The h Bar

ACuriousMind

12:00 AM

I don't think this is the case here, although the effect is close

0celo7

Does she caim to be a mother?

If so, she's up awfully late for that portion of the world doing things not related to kids.

ACuriousMind

Not explicitly

0celo7

@ACuriousMind ncatlab.org/nlab/show/Dolbeault+complex

Who doesn't know what ass is?

Danu

It'd be hilarious if this was the case

I'd be willing to entertain the joke :)

ACuriousMind

@0celo7 I think that was an attempt to show how immature we are, given the reply to Danu, but perhaps I've just got an overactive imagination.

0celo7

12:05 AM

@ACuriousMind 4chan is immature. We are not.

ACuriousMind

I agree, though I would find worse words for 4chan.

0celo7

@ACuriousMind Fun, entertaining, etc. are not bad words IMHO.

ACuriousMind

Obviously, those are not the words I had in mind.

But if you find it entertaining, I won't rain on your parade

0celo7

@ACuriousMind I won't complain if it rains, e.g., Benjamins.

Do Germans know what Benjamins are?

ACuriousMind

@0celo7 I'm trying to decipher that and see whether it can enlighten me about the wedge ;)

Sofia

12:07 AM

@Danu I am replying to you. You wondered about a question that I asked @0celo7. Yes, I asked as if I have asked an issue of language, any mature person.

ACuriousMind

@0celo7 Unless their surname is Franklin, no

0celo7

@ACuriousMind Oh lol nothing. It just mentions complex exterior derivatives.

@ACuriousMind C-note

Danu

@Sofia Ah, yes. I must admit that I found it quite funny that you were not aware of the word 'ass' :)

0celo7

@ACuriousMind Union of 100 singlet simoleons.

ACuriousMind

@0celo7 Don't you see that the "bicomplex" $\Omega^{\ast,\ast}$ there is precisely the $\Lambda^{p,q}$, and its elements are all written with the wedge. I suspect writing the symbol joining one complex to the other as a wedge is convention.

Danu

12:10 AM

...it's just such a useful word that one sees so much it's hard to imagine someone not coming across it, @Sofia

0celo7

@ACuriousMind I think that $\Omega$ is a section of $\Lambda$, but I get your point.

@ACuriousMind Benjamin = 5 Jacksons

(money)^

Still no clue?

Oh, I spoiled it

@Danu Have an internet cookie dollar.

Danu

12:12 AM

Americanized as f*ck :)

ACuriousMind

@0celo7 Yes, I think you are right, these are the sections, like DeRham is sections of the usual exterior cotangent algebra.

@0celo7 I had no clue till Danu said it

0celo7

@ACuriousMind Have you never been to FreedomLand, Inc.?

Danu

"I'm out for dead presidents to represent me"

ACuriousMind

Is Franklin on a dollar note, or something?

0celo7

@ACuriousMind Benji is the C-note

ACuriousMind

12:13 AM

@0celo7 Nope, never been across the ocean

0celo7

Jesus, George is on the $1.

ACuriousMind

@0celo7 What the heck is the C-note. A hundred?

0celo7

Abe is the $5.

Danu

Jay-Z - Dead Presidents [HQ/Explicit]

►

0celo7

@Danu Shockingly Americanized.

Danu

12:14 AM

@0celo7 Genuinely a classic.

0celo7

@Danu Forgot all about it, sad to say.

Danu

The video actually features Jay-Z and his 'friends' playing Monopoly---with real money though.

0celo7

Is there some special reason why when I go to the bathroom, Einstein the cat follows me in and starts rubbing up against my legs?

ACuriousMind

@0celo7 No, all cats do that

Danu

He clearly wants the D

ACuriousMind

1:24 AM

Some people...

Danu

@ACuriousMind A kind spirit... right? ;)

Kyle Kanos

Ugh. I am annoyed right now.

ACuriousMind

@Danu Do you mean kindred? I don't get the joke with *kind*^^

Kyle Kanos

The AutoReviewScript updated and now it doesn't work

ACuriousMind

Gotta looove "updates" like that

Stan Shunpike

1:31 AM

what is the autoreviewscript?

are all reviews autoreviewable

Kyle Kanos

It allows you to insert automatically generated text

That way I don't have to manually add in, "Please note that Physics.StackExchange ...."

