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00:00 - 14:0014:00 - 00:00

2:02 PM
Oh it goes back all the way to chapter 2, actually
It's the "tangent map"
Weird to not use $df$ or $f_*$
Maybe I should read all of it
Let's see if it's affordable
It is not
won't be reading it on the can for a while
 
I have it. Quite a worthwhile book
 
yeah
Lee seems to do fine books
 
Different Lee
 
Didn't he do the topological manifolds one
possible photo of Jeffrey Lee
 
2:17 PM
@Slereah that’s Jack Lee
You’re reading Jeff Lee
 
Too many lees
Not Jack Lee, apparently
But John Lee
 
John is often called Jack in the states
And he goes by Jack
 
wot
"John M. (Jack) Lee"
Well I'll be a monkey's uncle
Is his full name John Jacob Jingleheimer Schmidt
(his name is my name too)
 
Samuel Jacob?
 
^footage of John Lee
Lee uses $\jmath$
Disgusting
 
2:43 PM
Lee defines $\iota : E_p \to E$ and then writes $\iota (T_y E_p)$
Why is this allowed
$T_y E_p$ isn't a subset of $E_p$
Or is that supposed to be $\iota : T_y E_p \to T E_p$ here
But then there is $T_y \iota (T_y E_p)$
Which sounds like $\iota$ should indeed be a subset of $E$
 
@Slereah I’m in class right now, I’ll answer you in a bit
 
Is it because $T_y E_p \approx E_p$
no problem
It's no life or death situation
Fortunately I don't have to solve differential geometry at gunpoint
 
3:01 PM
Lee does indeed have the Koszul connection from the Ehresmann connection
But it takes a bit of math
 
@Slereah what page is the doubt
 
510
Lemma 12.8
 
@Slereah btw there are errata on his website
also additional materials
 
Yeah I know
The principal bundle stuff is there
 
there's a typo in the proof of Lem 12.8
what is your issue with Lem 12.8
 
3:15 PM
cf what I said
32 mins ago, by Slereah
Lee defines $\iota : E_p \to E$ and then writes $\iota (T_y E_p)$
 
he seems to be writing $T_y\iota(T_yE_p)$
which is defined by definition of $T$
 
Oh wait, is that $T_y \iota$ as in the tangent map of iota
Or is it the tangent bundle of the image $\iota (T_y E_p)$
 
clearly the tangent map of iota
 
I guess the first one since it would be $T_y \iota : T_y E_p \to T_y E$
 
the notation is shit, but what can you do
 
3:18 PM
This notation is confusing me
 
@Slereah that's right, I think
 
Does anyone else use this notation?
First time I'm seeing it
 
straumann
 
We need more letters to do math
 
@Slereah I got some shit yesterday for notational overload in the seminar
which went really well considering it was all from memory with no real plan
 
3:23 PM
How did the presentation go
 
really well, although the guy we were counting on to do two talks said he had no interest
which was quite a surprise
but there's still five of us so it can be done
 
I'll just fill in for him
I'll just ramble on about spacetimes
 
@Slereah we can skype you
 
probably not
 
How big was the audience?
 
3:27 PM
@skullpatrol the usual, 7 profs and a grad student
 
did you slander the noble profession of physicist
 
@Slereah I did!
others jumped in
best one was "of course there's no rigor in physics because then they can pretend their stuff makes sense"
 
Well it's harder to make sense when you can't invent the rules!
 
sense is not made, it evolves :P
 
For a given base manifold and fiber, can you have a fiber bundle for every Lie group acting on the fiber
Like if the fiber is $S$, is there a fiber bundle for the structure groups $D_n$
 
3:35 PM
so we're gonna prove the PMT this semester
 
Actually now that I think of it that might be the twisted torus
 
I want to do Poincare conjecture next semester
 
is it the one that's solved or still unsolved
 
solved in 2002 by Perelman
 
how bad is the proof
 
3:36 PM
but there's recent work to simplify the proof
@Slereah multiple hundreds of pages
 
Is the structure of the proof like
 
I don't know the proof
 
THEOREM : Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.
PROOF : [300 pages]
and that's the whole paper
 
no, you develop the theory of Ricci flow with surgery first
 
I wonder if there's any GR consequences to this
 
3:38 PM
classification of spatial topologies
 
yeah
I guess it means that the only two simply connected spatial topologies are $S^3$ and $R^3$
or something
 
the theorem is for compact manifolds
I don't know what the situation for noncompact ones is
 
Good thing string theory only has 2d compact manifolds
 
Hey, mind if I barge in with a quick question?
 
