@ACuriousMind What does an affine map $a:\mathbb{R}^n\to\mathbb{R}^{n+1}$ look like?

Is it just the embedding of an $n$-plane (or subset thereof) in $\mathbb{R}^{n+1}$?

@0celo7 No, the image need not be $n$ dimensional (affine transformations need not be invertible)

@BernardMeurer yes

@DanielSank Goddammit I closed the webpage I wanted to show you, sec

Oh, and hello too

@ACuriousMind Hmm...is there anything you can say about it beyond "it's affine"?

@0celo7 Yes.

@DanielSank Here, the paragraph before last

@ACuriousMind Ok, please do

The hell's a "ten-dimensional cubic lattice"

@0celo7 It's of the form $x\mapsto Mx+b$ for $M$ a matrix.

@ACuriousMind I know that

@0celo7 Well, then don't ask me to say "anything more" if you already know more. Be specific and stop wasting my time.

Yeesh

@BernardMeurer Ok.

@ACuriousMind I'm trying to verify that $pa:\mathbb{R}^n\to P^n\mathbb{R}$ where $p(v)=$ line spanned by $v$ and $0\notin\operatorname{im}a$ is injective.

I'll think about it some more...

@0celo7 That's not true, take $a$ to send everything to a single point that's non-zero, then $pa$ is clearly not injective. (More generally, injectivity of $f\circ g$ implies injectivity of $g$)

So unless you defined an affine transformation to be injective, the statement is false.

@ACuriousMind Hmm, I don't think the author did that.

But that's a good point...

I guess that would correspond to setting $M=0$? Yeah, that's affine...

@ACuriousMind Have you ever heard of the "affine parametrization" of $P^n\mathbb{R}$?

@0celo7 Uh, do you mean that there is a cover of the projective space by affine spaces?

@ACuriousMind No, it is claimed that $pa$ above is a chart.

I like the construction using homogeneous coordinates better.

(For one, it makes sense.)

@0celo7 Wait, is $a$ arbitary or given? Because I think for that you want $a$ to be $a: (x_1,\dots,x_n)\mapsto [x_1:\dots:1:\dots:x_n]$.

@0celo7 Yeah, the text is clearly missing the condition that the affine map be injective.

@ACuriousMind Ah, well, then it's clear.

So how do we know that every point in $P^n\mathbb{R}$ is in the image of some affine parametrization?

@ACuriousMind Is it true that one can always find an affine map $\mathbb{R}^n\to\mathbb{R}^{n+1}$ so that $v\in\mathbb{R}^{n+1}$ is in it's image?

@0celo7 For $q\in P^n\mathbb{R}$, choose any representant $v_q\in\mathbb{R}^{n+1}$ and any invertible matrix $M\in\mathrm{GL}(n)$, then set $a: x\mapsto Mx+v_q$.

@ACuriousMind $Mx$ is an $n$-vector.

@0celo7 Ah, you are right. Choose it as an $n\times n+1$ matrix of rank n, then.

@ACuriousMind Ok...hmm, is $a(x)$ parallel to $v_q$?

wat

I'm assuming you're trying to show that the line containing $v_q$ can be obtained by some $a$.

@0celo7 Why would you need the entire line?

@ACuriousMind You just need some vector parallel to $v_q$.

That's possible, too, but we don't need that

@0celo7 Yes. And $a(0)=v_q$.

for the $a$ I gave

@ACuriousMind Ah, so each affine parametriation has to be injective

But certainly other $a$s give different lines at $0$

so?

@ACuriousMind Uh

I don't know lol

Oh I'm stupid

@DanielSank Any idea?

Nevermind, thanks

@ACuriousMind Each pa having a different value at 0 is just each chart having a different origin

@0celo7 I'm not sure what you want to say by that, but it's probably right

Bjorn what's a ten-dimensional cubic lattice?

Uh, a lattice in ten dimensions that has a 10D cube as its unit cell?

His name is Bjœrn

We don't do that ligature in German

Only in bloody french afaik

@ACuriousMind We're not in Germany

@ACuriousMind But how could one build a 10 dimensional cubic lattice?

