The vast polar structure disperse quickly, probably an unstable structure. This supports a plane of dark matter cloaked satellite galaxies coexists with the vast polar structure

When loneliness literally make you feel more ill

The mental effects of climate change, and how to mitigate them

Floods can degrade water quality and costy denitrification plants have to be built, which eventually result in high price need to pay per water drunk

h e l p

What the hell is the structure group of the tangent bundle

Is it trivial or is it $GL(n, \Bbb R)$?

Good morning to everybody

@Slereah Hi, can you ask an answer please?

@Slereah I have a question that does not have an answer yet. Why can not I ask another question? A positive vote to my question might do something? physics.stackexchange.com/questions/322522/…

Hi Sebastiano. Generally speaking we like questions that involve fundamental ideas in physiscs i.e. help people to understand physics better. We tend not to like questions that just ask how do I do this calculation.

I don't think one can ask an answer

You can ask a question

Or say an answer

For my interpretation of our policy have a look at this post of mine on the meta

If you have a look at this Wikipedia article it gives you F in terms of E and B, so you just need to calculate F^2 then take the trace.

That should be routine, if a bit of a pain to do.

@JohnRennie Hi John. Unfortunately I'm following a university course only twice a month, and with utmost sincerity I would figure it out. I saw the article on wikipedia but do not know where to start since in the university physics course 22 years ago I have never done such operations.

Morning :-)

How is the chilling out going?

Eighteenth birthday! I had one of those once :-)

It was a long time ago!

Hmm, I'm 56 ...

And I don't feel old ...

The last few decades have seen enormous improvements in the health of people over 60.

Basically the generation that grew up with plenty to eat and access to free health care are now in their 60s.

So that generation aren't the broken down wrecks that their ancestors were at 60. They're now going on adventure holidays and buying sports cars.

I would generally interpret the boundary between middle age and old age as the point where increasing infirmity stops you from doing the things you used to enjoy, and that now happens a lot later.

@Kaumudi.H: I'm currently cooking a mixture of beef mince and smoked pork sausage that is going to make a sauce for tomorrow's meal. I know it's not your idea of good food, but it smells absolutely fantastic! :-)

It just needs about 20 minutes more simmering then into the fridge to keep until tomorrow.

@Sebastiano: I've just done the calculation and it took less than a minute. Can you give me some idea of where you get stuck trying to do the calculation for yourself?

A day early!

Midnight?

Ah, so technically that's tomorrow :-)

They're deliberately torturing you!! Families do that sort of thing :-)

I'm not sure I can wait until tomorrow to eat the sauce I'm making. I might give in to temptation and eat it today ...

I can't do that with my family. We're all old enough that we have everything we want - well, anything we might reasonably want, I still haven't got a Ferrari.

And I always give my niece Amazon tokens so she can buy whatever she wants.

Giving tokens always feels a bit like I can't be bothered to think of anything really good, but she much prefers tokens.

I honestly can't think of anything my niece really wants that she hasn't already got.

But then she's not particularly materialistic so she doesn't want that much.

My niece would say: very nice Uncle John now where are the Amazon tokens? :-)

My niece would say: very nice letter Uncle John now where are the Amazon tokens? :-)

That would be telling. Quite a lot by the standards of a 15 year old, though not much by the standards of a 56 year old.

She asked me if i could split them up so rather than a lump sum once a year she gets another batch of tokens every month. Then she can choose whether to spend them immediately or save them up for something big.

Amazon gift cards

Not recently. I do it very few years if I'm feeling bored.

But you get lots of other more famous John Rennies. There's one who writes for Scientific American, and there are a number of 18th and 19th century John Rennies who were Engineers. One of the London bridges was built by an engineer called John Rennie.

Rennie is a Scots-Irish name, and there are quite a lot of Rennies around. And given that the Scots-Irish were staunch Presbyterians they tended to name their sons with biblical names - John is obviously a common bibilical name since it's one of the Gospels and the writer of the Book of Revelations.

I rank pretty low on the roster of famous John Rennies :-)

I am certainly the most famous John Rennie on the Physics SE

No :-)

Howdy

@Kaumudi.H About an hour.

I need to head off and buy stuff for lunch some time between 12 and 1, and I'll be gone for a couple of hours. However I'll be back here mid to late afternoon BST.

Was there something you wanted to ask?

Ask now?

No problem. Just ping me and I'll see it the next time I log onto the chat.

@YashasSamaga What was your method for dynamically allocating a 2-D array that was compatible with normal syntax again?

