1:54 AM
@JohnRennie This just reminds of Toys R Us closing again...
Well then again I don't know if that happened in the UK

3 hours later…
5:35 AM
@SirCumference it closed here too. Not that I've been in a Toys'r'Us store for about a decade.
@danielunderwood no. It's something you assign to students once to teach them how wonderful Mathematica is.

3 hours later…
8:05 AM
I got a rep max yesterday, but no hat! That seems ... unfair!

8:56 AM
hello my droogs

9:19 AM
@JohnRennie You'll get it...in 15 days :)
I don't see any hat for hitting the daily cap though. :/

'tis a very jaunty chapeau

9:37 AM
And `tis the right way to don the blue hat ;)

1 hour later…
10:41 AM
"It is easy to see that only neat submanifolds can have tubular neighbourhoods"
Are neat submanifolds related to nice functions

11:28 AM
hi

@Slereah I'm disappointed they don't have pleasant neighbourhoods

@ACuriousMind it was the 80's, everything was tubular
(Actually it was in Hirsch so I guess it was a groovy neighbourhood)

12:05 PM
Hirsch why are you calling a submanifold $M$
That is very confusing

12:16 PM
How do you get the wizard hat
The secret one

@AvnishKabaj It's a secret

@ACuriousMind :(
@Blue there's an entire meta post on secret hats!

Sun Wukong should really be called "Controversial", sort of adopted from hereWELZ yesterday
Yesh, I managed to get it (the Sun Wukong)...love how controversial I am :D
@AvnishKabaj There's one such thread for each year and even a dedicated chat room for figuring out secret hats.
Someone should go get the James Bond hat. Let's see who gets it on Physics SE first. ;)
(I wonder if mods are allowed to cheat by manually deleting all comments :P)
In case you didn't know, the hats leaderboard is here.

12:34 PM
I'm going to have to change this hat. I keep seeing red up in the top bar and thinking there are notifications ...

@JohnRennie The waffle hat would fit you ;)
(for now)

@Blue I've already work the waffle hat and the peacemaker hat. The trouble is I only have four hats because I'm not that active on the main site these days.
I don't want to go through all my hats too quickly :-)

Ugh, we should totally have a nice HNQ coming up so that you can write one of your JR-special awesome answers. Fwiw, I see you're missing the Still Fresh hat. You can get it by joining any site.

12:49 PM
I wonder what motive in math or physics means.

@CaptainBohemian You mean this?
(not something I know about :P)
12

First, I'm not a physicist so I have just a little background in physics. I have been reading some noncommutative geometry books and papers (Connes, Rosenberg, Kontsevich etc) and a lot of high machinery from algebraic geometry such as étale cohomology and motives appears in such books, however I...

There's a PSE thread in case it helps you. I have no idea what they're talking about though.

@Blue I probably have read that article some time ago but didn't quite understand what it means.

We do have some mathematical physicists COBOL engineers around... :P

@Blue thank you. I will read it and let you see if I can understand it.

@CaptainBohemian This isn't my field and I wouldn't be able to help (so it wouldn't be of much use asking me questions). Anyway, hope it helps you. If you need clarifications on specific topics, it's best to post on the main site.

1:00 PM
@Blue I do find some posts in physics SE regarding diffeomorphism invariance require clarification.
I have been thinking about sending a mail to previous advisor to ask clarification for several weeks.

2 hours later…
2:33 PM
Anybody know a good optics book with worked examples?

3:13 PM
in Mathematics, 2 hours ago, by Akiva Weinberger

Clearly Griffiths is the pain one right? :p

3:34 PM
lol uh oh another Arianna Grande meme! yikes! o_O :P popbuzz.com/music/artists/ariana-grande/news/…

1 hour later…
4:39 PM
whomp

Unrelated: I was happy to see this today. An amicable community team is definitely one of those things that makes SE great.

weird question
wtf someone has >1 million rep...

@JohnRennie I don't think anyone told my professor about the once part. Either that or I messed up the calculation so many times that it seemed like I had multiple assignments
I will admit that dealing with indices briefly broke my brain back then

4:57 PM
@danielunderwood :-) It's not that the calculations are hard, but they're just so flipping long and you need to be ruthlessly organised to avoid any tiny mistake. Not fun at all.

fun beans

it's why I like the idea of diagrammatic notation for index calculations, simply as a way to get rid of dummy indices
unfortunately that's a scenario where the cure is probably worse than the disease...

