@ACuriousMind Let me give you an example.

I did the exercise in Bredon to prove that the topologist's sine curve is connected but not path connected.

The natural question to ask is "is that the only space that's connected but not path connected"

Then this becomes "what guarantees path connectedness"

@ACuriousMind But I don't know what this condition is

I want something $P(X)\Leftrightarrow X$ is arcwise connected

@ACuriousMind So the proof that connected $\not\implies$ arcwise connected using a counterexample is not satisfying

I'm somehwat following, but growing even more confused why you think "Why are continuous functions not differentiable?" is a meaningless question. It's disproven by the counterexample of the absolute value. But I want something that's equivalent to being differentiable! So the proof using the counterexample is not satisfying.

@ACuriousMind Ok, you're right, I don't think that it's meaningless.

I realized by proof used a counterexample :P

I'm just so familiar with that fact that it seemed natural to me.

So...why do you expect that other such why functions should have a more "satisfying" answer than that one?

What would a satisfying answer even be, can you give an example of a case where there is one?

@ACuriousMind No.

Not off the top of my head, at least.

Like I said, I don't question the logical validity of a disproof by counterexample.

Yeah, it sounds like you just not satisfied by logic.

Which is fine in many areas, but really not in mathematics

Booo

@ACuriousMind You should have come up with some way to determine the horizontal/vertical split of a $\mathrm{U}(1)$ bundle experimentally.

@0celo7 That would amount to showing the gauge invariant theory is not gauge invariant.

@ACuriousMind Come again?

Oh, you can't determine $A$ but up to some $\mathrm{d}f$.

Meh.

The horizontal/vertical split is exactly the data of the Ehresmann connection, which is equivalent to the data for the gauge field, but the whole point is that parts of the gauge field are unphysical.

@ACuriousMind Yes, I know.

I was almost done typing when you realized, deleting would have been inefficient :P

@ACuriousMind I had

ready, too

For when you asked

"Well why did you ask if you knew that"

I only ask you that if you say "I know" after getting an answer to a question, not when you make realizations on your own.

@ACuriousMind I can't help when you answer the parts I know!

...someone just flagged a bunch of accented us.

Huh?

Yeah, my reaction exactly

Accented us?

No, I don't know what you're saying.

Multiple iterations of the letter u with various accents on them

Uhhhh

What are you talking about

uüúùû

A message exactly like that

I know what an accented u is!

@ACuriousMind In chat or on the main site

@0celo7 I can't see flags on the main site

@ACuriousMind So someone flagged that on chat

Which chat?

Well, I can see some, but a VLQ flag on a post full of us would not be worth mentioning

@0celo7 Yes

Did the person who said that get banned?

@0celo7 Irrelevant

@0celo7 I don't think so

@ACuriousMind Not really!

@0celo7 Get 10k if you want to know where flags come from :P

@ACuriousMind If you can tell me about someone flagging us, I can tell you about salsa

@ACuriousMind I don't know enough physics/math to get rep

There are people who definitely have less of a clue and are happily marching towards it.

@ACuriousMind You do know I could not reproduce 80% of my answers, right?

I've actually looked up a thing, read the accepted answer, said "neat", and I was the one who wrote it.

I'm still not sure what to make of that, but even you at 10% has more of a clue than those

No recollection.

@ACuriousMind What, evidence man?

@0celo7 No, I'm not providing evidence

(and I would advise you not to guess :P )

@0celo7 You're not narcisstic enough to compulsively and regularly check your own answers, then ;)

@ACuriousMind Narcissistic? My memory is too poor to remember to be narcissistic.

See, you have to look at the bright sides!

What, the fact that I can't answer a single question on the front page right now?

:/

I could answer the electrical charge one, but it's a dupe

@0celo7 You're also sensible about dupes, an admirable trait!

@ACuriousMind I don't believe this. I look for things to answer, and there's nothing I can answer

(seriously, few things irk me more than when a question has a clearly visible upvoted duplicate comment below it and someone answers it with an answer that's essentially also already given to the duplicate)

That's just a waste of time for everyone who's involved

I'm confused by the second statement.

Coordinate free yes, but certainly not basis free.

And I think "basis free" is what we mean when we say "coordinate free"

You mean "Tetrads are a way of representing general relativity in a coordinate-independent fashion."?

Yeah, I don't get what that's supposed to mean, either.

@ACuriousMind Yes.

I can present GR without coordinates perfectly fine without tetrad. Just drop all the stupid indices :P

@ACuriousMind lol

You get the idea ;)

@ACuriousMind Let's see your index free version of $R_{abcd}C^{abd}R^{ce}v_e$

@ACuriousMind Are you gonna leave a comment on that

@0celo7 I'm too lazy to look up which of the slots of the Riemann tensor are which index :P

Oh, I see what his issue is.

@0celo7 I don't think so

@ACuriousMind It's $\langle \mathrm{d}x^i,...$

uh, forget it

no clue :P

@ACuriousMind Ah, I see what his confusion is. For you and me, a tetrad is just a set of vectors $\{e_i\}$ such that $\langle e_i,e_j\rangle=\eta_{ij}$

but those damn physicists put another index on the thing

so they get $e_i^\mu$

> Note: I have mainly read physics books which did not deal with differential geometry

I hate physicists.

@0celo7 Yeah

@0celo7 I'm also confused why he seems to think the tetrad and the vierbein are different things

@ACuriousMind I use whichever based on how Deutsch I feel at the time

The inherent symmetries are just Lorentz invariance on the $i$ index, right?