3:59 PM
Oh no it's president Giscard
 
and "42"
:-)
 
Yay someone got the reference!
If I've got a ~20 kev electron beam spinning around in a light magnetic field
Such that the radius of the orbit is on the order of magnitude of a meter or so
What factors will lead to the decay of the beam energy?
There's cyclotron/synchrotron radiation, naturally
 
@Giskard42 You mean something like a cyclotron?
 
@JohnRennie Yeah. Is cyclotron radiation going to be the main power draw?
I was thinking about what factors would prevent using an electron beam for energy storage - there's gotta be some high power loss factor, otherwise an electron gun and a magnet
would make a battery with unheard of energy density
 
@Giskard42 the power draw of the magnetic coils and/or their cooling system.
 
4:12 PM
@Slereah ...
The compactification thing is a 6 dimensional manifold
 
@EmilioPisanty That's not pulling energy off the beam though
I mean, magnetrons use permanent magnets and no cooling system, so for a low-energy beam that can't even be a large factor
 
@Giskard42 the electrons in the beam will repel each other so your beam will diverge and drift apart. You'd need some active focussing of the beam and that would take power. For a large electron density the focussing would be very difficult if not impossible.
 
@JohnRennie There we go. I knew it had to be impossible, because otherwise everyone would do it.
Thanks.
 
@JohnRennie Can I use $PdV= nRdT$ in a process with $PT= k$, k = constant?
 
Your expression $PdV= nRdT$ is only true if $V$ is constant.
 
4:22 PM
why so?
 
@BernardoMeurer you say you like non-protected keywords? I just had a line of code that was basically: data type type type.
 
@Abcd The ideal gas equation is $PV = nRT$ so $d(PV) = nRdT$
 
Okay, fine.
 
Each of the 3 type there is something different, and one is a keyword.
 
And $d(PV)$ is done with the product rule $d(PV) = PdV + VdP$
Oh ...
 
4:24 PM
yeah, I know that.
 
@0celo7 yeah but you don't have to sum over it
 
I meant $P$ has to be constant i.e. $dP=0$.
Oops :-)
 
Yeah, fine. I understood that.
 
But if $P = k/T$ then $P$ isn't constant if $dT \ne 0$
 
@JohnRennie $T= 1/P \implies dT = \ln P $? right?
No
 
4:36 PM
you integrated :-)
 
$dT = - p^{-2}$?, right?
 
There's a dP missing.
 
$dT = - P^{-2}dP$
 
@JohnRennie why?
 
Bah. Ninja'd again :-)
$T = P^{-1}$
$\frac{dT}{dP} = -P^{-2}$
$dT = -P^{-2}dP$
 
4:39 PM
can't we directly take infinitesmals on both sides of equation?
like here: $d(PV)= nRdT$
Here we don't differentiate.
We just take infinitesimals of both sides of the equation.
 
Sure, but you actually need to take it on both sides, then - you had an infinitesimal lhs but a finite rhs
And there is no such thing as taking infinitesimal without im- or explicitly differentiating
 
Okay, fine.
 
To wit: $d (1/P) = (d (1/P) / dP) dP = -1/P^2 dP $
(Excuse the terrible formatting, on mobile :P)
 
is this implicit differentiation?
 
not to mention using "To wit" :P
 
4:44 PM
@Abcd this is physicists commiting grave crimes against mathematical rigour :-)
 
@Abcd that's not a technical term, but that is what I meant by implicitly differentiating when "taking infinitesimals", yes. The proper mathematical treatment of this is via differential forms
 
@JohnRennie I don't get why treating infinitesimals like fractions always works fine...
 
@JohnRennie actually, this is perfectly rigorous once one realizes the "infinitesimals" here are just differential forms on thermodynamic state space.
 
@Abcd it just does. Accept it and move on :-)
 
@BernardoMeurer Well, I have a mac which means there is a POSIX core down there. I can test most POSIX related things but the OS uses more modern facility for some things.
 
4:47 PM
$df= (df/dx)dx $ does hold rigorously for forms, no shenanigans with fractions necessary
 
@Abcd just don't show any real mathematicians your working :-)
 
5:27 PM
-1
Q: I don't understand this

SkyWalker Can anyone tell me why I am banned from asking questions ?

