He pissed off shog9 if the rumor mill is to be believed @yuggib

@yuggib for the sake of it

Today we did Arzela-Ascoli on sigma compact spaces, used AA to solve a basic calculus of variations problem, and then the prof gave three examples for why directional derivatives are inadequate

We're apparently one or two weeks behind

@0celo7 I see

Arzelà-Ascoli (italian guys btw, one from my alma mater) can be actually proved in rather general situations

of course they just proved a very simple case

@yuggib we proved it on sigma compact metric spaces with the target a Banach space

@0celo7 reasonable, but not optimal ;-P

What's the best result?

Can you use nets to get it on any sigma compact topological space?

I'll write it down , but don't ask for a proof ;-P

By the way, Bourbaki is the source

Meh

I've been reviewing connections on frame bundles, in preparation for learning about spaces of constant curvature.

I'll have to learn some group/representation theory for that.

I don't foresee needing Bourbaki any time soon

Let $X$ be a topological space (resp. uniform), $\mathfrak{S}$ a cover of $X$, $Y$ a uniform space, $H$ a set of applications from $X$ to $Y$. Let us suppose that for any $A\in\mathfrak{S}$, the restriction to $A$ of all applications $u\in H$ is continuous (resp. uniformly continuous). Necessary are the conditions below for $H$ to be compact for the uniform structure of $\Sigma$-convergence, and sufficient if all the $A\in\mathfrak{S}$ are compact (resp. precompact):

Applications?

@0celo7 maps

Yeah that's how ours is formulated

Just with "uniform space"

well, it suffices that $X$ is topological and $Y$ is uniform to get the result.

Ok but the version we proved is sufficient for analysis/PDE, right?

The version quoted in Evans is the baby Rn one.

@0celo7 most of the times is sufficient yes

Most of the time?

I needed the general version for my research though

hmm

But I was studying functions from a generic locally convex space to a generic C* algebra.

Ok I'm not sure my interests are in that area right now.

Howdy

@0celo7 Say, uh...we cool?

Beats me

I thought ya said a few days ago you were angry at me

TBH I don't remember every conversation so it's hard to be mad at you

Okay cool

Wait, I am

Thanks for reminding me.

@ACuriousMind people who wear hats indoors are psychopaths

The worst of the worst, really

Although yesterday I saw a white guy with a fucking gold chain and gold watch. But otherwise respectably dressed. Probably a psychopath

That was maybe the worst

Ahh

Why am I such a misanthrope

@0celo7 Wait what

Unknown bug, flies like a moth

Cool?

@SirCumference what is unclear?

@0celo7 Why you're mad?

Oh. It should be clear.

Why would it be clear?

Cockroaches can look that thin?

We once caught a cat sized rat in our house

Well, not really the rat already died under the poison, and we are just picking up its corpse to dispose it

The water droplets is on my glass door. That bug was spotted when I was taking a bath and then after the bath I phtoograph it to see if I can identify what the hell it is

Anyone else agree that we need to stop teaching degrees in elementary school, and instead teach radians?

@IceLord why tho

Degrees have nothing over radians

Degrees are superior

@0celo7 Leave

Nice.

@IceLord Dude, where did you find those?

They're like a year old

I like how 1.5 years later I'm still telling you to read Shankar.

@IceLord

But yes, we need to kill degrees

And teach radians

We should also kill celsius and farenheit and replace them with kelvin

Yeah?

You didn't understand why the day changing by milliseconds was a problem

Forgive me for discarding your opinion on other unit related matters.

@0celo7 C'mon man, even you can't deny radians are more useful than degrees

Yes I can. I actively deny it. They're useful for different things.

In what ways are degrees better?

Enlighten me.

4 degrees is how many radians?

@0celo7 So radians are too big?

Give me the answer please

Fine, we'll make the "milliradian" too, which is the angle at which the arclength is 1/1000 of the radius. We all happy?

Or centiradian

Then we have the best of both worlds

@0celo7 About 7 "centiradians" :P

Ok so you see my point.

My point is we oughta improve our education system

We're teaching useless concepts

Degrees have a great degree (haha) of granularity

You can get "small" angles without horrible decimal places

@0celo7 So would "centiradians"

What the hell is a centiradian

ELI5

@0celo7 A unit I propose. It would be the angle at which the arclength is 1/100 of the radius

Arc length?

Works out pretty well, huh?

No, it's very abstract.

Consider a string of arbitrary length. One end of the string is fixed while the other end is in your hand. Why is it that when I pull the string upward & then back down to equilibrium, a transverse wave travels down to the fixed end? What is the physical cause of this wave? It seems like this is a self-propelling phenomena that continues onward until something stops it.

@Obliv Stop asking us your lab report questions

@0celo7 So are degrees.

@0celo7 we didn't have lab last week.

@SirCumference If you think cutting a circle in 360 slices is abstract, go back to school...

exam tomorrow though. I just want to know this for knowing it. It wont' be on the exam

@0celo7 It's arbitrary, rather. Why the hell would we divide it into 360?

Random as hell number.

because it has lots of prime divisors

Okay okay, but c'mon, would a centiradian really be that complex?

historically they took 365 days, then went down to 360 because it has more devisors

@SirCumference If I set you on a desert island and tell you to draw a radian, what do you do?

@0celo7 Draw about 1/6 of a circle. Better yet, if I ask you to draw a degree, what would you do?

Shoot

Draw 1/360 of a circle?

Unfortunately for you I have a freakish ability to partition a circle into exactly 360 pieces.

Good for you. Most people don't.

@SirCumference I can draw 90 degrees instantly. Then 45, then 15, then 5, then 1.

