@ACuriousMind

lolz

because that one can't've been asked before, can it

Excuse me I have problem with my browser in reading mathjax

@Student404Mus In general, there's always at least one CSCO: every Hilbert space has a basis {|ψ_n⟩}. Define  by Â|ψ_n⟩ = n|ψ_n⟩⟩, in this arbitrary basis. Then  forms a CSCO by itself.

@Student404Mus if you have greasemonkey/tampermonkey and chatjax++ and SOUP (dependency of chatjax++), it should be fine

Howdy

Ok

@Student404Mus do you have all of the above? (there are non-userscript alternatives, but this combo works for me out of the box)

@EmilioPisanty There are already like 2 dupse of that in the "related" side bar!

@sirC did you learn about PDF yet and expected/mean values of said PDF's?

@Obliv I'm already taking a stats class

so that's a yes?

Probably soon enough

Sorry @AndrasDeak I was mentioned Emilio

@AndrasDeak The bookmarklets work fine for me already without any monkey business

@AndrasDeak how to install the above tools

@Student404Mus You go to their webpages and you follow the instructions

@Obliv Why you ask?

if you don't provide more details there's very little more anyone can do to help

@ACuriousMind ah, possible. I've been using userscripts anyway

@Student404Mus what Emilio said. But as ACM noted, the bookmarklet version should be fine (whatever that is)

@Student404Mus did you try e.g. the instructions here math.ucla.edu/~robjohn/math/mathjax.html ?

@sirC I need to know why the mean of a random variable X is defined $\int_a^b xf(x)~dx$ where $f$ is defined on $[a,b]$

Just a moment

and $f(x)$ is a probability

@Obliv Do you understand why the mean for a discrete probability $p_i$ is $\sum_i x_i p_i$?

oh i figured it out. it's easier to think of it in terms of a riemann sum instead of an integral.

That integral is a direct generalization of that

yeah @acuriousmind I wasn't thinking of it that way at first for some reason.

@Student404Mus perfect timing of that message:D

Lol

Do people legitimately think the singular of "matrices" is matricee?

NOPE nvm.

Have they never seen the Matrix :/

just over the total probability which should be 1

@0celo7 well, there's people that think that the plural of 'baby Jesus' is 'baby Jesi'

It doesn't work

When I open the edited bookmark on the current chat window nothing happens

actually no idea why I said that. $\sum_i^n x_i~p_i$ yields the probability of $x$ in the interval $[i,n]$

nothing else involved in that

@Student404Mus That is the Top 1 Unhelpful Way to Ask for Help

@ACuriousMind the bookmarklets are the monkey business :-P

What's the problem

@DavidZ Did you realize monkey business was supposed to be a pun on the prompt to install greasemonkey? ;)

then to get the mean probability you get $\frac{\sum_i^n x_i~p_i}{\sum_i^n p_i}$ .. going to get food I'll look back at this later.

@ACuriousMind no, I missed that

Well, I guess it wasn't that funny :P

I got that. I will refrain from assessing the funniness though.

I wasn't paying much attention either

{\sum_i^n p_i}$

Anyone could help

You're missing an initial dollar

and a question;)

Just get a small loan of a million dollars

No I'm just trying to see if latex appears or not

But the same problem

@AndrasDeak could you help me please؟

You'll have to be more specific about what you tried for us to help you

@Student404Mus No, I was serious, I have no idea what you need help with

I m talking about latex language

your latex didn't render, but it was broken, as ACM pointed out

the same thing if I add a dollar: ${\sum_i^n p_i}$

Can't be displayed

@Student404Mus we're making progress:P

Nothing shown

So, what did you try to get it to show?

Any ask for help has to contain all necessary information, mostly because no mind-reading is allowed in this room;) If this was Stack Overflow, I'd ask you to provide an MCVE. In this case, this means "what did you do from among the many options to display mathjax"?

but step 0: Have you tried turning it off and on again?

I ll do

Look.. I explain: my mobile doesn't support drag and drop OK? So I copied and pasted the link address of each given link in the webpage you directed me in the bookmarks and I have clicked many times on each of the bookmarks mentioned

Ohhhhh, I don't think there's an easy way to get LaTeX working on a mobile.