Morning

Indices are one of those things that I never understood what my problem using them was after I figured it out
@Semiclassical like the Penrose diagrams?
Well Penrose tensor diagrams
Not the spacetime diagrams

right
the idea of trading dummy indices for connected lines is attractive
but in practice I never had to deal with so many dummy indices that it mattered

5:04 PM
Does anyone apart from Penrose and his students use those diagrams?

no clue
which is not exactly a testament to their efficacy

The first time I ever saw them was in Penrose's book The Road to Reality. I read that section, thought neat and moved on.

lol
that's how I came into them as well, but I played around with them a bit more than that

Yeah that's where I've seen them too

5:23 PM
When your program is telling you that, after 61 of 63 steps, you've got a polytope with 23289 vertices (and you're sure to pick up more in the last two steps)
you're either doing something awesome or you've done something wrong in a previous life
3

You were reincarnated as a physicist? That's terrible. I was a boll weevil in my previous life and even I thought this life was a step backwards :-)

Being a boll weevil sounds fun
You get to eat tasty stuff

given how many career changes a physics grad student may end up making
"reincarnated out of a physicist" sounds more apt
2

lol

at least this version of the program is telling me how much hell I'm in for. the previous one basically just started staring off into space when I told it to do all 63 steps at once
this one gets 61 of the 63 steps done quickly
it's just the last two which make Sagemath break out in a cold sweat

5:32 PM
@Blue they eat cotton don't they? If you think cotton is tasty you urgently need to stop eating at the college canteen.

Say we have $\nabla \times \frac{\partial \vec{H}}{\partial t}$. I forgot under what condition we can pull the $\frac{\partial}{\partial t}$ out and write it as$\frac{\partial}{\partial t} (\nabla \times \vec{H})$

component-wise, the first expression is just $\epsilon_{jkl}\partial_j \partial_t H_k$

@JohnRennie Boll weevils sure have a different notion of tasty, than humans ;)

So as long as you can commute space and time differentiation, you're fine
(Which I think is not a problem, since you're doing $\partial/\partial t$ not $d/dt$)

@Semiclassical When do they commute though? I've forgotten calculus :/

5:35 PM
They commute under standard physicist assumptions :P
tbh I don't remember

This is mainly in the context of Maxwell's equations

If you're in a context where your spatial points aren't changing in time, I think you're fine

$\nabla \times \nabla \times \vec{E} = -\mu \nabla \times \frac{\partial \vec{H}}{\partial t}$

by contrast, suppose (x,y,z) were the position of a particle in time, and H(x,y,z) was the field experienced by said particle
then x,y,z would indeed be functions of time and therefore you'd probably be using d/dt not $\partial/\partial t$
absent that, I think you're in the clear

@Semiclassical Ah, that makes sense

5:42 PM
("partial derivatives commute" is pretty standard in physics)

Wow, two new hats and both are secret hats.

Just found it:
It's has a name - Clairut's theorem
Is that right?

yeah, sounds right

Basically that would apply to the curl components along the three axes

right

5:47 PM
MAXWELLLLLLLL MJENKINS

@JohnRennie Yay!
Trying figuring out how you got the "Clean Up Duty" and "Propel Thyself" hats :D
I don't think it's public yet
I'd guess the Clean Up Duty hat is for your recent revisions - physics.stackexchange.com/users/1325/john-rennie?tab=activity

Finished step 62! The vertex count is now up to 89905

So, umm, the $\nabla^2\vec{E} = \mu \epsilon \ddot{\vec{E}}$ & $\nabla^2\vec{H} = \mu \epsilon \ddot{\vec{H}}$ equations only hold under the physicist assumptions of continuity of second order partial derivativates? I thought they're more general than that

oh, and these are vertices in RR^63
@Blue think so
a mathematician would probably be a lot more careful in explaining how the wave equations emerge out of Maxwell's equations, and what assumptions are necessary
I think that's as much generality as one worries about in practice
but you'd need to consult someone who does PDEs on a more regular basis

Yeah, consulting a math book would be better. Unfortunately I don't know of any electrodynamics book for mathematicians
Griffiths doesn't look too good

5:59 PM
yeah

Oh right. Some PDE books deal with this stuff
0celo would have known :/

Jackson has more mathematical detail
But it's Jackson

yeah, and Jackson's details are usually not in the realm of "rigorous assumptions"
it's more in the realm of "here's all the tedious stuff you can solve exactly that would be too complicated for an undergrad course"

