The h Bar

0celo7

15:01

@yuggib orly

proof?

is there a bijection from $\mathbb{R}^2$ to $\mathbb{R}$?

Slereah

Same cardinality, so probably?

Not sure what tho

0celo7

@Slereah that's circular

Slereah

Hm

I can think of one

0celo7

yes?

Slereah

It relies on

DECIMALS

0celo7

15:02

huh?

Slereah

Take two real numbers $0,a_1a_2a_3a_4...$ and $0,b_1b_2b_3b_4...$

yuggib

@0celo7 let $A$ and $B$ be two sets, then $\#(A\times B)=(\# A)\cdot (\# B)$

Slereah

The function to $0,a_1b_1a_2b_2a_3b_3a_4b_4...$ is a bijection

0celo7

@yuggib uh so the cardinality of the plane is $\aleph_1^2$?

Slereah

ALTHO

0celo7

15:04

@Slereah wait a moment

Slereah

does that work since a real number can have two decimal representations

0celo7

write $1/2$ in deicmal form

Slereah

Well I guess just pick one

$0.50000000$?

0celo7

why . there

but , above

yuggib

@0celo7 1) the cardinality of $\mathbb{R}$ is not known to be $\aleph_1$

Slereah

15:05

@yuggib Depends what axioms you use!

0celo7

@yuggib why not

yuggib

it is $2^{\aleph_0}$ for sure

Slereah

Also the point is that R and R^2 have the same cardinality :p

Secret

@yuggib does the same idea works for $\mathbb{R}^n$ also thus proving that the cardinality of $\mathbb{R}^n$ is the same as $\mathbb{R}$?

0celo7

@yuggib do you like Mythbusters

@yuggib proof?

yuggib

15:06

in cardinal arithmetics, $\aleph_{\alpha}\cdot\aleph_{\beta}=\max\{\aleph_{\alpha},\aleph_\beta\}$

0celo7

the fuck

you have to prove this stuff

@yuggib can one prove it directly

Secret

what about $\mathbb{C}^n$ is it the sam as $\mathbb{C}$ in terms of cardinality?

0celo7

@Secret well certainly $\mathbb{C}\cong\mathbb{R}^2\cong\mathbb{R}$

so it should work the same way

yuggib

@0celo7 these are standard results

0celo7

not in America

yuggib

15:08

anyways, if you want a direct proof you can find plenty just searching for them on the web

or on math.SE

0celo7

looking, can't find any

yuggib

5

Q: Cardinality of $\mathbb{R}$ and $\mathbb{R}^2$

I am working on this exercise for an introductory Real Analysis course: Show that |$\mathbb{R}$| = |$\mathbb{R}^2$|. I know that $\mathbb{R}$ is uncountable. I also know that two sets $A$ and $B$ have the same cardinality if there is a bijection from $A$ onto $B$. So if I show that there ex...

and references therein contained

0celo7

>elementary

paper cuts are literally Satan

yuggib

@0celo7 it's not non-elementary

0celo7

@yuggib it's PhD level

yuggib

15:16

@0celo7 nah, it's the most elementary part of set theory

0celo7

@yuggib wrong

what would you know about it

@yuggib what do you know about lie groups

yuggib

@0celo7 almost nothing

0celo7

why

yuggib

because I never studied them in a mathy way, only in physics

0celo7

so you know negative things about them

yuggib

15:21

in which sense?

0celo7

@yuggib ok so under the adjoint rep of a Lie group $G$ is the lie algebra $\mathfrak{g}$ a $G$-module?

just getting terminology straight

yuggib

I said that I do know almost nothing about them

0celo7

@yuggib the things you know about them probably only hold for unitary and orthogonal groups

and even then it's probably wrong

yuggib

maybe

I had a mathematics course about Lie groups also, actually

0celo7

@Danu was Chern a really cool guy

yuggib

15:24

but I forgot everything, they are essentially differentiable manifolds if I recall correctly