Although more tech-savvy people might know one

I'm not aware of any, but then again I never tried

But in other webpages it works

It works fine

That's because they have the thing that displays the LaTeX built in. The makers of SE chat didn't do that for chat

The problem is just in chat section

So what do mean by Chatham++

Chatjax++ sorry

When I click on start mathjax in math.ucla.edu/~robjohn/math/mathjax.html. the coded text appears as it should be

@sirC tell me something interesting about astronomy

@Obliv Ok...

uninteresting.

The Universe is expanding at an accelerating rate

This has tons of cool side effects

I already knew that. What is interesting that I don't know?

@Student404Mus if you click on the link in the chat room description it explains everything

For example galaxies can recede from us faster than light

@Obliv I assumed you didn't know that, but fine, gimme a minute to think

@SirCumference not everyone agrees :P

@Obliv According to some hypotheses, there once existed quasi-stars long before regular stars. These things would be thousands of times more massive and larger than regular stars. They also had black holes in their centers, and they remained bright thanks to the accretion disk of the black hole, not due to nucleosynthesis.

So that's pretty sick

That is interesting, I'll admit. But, we already talked about this before. I'll ask a question instead. What causes some stars to be larger than others? What causes planets to form? What would be the reason for why theorized supermassive blackholes , such as the one in the center of our galaxy, form?@sirC

question(s)

answer what you can

@Obliv Which first

Crap, caps

@Obliv I'll go from last to first

Whichever you feel like you can answer. I'm testing your knowledge and hopefully you learn something new while I do, too. It's to stave off boredom while I learn more integral applications/properties

How did supermassive black holes form, you ask?

That's a major unsolved problem in astrophysics.

We have no idea how they formed in the early Universe. The hypothesis I just showed you tries to answer that question, by stating that the black hole will eventually grow to consume the rest of the quasi-star.

The first two questions would require me to go off for a few paragraphs

The first in particular needs to be clearer

Are you talking about main-sequence stars only?

I don't know what that means. @sirC

@Obliv K cool :D

I get to educate someone in the ways of astronomy :)

Also, how common are those supermassive blackholes

@Obliv We think they are in the centers of most galaxies

Especially the more massive ones

@Obliv Right, so first I'll teach you how stars form

That's actually an open question too...

But the leading model is something called nebular theory (or nebular hypothesis)

@Obliv That's a difficult question to answer because we basically have no direct evidence of black holes, the closest we have are the recent gravitational wave detections.

It's funny that people talk about black holes so casually given that we've never actually seen one, compared to how tentative we talk about many quantum phenomena

@acuriousmind Oh yeah.. that is true. We cannot detect any EM radiation from them.

gravitational lensing would be indirect evidence?

@ACuriousMind Eh, @JohnRennie says that none exist in the Universe since event horizons take an infinite amount of time to form

@Obliv Gravitational lensing happens around large mass concentrations, but it's not required that the mass be so dense as to be a black hole

Which is true according to the OS metric

@Obliv That occurs among things like dark matter clumps too

@acuriousmind Yes but most mass will emit some form of radiation, right? If you cannot detect such radiation yet the lensing is strong (not sure how you could figure this out), maybe it can be assumed to be a theorized black hole?

Right, so back to stars

@SirCumference Well, the Schwarzschild and Kerr black holes certainly don't exist because they're eternal, but that doesn't mean there aren't time-variant versions of them. Electromagnetic perfect plane waves also don't exist because all waves must be emitted from somewhere, yet they're still a useful approximation and we will talk about "plane waves".

@ACuriousMind I was talking about time variant black holes

Take the OS metric for example. It says that apparent horizons can form, but they would take an infinite amount of time to reach the point of the absolute horizon

@Obliv as we currently believe, most mass in the universe doesn't radiate. You could even call it dark.

By definition, the apparent horizon will not reach the absolute horizon in any finite time

@Obliv Uh, that's not true. Take for instance the earth, or any other planet. We can't detect planets by their emissions, we mainly detect them by the influence they have on their stars.

@sirC while you're at it, can you explain the evidence surrounding dark matter, how it was discovered/theorized and alternative models to describe it?

@Obliv Yes!

I love this part!

Nobody steal it from me!