13

Is there any textbook (preferably not written by a physicist) on classical electrodynamics which gives a rigorous (by the standards of pure mathematics) treatment of (a part of) the topics found in the standard (nonrigorous) physics textbooks such as Jackson? (I don't want to see anything like $\... At least two people have recommended the DeWitt text to me. Not sure how far that goes into this stuff, but maybe worth a try. > In volume I, chapter Vbis ("Connections on a Principal Fibre Bundle") classical electrodynamics is treated as gauge theory on certain fibre bundles. neither of those two answers seems very relevant tbh 6:03 PM True :/ > I don't want to see anything like$\delta(x)$, the text should use distribution theory whenever necessary. The relation of electromagnetism to algebraic topology and to bundle theory is significant, to be sure$\rho = \delta^3(x)$but what you're asking for is rigor in the realm of PDEs, not in the realm of topology @Semiclassical That's right 6:05 PM as such, I don't think either of those answers are very helpful still waiting for my program to finish the last step, lol i've no good idea of how huge this thing will end up being but the combinatorial explosion of the last few steps has been significant @Semiclassical In a conference? no, I mean program in the sense of scripting Ooh What are you doing? I'm literally waiting for this last line to run polyhedra nonsense, lol Suppose you've got an experiment with some set of outcomes in the present case, each outcome will be a set of three numbers from the set -2,-1,0,1,2 So that's 5^3 outcomes. (I actually end up only caring about half of them, but I won't worry about this.) I can then assign a probability distribution to this set of outcomes. I've got certain constraints that need to be fulfilled, each of which is some linear function of the probabilities. Sounds interesting :D 6:13 PM Geometrically, I can think of that like so: Each probability distribution is a set of 5^3=125 nonnegative numbers which sum to 1. Mathematically, that's the 124-simplex in RR^125. Each constraint then corresponds to some hyperplane in RR^125. Collectively, these constraints turn out to produce a cone in RR^125. And that cone happens to lie in the$\sum_k p_k =1\$ plane, so any point in the cone is normalized as a probability distribution
however, that cone is too large: It includes points where the probabilities would be negative
so I need to restrict the cone to the nonnegative orthant in RR^125
(In fact, it's actually 125/2 = 63 (rounding up) so it's in that sense half as bad as one might imagine. still horrible but I'll take what I can get)
So I tried to have Sagemath compute the nonnegative part of the cone, i.e. what the vertices of the resulting convex set would be
however, it can't actually do that---too much memory I think
so instead I'm having it do it component by component: Take the cone and restrict it to have first coordinate nonnegative. Then take that result and restrict it to having the second coordinate nonnegative, etc
which would be bloody tedious to do by hand but that's what programs are for
turns out that Sage can do the above fairly quickly for most of the components, but once one gets to the end it slows down a lot
to the point that I'm still waiting for it to carry out the very last constraint
(of course, that means I get to be paranoid about it stalling out and not telling me...)

I'll never understand why the phrase is "integral multiple" instead of "integer multiple"

6:29 PM
i use the latter as well tbh

7:12 PM
@blue welp. it finished, yielding: "A 56-dimensional polyhedron in QQ^63 defined as the convex hull of 553664 vertices"

sounds legit

Now time to map these into 3D and see how many of them end up actually mattering :P

question: do 3D modeling software generally do the 3D rendering process as well or is it generally that the two processes are done by separate software?

Well they all have a live render. I'd imagine most or all of them have a rendering engine to export ray-traced stuff, but I'm not 100% on that. I'm fairly sure blender does

so is it common to use one software to model a scene
and then use multiple different software to render that scene to see which one renders better or something?

7:17 PM
uhhh
Well for a game, the engine will render it. I'm not sure about movies. But I think as far as research goes, there may be some standard models
There's a famous teapot scene

hmmm

There's the Stanford bunny

this brings me to another point I guess...are all computer shapes polygonal...
like using smaller and smaller polygons to approximate a smooth surface...

Everything I've seen is triangles. I suppose you could do something like build up an abstract representation of a sphere and use that to calculate things like normal vectors
I'm not terribly familiar with representations though

fun beans
I feel like the problem of 3D render is too intimately tied to the modeling process to really be separated from it...
unless you demand strict uniformity in the modeling process

7:25 PM
Yeah I think the modeling programs may generally export to triangles as well. At least I think OBJ files are sets of vertices that form triangles...it's been quite a while though

well I guess you'd just have a scenario where one rendering software must be made to be able to input multiple different file formats or something...like a PDF viewer that can also read word docs, excel, PS files, jpegs, etc...

Like if you wanted to know that something was originally a sphere/cylinder/whatever, you may have to parse the file format of the modeling program

yeah

There's also different types of modeling on that. Or at least there is on the engineering side of modeling

if one set of modeling programs are all polygonal based and export vertices of polygons, then you write some modeling software that actually calculates smooth coordinates and expect the rendering engine to discretize the process into pixels that seems like a big difference
hmmm

7:27 PM
waiting for sagemath to multiply out a 553664-by-63 matrix and a 63-by-6 matrix
(actually, that's probably not what's slowing it down. it then needs to find the convex hull of the resulting 553664 vertices in 6D space...i am not being very nice to sage today)

Well a rendering engine is kind of responsible for changing things into pixels either way. Your input representation is just different. Though I don't know how practical it would be for on the fly processing, so the rendering engine may have to break it down to a polygon-based representation anyway if you're doing realtime rendering

yeah that's what I'm saying
maybe if you change the way you input though you could change the way you render as well

1 hour later…
8:43 PM
@blue finally finished it. the final object I get is a 3D polytope with 68 vertices:
(it's like a tetrahedron with additional faceting)

9:20 PM
loool is it normal for so many people to decline being WH chief of staff...

I think the normal situation would be anyone that was offered would take it
But we're, uh, not in one of those

@Semiclassical Wonderful! :D

whole floor sealed off in a court in D.C... speculation abounds!

10:03 PM
@Pieter or someone... could you help me? I've heard that the hall coefficient of about half metals is negative, so it means that holes are the main charge carriers in half the metal, electrons in the other half. does it even make sense? if so, why do people claim that electrons are the main charge carriers in metals while in reality it's totally dependent on the metal? e.g. nickel and platinum have holes while iron has electrons as charge carriers

10:13 PM
ohhhh man