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user116211
12:00 PM
Seeing ally, I'm missing Barrycenter ;/
 
Good lord the chat log
You guys have been prolific this morning
 
yes, we have been walking around in the Poincaré group recently
 
Don't do that, you might get spun around
 
When I solve physics problems and get confused by something changing, I have a tendency to turn it into a "static" problem by plotting out all the possible changes as if they are points, and then represent that change as a trajectory through these points.

It often give me a better idea on what is happening, since I am kinda a computer and can only possess one step at a time

(This is why I suck at dynamical systems, too many things happening at the same time)
Basically my philosophy is Change = trajectory through points in parameter space
 
12:18 PM
@ACuriousMind If we have a vector field converging to a point, like if we take the "everywhere north pointing" vector field on the sphere, will the index at the zero be $(-1)^n$ because it's basically a reflection in all directions at that point
 
@0celo7 Sinks in n dimensions have index $(-1)^n$, yes.
 
@ACuriousMind Yes but why
and how do you know that
 
I'm really not in the mood to give a derivation of that
I have to leave in a few minutes, anyway
 
@ACuriousMind what's the legit definition of a sink
I'll try to figure it out myself
 
Is the divergence operator defined on vector fields on manifolds?
 
12:25 PM
@Secret On Riemannian manifolds
 
In that case, a sink is where the divergence is negative
 
Going from the Riemannian divergence to the topolgical index will be nigh impossible without help
Maybe I should stop skipping ahead in this book
He might explain it somewhere...
 
NB below is what we have gone through a few hours ago before you arrived. (Text version you already read in the chat log)
 
I did not read the chat log
The chat log is too long to be read
 
Short text version: Two ways to think about how an object changed motion when we change frames: 1. A field of fictious force act onto the object to brought its motion to the final state such that it matches the frame when we finsihed changing frames
 
12:32 PM
o.O a pair of pants literally just fell out of my closet
they were hanging up and just fell out
 
2. The specifics of the motion is already assigned to each frame, thus changing frames means you are just flipping through this sequence of frames until you get to the desired one
1 and 2 can derive each other
 
@Secret how do pants just fall out of the closet
spooky action at a distance indeed
 
no idea, except it happens to me too. Perturbation on the conformation of the hanger perhap, causing it to slide out
 
"Chat interview featuring guest speaker Slereah in 4 days" Is this true?
 
Yes.
 
12:44 PM
What is this some kind of Demo content?
 
No
It's all a lie
 
Everything he says is a lie :P
 
@Slereah Is it a quantum event?
@JohnRennie Can I ask you a programming question?
 
@HariPrasad yes of course, though I only know a limited range of languages ...
 
@JohnRennie Is there any way that I can measure the length(distance) that a mouse scroll wheel has covered using C++
 
12:53 PM
No need to shout
and yes
 
Which operating system and what class library?
I mostly program for Windows and there are WIN32 API calls to get the cursor position
 
@JohnRennie Can you just give me an example
 
OK, whenever the mouse wheel is scrolled it sends a WM_MOUSEWHEEL message to whatever window has the focus, and that message contains the amount scrolled.
I don't think there's a call to get the wheel position because the wheel doesn't have a position. All you get the the amount the wheel has moved.
 
the mouse wheel is a gauge theory??
 
@JohnRennie Thats fine. I tried asking this on the c++ chat room on stackoverflow but the didn't give me any answers. Maybe because they are not interested. :(
 
12:57 PM
@0celo7 well, it has a U(1) symmetry :-)
Is this what 0celo7 would mean by REKT?
Thanks for the conversation, I really had to go to lunch, but judging from the comments, I suppose you are not interested in a discussion. It was very useful, anyway to see the actual point you are making here.Thanks again! — ally 50 mins ago
Or is that just dissing? :-)
 
@JohnRennie No
 
Mouse scroll doesn't have $U(1)$ symmetry >:|
It has $D_n$ symmetry, if anything
 
You made an intelligent comment, that's not rekt
@Slereah what's that
 
@HariPrasad what's the context, what are you programming in?
 
Polygon rotation group
 
12:59 PM
Dihedral group?
 
yeah
 
@JohnRennie what's that
@Slereah my mouse scrolls continuously
 
Group of rotations leaving regular polygons invariant
then it might be broken
 
@JohnRennie I am trying build a tool to measure the distance from on point on floor to another by just rolling the mouse through the path
 
@Slereah nope, it's by design
it's a Gaming Mouse
 
1:00 PM
@0celo7 yes but it's not capable of infinitely fine movements
so it's effectively a polygon not a circle
 
@JohnRennie sure it is
 
@HariPrasad what are you programming in? Are you writing in C++ and hitting the WIN32 API directly, or are you using a class library?
@0celo7 there is a rotation angle below which it will not generate a message to the OS
 
@JohnRennie Writing in C++ but trying to find some library to make this possible
 
That angle is effectively the polygonal angle.
If it was me I would write a CMouseWheelDistance class that created a window, gave it the focus then watched for the mousewheel messages.
 
@JohnRennie Some guy on stackoverflow said to backtrack the IP address of mouse. I have no idea what he said.
 
1:03 PM
Oh, hang on, that's not the mouse wheel.
You're looking at how far the mouse has moved i.e. the mouse position
 
@JohnRennie NO! I just want to measure how many rotations the mouse wheel has made :)
 
@JohnRennie Nope :)
 
You mean the wheel on the top between the buttons?
 