Nor interrupt

@acuriousmind Is that due to the low-mass of the planet? Or their composition?

better type fast @sirC ;)

@Obliv they're cold

@Obliv Right, so we were observing numerous galaxies and we wondered, Why aren't these galaxies compressing under their own gravities?

oh true.. Forgot that part. @andras

@SirCumference and the obvious answer is rotation:P

We realized that in these galaxies were billions of stars

@AndrasDeak And yes, the answer is rotation :P

Is it? I was trying to mess with you. Sorry, go on:D

@Obliv I don't understand the question. A star emits radiation because its composition is such that the pressure and temperature in it drives processes that emit radiation. A planet doesn't, it's not dense enough to be hot enough for fusion and most of its elements aren't suitable for fusion, either

@Obliv So these stars were orbiting the galactic centers, with the more distant stars orbiting faster to keep up with the closer ones

Then we wondered: Say, these stars near the edge of the galaxies are going really, really fast, and gravity is weaker as you get farther from the galactic center. Shouldn't these stars be flying off?

We realized something invisible must be gravitationally holding the stars to the rest of the galaxy

That invisible stuff was named "dark matter"

@acuriousmind So, then the question becomes: can there be really massive planets that are not dense enough to become stars/black holes?

@Obliv That's not the question (after a certain mass the gravitation will take care of making it denser)

@sirC So the observation was stars that were orbiting around a galactic center? Couldn't the explanation just as well be a super massive blackhole?

@Obliv Usually, SM black holes are thought to be inside the galactic center

(SM being supermassive)

You have to realize that we observe gravitational lensing mostly around far-away objects. You can't resolve whether the mass causing it is sitting at a single spot or spread out over a few solar systems.

We were wondering why the most distant stars, which orbit fastest around the SMBH and where gravity is weakest, weren't flinging off into space

We realized something we can't see must be gravitationally holding them

@ACuriousMind especially that astrometry is non-trivial to say the least

@sirC orbit the fastest or have the most tangential velocity?

@Obliv I meant the latter, sorry

Tired :P

@AndrasDeak Almost no measurement done in the sciences in the last few decades deserves to be called trivial ;)

But they have the same orbital period, so yes they must have more tangential velocity

well there's non-trivial and there's non-trivial:P

That doesn't disprove thinking of SM black holes instead of dark matter for that explanation.

@Obliv SMBHs aren't massive enough to hold objects such fast-moving and distant objects.

@SirCumference chop chop or I'll interfere:P

We're talking dozens of thousands of lightyears

@sirC just theorize it to be bigger.

and that won't be good for anybody, I don't know anything about astronomy

@AndrasDeak that's a non-trivial statement

@Obliv Then the closer objects would be sucked in

@ACuriousMind obviously

Like us, possibly

not if they have fast enough tangential velocity

@Obliv Except we don't.

Not from what we've observed

so what's different if the mass is dark matter instead of a SMBH, you'd still need the same amount of speed to overcome the gravitational force

@Obliv Wait what

@AndrasDeak Surely you mean trivially ;)

I don't have a license to overdo it here

@Obliv OK, keyword: distribution

@Obliv It means there is likely a dark matter halo near the edges of the galaxy

Where dark matter is more plentiful than it is here

@AndrasDeak This is my show ಠ_ಠ

@AndrasDeak I misread it

:D

Then I got my head screwed on

:P

blatant miscommunication makes me cringe

@Obliv But yes, Andras is right

@andras Oh right because the force is dependent on the inverse distance squared.

Dark matter is more distributed near the edges of the galaxies than near the center

That sounds like a lot of complicated mathematics @sirC

dark matter distribution models to fit the observations, that is

@sirC competing models: go!

@Obliv It is. That's why we have things like the Oort constants and a whole field based on galactic movement

Well, subfield

you mean subspace

@Obliv Any other questions?

@AndrasDeak yess, this room needs more Trek references :)

yeah, I want to know if you know any competing models for this explanation. @sirC also the explanation for planet formation & star formation afterwards.

@Obliv Yeah, there are loads, like dark fluid

Though going into them would be out of my area of knowledge, since these are non-standard

@sirC is the SMBH necessary in the galactic center for this dark matter description to work?

if not, would there be a higher concentration of DM in the center to explain the rotation?

is this a normal spherical rotation, btw?