@BernardoMeurer int* board[BOARD_SIZE]

Then:
for (i = 0; i < BOARD_SIZE; i++)
  board[i] = (int*} malloc(BOARD_SIZE*sizeof(int));

Ah, yuck :P for-looping callocs gives me shivers

it's such a nice opportunity for blowing things up

I agree. Use a single array, do your own pointer arithmetic and wrap it all ina struct and a few associated functions.

inline the functions and it should be as fast as a native 2D array

@JohnRennie I want to replace the whole board variable with a nice struct, but I want to have the project working first

so if I can't rewrite the logic for using the struct I can still deliver it and get my grade

@Slereah It's $\mathrm{GL}(n)$ for a generic manifold, reducible to: $\mathrm{GL}_+(n)$ for orientable, $\mathrm{O}(n)$ for Riemannian, $\mathrm{SO}(n)$ for orientable Riemannian and the corresponding special holonomy groups for orientable Riemannian with special holonomy.

@BernardoMeurer ideone.com/axi6aG

@BernardoMeurer I made a typo in line 15, the sizeof must have (int) instead of (int*).

It wouldn't matter because size of pointer = size of int

but it is still bad code :p

@BernardoMeurer I also forgot to add free :P

@JohnRennie You can do the malloc once and then manually fix the indirection table :P

It probably doesn't matter because the allocation is done only during initilization.

It might have made a difference if the number of rows and columns were a big number. Having arrays of columns stored at different locations would cause the CPU to flush the cache.

@BernardoMeurer Try this:

#include <stdio.h>
#include <stdbool.h>

typedef struct _Board
{
  int size;
  int* cells;

  int  (*get)(int, int, struct _Board*);
  void (*set)(int col, int, int, struct _Board*);

} Board;

inline int _BoardGet(int col, int row, Board* this)
{
  return this->cells[col*this->size + row];
}

inline void _BoardSet(int col, int row, int value, Board* this)
{
  this->cells[col*this->size + row] = value;
}

bool _BoardInit(int size, Board* this)
{
  this->size = size;
  this->cells = (int*) malloc(size*size*sizeof(int));

@ACuriousMind why are you telling him things

@0celouvsky Because I like to tell people things?

That's...kind of why I'm here :P

That and supporting @AccidentalFourierTransform's upcoming communist uprising

@JohnRennie _BoardSet and _BoardGet won't be inlined because you are using its address.

He's having an uprising?

@skullpetrol I'm just going by the star board

@ACuriousMind I hadn't heard the thing about holonomy, how does one prove it?

@Slereah It is GLn(R)

Ah, ACM gave a better answer.

@0celouvsky The reasoning is exactly the same as for why the Riemannian case has merely $\mathrm{O}(n)$.

Hi guys

o/

How's it going?

i'M CONFUSED.

rip

@Danu About the location of caps lock?

lol

anything

I have $TZ=T\pi\oplus \pi^*(T M)$

where $T\pi$ is the rank 2 (real) vertical tangent bundle ($Z$ is a fibration over $M$)

Then $p(Z)=p(T\pi)\cdot \pi^* p(M)$ ($p$ the total Pontryagin class)

Since $T\pi$ is rank 2, it only has $p_1$ hence $p_2(Z)=p_1(T\pi)\pi^*p_1(M)+\pi^*p_2(M)$. But my supervisor told me that $p_2(Z)=\pi^* p_2(M)$ and all the computations come out right if I take that.

Neither of the $p_1$'s is zero though, and their cup product isn't either. WTF

Am I doing something stupid?

$p_2(T\pi)$ is trivial?

(I dunno anything about Pontryagin classes but I understand some axioms)

It's rank 2, $T\pi$, so it only has $p_1$

Ahh, ok.

I dunno

@ACuriousMind Hmm? I use gram-schmidt in charts

that gives you SO at best

what am I missing?

[Warning, the following naive idea may not necessary make sense]

(NB I put light cones on the loop so that people won't think I am making a jump there, as jumps like that are not allowed by GR)

@ACuriousMind hello there comrade

WAKE UP PEOPLE

WE STILL LIVE UNDER THE DICTATORSHIP OF CAPITAL

::drinks blood of child worker::

yes, it's wonderful

workers of the world, unite

@0celouvsky Oh, okay, then it's not the same reasoning. I was thinking of the following general fact: If you've got a tensor that is stabilized (left invariant) by some subgroup of $\mathrm{GL}(n)$ at every point, then you can reduce the structure group to that subgroup.

In the Riemannian case, the metric itself is that tensor, stabilized by $\mathrm{O}(n)$

Til

How does one prove that?