@0celo7 As your angles get smaller and smaller, it gets harder to be precise.

Ah, but my circle is in a corn field made by aliens with arbitrary precision.

At least with a radian you can approximately draw 1/3 of a semicircle.

Czech mate.

@SirCumference The whole point is that your one radian is too large to be useful.

@0celo7 Then use the "centiradian" unit I proposed.

You need to draw a centiradian since that's the system you're proposing.

And actually...isn't a centiradian smaller than a degree? So that would be much harder than what I proposed.

@0celo7 Sure. Just draw a radian, then draw 1/10 of that, then draw 1/10 of that.

You'd split it up into 100.

Is your radian 1/6th of a circle?

No, 1/2pi of a circle

Ok, so you're approximating in the first step.

It can be approximated as 1/3 of a semicircle.

Degrees involve no approximations of that type.

So once again, I win.

@0celo7 So are you. You think you can perfectly draw a degree?

You're splitting it up into smaller and smaller units.

Yes. Any degree I draw will be better than any centiradian you draw.

Bottom line is: centiradians would be just as intuitive as degrees, and more useful in mathematics

They're not intuitive at all.

Something something arc length, then divide by 100?

Nor are degrees!

Divide the circle into 360 parts. What's so damn hard about that?

Try dividing anything into 360 parts!

It's a huge and arbitrary number

You're trying to divide the circle into like 2pi/100 parts or something!

@0celo7 It's easier to draw 1/3 of a semicircle, and divide by 10 twice then to divide a circle into 360.

What?

The 1/3 is an approximation, what do you not get about that?

@0celo7 Can you perfectly draw a degree?

Also I think dividing by ten (twice!) is way harder than what I proposed.

Good point.

I can approximately draw a centiradian, just like you can approximately draw a degree.

Goddammit

I have to go anyways.

I don't know why he does this.

@0celo7 There's a madness to my method.

First with the seconds thing, now with this.

@IceLord Honest to God, I have classes.

Not much I can do about it, though I'd love to debate this.

I don't remember him using them at all, tbh

→ 1 message moved to Trash

...

Oh man I've made Danu mad

(no biggie, 0celo7, but no point in bringing it up)

→ 3 messages moved to Trash

@Danu Don't entertain him.

He can't know we're the same person.

I'm not entertaining anyone :)

We can't let him.

@SirCumference Are you saying you're Danu

He wish

@0celo7 You may never know

If you're Danu, then Danu should be ashamed of himself.

Ouch

Jesus

@SirCumference yeah that was a bit much

so when are mods being elected?

I'm not answering vague questions like that.

I already told you I don't know how to do that.

If you know how to do it, why are you asking me?

Lol

@IceLord EoM of your theory.

@IceLord what what? :o

ah ...agree, eom

what is a correct description of the wave speed of a mechanical wave?

I'm not sure $v = \sqrt{\frac{B}{\rho}}$ suffices

why would it not suffice

isn't there one in terms of the tension?

yeah but that's for a string only

that's the one for a sound wave

ok I took this last semester and instantly forgot everything

Okay in general, then, $v = \sqrt{\frac{\text{elastic property}}{\text{inertial property}}}$

is this it?

I'd have to dig out my notes which are a mile away.

Did you try Google?

First thing I do whenever I have a question

After asking ACM, that is.

the wiki page is bare bones

no equations

that's not good.

doesn't even talk about wave speed

did you look up wave speed separately?

yeah I'm getting two results. Group & phase velocity. I think I'm looking for the group one

but it's given by $v = \frac{\partial \omega}{\partial k}$ like what

oh maybe that makes sense. $\omega = \frac{v}{r}$ $k = \frac{2\pi}{\lambda}$

it is a space of functions

@mafia i just read a few sentences from the wiki page. Do all functions in this space share the same domain and codomain?

what do they mean by of the same 'kind'

@Obliv Yes.

@Obliv Continuous, Lipschitz, $\alpha$-Hölder, etc.

I hate learning half ass physics sigh

I wish I could just learn the real stuffs

Few people can dive into the real stuff without first whetting their skills on simplified model. Very few.

Happily many of the simplified model have a lot of application to real systems.

My personal whinge for the day is over the disparity in communicating the basic results of theoretical physics to the general populace and the utter lack of success in making them even vaguely aware of the limits and successes of experimental science.

For most people Mythbusters is as sophisticated as it gets. And while I love the show, it ain't exactly working to exacting standards even on it's best days.

@dmckee it's hard to have people appreciate something that they aren't familiar with. Reminds me of showing friends dance videos or other high level skills that they are not familiar with. They simply think it's 'cool' but don't really understand/appreciate it.

...dance videos?

les twins, krump etc

not ballet :D

@Obliv Well, yeah. It takes a degree of expertise to make expert judgements. I mean, I can tell a very good pianist from a a pretty good one. But I can't sort out the contestants at a international competitions.

@dmckee I think trying to explain the successes of experimental physics to the general public will be very difficult if you're throwing out words & ideas around that they've never heard of/studied. So, the success of modern physics is probably going to go mostly unnoticed to the people. I'm still unaware of most of it and I'm a second year physics student so..

Good luck :D

hello my droogs

hi @slereah

I was wondering about something the other day.. I know that if you have a classical time varying signal, its power spectral density will be symmetric around 0 frequency. This is why your spectrum analyzer only shows the positive part, the negative part is redundant. But if one has a complex signal, such as often encountered in quantum systems, the PSD can be asymmetric around 0, leading to differences in absorption and emission.

Is there a way to make a voltage signal that would have such an asymmetric PSD? Maybe using two channels and some phase relation?