The h Bar

Slereah

3:00 PM

either you get a weird tiny fraction $\frac{d}{dt}$ or you get an awkward line fraction $d/dt$

Secret

Wringing out a Water Soaked Washcloth in Space | CSA Science HD Video

►

Slereah

I need to talk about trousers

Balarka Sen

hey, that's the space oddity guy

Slereah

Does the topology of the trouser spacetime equals to $(S \times R) \# (S \times R)$

not sure it does

trying to find a description of the topology without using cobordisms

Balarka Sen

it's a thrice punctured sphere

0celouvsky

3:06 PM

@BalarkaSen The proof goes something like this: First show that $\mathscr B^\times$ and $\mathscr U$ are homotopy equivalent. (Use Gram-Schmidt for this.) Show that $\mthscr B^\times$ is path connected. For this you can use the spectral theorem for unitary operators, or a more complicated geometric argument. For a compact space $X$, you show that $[X,\mathscr B^\times]=0$. This proof has two steps: you first show that you can deformation retract the image of $f:X\to\mathscr B^\times$ onto [...]

Slereah

@BalarkaSen a good description

Fawad

Hi chat

Slereah

hello

0celouvsky

[...] a finite dimensional simplical complex in $X$. Then you use a geometric technique from the path connected proof to get the homotopy to the trivial map $x\mapsto \mathrm{id}_H$. Finally, you use $[X,\mathscr B^\times]=0$ to show that $\mathscr B^\times$ is contractible. I don't know how that proof goes.

Fawad

Wave equations are drawn on 3-dimeansionsal?

x,y,t ?

0celouvsky

3:08 PM

I think you somehow approximate $\mathscr B^\times$ by compact spaces and eventually get $[\mathscr B^\times,\mathscr B^\times]=0$ but I'm not sure.

Slereah

I wonder if there's a Latex package with an even fancier script than mathscr

gertian

@ACuriousMind I'm back, still no elaboration on this ? :)

Slereah

let's check the comprehensive guide to latex packages

0celouvsky

@BalarkaSen According to this book the final step requires a careful study of the nerve of an open cover of $\mathscr B^\times$.

@BalarkaSen Still don't believe it :(

Slereah

Fawad

3:12 PM

Sorry for typo of "dimensional"

0celouvsky

@BalarkaSen nLab says $\mathscr U(\mathscr H)$ is very different than $\mathrm U(\infty)$.

Slereah

Is it possible to ask the mathjax people to include this package

Balarka Sen

So you essentially want to prove $B^\times$ is contractible.

Slereah

I want \mathghost for Fadeev Popov fields

0celouvsky

@BalarkaSen Yeah, step 1 shows that this implies $\mathscr U$ is as well.

Balarka Sen

3:13 PM

Ok, I don't know. vOv

0celouvsky

@Slereah Lol. [abstract nonsense] Proof: $\mathghost$.

@BalarkaSen I was just telling you something I found interesting, apologies

Slereah

the math witch is better for proofs

it is magic

I'm not sure how it got in the big official review of latex symbols

the rest of the document is mostly a neverending list of relation symbols, arrows and integral signs

Physics Guy

LOL

0celouvsky

> The unitary Fourier transformation $F:L^2(\Bbb R)\to L^2(\Bbb R)$ can be written as $$F=i\mathrm{id}\oplus-\mathrm{id}\oplus-i\mathrm{id}\oplus\mathrm{id}.$$

What?

Slereah

$i\mathrm{i}\mathfrak{i}\imath$

this package is great

neat

Also what the hell are those

Physics Guy

3:24 PM

tieinfinity?

Sir Cumference

> That is the magic of animals. They can be friends and food.

That is one hell of a quote

Physics Guy

@SirCumference Your username is funny.

Sir Cumference

Thanks :)

Slereah

The many faces of the electromotive force

Physics Guy

@Slereah Where do you get those?

Slereah

3:27 PM

anorien.csc.warwick.ac.uk/mirrors/CTAN/info/symbols/…

One of the package has a \Pentagram

Another useful symbol to have

0celouvsky

@ACuriousMind this book is truly

OH MY GOD

Please ban me

user228700

@JohnR: Finally finished FBaWTFT (screenplay) and it is absolutely wonderful! I really feel that you'd love it.

John Rennie

@Kaumudi.H Ah, Fabulous Beasts - it took me a few moments to decode the acronym :-)

user228700

I'd lend you my copy but there's quite a lot of sea in between our houses.

Slereah

ACuriousMind

3:31 PM

@0celouvsky Why does that keep happening?

user228700

@JohnRennie Oops, sorry.

ACuriousMind

Are you accidentally hitting enter?