Stan Shunpike

So like comments reminding people not to do things....

Kyle Kanos

Right

But it makes it so that I don't have to type it in every time I need to do so

ACuriousMind

@StanShunpike It's the reason Kyle's comments begin to sound robotic when you've read them for the hundredth time ;)

Kyle Kanos

Because it is robotic

Stan Shunpike

1:33 AM

Yeah, that explains it. I just thought it was because he was boring :-o :p

Kyle Kanos

And it's now effing annoying

Stan Shunpike

Can you undo the update?

Kyle Kanos

I had to go back to the repository (fortunately on GitHub) and install the previous version

ACuriousMind

@StanShunpike lol

Physicists can be boring, but not that boring

Stan Shunpike

@KyleKanos did it work?

Kyle Kanos

1:38 AM

Yes

And fortunately my replacement text (the common HW one) was still there

Stan Shunpike

That's good. I hate extra work for mods. I was really amazed actually yesterday...I was in one of the CS chat rooms for the first time. and I saw people chatting about whether to protect a question. And I didn't realize people actually posted crap answers. That's so stupid. But they were discussing how it was going on and it just baffles me people have the time to post useless stuff.

ACuriousMind

@StanShunpike You don't see discussions about protection here because almost everytime I think oh, that should probably be protected, I find that Qmechanic beat me to it ;)

Kyle Kanos

Yeah, some of it is the HNQ effect

Seeing an interesting title (and post) via the Hot Network Question list leads to plain bad answers

I remember there was someone who asked virtually the same question as a HNQ but with one minor tweak. I VTC'd as a duplicate and the guy got a little offended

Stan Shunpike

@ACuriousMind QMechanic is like a wizard lol

Mysterious, we don't know where he's from, he seems to know things in advance, and he pulls answers to stuff out of thin air.

ACuriousMind

@StanShunpike abstrusegoose.com/253

Stan Shunpike

1:47 AM

@ACuriousMind lolol that's hilarious

ACuriousMind

And I believe he pulls the answers out of his knowledge and books, there are always references ;)

Stan Shunpike

It's true. He asked me to provide page numbers in my answer.

@KyleKanos Really? I'm amazed making the HNQ actually makes a difference. I guess though there are a lot of SEs so I don't really appreciate how many people that actually reaches

@ACuriousMind I thought that was homotopy....

Kyle Kanos

@StanShunpike I've visited a fair few of the sites due to HNQ

Pretty much any Harry Potter, Marvel/DC, or Tolkien question gets me over to SciFi

ACuriousMind

I think gaming.SE has made a sport of making clickbaity titles like "Is there a downside to killing everyone I meet?"

Stan Shunpike

lolol omg that's such a crafty way to get people to click on stuff

Kyle Kanos

1:52 AM

@ACuriousMind Or if there is a downside to forcing someone to marry you

Stan Shunpike

and ppl do it

you see ads online with titles just like that

and i never click on stuff like that, but some ppl must

ACuriousMind

Yeah, these ads wouldn't exist if there weren't some people who click them

Kyle Kanos

Someone's bitter:

0

A: Stark Effect in Hydrogen (solution with Mathematica)

Wow, thanks for nothing, Physics stack exchange ... I posted this question on Mathematica stack exchange first because I didn't even realize there was a Physics one. And I didn't have my hopes up because it was kind of off topic there even more so than it could've ever possibly been here, but at ...

Stan Shunpike

Should I flag this lol?

ACuriousMind

::shrugs:::

@StanShunpike Well, technically, it is an answer to the question since they point out their mistake.

So it's not not an answer.

Stan Shunpike

1:54 AM

But could we edit that?

Like if I were a first-timer, I would be put off by that

Kyle Kanos

@StanShunpike yes

Stan Shunpike

Yes to flag, or yes to edit

?

ACuriousMind

Yes to edit. (You would see the arrow if you weren't on mobile, I guess :P )

Kyle Kanos

@StanShunpike Sorry, it links correctly for me. Yes to edit

Stan Shunpike

lol mobile, ah the disadvantages. but i'm not complaining, i learn a ton. it works great. i actually only got a smart phone 6 months ago and I'm really loving having internet access wherever i go.

I can go on SE anywhere

So is it true LHC is on again?

I saw Lubos posted something about it yesterday.

ACuriousMind

1:59 AM

Probably, I don't know.