Say you've got a tensor $\phi\in (\mathrm{R}^n)^{\otimes k}\otimes(\mathrm{R}^n)^{\otimes l}$ that's stabilized by $G\subset\mathrm{GL}(n)$.

Then choose a trivializing cover $U_i$ of the frame bundle with sections $s_i$

So if I have a tensor field $\Phi$ on the entire manifold that's stabilized by $G$ at every point and is locally $\phi$, I can pull it back by these sections

The compatibility condition with the transition functions is $\phi = (s_i^\ast)^{-1} s_j^\ast \phi$

So $\phi$ is stabilized by the transition functions, hence the transition function can be chosen to lie in $G$, which is precisely what reducing the structure group is.

Is this a tensor field?

Oh, I didn't read

@ACuriousMind btw, did you figure out how to prove the parallel spinor thing?

@0celouvsky Which one?

@ACuriousMind sufficiency of G2 holonomy

@0celouvsky The issue was that the associated fixed point in the spinor representation might not lift to a globally defined spinor field?

@ACuriousMind Yeah. It's more or less clear how to extend it, just do it along geodesics.

But it's not clear that this is unique unless the manifold is complete

And that the result is, well, parallel. It seems difficult to show it's even smooth.

I'm thinking you do the above in reverse: Reduce the structure group to $G_2$, which we can do since we know it's necessary, trivialize the spinor bundle and pick smooth sections, pull the constant spinor at a point back by those sections, since the transition functions act trivially there's no issue in gluing to a global field, there's your holonomy-invariant spinor field

One might also be able to just invert the equation that gives the 3-form in terms of the parallel spinor - I just said I'm not sure whether that's possible, but it's not a differential equation, so I suspect it might just work algebraically, I haven't looked

In a way, my first construction is a generalization of the always-existing zero section of a vector bundle - the vector bundle has structure GL(n), and the 0 is stabilized by it, so you can always get a global section since the transition conditions are trivial

That, then, is also the obstruction to the global section of a principal bundle - by definition the action on the fiber has no fixed points, and in fact a principal bundle with a global section is trivial for that reason

@JohnRennie Why did you make those functions inline?

Attempting compilation I get:

/usr/bin/cmake --build /home/meurer/src/Cexamples/cmake-build-debug --target Cexamples -- -j 8
Scanning dependencies of target Cexamples
[ 50%] Building C object CMakeFiles/Cexamples.dir/main.c.o
/home/meurer/src/Cexamples/main.c: In function ‘_BoardInit’:
/home/meurer/src/Cexamples/main.c:25:46: warning: conversion to ‘long unsigned int’ from ‘int’ may change the sign of the result [-Wsign-conversion]
     this->cells = (int *) malloc(size * size * sizeof(int));
                                              ^

I guess he doesn't like his functions to be out of line? :P

@ACuriousMind -.-

greenend.org.uk/rjk/tech/inline.html

@JohnRennie Apparently having them as inline causes it not to compile on the basis of the previous log

Removing inline they work fine

Ah, MS compiler treats this different than GCC with C99 standard

or GNUC

Maybe replace with static?

@ACuriousMind Why is it parallel?

Hi, I've a doubt about how to get the torque from cross product result. If you would like to help me this is the link physics.stackexchange.com/questions/322664/…

what do you think why bodies with different mass fall with the same g even though body with more mass has more force of attraction than that of the body with lesser mass?

@defalt F=ma

Mass cancels on both sides

More mass requires more force to accelerate. So there's more force, yes, but it has more inertia too.

@0celouvsky Because if $\psi$ is invariant under holonomy, that means that with the parallel transport operator $\Gamma$ along curves $\gamma$ we have that $\Gamma_\gamma \psi(\gamma(0))$ does not depend on the curve chosen at all and must be $\psi(\gamma(1))$. Therefore parallel transport acts trivially on the object and the covariant derivative vanishes, since it measures the difference between the parallel transported version and the actual version.

@0celouvsky yeah exactly, I wonder why nobody was able to answer when I asked this in my seminar. 100% of people in that hall were not able to answer..People forget about inertia

It's natural to forget what you don't use regularly, no?

@ACuriousMind yeah; I'm having trouble seeing why the curve shouldn't matter

@0celouvsky Fix some other curve $\epsilon$ in the opposite direction. Then for every other curve $\delta$ we have $\Gamma_\gamma \Gamma_\epsilon = \Gamma_\delta \Gamma_\epsilon$, and since the $\Gamma$ are isomorphisms between the fibers they are invertible and we get $\Gamma_\gamma = \Gamma_\delta$.

