« first day (2962 days earlier)      last day (1950 days later) » 

Sir Cumference
Sir Cumference
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
 
Secret
Secret
2:48 AM
 
 
3 hours later…
John Rennie
John Rennie
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…
John Rennie
John Rennie
8:05 AM
I got a rep max yesterday, but no hat! That seems ... unfair!
 
Slereah
Slereah
8:56 AM
hello my droogs
 
Anonymous
9:19 AM
@JohnRennie You'll get it...in 15 days :)
 
Anonymous
 
Anonymous
I don't see any hat for hitting the daily cap though. :/
 
Slereah
Slereah
I like how your hat is slightly askew
'tis a very jaunty chapeau
 
Anonymous
9:37 AM
And `tis the right way to don the blue hat ;)
 
Slereah
Slereah
10:41 AM
"It is easy to see that only neat submanifolds can have tubular neighbourhoods"
Are neat submanifolds related to nice functions
 
Akash. B
Akash. B
11:28 AM
hi
 
ACuriousMind
ACuriousMind
@Slereah I'm disappointed they don't have pleasant neighbourhoods
 
Slereah
Slereah
@ACuriousMind it was the 80's, everything was tubular
Or rad
(Actually it was in Hirsch so I guess it was a groovy neighbourhood)
 
Slereah
Slereah
12:05 PM
Hirsch why are you calling a submanifold $M$
That is very confusing
 
Avnish Kabaj
Avnish Kabaj
12:16 PM
How do you get the wizard hat
The secret one
 
ACuriousMind
ACuriousMind
@AvnishKabaj It's a secret
 
Anonymous
 
Avnish Kabaj
Avnish Kabaj
@ACuriousMind :(
@Blue there's an entire meta post on secret hats!
 
Anonymous
Sun Wukong should really be called "Controversial", sort of adopted from here — WELZ yesterday
 
Anonymous
Yesh, I managed to get it (the Sun Wukong)...love how controversial I am :D
 
Anonymous
12:21 PM
@AvnishKabaj There's one such thread for each year and even a dedicated chat room for figuring out secret hats.
 
Anonymous
Someone should go get the James Bond hat. Let's see who gets it on Physics SE first. ;)
 
Anonymous
(I wonder if mods are allowed to cheat by manually deleting all comments :P)
 
Anonymous
In case you didn't know, the hats leaderboard is here.
 
John Rennie
John Rennie
I'm going to have to change this hat. I keep seeing red up in the top bar and thinking there are notifications ...
 
Anonymous
@JohnRennie The waffle hat would fit you ;)
 
Anonymous
12:36 PM
(for now)
 
John Rennie
John Rennie
@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 :-)
 
Anonymous
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.
 
Captain Bohemian
Captain Bohemian
I wonder what motive in math or physics means.
 
Anonymous
@CaptainBohemian You mean this?
 
Anonymous
(not something I know about :P)
 
Anonymous
12:52 PM
12
Q: How algebraic geometry and motives appears in physics?

user40276First, 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...

string-theory mathematical-physics non-commutative-geometry algebraic-geometry category-theory
 
Anonymous
There's a PSE thread in case it helps you. I have no idea what they're talking about though.
 
Captain Bohemian
Captain Bohemian
@Blue I probably have read that article some time ago but didn't quite understand what it means.
 
Anonymous
We do have some mathematical physicists COBOL engineers around... :P
 
Captain Bohemian
Captain Bohemian
@Blue thank you. I will read it and let you see if I can understand it.
 
Anonymous
@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.
 
Captain Bohemian
Captain Bohemian
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…
Jake Rose
Jake Rose
2:33 PM
Anybody know a good optics book with worked examples?
 