0celo7

I just noticed do Carmo dedicated his riem geo book to him

@yuggib yes

yuggib

and the algebra is the tangent blah blah

0celo7

@yuggib tangent space at the identity

or the left-invariant sections of the tangent bundle

yuggib

as I said before, geometry is boring

0celo7

:o

take that back

yuggib

15:26

never

suggested readings for you:

link.springer.com/book/10.1007%2F3-540-44761-X

0celo7

fuck that

yuggib

you need to read the first, so you will finally understand something about sets

no prerequisite needed

0celo7

why do I need to know things about sets

only pure math people care about that

yuggib

you are a math major

and you always consider sets in doing math

0celo7

@yuggib so

I have no intention of doing pure math

yuggib

15:28

second reading:

alainconnes.org/docs/book94bigpdf.pdf

0celo7

@yuggib what the fuck

yuggib

there are some parts of that type of geometry that are interesting

0celo7

I'll never be able to understand that

so you telling me to read that is pretty dickish

yuggib

sure you'll be able to understand that

0celo7

no

yuggib

15:30

plenty of cohomology, $K$-theory, $K$-cycles etc

0celo7

I can't understand that either

yuggib

From the intro: "The theory, called noncommutative geometry, rests on two essential points:
1. The existence of many natural spaces for which the classical set-theoretic tools of analysis, such as measure theory, topology, calculus, and metric ideas lose their pertinence, but which correspond very naturally to a noncommutative algebra. Such spaces arise both in mathematics and in quantum physics and we shall discuss them in more detail below; examples include:
a) The space of Penrose tilings
b) The space of leaves of a foliation

you can't say that it is not interesting

0celo7

I don't see where the GDP is

yuggib

you are extremely narrow-minded

0celo7

how so

I'm not interested in abstract nonsense

yuggib

15:37

you're not interested in fundamental things, but you always ask for proof of everything

Slereah

mb go there then

Secret

http://math.stackexchange.com/questions/1240056/approach-on-solving-limit-equation-systems-and-finding-some-f-given-assymptotes

The question is unusual in that a graphical solution is often easy to found, but (at least me) have no idea how to do it algebraically

In terms of problem solving I am always interested in the interplay between graphical methods and algebraic methods

Slereah

yuggib

and demand that the proofs should be done only by what you are interested in

Slereah

0celo7

15:38

@yuggib I am interested in fundamental things

just not noncommutative geometry

yuggib

which mathematical fundamental things are you interested in?

not set theory

0celo7

wait what are the fundamental things

Slereah

The GDP

yuggib

the things that build the foundations of mathematics

0celo7

@Slereah good answer.

@yuggib like what

Slereah

15:39

economics.stackexchange.com/questions/tagged/gdp

mb try here

0celo7

oh yesssssss

yuggib

@0celo7 set theory, category theory, model theory, logic, abstract algebra

Slereah

9

Q: What is the Gross Domestic Product (GDP)?

I suppose GDP is supposed to create a measure of a country's wealth/welfare, something easily indexable. But how exactly is it composed? And is its composition disputed? How good is it at measuring a country's economic well-being?

macroeconomics gdp

0celo7

@yuggib model theory?

yuggib

Model theory

In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic. The objects of study are models of theories in a formal language. We call a set of sentences in a formal language a theory; a model of a theory is a structure (e.g. an interpretation) that satisfies the sentences of that theory. Model theory recognises and is intimately concerned with a duality: It examines semantical elements (meaning and truth) by means of syntactical elements (formulas and proofs) of a corresponding...

0celo7

15:40

> GDP=C+I+X−M+P

This the best equation.

@yuggib I'm not interested in fundamental things

Secret

I am usually interested in abstract algebra, on how wild can axioms get to give algebraic operations with very unusual properties (the naive overgeneralisation of this "hobby" often cause me to stumble upon category theory)

yuggib

@0celo7 but since they are at the foundation, you often come in contact with them

0celo7

@Slereah how the heck do you get the adjoint rep on the Lie algebra from the one on the Lie group by differentiation

like $\mathrm{Ad}(g)X=gXg^{-1}$

how exactly is $\mathrm{ad}(Y)X=[Y,X]$ related to that

@yuggib yeah, so?

I see no reason to study any of them on their own

yuggib

@0celo7 So having a basic knowledge of them is useful in order to do mathematics in general

0celo7

what's your point

yuggib

15:45

even applied math

0celo7

bullshit, no applied math person needs category theory

like 10 people actually need category theory

and of those 0 are doing meaningful stuff

yuggib

maybe, but every applied math person needs to know sets and their properties

0celo7

but not cardinal numbers

yuggib

and some basic properties of algebraic structures

0celo7

I'm taking an algebra course

right now

Secret

15:46

On the more applied side of things, I have a very slight interest in mathematical education, in order to show the kids that maths is not scary

yuggib

@0celo7 why not? they can come in handy when considering sets

0celo7

interesting math is scary though

@Slereah Is it the following: let $g=g(t)$ be a curve through $e$ at $t=0$ with derivative $Y$, then $\mathrm{ad}(Y)X=\frac{\mathrm{d}}{\mathrm{d}t}|_{t=0}\mathrm{Ad}(g)X$?