@JohnRennie Oh yes this struct will be awesome

I'm implementing a "method" that returns a row or column

Does struct = structure?

btw @Qmechanic @DavidZ @JohnRennie @AccidentalFourierTransform @KyleKanos @rob, here's some feedback from EE.se on stuff they weren't very keen on

::nods::

nice

physics.stackexchange.com/questions/318840/… physics.stackexchange.com/questions/305383/about-joule-thief physics.stackexchange.com/questions/304226/… physics.stackexchange.com/questions/302829/…

@EmilioPisanty Why don't I get a mention :(

@BernardoMeurer because you're not on the VTC list on any of the EE questions here

@EmilioPisanty I'm such a pleb I can't even see that page lol

@ACuriousMind ah, of course

@BernardoMeurer frankly, it's not all that interesting

Me too :(

@ACuriousMind to show smoothness though...I guess one should show it's $C^\infty$ along every curve through a given point

@0celouvsky Parallel transport is smooth, no?

@ACuriousMind Yes, but I must have a completely wrong picture of this in my head

I'm picturing $S^2$ with a bunch of great circles

we have $\psi$ defined on these great circles

How do we differentiate "transversally"

parallel transport gives smoothness along curves

we want a smooth spinor field

@0celouvsky No one says we need to define "along great circles". You can define along any curve

So it's also smooth along any curve

@ACuriousMind So is smoothness along every curve equivalent to smoothness? Should be, all the partials will be smooth.

@ACuriousMind yeah, that's what's messing me up

I've had the wrong picture

No geodesics here, the argument doesn't rely on the Riemannian structure at all, it works for any vector bundle with connection that has fixed points of the holonomy group

@ACuriousMind had a bounce from math.se, too physics.stackexchange.com/questions/313960/…

@JohnRennie Oh wow this is going to make everything much nicer

@ACuriousMind appears so, yeah

I can just make movement, game over, and so on all elements of the board!

Woah

This is going to be GREAT

@EmilioPisanty Can't fathom why, though, I see unclosed questions of that type there regularly, and I cannot see the reason because the migration target is already deleted.

Ugh, I'm stuck in algebraic geometry hell again

@ACuriousMind yeah, this 404s for me as well, so no idea

@JohnRennie Time to rebuild this thing using struct powa

@BernardoMeurer Cool :-)

how's that for not mincing words?

@JohnRennie How do I free the struct in the end just free(board)?

I inlined the functions before I made them struct variables. As Yachas said somewhere above, by making them struct variables that defeats the inlining anyway because of the layer of indirection. So just remove the inline.

@BernardoMeurer There's no destructor for structs in C99. Either don't bother, and the memory will be freed when the program exits, or explicitly call a destructor function.

Yes, just free(board).

I'M SO EXCITED

THIS WILL BE TOTES GORGE

I'd be inclined to fork a new project, or at least a new branch, before you head out on this path ... Just in case!

I just backed up the previous code

and pushed my changes

what the hell does it mean for current to lead voltage

it's clearly not the obvious thing

@JohnRennie Actually I'll just rewrite this thing

It needs some good refactoring anyway

I must be retarded

in that picture, the description is clearly wrong

wkipedia is clearly wrong

what the hell is going on

?????????????

it's most definitely lagging

No it is leading.

e.g. the voltage peaks a time $\phi/\omega$ before the current does.

I don't know what fucking picture you're looking at, but in the one I see the peak for $I$ comes before that of $V$

that's fucking leading current

Black is voltage. Yes?

oh

never mind

@BernardoMeurer refactoring - noun, a method of ensuring code never gets shipped :-)

@EmilioPisanty : Noted. Yeah, Several of those questions should probably just have been closed immediately rather than unsuccessfully migrated.

@BalarkaSen shoelaces of the world, untie!

@BernardoMeurer What compiler are you using?

The keyword inline by standards is supposed to hint the compiler to inline but not to force it to inline.

Your compiler saw the keyword inline and really inlined it. When it encountered the function, it couldn't find it because it had already considered it for inlining. Inlined functions don't have addresses.

Dumb compiler.

In GCC, you use the _ _ attribute _ _ tag to force the compiler to inline and in MSVC you use __forceinline to force the compiler to inline.

Just inline tells that compiler to consider it for inlining but does not force it to. It is up to the compiler.

Moreover, the keyword inline is rarely used because modern compilers know better than the programmer. It does the optimizations automatically unless you explicitly tell it to not do so.

According to his statement made at 2:50 of this Feynman and Gell-Mann had offices next to each other for 33 years!