@BernardMeurer What, exactly, do you mean by "build"? (You certainly can't build one in physical reality, unless string theory is right ;) )

relality?

Oh, I never know whether it's a typo or a word with you guys

@ACuriousMind How do you build a lattice on the compact dimensions

@0celo7 veeeery carefully and with tiiiny tweezers, I guess

@ACuriousMind I'm asking because bloody dwave is talking about building a computer based on that

@ACuriousMind That seems like PhD level craftsmanship

craftsmanshit

@BernardMeurer I can't find the words "cubic" or "lattice" in that article

@ACuriousMind paragraph before last, that's if germany's copyright didn't censor it

Rekt

@BernardMeurer Oh, I missed that it has two pages :D

@ACuriousMind Failure will not be tolerated! Jk, I'd be dead long ago if that was the case

They don't say they are building a 10D cubic lattice. They say they are building something that has the connectivity of a 10D cubic lattice, which is just a statement about how the nodes of their lattice are connected.

But how can one achieve the connectivity of a 10D cubic lattice in 3D?

Carefully

@BernardMeurer Why would you think one can't?

@ACuriousMind I'm limited

@BernardMeurer As an example, you can convince yourself that you can get the connectivity of a 3D cubic lattice in 2D: Connect one node to six others, then connect twelve pairs of them to twelve other nodes, and so on. The connections will cross, but you have to just declare that they can cross without there being a node there (and in 3D you don't have that problem, this is a problem specific to 2D)

Ooooh I can see it now

Makes sense yeah

ACM is also a graph theorist

@0celo7 I just have a solid foundation of knowledge :P

@ACuriousMind I tend to believe you have a solid foundation of most things

@BernardMeurer Any idea what?

@DanielSank, ACM explained it to me; I was confused on what did they mean with a 10D cubic lattice; turns out I had missed the word 'connectivity' in the text

anybody remember the relation in stat mech for ideal noninteracting systems, there was PV = - k_B *T *ln(___) and I've completely forgotten where it came from

basically I'm trying to show PV = 2/d <E> for Boltzmann ideal gases, ironically I did it right for fermi gases already

d = dimensions

well, i did for 3d fermi gases

@user507974 Just a general tip, use \$ for $LaTeX$, makes things easier to read

\$ ~mathemagics~ \$

I tried to keep up with the general notation but had forgotten if it was dollar signs or double dollar signs here

For god's sake can someone just stab meta?

@BernardMeurer that is a good idea though... for a lot of people physics is kind of unlearning all the little things you learned incorrectly

while creating a framework for the right things

and to understand why they are right

@user507974 I'm not in angst about the idea, I do like it as well, I just hate when meta self promotes

oh

@BernardMeurer I think you mean $\LaTeX$.

man, next week i start on another 240 pg notebook for stat mech...

@0celo7 Keep my shirt in mind

@user507974 No class till August here

@BernardMeurer What?

@BernardMeurer You didn't see what I removed?

Nope

Ok.

@ACuriousMind You disliked that meta post! Quit ruining Christmas man

@BernardMeurer hmmmm?

I know you did you evil german grinch

This is you!

Krampus!

Nah, I don't care whether or not you think I downvoted that, I'm puzzled why you think downvoting a meta post is somehow an evil thing to do

@BernardMeurer Jesus

Not any meta post, some deserve downvoting

That one didn't imho. I just wanted an excuse to call you krampus really

@BernardMeurer Standard announcement: Downvotes on meta mainly reflect disagreement with the content of the post, not that the post is badly written/stupid/effortless/whatever else.

That's also who votes on meta have no influence on rep at all

Meh, krampus

@ACuriousMind im sure those types of posts also get downvoted

Can I get an opinion?

an opinion

did i do well?

@SirCumference yes

>_>

@SirCumference Not an honest one

@SirCumference Try the philosophers, we're fresh out of opinions

All right, well I'm working on an promotion ad for the astronomy SE. Is this one good?