@yuggib you're not going to convince me to read a whole book on set theory

we do a lot of set theory in intro topology

@yuggib did you know that some math programs don't require you to take analysis

yuggib

@0celo7 it is not so surprising

for many pure mathematicians analysis is not useful

0celo7

really?

yuggib

for example they told me that Sir Atiyah was of that opinion

and then he "destroyed" the english analysis tradition

0celo7

15:54

his most famous theorem is about fucking analysis on manifolds

@yuggib what does that mean

how does one man destroy it

yuggib

because nobody was encouraged to do analysis

0celo7

@yuggib now if you sent me a book on the AS theorem, I would read it

or try

it's on my list of thesis topics

@yuggib but how do you do topology or geometry or PDE or like any useful math without analysis

yuggib

@0celo7 you can do topology and geometry without analysis I think (or at least hiding analytic concept as much as possible)

of course PDEs are just a branch of analysis as is usually defined

0celo7

from a pedagocial standpoint topology must be hell to teach if the students haven't had analysis

yuggib

so you can't

0celo7

15:58

and it's really hard to do geometry without analysis, it rears its ugly head all the time

yuggib

@0celo7 no, topology can be so abstract that no analysis intuition may come to help ;-P

0celo7

wait, are you considering metric space topology as analysis?

I am

you need "compact metric spaces are complete" in Riemannian geometry

yuggib

don't know, I would call it topology and not analysis

Secret

math.lsa.umich.edu/~idolga/soviet74.pdf

Algebraic topology

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. == Main branches of algebraic topology == Below are some...

yuggib

according to wikipedia, the main branches of analysis are: theory of real and complex functions, func analysis, diff eqns, measure theory, numerical analysis

I think that they are overlapping with many, but not all, other branches of math

Secret

16:03

my problem with analysis is that it is not chunky, i.e. too many things happening at the same time to keep track of my calculations,, and then I fall behind

0celo7

What?

@yuggib complex analysis is important in complex geometry

And twistor theory

yuggib

yeah, I think that also algebraists/geometers need to know at least real and complex analysis

and some parts of functional analysis are deeply interconnected with topology

so it is difficult to separate the disciplines exactly

let's say that most geometers and algebraists can live, in my opinion, without measure theory, diff eqns and definitely numerical analysis

Secret

I wish I wil be able to improve my analysis in the coming semester, all my functon related hobbies are related ot it, not to mention solving real life problems

There are just too many times I ran into problems of unable to explore an interesting mathematical function because I am not good at analysis

thus "not sure where I have walked"

0celo7

@yuggib I was told by my adviser that measure theory is a must for higher geometry

But he's a geometric analyst

So he might not be trustworthy there.

yuggib

@0celo7 to be honest, I don't know exactly what algebraists/geometers do

0celo7

16:09

Me neither.

yuggib

surely you can do some mathematics without knowing analysis (almost) at all, but your point of view would be very limited

0celo7

my analysis prof should iron his shirts

He's looking very wrinkled today.

Brb lecture.

yuggib

:-D

0celo7

17:36

@yuggib I think I passed out a few times in that lecture

Bernard Meurer

17:46

@0celo7 Your sister just asked me why don't you act like a normal person

I had no answer

0celo7

@BernardMeurer what the fuck

GPhys

@FenderLesPaul Waiting for 4 schools, heard back from the other 7

@FenderLesPaul one of those hasn't sent out anything, the others I missed the first round

@FenderLesPaul I got into my ~2/3 AND ~3/4 choice though

didn't get into my first choice (rip), but no complaints

Bernard Meurer

18:01

@GPhys Which ones are you still waiting on?

0celo7

18:47

@ACuriousMind if you love me, you'll check out my proof

And tell me that it's horribly wrong.

ACuriousMind

I don't love you, and what little brainpower I had available today has been drained already, so I'd prefer not to think hard in the next hours

Bernard Meurer

@ACuriousMind I'm a master at not thinking, I can teach you the skills

ACuriousMind

Thanks, but I'd also prefer to leave my kitchen and other possessions unburnt.

