0celo7

What is $R$?

Sir Cumference

@bl00 That's unrelated

He answered my question

user218912

1:37 AM

oh

heather

$\bb R$

user218912

okay XD

Obliv

@SirCumference dangit man I wanted to keep low rep like @bl00

heather

I mean, however you do the set of all real numbers

Obliv

What happens if you remove those upvotes? lol

Sir Cumference

1:38 AM

@Obliv That's...not the "thank you" I expected...

0celo7

@heather no

it's the line $y=x$

user218912

@Obliv I should have the low profile badge.

0celo7

in the plane $\Bbb R^2$

Sir Cumference

@Obliv You still get 100 rep for every site

Obliv

I don't deserve reputation as a filthy undergraduate physics student @sirC but thanks.

Sir Cumference

1:38 AM

And for new accounts you make on sites

0celo7

because if you take an $x$ and a $y$ on that line, then $yRx$

heather

@0celo7, okay, what? I don't quite understand.

Sir Cumference

@Obliv Well you get more permissions, like upvoting and commenting, on every SE site

Not downvoting though :/

0celo7

@heather here $yRx$ means $y=x$

heather

Right

0celo7

1:39 AM

So we want the subset of $\Bbb R\times\Bbb R$ such that $x=y$ for $x\in\Bbb R$ and $y\in\Bbb R$

but that's clearly just the diagonal line

Sir Cumference

@Obliv I'm a "filthy" undergrad student and I have 4k on Astronomy

Heather's a middle schooler and has 3.7k here

heather

oh, right! Oh! That makes sense now!

0celo7

So now consider the relation $\le $

We want $y\le x$

Sir Cumference

@Obliv But did you actually know that happens when you reach 200 rep?

0celo7

I know you've graphed that in algebra

Obliv

1:40 AM

@sirC not at 200 rep but I've heard that something like that happens at some point.

user218912

@Obliv if JD has like 5k, then it's not even an issue.

Obliv

rekt

Sir Cumference

@Obliv Wait, you're a girl?

Thought you were a guy

user218912

what?

0celo7

what?

Obliv

1:41 AM

yes, is that a problem?

Sir Cumference

Obliv's pic

Nah, 'course not

Obliv

I'm that girl in the picture.

0celo7

Oh

heather

@0celo7, yes, it sounds familiar, but I'm unsure...

0celo7

@heather these are the guys you want to avoid btw

2

Sir Cumference

1:42 AM

I just always hear a guy's voice when I read posts from anonymous people

user218912

just like how ACM is the girl in his profile image.

heather

@0celo7, who?

Sir Cumference

Even Heather

0celo7

@SirCumference sexist

@heather everyone in here

Obliv

@bl00 exactly. and @0celo7 is a cat. And @sirC is a slice of pie

2

Sir Cumference

1:42 AM

@0celo7 It's what I hear in my head

My own voice

So I project that onto other people

0celo7

@SirCumference then your head is sexist

2

Sir Cumference

...

user218912

@Obliv I'm thanatos. :D

0celo7

@heather let me draw it

PhD art skills

Obliv

I am gender fluid. I sexually identify as a fluid.

0celo7

1:44 AM

user218912

@Obliv look how badass I am youtu.be/EYdPy8da27s?t=7m11s

user218912

@0celo7 that shading is beautiful.

0celo7

@heather

heather

@0celo7, oh yeah, duh! I haven't done that in forever.

0celo7

that's $y\le x$

I hope!

heather

1:45 AM

Yeah, I think that's right

Obliv

@bl00 oh that's what it was from. So your old old old profile picture was the same dude as well?

0celo7

Right, so "relations" between sets $A$ and $B$ are just subsets of $B\times A$.

user218912

@Obliv yes.

heather

@0celo7, yeah, that makes sense now. So those points shaded are a subset of the overall set.

Sir Cumference

Can we just go, I dunno, 5 mins without discussing math?

0celo7

1:47 AM

@heather So a function $f$ between $X$ and $Y$, written $f:X\to Y$, is a relation on $Y\times X$ such that $yfx$ and $y'fx$ implies $y=y'$.

I.e. to each $x$ is only related one $y$.

user218912

@SirCumference math is boring. :(

Sir Cumference

@bl00 'Course it isn't

0celo7

This is the "vertical line test" abstracted

Sir Cumference

It's just insane to talk only about math

heather

Okay, so let me see if I've got this straight.