@ACuriousMind wait...this just in, a whole new load of opinions arrived today

@SirCumference I dislike the front choice

its out of this world but there should totally be blue letters

@BernardMeurer font?

and the colors for the link on the bottom

Hmm...yeah

yep, that's what I meant, my bad

Any font ideas?

Or colors for the link?

I like very clean fonts

fonts2u.com/space-and-astronomy.font

This one sounds fitting

um

That reminds me of something...

i like the font used for the sci fi one

Can't remember the movie title

@SirCumference The ".com" is unreadable, and I think sans serif fonts look better for such a purpose, but I like the imagery

sci fi SE

@SirCumference The image's resolution is also a little low

But it's looking pretty cool man, good work

also the font choice for physics might work too

That's the big problem

@BernardMeurer No, 300x250 px is the prescribed resolution

I gotta figure out how to keep it under 40KB

The only way to do so is to make it like:

@ACuriousMind how do you know that

@ACuriousMind I was about to ask whether it was made to fit a resolution

ACM is a graphics design artist too

@0celo7 By looking at the Community Ad thread

Which looks horrible

@ACuriousMind whaaaaaa

@BernardMeurer 300x250 px and 40 KB are the limits.

Sigh...if only I could keep it at 50KB. It'd look a lot better

@ACuriousMind You should teach a google course at your uni

@SirCumference Did you check that font out?

@0celo7 I'm not a graphics design artist

I just know how to use Photoshop

I use GIMP

Yeah, trying it out. I did some weird stuff so I'll be making a lot of changes to fix the font

@0celo7 I actually did most of the work on our end-of-school yearbook...

FREE SOFTWARE

AAAAAAAAAA

@ACuriousMind wtf

Is ACM the superior being?

@0celo7 I bet he's also tall, fit and resembles George Clooney

@BernardMeurer What font colors for the link?

@BernardMeurer Nah, I'm of average height and rather scrawny.

Something that's visible, try some colors out

The problem I had with the one you used was that it didn't contrast enough

@ACuriousMind average?

how tall, in real units please

@ACuriousMind German average?

Finding colors that represent the entirety of space and the Universe is tough

@SirCumference the universe is mostly black

Dammit that's smart

@0celo7 1.75m give or take 2cm

But black ain't a color

@ACuriousMind REAL units

It's the lack of light

@0celo7 that's racist

Or lack of color

That's not racist

@BernardMeurer what

@0celo7 It's a color, and you're racist too

the fuck?

colorist actually

If anything I had a problem with black people being called "colored" in history

Not only is it racist, but it's scientifically inaccurate

@SirCumference Why

White is all the colors

Black people are not black

So they're "colored"

I know

They're dark brown

But if you call something black, you can't call it "colored"

Of course I can

I don't know if this is about art or physics

Okay

It's about you being nitpicky

Does a black hole have color?

Exactly

Maybe I'm a pretentious prick

But still...

@SirCumference what the fuck does that have to do with anything?

@SirCumference You're mixing your magics up

What are we talking about?

Making a big deal out of this

@SirCumference Are you on something?

'Course not

@ACuriousMind Ok, you're 5.74147'

All right. Is black a color?

what is a color

Dictionary: the property possessed by an object of producing different sensations on the eye as a result of the way the object reflects or emits light

ok, so black is such a sensation

so black is a color

end of discussion

Things that absorb light are black

Okay let's talk serious

@ACuriousMind according to el Google I'm 1.88m

Theres RGB for light and CMYK for color/pigment

@BernardMeurer Anyway, this is what yours looks like

black is not a color in RGB

but is in CMYK

done deal

@SirCumference I think that looks pretty cool

Stop being clever

Hmm...

I think you have a lambda where an "A" should be.

@SirCumference Some would argue I'm yet to begin

You should fix that.

Lemme test sans serif

@0celo7 I know. That's the font

@0celo7 It's cause lambdas are badass

@SirCumference You should fix that.