0celo7

@ACuriousMind I'm genuinely hurt

0celo7

19:08

@ACuriousMind ugh I keep bumping it

I keep finding little errors

ACuriousMind

Yeah, that happens. If you don't want to bump it constantly, note the errors, but don't edit it, but wait a bit, read it again, note the errors, and repeat until you've either lost the will to live or think you're not going to find any more. Then finally edit it.

0celo7

@ACuriousMind I would appreciate if you read it eventually. I probably put in 100x more effort/upvote than you did for your muon answer :P

@ACuriousMind that makes sense

ACuriousMind

I will read it eventually, but I'm really not in the mood for tracing signs and definitions right now.

Bernard Meurer

@ACuriousMind FYI I only set my kitchen on fire 3 times okay?!

And one of the fires started with me trying to make plasma using a grape and a microwave oven

so not even cooking

(Yes it worked)

0celo7

@ACuriousMind I understand.

If you trace them enough you'll go insane.

Slereah

19:23

Do you ever just look through lists of equation solution

Try to find one you'd think would make a good physics problem

Bernard Meurer

@Slereah That's not weird enough for me to occupy my time with

Slereah

Do you ever steal mailboxes to have sex with

3

Bernard Meurer

I'd consider it if it involved doing that on top of a wild cat or a rhino

Slereah

the cat can watch

Bernard Meurer

And just a tip, the best mailboxes are those rectangular ones, real nice fit

@DanielSank blog.takipi.com/5-scala-puzzlers-that-will-make-your-brain-hurt

Danu

19:32

hey hey hey

Bernard Meurer

sup @Danu

0celo7

Dammit found another typo

Danu

@0celo7 No need to let us know every time ;) we all make typos (and sometimes discover them!)

@BernardMeurer I just got back to Munich after a small vacation

(pretty sad right now, sigh)

Bernard Meurer

Oh come on, don't be a downer, Munich is a p cool place to live

0celo7

@Danu but now I'm gonna bump it again

Danu

19:36

@BernardMeurer Meh

0celo7

Munich is in Bavaria, there's like 5 places worse than in it in the world

And many thousand better

Bernard Meurer

@Danu Wanna switch? :p

@0celo7 I had a dream I got accepted to UPenn last night

that can only mean I'm not getting in

0celo7

@BernardMeurer if you go there we're never gonna get to hang out

Bernard Meurer

@0celo7 There's such thing as planes, and I didn't apply to anywhere close to Tennessee

I really want to go to penn

I'd chop an alfredo for it

0celo7

@BernardMeurer but I'll probably go to CA more often than to PA

That's what I'm saying.

John Duffield

19:49

@0celo7 : LOL, I couldn't resist.

0celo7

Someone downvoted it

Really

Bernard Meurer

@0celo7 But UPenn dude

UPenn

They have a program that sends us padawans to the LHC

I'd strangle a baby panda to stay at the LHC working on their Python stuff

FenderLesPaul

@GPhys Nice to hear you got into some of your top choices

Best of luck! :)

glS

20:07

how is this question "too broad"? If anything, I would have said it's too narrow, or possibly unclear

ACuriousMind

@glS I actually voted unclear what you're asking. I don't see at all why you think you can't use density matrices in "second quantization" (and the comments don't make that clearer). Every time you got a Hilbert space, you can consider density matrices on it, I don't get the problem

0celo7

@ACuriousMind you don't see the issue

Haven't said that one in a while

JokelaTurbine

Have any one here ever had a thought WHY Grigori Perelman simply uploaded his genious solution only to ArchivX, without ever bothering to publish it properly? Or have any of you ever even read i.e. the Opus Majus from Roger Bacon from Year 1267? And if Yes, what might have bin your own thoughts about this?

glS

@ACuriousMind well I'm failing to make myself clear, that is evident. Did you have a look at the last things I wrote on the related chat room? chat.stackexchange.com/rooms/36428/…

@ACuriousMind mine is a very "practical" problem if you want: I'm failing to see how would you actually do the HOM calculation I showed (which is the most simple example I could think of which presents this kind of phenomenology) without "exiting" the density matrices formalism, as I (tried to?) clarify in the above linked chat

Danu

20:23

@JokelaTurbine He despises the mathematical community, and does not want to be part of it any longer.

glS

@ACuriousMind Also probably there is a problem of terminology with what "second quantization" means. I basically mean the use of creation operators to represent a state and compute its evolution

ACuriousMind

@glS I think you're asking for something that's impossible. If what you know about your system is what states it starts in, then why do you expect you can get the density matrix without writing it as the projector of those states?