Stan Shunpike

lol I take it your not one of the "experimentalists" as Particle Fever calls them

ACuriousMind

@StanShunpike Nope, not really. If they get interesting results, I'll hear of them soon enough.

Stan Shunpike

Lol, for me it's sorta like a sporting event. I like to watch all the hype

I love sports.

ACuriousMind

Whether they're currently upgrading or running LHC is not all that interesting, I think

@StanShunpike Heh, go for it, then. I don't like sports :P

Stan Shunpike

Not a fan of the Bundesliga?

ACuriousMind

2:05 AM

@StanShunpike Nope. Although, at times, it seems every other German is :D

0celo7

@ACuriousMind Do you not like soccer in general or just German soccer?

@ACuriousMind Your theorist is showing.

ACuriousMind

@0celo7 Soccer in general as a subset of sports in general. I just don't get what's interesting about watching other people do sports.

@0celo7 Yeah, he needs some air at times.

Stan Shunpike

Amazing athletes make amazing plays. Have you ever heard of ESPN's sports science segments?

@ACuriousMind youtube.com/watch?v=i6T49kBZ6wM

But maybe you won't find it interesting.

@ACuriousMind I'm still not sure what a wedge product is. Any chance you know a convenient way of explaining it?

ACuriousMind

@StanShunpike Yep, my reaction is: meh

@StanShunpike Do you know what a tensor product is?

0celo7

@ACuriousMind ::Unwraps noose rope::

ACuriousMind

2:15 AM

@0celo7 Good thing there's an ocean between us, then.

0celo7

@ACuriousMind ::grumbles::

Stan Shunpike

@ACuriousMind not really, but I'm trying to learn about them. Wikipedia defines them using free vector spaces and everyone I talked to said that wasnt needed

Ted Shifrin said I should just use matrices in the beginning but I think if I could learn tensor products it would just be more efficient.

I don't know what an ideal is either.

Tensor products and ideals seem like the key ingredients for defining a wedge product

ACuriousMind

@StanShunpike Understand the tensor product first, then, the wedge is defined out of it. As a slogan, $\wedge$ is the antisymmetrization of $\otimes$.

And, unsurprisingly, I would disagre with the people you talked to, the proper definition of the tensor product is as the free space on a certain basis.

Or as multilinear maps, take your pick

Stan Shunpike

Multilinear maps!

I know what those are

Those I am comfortable with

ACuriousMind

Good. The tensors of degree $k$ on a space $V$ are just mulltlinear maps that eat $k$ arguments from $V$, alright?

Stan Shunpike

2:21 AM

Sure, that makes sense.

Does that mean they take in both $k$-vectors and $k$-forms?

ACuriousMind

@StanShunpike no forms here. For forms, you need the wedge

A $k$-tensor takes $k$ vectors as arguments

Stan Shunpike

Ah, really? I thought it took both. No wonder I am confused.

So a $k$ tensor only accepts $k$ vectors?

ACuriousMind

@StanShunpike Yes. A $k$-tensor takes $k$ different vectors as its arguments, it is a multilinear map $V\times\dots\times V \to \mathbb{R}$

Stan Shunpike

Okay, that's very helpful. I have been confusing that point. So no forms yet.

I got confused because schutz says forms behave like vectors

0celo7

@ACuriousMind D: Remember the rug!

ACuriousMind

2:26 AM

@StanShunpike Now, you can take $k$ $1$-tensors $t_i$ and build a $k$-tensor $t$ out of them as $t(v_1,v_2,\dots,v_k) := t_1(v_1)\cdot t_2(v_2)\cdot\dots\cdot t_k(v_k)$.

@0celo7 I'm not doing your weird complex geometry here :P

Stan Shunpike

@ACuriousMind What operation is $\cdot$ here?

Is that just dot product?

ACuriousMind

@StanShunpike Multiplication in $\mathbb{R}$

Stan Shunpike

OH

I get it

ACuriousMind

Remember, a $1$-tensor that has eaten a vector is just a number

Stan Shunpike

okay yeah that makes perfect sense

ACuriousMind

2:30 AM

@StanShunpike: Now, you have to observe that a) the $1$-tensors are just the dual space of $V$, since they're linear maps $V\to\mathbb{R}$, which is the definition of the dual, and so they have a basis $t_i$ and a vector space and that b) $k$-tensors are also a vector space (in the sense that they satisfy the vector space axioms)

0celo7

@ACuriousMind Complex geometry is all mine.