Obliv

1:48 AM

I think google is in my head. As soon as I type something it knows exactly what I want..

heather

@0celo7, You can have a relation called a function. But this relation must "map" (that's the correct use of the term, right?) every $x$ to a unique $y$.

user218912

@Obliv I think that's a new feature, based on what you searched before.

0celo7

@heather YES

Obliv

Kind of creepy. eric schmidt knows me personally :(

heather

Victory!

user218912

1:49 AM

@Obliv who is that?

0celo7

@Obliv @bl00 @SirCumference sorry I have a new apprentice

heather

Apprentice? Who?

user218912

:(

Sir Cumference

@0celo7 You weren't exactly training us...more laughing at our ignorance...

0celo7

@heather You

Obliv

1:49 AM

the crazy guy that works at google that said "If you have something that you don't want anyone to know, maybe you shouldn't be doing it in the first place;"@bl00

heather

@0celo7, cool! I'm excited already. (Well, I mean, I was excited before hand)

user218912

@Obliv lol

0celo7

Ok, not sure why were doing functions actually

heather

I think it was because of metric spaces

0celo7

Oh right!

heather

1:50 AM

And I didn't know what a metric was

Obliv

@heather run away @0celo7 is going to turn you into another him.

user218912

and your eye will get all broken.

user218912

D:

heather

@Obliv, though hopefully I'll go to the doctor when I need too =)

@0celo7, so, Master Yoda, what next?

Sir Cumference

You're gonna be a math purist

0celo7

1:52 AM

Ok, so a metric space is a set $X$ with a function $d:X\times X\to\Bbb R$ such that (i) $d(x,y)=d(y,x)$ for all $x,y\in X$, (ii) $d(x,y)\ge 0$ with $d(x,y)=0$ if and only if $x=y$, (iii) $d(x,y)\le d(x,z)+d(z,y)$ for all $x,y,z\in X$.

heather

@SirCumference, nah. I love physics too much.

Sir Cumference

A girl version of 0celo. 0cela.

0celo7

So that needs to be explained

Obliv

A+ teaching @0celo7

user218912

@SirCumference lol

heather

1:52 AM

@0celo7, whew! Okay, so $d$ is a function

0celo7

$d:X\times X\to\Bbb R$ means that $d$ takes two points of $X$ at once

and assigns a real number

heather

and it maps the set of coordinates created by X x X to R, right

0celo7

$d$ is the metric or distance function

heather

okay, so...oh, that makes sense.

0celo7

@heather ordered pairs

Obliv

1:53 AM

gotta go. night folks

heather

@0celo7, right.

Gotta remember that.

user218912

@Obliv night

0celo7

So given $x,y\in X$ the symbol $d(x,y)$ just means the distance between them

Sir Cumference

@0celo7 I'm so used to seeing $d$ followed by variables as derivatives, it threw me off

heather

So the function follows the rules that d(x, y) = d(y, x)

0celo7

1:53 AM

right, these are all "reasonable"

The distance between $x$ and $y$ is the distance between $y$ and $x$

heather

which makes sense because it is creating coordinates from X times itself

and stuff

and what you said

0celo7

(ii) means the distance is always positive

Sir Cumference

Anyone here ever tried corn with ketchup?

Tastes darn good

0celo7

unless the two points are equal, in which case the distance is 0

heather

distance can't be negative, distance is 0 only if they are the same ordered pair

right

0celo7

1:55 AM

(iii) is called the triangle inequality

I'll draw a picture unless it's obvious

heather

okay, I've heard of it but I don't know what that means

pictures are good

0celo7

so the lines here represent the distances between the points

heather

Oh, I get it now, the bottom can't be longer than the top, basically

0celo7

the top?

heather

that makes a lot of sense

well, the right two lines

0celo7

1:57 AM

it means taking a detour through $z$ will never shorten the path

heather

yeah

0celo7

it can be the same distance

but never shorter

heather

so a metric space is just a way of defining distance

0celo7

yes

many spaces are metric spaces

and they're the first examples of topological spaces we will encounter

now you should have a question about manifolds

heather

one moment

okay, I'll think about this overnight

my mom is telling me I need to go to bed, sadly

but my question would be

1. what is a "space"?

user218912

1:59 AM

is it past your bedtime? hehe

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