Semiclassical
Semiclassical
3:13 PM
in Mathematics, 2 hours ago, by Akiva Weinberger
user image
 
bolbteppa
bolbteppa
Clearly Griffiths is the pain one right? :p
 
Semiclassical
Semiclassical
lol
 
vzn
vzn
3:34 PM
lol uh oh another Arianna Grande meme! yikes! o_O :P popbuzz.com/music/artists/ariana-grande/news/…
 
 
1 hour later…
enumaris
enumaris
4:39 PM
whomp
 
Anonymous
Unrelated: I was happy to see this today. An amicable community team is definitely one of those things that makes SE great.
 
enumaris
enumaris
weird question
wtf someone has >1 million rep...
 
danielunderwood
danielunderwood
@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
 
John Rennie
John Rennie
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.
 
enumaris
enumaris
fun beans
 
Semiclassical
Semiclassical
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...
 
Sir Cumference
Sir Cumference
Morning
 
danielunderwood
danielunderwood
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
 
Semiclassical
Semiclassical
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
 
John Rennie
John Rennie
5:04 PM
Does anyone apart from Penrose and his students use those diagrams?
 
Semiclassical
Semiclassical
no clue
which is not exactly a testament to their efficacy
 
John Rennie
John Rennie
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.
 
Semiclassical
Semiclassical
lol
that's how I came into them as well, but I played around with them a bit more than that
 
danielunderwood
danielunderwood
Yeah that's where I've seen them too
 
Semiclassical
Semiclassical
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
2
 
John Rennie
John Rennie
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 :-)
 
Anonymous
Being a boll weevil sounds fun
 
Anonymous
You get to eat tasty stuff
 
Semiclassical
Semiclassical
given how many career changes a physics grad student may end up making
"reincarnated out of a physicist" sounds more apt
 
Anonymous
lol
 
Semiclassical
Semiclassical
5:30 PM
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
 
John Rennie
John Rennie
@Blue they eat cotton don't they? If you think cotton is tasty you urgently need to stop eating at the college canteen.
 
Anonymous
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$\frac{\partial}{\partial t} (\nabla \times \vec{H})$
 
Semiclassical
Semiclassical
component-wise, the first expression is just $\epsilon_{jkl}\partial_j \partial_t H_k$
 
Anonymous
@JohnRennie Boll weevils sure have a different notion of tasty, than humans ;)
 
Semiclassical
Semiclassical
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 $d/dt$)
 
Anonymous
5:35 PM
@Semiclassical When do they commute though? I've forgotten calculus :/
 
Semiclassical
Semiclassical
They commute under standard physicist assumptions :P
tbh I don't remember
 
Anonymous
This is mainly in the context of Maxwell's equations
 
Semiclassical
Semiclassical
If you're in a context where your spatial points aren't changing in time, I think you're fine
 
Anonymous
$\nabla \times \nabla \times \vec{E} = -\mu \nabla \times \frac{\partial \vec{H}}{\partial t}$
 
Semiclassical
Semiclassical
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
 
Anonymous
5:41 PM
@Semiclassical Ah, that makes sense
 
Semiclassical
Semiclassical
("partial derivatives commute" is pretty standard in physics)
 
John Rennie
John Rennie
Wow, two new hats and both are secret hats.
 
Anonymous
Just found it:
 
Anonymous
 
Anonymous
It's has a name - Clairut's theorem
 
Anonymous
5:45 PM
Is that right?
 
Semiclassical
Semiclassical
yeah, sounds right
 
Anonymous
Basically that would apply to the curl components along the three axes
 
Semiclassical
Semiclassical
right
 
enumaris
enumaris
MAXWELLLLLLLL MJENKINS
 
Anonymous
@JohnRennie Yay!
 
Anonymous
5:47 PM
Trying figuring out how you got the "Clean Up Duty" and "Propel Thyself" hats :D
 
Anonymous
I don't think it's public yet
 
Anonymous
I'd guess the Clean Up Duty hat is for your recent revisions - physics.stackexchange.com/users/1325/john-rennie?tab=activity
 
Semiclassical
Semiclassical
Finished step 62! The vertex count is now up to 89905
 
Anonymous
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
 
Semiclassical
Semiclassical
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
 
Anonymous
5:59 PM
Yeah, consulting a math book would be better. Unfortunately I don't know of any electrodynamics book for mathematicians
 
Anonymous
Griffiths doesn't look too good
 
Semiclassical
Semiclassical
yeah
 
Anonymous
Oh right. Some PDE books deal with this stuff
 
Anonymous
0celo would have known :/
 
danielunderwood
danielunderwood
Jackson has more mathematical detail
But it's Jackson
 
Semiclassical
Semiclassical
6:01 PM
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"
 
Anonymous
13
Q: Mathematically rigorous text on classical electrodynamics.