Stan Shunpike

@ACuriousMind Yes, I follow.

@0celo7 I think Danu was considering taking a course on that.

ACuriousMind

@StanShunpike Good. Now, let's denote the $2$-tensor I can construct out of pairs of $1$-tensors $t_i,t_j$ as $t_{ij}(v_1,v_2) := (t_i\otimes t_j)(v_1,v_2) := t_i(v_1)\cdot t_j(v_2)$.

One can show that all the possible combinations $t_i\otimes t_j$ form a basis of the space of $2$-tensors.

With me so far?

Stan Shunpike

I think so. we started off by constructing $k$-tensors out of $1$-tensors. Now we are saying that this $2$-tensor is simply a construction out of these. Does this mean it forms a vector space?

ACuriousMind

@StanShunpike This $2$-tensor is just a special case of the earlier construction. You agreed that the $k$-tensors abstractly form a vector space. I now claim that the basis of the space of all $2$-tensors is given by these $t_i\otimes t_j$.

similarily, all possible combinations $t_i\otimes t_j\otimes t_k$ are a basis for the space of $3$-tensors, and so on

Stan Shunpike

2:38 AM

Makes sense.

Yes, I follow.

So wait, for $g = -t \otimes t + x \otimes x + y \otimes y + z \otimes z$ that works then because we can just add those elements and they form a $2$-tensor?

We can add them because they form a vector space?

ACuriousMind

@StanShunpike Exactly

Stan Shunpike

YES!

Awesome :)

ACuriousMind

And every $k$-tensor can be expressed as a sum over the basis $t_{i_1} \otimes \dots \otimes t_{i_k}$ made of the $k$-fold combinations of the basic $1$-tensors.

Stan Shunpike

Yes, that makes sense.

That's awesome. I love it.

NeuroFuzzy

Haha ohhh @0celo7 consider, say, the sequence of partial sums of (1,2,1,3,1,4,1,5,1,...). ie the sequence 1,1+2,1+2+1,1+2+1+3,... then you can have arbitrarily large gaps. Lim sup gap size =infinity. But after every gap comes a gap of size 1! Nothing more to it than that.

Stan Shunpike

2:43 AM

@ACuriousMind Is that the basic idea behind the tensor product?

ACuriousMind

@StanShunpike That, uh, basically was it

NeuroFuzzy

Re a much earlier conversation between you and Danu (?) I can't cite 'cause I'm on my phone.

0celo7

@NeuroFuzzy I see.

Stan Shunpike

@ACuriousMind So what is an ideal?

ACuriousMind

@StanShunpike Oh, that would require a bit of ring theory. I'd now just define the wedge by $s\wedge t := s\otimes t - t\otimes s$.

Stan Shunpike

2:48 AM

Hmm, amazing. That's awesome. I'm going to have to study the tensor product part to appreciate the wedge part, but that's a really nice way to go about it. Yay! I have a book on exterior algebras coming so this is great. I will hopefully be able to get more out of it now.

@ACuriousMind My uncle gave me a book Topics in Algebra i think it's called

Rings baffle me frankly. I don't know what to do once a group loses it's abelian nature. In fact, I still don't get why rotations aren't abelian. I think that's what I remember someone saying

ACuriousMind

@StanShunpike Then I'm certain you will learn what an ideal is then

0celo7

@StanShunpike You can rotate your body to check this.

Stan Shunpike

Try me. How? What's an example?

ACuriousMind

@StanShunpike Rotating something first about the $y$-axis by 90° and then about the $z$-axis by 90° isn't the same as doing it in the reverse order

0celo7

End of the third chapter in Zee IIRC

He has a picture.

Stan Shunpike

2:51 AM

Hmm...

Yes, indeed it isn't the same.

ACuriousMind

Abelian groups are boring, they're just sums of copies of $\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$ :P

Stan Shunpike

I think this stuff is fascinating, I just haven't gotten into it yet. I think I need to do some proofs. I haven't yet tried doing the problems in several books.

music was what got me interested in group theory.

Because I always come back to Do.

I always wanted to know

why certain notes are preferred

in certain combinations and if there were ways to describe that through group theory

Anyways, neat stuff

@ACuriousMind When did you first start learning about physics?