Conversely, if e.g. you're doing QFT at finite temperature, what you know about your system is $\beta$ and the Hamiltonian $H$, so you can write the density matrix as $\exp(-\beta H)$, but it's pretty impossible to write down the actual states in that mixed state without going through first writing that matrix.

Bernard Meurer

@JokelaTurbine Ever heard of mad geniuses? Perelman has done what a number of others like him did before, just look at Wittgenstein or Schopenhauer if you shift to philosophy, the former lived alone in the middle of Norway and the latter had only a dog for a companion throughout life (which people would mockingly call "Mrs. Schopenhauer"). Go figure what goes through their minds

0celo7

@Danu why

I despise the textbook and journal price setters

ACuriousMind

@BernardMeurer Pretty sure Wittgenstein didn't live in the middle of Norway :P

At least not for most of his life

Bernard Meurer

20:29

@ACuriousMind While writing some of his works he did

Google Wittgenstein norway hut

glS

@ACuriousMind I don't expect that. My point is that for example describing a state as $a_0^\dagger a_1^\dagger \lvert 0 \rangle removes the "issue" of having to symmetrize the state, which I would have had to do in the bra-ket formalism: $\frac{1}{\sqrt 2} ( \lvert 0,1 \rangle + \lvert 1,0 \rangle)$. Now consider mixed states described in the density matrix formalism: to properly write the density matrix of the above state I now have to use 4 projectors: (...)

Bernard Meurer

@ACuriousMind And nontheless Wittgenstein was an absolute recluse

glS

... $\rho = \lvert 0\rangle\langle 0 \rvert + \lvert 0\rangle\langle 1 \rvert + \lvert 1\rangle\langle 0 \rvert + \lvert 1\rangle\langle 1 \rvert $. This becomes hard when we have to deal with mixtures of such states. Hence my question: isn't there a better way to deal with this?

ACuriousMind

@glS Why do you not write $\rho = a^\dagger_0 a^\dagger_1 \lvert 0\rangle\langle 0 \vert a_0 a_1$?

glS

@ACuriousMind mh. That may actually be exactly the answer I was looking for (which is actually also what Mark Mitchinson suggested, yes, but for some reason I didn't catch that a few hours ago, probably because there were other things I was not getting). We may then proceed evolving "indipendently" each one of the creation operator in the usual way... let me try to do the calculation but I'm quite sure that that is the answer, thanks

@ACuriousMind do you mean to write that to "second-quantize" the $\rho$ I wrote just above? because in that case the elements do not seem to come out right

ACuriousMind

20:45

@glS What do you mean "the elements don't come out right"? If you want the density matrix corresponding to $\lvert \psi \rangle = a_0^\dagger a_1^\dagger\lvert 0 \rangle$, it's what I've written there.

0celo7

@ACuriousMind how would you know

glS

@ACuriousMind oh, ok, but that is not the $\rho$ I wrote above here in chat, which is the density matrix of a state of the form $\lvert 0 \rangle + \lvert 1 \rangle$. Anyway, the concept should be easily generalizable, let me try

ACuriousMind

@0celo7 Because I seemed to recall he worked in Cambridge

0celo7

@ACuriousMind how would you know

Bernard Meurer

Wittgenstein had a shack where he wrote his first book I think in norway

dunno the name of the book anymore

ACuriousMind

20:48

@0celo7 Because I am an educated person.

Bernard Meurer

tractatus or something

ACuriousMind

logico-philosophical

0celo7

@ACuriousMind that's pretty insulting

Bernard Meurer

Exactly @ACuriousMind

I wanted to start reading some of his stuff, but I can't finish Schopenhauer's complete work

ACuriousMind

@0celo7 What kind of answer did you expect? I read it somewhere, I learnt it in school, someone told me...I don't know where I got every single bit of (mis)information I have from

0celo7

20:50

expected answer: "I read it somewhere, I learnt it in school, someone told me..."

answer I got: "oh I'm educated"

@ACuriousMind can I ask a probably stupid question

Bernard Meurer

Asking to ask a question is already stupid

0celo7

:^)

ACuriousMind

@0celo7 You should know by now that I consider "Can I ask a question?" to be among the stupidest questions ;P