Slereah

the hell are those

John Rennie

@Kaumudi.H If you think it's good reading, bearing in mind that I haven't seen the film, then I'll grab a copy from that nice Jeff Bezos.

Slereah

they have symbols for the Bose distribution and for the Fermi distribution

user228700

3:33 PM

@JohnRennie I dunno what "good reading" is supposed to be but I can assure you that JKR has written it beautifully and there is no need to watch the film to piece together that universe in your mind.

user228700

And if you love it, maybe you'll even watch the film eyy! (:-P)

0celouvsky

@ACuriousMind I don't know but it keeps happening here and in text messages too

user228700

Hmm but I suggest you at least look at pictures of the creatures because that would make for a better experience, I feel.

0celouvsky

@ACuriousMind but this book is pretty fascinating. From functional analysis to index bundles to signals processing

Fantastic book!

Slereah

perfect math symbols

0celouvsky

3:37 PM

@ACuriousMind allegedly there's a deep relation between signals processing and K theory

Slereah

user228700

@JohnR: This page should help.

Slereah

What

0celouvsky

Lol

Ben Niehoff

can one do \left \Marge ... \right \Marge?

Slereah

3:40 PM

yes, you can

John Rennie

@Kaumudi.H I'm heading off to my mother's house for Easter on Wednesday, so I'll take a copy with me to read there. Just to check, it is this one isn't it:

Slereah

Also good

Fawad

Hello @JohnRennie

Ben Niehoff

ah, my regular cursive E looks just like the emf symbol

in fact I'm not sure why one wouldn't just use \mathscr{E}

user228700

@JohnRennie That's the one :-)

user228700

3:42 PM

I hope u love it! (Please don't hate me if u don't though :-P)

Fawad

My physics sir said if $y=a\sin (\omega t - (-kx) ±\varphi)$ then wave travelling in negative direction. But in my book it says if $y=a\sin (\omega t +kx +\varphi)$ then wave travelling in negative direction. Which is correct?

@JohnRennie ^

Slereah

$-- = +$

Fawad

(｡>﹏<｡)

John Rennie

@Fawad $-(-kx) = kx$ so both are correct.

Fawad

Oh,wait

$y=a\sin (kx-\omega t +\varphi ) $ is correct or $y=a\sin (\omega t -kx ±\varphi ) $ is correct representation of wave?

Yashas

3:48 PM

both are correct

John Rennie

@Kaumudi.H I'm sure I will like it. Reading a screenplay will just take a bit of getting used to.

Slereah

The phase is unimportant for the direction

Yashas

^

user228700

@JohnRennie Only a bit. I got used to it about 10 pages in (and there's a glossary at the back).

Fawad

My teacher used latter equation in everyplace.

ACuriousMind

3:49 PM

@Fawad What do you mean by "correct"? Have you thought about what the difference between the two is, physically?

Yashas

you can change the phase angle to account for the change in sign of (kx - wt)

Slereah

I'm not even sure why you'd put $\pm \phi$

Yashas

@Fawad It is just a convention; I use $y=Asin(\omega t-kx + \phi)$ always

Slereah

Since $\phi$ can be any value anyway

Yashas

Use which ever you are comfortable with

If you want to change the equation from wt - kx to kx-wt, just add a pi

Fawad

3:51 PM

@ACuriousMind no,I don't even know is wave equation drawn on 3-dimensional? x,y,t ?

And negative before kx ?

Yashas

@Fawad the equation you wrote represents a travelling wave in two dimensions

@Fawad The only important sign thing you need to remember is: if kx and wt have the same sign, the wave travels in the negative-x direction; if kx and wt have opposite signs, the wave travels in the positive-x direction.

ACuriousMind

I don't know what it means for an equation to be "drawn", but your equation there describes the time evolution of a transversal wave in two dimensions.

Yashas

@Fawad And as far as I know, 3D waves is not in the regular high school syllabus. I am not sure if you are preparing for JEE though.

John Rennie

On topic?

1

Q: Which of Euclid's postulates can be relaxed, to take us closer to the laws of physics?

Which of Euclid's postulates can be relaxed, to take us closer to the laws of physics? Euclid's 5th postulate states that parallel lines never meet. There are many equivalent ways of stating it, given the other postulates - perhaps most simply "the sum of the internal angles of a triangle is 18...

geometry

Fawad

Sorry,internet is slow

Balarka Sen

3:55 PM

@Fawad Graph of the equation lives in the (x, y, t) space (aka R^3), yes. But that's not the point. The graph of the t = t0 slice describes the (travelling) wave at that specific time.

gertian

@JohnRennie I think it is. And I find it an interesting question actually.
As for the answer ? Local parralel lines may cross instead of they may never cross.

Yashas

I took my 3mg of melatonin tab.

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