ACuriousMind

Well, if you let the mathematician work long enough, they will describe everything ;)

Stan Shunpike

lol

I'm curious because some people started very early.

Lubos said he was thinking about this stuff when he was 10. But I grew up in a family that didn't really know much about it.

ACuriousMind

@StanShunpike I'm not sure. I soaked up what my father told me, but my parents are both chemists, so that was only rarely physics. My contact with physics is only through school, I think.

Probably 6th or 7th grade, but I was never someone who thought much about these things. It was good to know that there was knowledge out there, but it could wait.

Stan Shunpike

3:02 AM

@ACuriousMind So I'm still struggling to get a grasp on what the current working framework is for understanding blackholes. Is the Schwarzchild metric a tool used for defining blackholes?

I just mean

from what I have heard, GR fails to describe blackholes to some extent.

ACuriousMind

@StanShunpike Oh, don't ask me that, I don't know. My understanding of GR is...superficial

Stan Shunpike

@0celo7 Okay, what say you?

@ACuriousMind Does GR interest you? I read somewhere (maybe your profile) that you like gauge theories or something like that...

0celo7

@StanShunpike Correct.

We really haven't solved black holes, because, as @ACuriousMind so elegantly puts it, we use hokus pokus curved spacetime QFT.

Stan Shunpike

What do you mean?

0celo7

@StanShunpike We don't really know what happens at the horizon.

Kyle Kanos

3:06 AM

Oh, BTW: the baseball game was fun

Stan Shunpike

@KyleKanos What are you talking about?

Kyle Kanos

There was a surprising number of injuries

0celo7

We don't have any direct evidence of Hawking radiation.

Kyle Kanos

@StanShunpike I took my son to his first baseball game

Stan Shunpike

@KyleKanos That's awesome! What teams played? My aunt and her family are seeing opening day for cubs cardinals. She is a die-hard cardinals fan

Kyle Kanos

3:07 AM

Clemson vs Notre Dame

Stan Shunpike

That's cool

Kyle Kanos

Eh, Clemson lost

5-1

ACuriousMind

@StanShunpike It conceptually sounds like something that would interest me, but I think I've been deterred by a bad lecture on it, and now I'm so immersed in quantum theories that my interests don't go in that direction anymore.

I mean, it's classical. Ew. ;)

Kyle Kanos

@ACuriousMind It's not classical, it's general ;)

Stan Shunpike

Lol

@0celo7 But what is a black hole?

That's what I'm confused about. What's our definition of it?

0celo7

3:09 AM

@ACuriousMind It's probably for the best. We don't have any other gauge theory specialists who frequent the chat.

@StanShunpike Roughly, a region of spacetime that is causally disconnected from the rest of spacetime.

Kyle Kanos

@StanShunpike Isn't it any object whose escape velocity is $\geq c?$

0celo7

I don't have the precise topological definition memorized.

user54412

@StanShunpike The event horizon separates regions of spacetime based on whether there null paths to null infinity

Kyle Kanos

^there's an "expert"

:D

Stan Shunpike

@ChrisWhite Is what Kyle said captured in that statement then?

0celo7

3:12 AM

@StanShunpike Yes. If there is no path to null infinity inside of the horizon, then light from inside the black hole can't join light from the outside off in the distance.

user54412

I'd argue that escape velocity is a misleading way to think about things. In particular, in a Newtonian universe with an arbitrary speed limit of c, you could still escape from a black hole.

user54412

After all, with continuous thrust, you can escape at any velocity

ACuriousMind

@0celo7 Oh, I'm probably "advanced", but not a specialist. I'll call myself a specialist when I understand everything in, for example, here.

user54412

Moreover, even without continued thrust, launching yourself at less than the escape velocity moves you some distance off the surface, which is decidedly not the case with GR and black holes

0celo7

@ACuriousMind But no one cares about that :P

ACuriousMind

3:14 AM

lol, alright

0celo7

@ACuriousMind I meant a specialist to serve my needs.

Egocentrism and all that.

ACuriousMind

I serve your needs? Now I feel dirty.

0celo7

@ACuriousMind You dissed GR. You should.

NeuroFuzzy

@ACuriousMind Hey! No one ever told me that!

0celo7

@ChrisWhite Interesting, I never thought about it like that!

@ChrisWhite Quite true. Nice observation.