A = lambda for some reason

You fix it. Send me the new version of the font

@0celo7 Quit being nitpicky

Lol...that reminds me - they're building a new building for the mathematicians here, the Mathematikon. The font above the entrance replaces the As by $\Lambda$s, which led to endless discussions in the commitees :D

apparently the designer did not expect mathematicians to throw a fit about that

@ACuriousMind That's with your font suggestion

@ACuriousMind That should've been expected

@BernardMeurer This is yours when it meets the 40KB limit

@SirCumference Well, I like that better. The yellow is still a bit hard to read, but that's a bad sequence of colors (black-white-blue) there to have a single color be readable in any case.

@SirCumference I never quite liked Sans Serif. You could check this out too.

@ACuriousMind Hmm...what do you suggest?

Should I just put the psd up for ya'll and you can change it?

Perhaps slighly move the Earth to the right so that the text is completely on the space?

Also, if you'll do the color change on the link make sure only the word "astronomy" is in a different color, not "astronomy."

@SirCumference learn any interesting calculus lately

@BernardMeurer what about you

@0celo7 What about me?

@0celo7 Yep, a bit more on improper integrals

All right, gimme some colors for the link

Something on that image is bothering me and I have no idea what it is

Here. I'll send ya'll the psd

>ya'll

What state are you from

New York...

I'm just too lazy to say you all

You're also too lazy to spell it correctly, it's y'all

Excuse me

haha

We ain't gon have a yank use a word he can't spell

Well, I'm gonna format my machine now folks

talk to you all in a few

@BernardMeurer @ACuriousMind mediafire.com/?iayo02dllhpc37p

Compile the kernel?

@0celo7 uhum

Wanna do some finicky stuff that require a full recompile

so I'm using the opportunity to also clean all the garbage

In reference to the above

ars.userfriendly.org/cartoons/?id=20010425

I grew up in Texas, but I mostly only drawl in places where they don't know the many ways to conjugate 'y'all'.

@dmckee I like "y'all're"

@0celo7 Perfectly good word. Very useful in day to day conversation.

No one knows how to conjugate it, pronouns are declined, not conjugated ;P

@ACuriousMind Leave.

I decline your presence

@ACuriousMind I knew. Or at least I knew that conjugate wasn't right. But if I was trying to be correct I'd have guessed at "inflected". Never real payed enough attention to grammar.

Well, inflected is correct also, that's the more general term for changing words according to grammar

@ACuriousMind are you in any way related to CuriousOne?

Ha!

@Sidarth Nope (except that I think he is also German)

hmm...how so?

@ACuriousMind I think there's a German postdoc on our campus...

I heard Lang talking in ye olde lingua to someone.

@Sidarth Moderately wild guess based on some comments

ok

still am curious as to how you say hes german @ACuriousMind....if you want to elaborate, do so....im all ears....

Germans can spot Germans.

i can get that much @0celo7....but how?

Germanvision

:|

It's simple

@Sidarth There are certain constructions

?

but ppl answer in english...

Nein

@Sidarth When you directly translate some stuff is sounds strange.

And there are "typical" errors

and curiousone did that?

@Sidarth Likely.

hmmm

care to anybody?

and dont look at the comments....;)

egh

maybe next time when i actually read up on ligo

im going to have to soon anyways since im starting an internship at least tangentially related to it

oh, he just doesnt get geometry

eh, still too much effort

hmmm

mmhmmm

so wassup @BernardMeurer

In general do you mean?

yeah

Working on some code, preparing a linux kernel; why?

just asking..:)

im watching the science of interstellar...

Alright

hmmm

@ChrisWhite Where do you work again?

yeah chris ...where?

and wth??

Dammit, not in a bikable distance from SF

@BernardMeurer SF?

@0celo7 If everything goes as planned I should be there by August top

@ChrisWhite any explanation on the 5 d torus thing?

what is SF

If things go 99% as planned I'll be at Penn

San Francisco you numbnuts

@BernardMeurer AFAIK U Penn is not in SF

yes.......I get it completely....hmmm

@ChrisWhite Tried using photoshop for it and 5 online sites

All giving me the same result

@0celo7 but Berkeley is-ish

@BernardMeurer what