Alexander GrothendieckIs 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 $\...

reference-request mathematical-physics
 
Anonymous
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.
 
Anonymous
> In volume I, chapter Vbis ("Connections on a Principal Fibre Bundle") classical electrodynamics is treated as gauge theory on certain fibre bundles.
 
Semiclassical
Semiclassical
neither of those two answers seems very relevant tbh
 
Anonymous
True :/
 
danielunderwood
danielunderwood
6:04 PM
> I don't want to see anything like $\delta(x)$, the text should use distribution theory whenever necessary.
 
Semiclassical
Semiclassical
The relation of electromagnetism to algebraic topology and to bundle theory is significant, to be sure
 
danielunderwood
danielunderwood
$\rho = \delta^3(x)$
 
Semiclassical
Semiclassical
but what you're asking for is rigor in the realm of PDEs, not in the realm of topology
 
Anonymous
@Semiclassical That's right
 
Semiclassical
Semiclassical
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
 
Anonymous
6:08 PM
@Semiclassical In a conference?
 
Semiclassical
Semiclassical
no, I mean program in the sense of scripting
 
Anonymous
Ooh
 
Anonymous
What are you doing?
 
Semiclassical
Semiclassical
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.
 
Anonymous
Sounds interesting :D
 
Semiclassical
Semiclassical
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...)
 
Sir Cumference
Sir Cumference
I'll never understand why the phrase is "integral multiple" instead of "integer multiple"
 
Semiclassical
Semiclassical
6:29 PM
i use the latter as well tbh
 
Semiclassical
Semiclassical
7:12 PM
@blue welp. it finished, yielding: "A 56-dimensional polyhedron in QQ^63 defined as the convex hull of 553664 vertices"
 
enumaris
enumaris
sounds legit
 
Semiclassical
Semiclassical
Now time to map these into 3D and see how many of them end up actually mattering :P
 
enumaris
enumaris
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?
 
danielunderwood
danielunderwood
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
 
enumaris
enumaris
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?
 
danielunderwood
danielunderwood
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
 
enumaris
enumaris
hmmm
 
danielunderwood
danielunderwood
There's the Stanford bunny
 
enumaris
enumaris
this brings me to another point I guess...are all computer shapes polygonal...
like using smaller and smaller polygons to approximate a smooth surface...
 
danielunderwood
danielunderwood
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
 
enumaris
enumaris
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
 
danielunderwood
danielunderwood
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
 
enumaris
enumaris
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...
 
danielunderwood
danielunderwood
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
 
enumaris
enumaris
yeah
 
danielunderwood
danielunderwood
There's also different types of modeling on that. Or at least there is on the engineering side of modeling
 
enumaris
enumaris
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
 
Semiclassical
Semiclassical
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)
 
danielunderwood
danielunderwood
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
 
enumaris
enumaris
yeah that's what I'm saying
your input representation is different
maybe if you change the way you input though you could change the way you render as well
 
 
1 hour later…
Semiclassical
Semiclassical
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)
 
enumaris
enumaris
9:20 PM
loool is it normal for so many people to decline being WH chief of staff...
 
danielunderwood
danielunderwood
I think the normal situation would be anyone that was offered would take it
But we're, uh, not in one of those
 
Anonymous
@Semiclassical Wonderful! :D
 
enumaris
enumaris
whole floor sealed off in a court in D.C... speculation abounds!
 
Kentucker_Filled_Turkey
Kentucker_Filled_Turkey
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
 
enumaris
enumaris
10:13 PM
ohhhh man
 

« first day (2962 days earlier)      last day (1950 days later) »