ACuriousMind

3:18 AM

@NeuroFuzzy It's just the structure theorem for finitely generated modules applied to $\mathbb{Z}$-modules ;)

Stan Shunpike

@ACuriousMind is an ideal domain related to ideals?

ACuriousMind

@StanShunpike Yeah, a principal ideal domain is a domain which every ideal is a principal ideal.

...which probably tells you nothing :D

Stan Shunpike

Peter piper picked a peck of pickle peppers.

That's about as much as I got out of it

ACuriousMind

Thought so, but I don't have an easy explanation, sorry

Stan Shunpike

That's okay, I will do some studying before I ask

I don't like to ask until I feel like I have a chance to get it.

Too much to ask for someone to explain. But if I'm on the cusp, then I ask away.

NeuroFuzzy

3:24 AM

@ACuriousMind so what the heck do ideals have to do with physics???? I've been learning about them (ideals over commutative rings, specifically)

I actually have a final on them tomorrow morning...

Stan Shunpike

My English teacher at Caltech said she was the first person to take Feynman to Huntington Library where they keep a copy of Newton's principia. She said Feynman took the Principa and started reading it. He came to a page where he saw some problem. He thought through the proof and turned the page, only to find Newton had done the same proof.

@ACuriousMind ^

ACuriousMind

@NeuroFuzzy Uh...they're things you can divide out of rings, since they're the kernels of ring morphisms, and it often happens that you want to consider the equalities in some algebra (which is essentially a ring with additional structure) "up to" something, and the way to make that precise is to divide out the ideal these somethings lie in...I don't have a physical explanation of what they are, and I don't know whether there is one.

NeuroFuzzy

That makes perfect sense to me.

ACuriousMind

Oh. Good :)

NeuroFuzzy

I guess the problem is then that I don't know where rings pop up in physics

Stan Shunpike

3:30 AM

@ACuriousMind What does the phrase "up to" mean in mathematics? I hear it all the time. Like "up to isomorphism" or something like that. The only association I make with it is "up to no good" lol

ACuriousMind

@StanShunpike The prime example is "clock arithmetics", i.e. $\mathbb{Z}/n\mathbb{Z}$. Take some number n, for example 8, and say that two numbers are equal if their difference is a multiple of 8, that is $4 = 44$ "up to $8\mathbb{Z}$".

"up to" means stuff differs only in respects you don't care about, generally

@NeuroFuzzy Yeah, that's a bit difficult to see, and you can live a happy physicists' life without ever knowing what an ideal or a ring is, I think.

You can't live a happy mathematical physicists' life, though ;)

NeuroFuzzy

@ACuriousMind One could, but I can't. Because that would mean I'd fail my class. :P

I really like what I've seen of group theory so far.

ACuriousMind

Oh, well. You'll survve :)

0celo7

@StanShunpike The precise topological definition of my earlier black hole definition is $B:=M-J^-(\mathcal{J}^+)$ where $J^-$ is the causal past and $\mathcal{J}^+$ is future null infinity.

Stan Shunpike

Where is that from?

0celo7

3:40 AM

Straumann.

Stan Shunpike

lol that's it I'm getting it

0celo7

@StanShunpike Nah, he doesn't explain what the hell that means.

I just new the page it was on :p

He just cites Hawking, Penrose and Wald I think.

This is equivalent to what Chris White said in words.

Stan Shunpike

Oh, I get it.

That's really cool.

Wald has some sections on causality. are they good?

0celo7

@StanShunpike Yes, but demanding.

Stan Shunpike

@0celo7 He does put them in the advanced section.

I'm not surprised.

0celo7

3:43 AM

I just had an interesting idea. Since there are points in our universe which appear to be moving away from us at a speed faster than that of light, does our universe satisfy the Newtonian definition of a black hole?

After all, to escape our universe in the Newtonian sense, we would have to go faster than light.

@ACuriousMind Does this sound sufficiently crackpot?

Stan Shunpike

lol

ACuriousMind

@0celo7 I'm not sure. Throw in a bit obscure notation, perhaps?

0celo7

@ACuriousMind Wrap it up in a bow and drop it on 12262's doorstep?

He'll make sure everyone properly defines $c$ first, of course.

One must really understand $c$ before any progress can be made. Everyone is an idiot and obviously does not understand GR.