0celo7

@ACuriousMind my bad, poor memory

ACuriousMind

I honestly don't know whether I believe that

0celo7

20:54

@ACuriousMind Ok, so we have the Cartan-Maurer form

now if this form were a connection, it would be flat

so suppose that it IS a connection

does the resulting horizonal/vertical split do anything cool

ACuriousMind

It's a connection on $G$ considered as the principal $G$-bundle over the point

So there is no split, the horizontal subbundle is zero-dimensional

0celo7

hmm

ok, not very interesting

@ACuriousMind lol

@ACuriousMind Ok, so what exactly is the relationship between $\mathrm{Ad}:G\to\mathrm{GL}(\mathfrak{g})$ and $\mathrm{ad}:\mathfrak{g}\to\mathrm{GL}(\mathfrak{g})$? I thought it was $\mathrm{ad}(Y)X=\frac{d}{dt}|_{t=0}\mathrm{Ad}(g)X$ where $g=g(t),g(0)=e,\dot g(0)=Y$

ACuriousMind

That looks correct

0celo7

OK, but his book has it as an exercise to show that's true

they define $\mathrm{ad}$ "by taking the derivative"

it's very confusing

Look at exercises A.4.5 and A.4.8 1.

ACuriousMind

@0celo7 Well, the definition of $\mathrm{ad}$ is as the differential of $\mathrm{Ad}$ at $e$.

0celo7

21:02

I solved A.4.5 but accidentally used A.4.8.1

@ACuriousMind ok, so you view $\mathrm{Ad}$ as function on the manifold in one case

and $\mathrm{Ad}(g)$ as an operator on the vector fields in the other case?

ACuriousMind

If $\mathrm{Ad} : G\to\mathrm{GL}(\mathfrak{g})$, then $\mathrm{Ad}(g)\in\mathrm{GL}(\mathfrak{g})$. I don't understand the question.

0celo7

@ACuriousMind Hmm, well, I guess I don't know how to calculate $\mathrm{d}\mathrm{Ad}|_e$

Stan Shunpike

@0celo7 u got a spotify playlist?

0celo7

except for what I just did via the derivative and using a curve

but I think that's cheating

@StanShunpike don't have spotify

ACuriousMind

@0celo7 Why not? You know how to compute the differential of a smooth map, no?

0celo7

21:07

@ACuriousMind in coordinates via a Jacobian or abstractly using a curve

is there another method that I've forgotten?

ACuriousMind

@0celo7 No

so why do you say you don't know how to compute it?

0celo7

Because I did it using a curve and that's a separate exercise

So I think the authors want me to use a different method

So should I chartify $G$ and work in coordinates?

ACuriousMind

How am I supposed to know what the authors "wanted" you to do?

0celo7

@ACuriousMind MAGIC

@ACuriousMind so you think my solution is adequate?

ACuriousMind

Yes

0celo7

21:21

@ACuriousMind lol I just bumped the answer

and I'll do it again in a few minutes

ACuriousMind

Not your problem the authors apparently didn't realize that they just put the same exercise twice :P

0celo7

I should have fixed the typos and done requested clarifications in the same bump

oh well

@ACuriousMind yeah

@ACuriousMind Sigh...the proof is wrong.

John Duffield

Mathematical proof isn't scientific evidence. It's all "lost in maths" abstraction anyway. None of those things exist.

0celo7

@JohnDuffield what are you talking about

John Duffield

Anybody want to talk physics?

0celo7

21:36

I take it you gave me a -1?

Bernard Meurer

Oh god not again

3

John Duffield

@0celo7 : I'm talking about physics.

@0celo7 : yes, I was going to make some comment to justify it but didn't get round to it.

0celo7

@JohnDuffield please do

help me figure out this sign error while you're at it

Hmm, two negatives make a positive

@ACuriousMind I think I made the glorious mistake of an even number of sign errors :D

ACuriousMind

Haha

Every result is only correct up to an even number of sign errors ;)

0celo7

I just lifted a Riemannian result from Lee

$\langle N,N\rangle=\pm1$ in GR, not just $1$

John Duffield

21:41

@0celo7 : there aren't really any signs there. We talk about positive charge and negative charge, but they aren't positive or negative really, just as cyclones and anticyclones aren't positive or negative.

0celo7

@JohnDuffield lol

John Duffield

It's looking "under the math", and it isn't funny, it's physics. Learn to ask yourself what a term actually means in this real world.

0celo7

No, it's not physics

It's a math question

ACuriousMind

@JohnDuffield The question is about Stokes' theorem on Lorentzian manifolds and the correct sign for the normal vector. Learn to recognize when a question talks about something you have no knowledge of.

0celo7

@ACuriousMind Well put

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