Or Lorentz covariance

Or whatever the hell Lorentz stuff is called

I'm not sure what an "inherent symmetry" of something that's not a Lagrangian or Hamiltonian or action is supposed to be

@ACuriousMind Yes

whatever

But, I think you understood the right thing there - since the tetrad diagonalizes the metric and Lorentz transformations commute with the Minkowski metric, applying a Lorentz transformation to a tetrad produces another tetrad.

I'll write an answer, he'll complain about the math, I'll read my book on 18th century ghosts

@ACuriousMind I know, and I think that's what he means.

Of course not

Compact spacetime crap

@ACuriousMind I just had an 18 hour text response delay

She's good at this

@ACuriousMind Tetrads are greek and vierbein are german, obviously

you should write tetrads with greek indices and vierbeins with Fraktur indices

Lol

@Slereah How do I transform between them?

A dictionary

:D

Beautiful, thank you

$D^\mu_\mathfrak{M}$

Oh jesus

That's as bad as emoji indices

Don't make him post the telephone operator again

But that joke is comedy gold

@ACuriousMind I really do think Lang was ejected from Germany for having no sense of time or punctuality

In the last group meeting he was supposed to leave 30 minutes in, but after an hour and a half he said "meh the meeting (other thing) wasn't that important anyway"

Academics are excused from the German clockwork mentality, I think. They're all supposed to be strange cloudcuckcoolanders with fuzzy hair, anyway

"cloudcuckcoolanders"

That makes no sense in any language I know :P

tvtropes.org/pmwiki/pmwiki.php/Main/Cloudcuckoolander

You made that up

There's a TVTropes link right in front of you, I didn't make that up :D

You could have written that

Wait a moment

you know what a cloudcuckcoolander is but didn't know BTFO?

I've already forgotten again what that stands for

blown the fuck out

Ah

Well, it doesn't sound as nice as cloudcuckcoolander

i.e. what D.J. Trump does to everyone

Which is a nice word because it's so close to the German expression of living in the Wolkenkuckucksheim

No, I didn't make that up, either

It scares me how little German I remember

It's only been 5 years

@0celo7 It's not a common expression

@ACuriousMind Is your mic working?

@0celo7 Yes, but I need the headphones for something else right now

@ACuriousMind Right now?

I was not suggesting we talk now

Okay, then simply "Yes" :P

I'm reading about intrigue and murder in the 18th century

Haha

Your readings sound like they are getting more awesome

But they probably aren't, right?

I think Mr. Morton was still the best :D

But there are ghosts and dead people in this novel

"ghosts"

The prof spoiled that there's a rational explanation for everything

Oh no, he spoiled life! :O

Oh, you mean in the novel :D

It's one of those enlightenment era novels where the morals of the story are "ladies, keep your knees together" and "ghosts aren't fucking real"

Never heard of those

@ACuriousMind Did you know that Jefferson took a Bible and cut out all the parts that referenced Jesus being the son of God and miracles

I have heard such a story, but I didn't hear it with Jefferson, I think

Do you even know who Jefferson is?

@0celo7 The Son of Jeffer.

@ACuriousMind Yeah, the functional analyst.

All hail Jeffer!

@0celo7 that's Jaffe

At least I think you mean Jaffe, I know no Jeffer

@ACuriousMind Jeffer $\cong$ Jaffe

IN WHICH CATEGORY?

@ACuriousMind Calm down.

In the category of people with strange names.

C'mon, the suspense is killing me - what are the morphisms?

@ACuriousMind Identity except for the one which carries Jeffer in to Jaffe.

then they are not isomorphic

@ACuriousMind Dude, can I please read this awesome novel

I don't have time to prove you wrong

@ACuriousMind Holy shit all of the kids died

Ok this is a pretty crazy book after all.

@ACuriousMind You never read any enlightenment era books?

@0celo7 Not a novel. From that era, we read plays like Nathan der Weise from Lessing and Don Carlos from Schiller (although he is technically Sturm und Drang, not enlightenment, although the former is heavily influenced by the latter)

They don't have those morals you are talking about, they are generally more about tolerance, the usage of reason and the overcoming of the traditional structures

@ACuriousMind Hmm, this might be late enlightenment / gothic

Whatever I'm even worse at literature than physics

I'm the JD of literature

@0celo7 I think the issue might be more that German enlightenment literature was a bit different from the English one, but I don't know either

@ACuriousMind I read Der Schimmelreiter back in the day

Ever heard of it?

Heard yes, read no

I'm trying to remember what year that was.

Eighth, probably.

I don't recall the name of my German teacher at the time.

Frau something

Ugh that's gonna bug me now

@ACuriousMind Would it say who my teacher was on my report card

I don't know if there's an English word for that

It's sad that you think you have to translate everything for me

The English word is "homeroom teacher"

@0celo7 No, I hate it when I don't know words, nothing to do with you :P

It happens the other way around, too. Yesterday, I couldn't for the life of me come up with what the hell a "conserved current" is in German.

@ACuriousMind Ok, well now you know the word

It's erhaltener Strom, but it sounds wrong.

I would have said konservierter Strom

Yeah, konserviert means "preserved" not "conserved"

@ACuriousMind Same root as the German word for "jam"

I think

Wait, is Marmelade the German word

The con-/pre-served words are quick tricky

@0celo7 That and Konfitüre

A "preservative" is a Konservierungsstoff and a Präservativ is a "condom".

@ACuriousMind Ah!

"Konservierungsstoff"

That's what I was thinking about

Uhhh...I never said anything other than Kondom for "condom"

Well, Kondom is the usual term

Ok, so is Präservativ the word for "contraceptive"?