NeuroFuzzy

It's the number of meters per meter, of course.

0celo7

Also, you have to define axiomatically the clock you are using.

Otherwise, we're just dumb engineers.

@NeuroFuzzy Go home, childish engineer.

NeuroFuzzy

3:53 AM

@0celo7 Hey! Some of my best friends are engineers! And, well... OK, they are a bit special.

0celo7

@ACuriousMind I have this urge to \mathrm every post I see now.

Stan Shunpike

@0celo7 lol isn't your whole family engineers?

0celo7

@NeuroFuzzy As a future engineer, I have to clarify that I was mocking someone.

There's a troll on this site who wrote a whole page axiomatically defining what a clock is.

NeuroFuzzy

@0celo7 Just playing along. I think i read some of his posts before too.

0celo7

He said the OP could not know what he was asking because he did not truly know what a clock is.

NeuroFuzzy

3:55 AM

Does he assume choice?

0celo7

@NeuroFuzzy I have no idea.

NeuroFuzzy

that was the funniest thing I read all day

oh my god I'll have to use that some time

thanks ;D

0celo7

Welcome.

I have to sleep now.

NeuroFuzzy

night!

ACuriousMind

@0celo7 Welcome to my world ;)

And good night

I should probably get to sleep, too.

Sun's almost coming up :P

Stan Shunpike

3:58 AM

bye!

Stan Shunpike

6:52 AM

@ACuriousMind I just went back over the notes I took on tensor products. And then the definition of the wedge product you gave. Here's what I don't understand.

@ACuriousMind the tensor product was defined as $t_i,t_j$ as $t_{ij}(v_1,v_2) := (t_i\otimes t_j)(v_1,v_2) := t_i(v_1)\cdot t_j(v_2)$

But dot product is commutative

And the wedge product definition you gave was

$s\wedge t := s\otimes t - t\otimes s$

So if I let $a$ be the tensors and I write $s = a_i(v_1) \cdot a_j(v_2)$ and $t = a_k(v_3) \cdot a_l(v_4)$, then

Damn sorry let me rewrite that

What I'm trying to say is that

$s$ and $t$ are the tensors so we just write them as a dot product

So that would mean

$s\wedge t = s \cdot t - t \cdot s = 0$

@ACuriousMind there we go, I got it. What I just wrote. And that doesn't make any sense. I must be misunderstanding something conceptually

Forget the part involving $a$ that was a mistake.

user54412

7:17 AM

@StanShunpike I think you just need to keep track of all your products and what's acting on what.

user54412

start with $s \wedge t = s \otimes t - t \otimes s$

user54412

then $(s \wedge t)(u,v) = (s \otimes t)(u,v) - (t \otimes s)(u,v) = s(u) t(v) - t(u) s(v)$

user54412

In other words, there's no dot product between $s$ and $t$. Your "dot" product is just the multiplication in the base field, whatever it is. $s(u)$, $t(v)$, etc. are scalars in this field and so can be multiplied in this way.

Stan Shunpike

@ChrisWhite but doesn't that still leave me with the result being zero?

Stan Shunpike

7:40 AM

In other words, if they are multiplied in the base field, its still $st - ts = 0$

Stan Shunpike

8:13 AM

@bolbteppa any thoughts on the above?

Danu

11:24 AM

@ACuriousMind That he's just so nice to want to solve the problem. Not really a good 'joke'

@ACuriousMind Have you ever done sports at a semi-serious level?

@NeuroFuzzy Theere we go :)

@StanShunpike Rotate a cube, or your phone...

Danu

11:52 AM

@ACuriousMind I'm not sure one ever can ;)

@0celo7 Oh, you think $c$ is your ally, but you merely adopted $c$. I was born in it, molded by it. I didn’t see Newtonian mechanics until I was already a man.

@StanShunpike Dude, $s(u)\neq s(v)$, and the same holds for $t$

Why would it be zero?

Also hah caught up on chat

Mornings/early afternoon in EU is the perfect time for that---nice 'n' quiet.

Stan Shunpike

12:56 PM

@Danu dude, (1) you said dude a lot and (2) dude I didn't see that the inside of the vectors dude flipped dude. So dude no wonder its not zero dude. Dude, I think that like dude that answers the question dude.

Dude where's my car?

Kyle Kanos

Stan Shunpike

This scene...

Dude where's my car tattoo

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