 
5:41 PM
what is the topology of the thermodynamical space, though
Is it $\Bbb R^3$
Is it that contact manifold thing from thermogeometrodynamics
 
Anonymous
6:39 PM
@JohnRennie I was using srand(time(0)) as a seed whenever I needed to generate random number. However, the problem is that it returns the time in seconds. I need a new random number within a certain range (0.0-100.0) every time a certain loop executes (which I presume to be several times a second). srand(time(0)) just doesn't have good enough resolution for my purpose. Any trick to get past this?
 
i forget why $a = -1$ in $(L_0 + a)|\psi> = 0$ :(
 
@Blue you only call srand once. After that each call to rand returns a new rndom number. There is no need to call srand again.
 
Oh yeah spurious state stuff
 
Anonymous
@JohnRennie Oh lol. I was doing it wrong all this time. Gotcha, thanks :)
 
7:00 PM
@Slereah time to write a 1 hour talk in 1 hour
that should work out
 
Perfect alignment
 
ola
 
7:57 PM
@ACuriousMind Hehehehe, beautiful!
@dmckee I managed to fix the bug :)
A lingering -1 from initial debugging
Only triggered when two random bools were true
 
Anonymous
@BernardoMeurer Need some C help. Any idea how to seed srand() with nanoseconds or at least microseconds? In my program I'm getting some very similar values in consecutive iterations but iterations which are further apart have different values. I called srand() just once in the program as JR suggest but even then it doesn't seem to work very well.
 
@Blue Don't use rand()!
Are you on a POSIX-compliant machine?
i.e. BSD, MacOS, Linux
 
Anonymous
I have Ubuntu, but currently on Windows
 
Anonymous
You can tell me what to do on Linux though
 
Alright, here's my function to generate numbers on POSIX machines
On windows you can write code that calls a syscall that does the same thing, ask @JohnRennie for it, in fact it would be nice to complete my function
 
8:11 PM
@Slereah didn't work out
I did write two pages
I wonder if I'll have enough time for even that
this should really be a 2 hour affair
 
guess you'll just have to improvise
 
static bool HAS_URANDOM = true; // Global

unsigned int random_uint() {
    unsigned int r_uint;

    FILE *f = fopen("/dev/urandom", "r");
    if (f == NULL) {
        if (HAS_URANDOM) {
            printf("---- Failed loading random generator device /dev/urandom. Defaulting to rand().\n");
            srand((unsigned int) time(NULL));
            HAS_URANDOM = false;
        }
        r_uint = (unsigned int) rand();
    } else {
        fread(&r_uint, sizeof(r_uint), 1, f);
        fclose(f);
@Blue That
And if you want a range
// Inclusive range
// stackoverflow.com/a/17554531/2080712
unsigned int generate_int(unsigned int lower, unsigned int upper) {
    unsigned int r_uint;
    const unsigned int range = 1 + (upper - lower);
    const unsigned int buckets = UINT_MAX / range;
    const unsigned int limit = buckets * range;

    if (range >= UINT_MAX) {
        fprintf(stderr, "Range too big!\n");
        exit(EXIT_FAILURE);
    }

    /* Create equal size buckets all in a row, then fire randomly towards
     * the buckets until you land in one of them. All buckets are equally
 
Anonymous
@BernardoMeurer This one looks good
 
Anonymous
Trying
 
Anonymous
Thanks
 
8:14 PM
It relies on the previous one
@JohnRennie Could you help me finish that random_uint function?
What's Window's version of /dev/urandom?
 
9:23 PM
Does it hve one
9
Q: /dev/zero equivalent in windows?

MatthewI am trying to use the windows version of dd to copy a RHEL iso to a USB stick. However, I wanted to zero out the drive first to ensure there is no filesystem on it before writing it out. Is there an equivalent of /dev/zero in windows that I can use as the infile?

 
10:05 PM
@BalarkaSen the $\mathcal Op$ notation would be helpful for me but it looks so awful
maybe $\mathscr{Op}$
 
@Slereah I was thinking the Win32API has some provisions to generate good random numbers
 
@0celo7 I think it's the root of many-a-confusions
You reading E-M again?
How did your talk go
 
@BalarkaSen no
@BalarkaSen very well
@BalarkaSen well here I really just want any open set containing a point
 
10:22 PM
@0celo7 You giving talks left and right aren't ya
 
@BernardoMeurer people like to hear what I have to say
 
11:28 PM
Perhaps, they also like how you say it.
 
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