@JohnRennie yup
 
So you're going to turn the mouse upside down to do the measurement?
 
1:06 PM
@JohnRennie Exactly
 
Fine, in that case do what I suggested, create a window and process the WM_MOUSEWHEEL messages
@0celo7 Proof?
 
@JohnRennie Thanks I'll try
 
@JohnRennie what kind of dumb question is that
 
@0celo7 I learned from the master
 
@JohnRennie uh, @ACuriousMind ?
 
1:09 PM
@JohnRennie Got it. "GET_WHEEL_DELTA_WPARAM" msdn.microsoft.com/en-us/library/windows/desktop/…
I am coding :D
 
General relativity, string theory and the WIN32 API. Truly I am a God like being.
One day I hope to explain why kinetic energy is frame dependent.
 
@JohnRennie implying you know anything about GR...do you even know that proof that $\Bbb R^n$ is paracompact
(if you do, let me know)
 
@0celo7 yes, but it's a secret
Einstein told me on his deathbed but he swore me to secrecy
 
I doubt he actually knew the proof
Now someone will tell me it's because of local compactness + Hausdorff
+ second countability
but I want a proof from first principles
 
1:28 PM
Right, I'm about to cycle into town but ... there are thunderstorms in Chester at the moment. So if you never hear from again that probably means my bicycle tyres weren't as insulating as I had hoped.

Wish me luck.
 
@JohnRennie Good Luck Sir
 
@Slereah what about Rn
 
Same proof with an n-cube?
 
Maybe
 
1:46 PM
@Slereah do we know of all of the GR books
or are there more GR books out there
 
there's plenty
 
math heavy ones?
 
Probably
 
I think the most advanced one mathematically is Choquet-Bruhat
 
It's lady GR tho
 
1:48 PM
that's rayciss
 
GR is kind of a sausage fest
What GR lady is there outside of Choquet Bruhat
 
science is kind of a sausage fest.
 
depends
lots of ladies in biology
 
maybe not biology
yeah
wonder why
 
2:07 PM
You know
I understand why Einstein had Marcel Grossmann
When you do a physics you want to keep a math guy to take care of the math
 
2:18 PM
@Slereah but the GR that Albert did had no math in it
I don't think he could even write one
damn alfreb
 
user116211
@0celo7 Hmmm
 
@MAFIA36790 I care.
 
@Slereah E is not equal to mc^2
 
@HariPrasad lol
 
user116211
Do you love his futile arguments based on no ground? I'm tired of that.
 
2:26 PM
Don't get smart with me young man
 
user116211
Hopefully we are at peace now.
 
@MAFIA36790 I do.
@MAFIA36790 :(
 
user116211
::sigh::
 
Hot damn Milnor you're too slick
 
vzn
@MAFIA36790 seriously? imdb.com/title/tt1497563
 
2:36 PM
@Slereah jesus why is the index of a sink $(-1)^n$
 
What's a sink
 
sink of a vector field
@Slereah It has to be because a sink is homotopic to an orientation reversing diff in odd dimensions
how how to prove that
 
lol
 
user116211
great
 
2:41 PM
a useful site to have around
 
@Slereah Is the determinant of a matrix at all related to the trace
 
user116211
@vzn Physicists are not hoarders ;/
 
In general, I'd guess not?
Errr
No I can't really think of any deep thing that would link the two
 
Ok I have to calculate the index of a source
then the index of a sink will be $(-1)^n$ that
because $v\mapsto -v$ turns a source into a sink
Well, it's clear that I can consider a disk $D^n$ with the outward pointing normal
now the Gauss mapping of that thing is a diff onto $S^{n-1}$
and that has degree $+1$
then by flipping each coordinate axis I get a factor of $(-1)^n$
So the index of a sink is $(-1)^n$. @ACuriousMind I figured it out.
@Slereah oh lord there's a song on that too
:DDDDDD
@Slereah Hmm, now I have a better question for you
Consider a vector field $v$ on $\Bbb R^n$ with a zero at the origin
Suppose on the unit sphere, $v$ points everywhere outwards
 
supposes
 
2:48 PM
What is the sign of the divergence of $v$
It has to be positive, but why
 
On the sphere?
 
@Slereah on the disk, ideally
 
Hm
How do you define the divergence
 
$\operatorname{tr} \mathrm d v$
 
The old physicist way to define it is as the flux on a surface, with the limit of 0 volume
 
2:51 PM
because $v:\Bbb R^n\to\Bbb R^n$ its derivative is defined
well now hold up
hmm, don't hold up
 
Oh
What about
Stoke's theorem
 
Yes that's what I'm using
i guess you can argue that since $v$ points outwards, $v\cdot dS$ is positive?
 
Since the flux is outward, you have $\int v d\Sigma > 0$
 
indeed
 
So $\int dv > 0$
So...
where to go from there
 
2:55 PM
But that doesn't mean it's positive everywhere in $V$
 
yeah
 
But it should be
 
Should it?
 
@Slereah it should at least be positive at the origin
 
Can't we have like a ring inside where $v = 0$?
arbitrarily many such rings
 
2:57 PM
I'm defining $v$ to have only one zero
 
Ah, then that's easier, I think
 
@Slereah that's how Arnold defines the exterior derivative
 
If it's continuous and only has one zero, then I think $\int dv > 0$ implies $dv > 0$
 
No
 
Why not
 
2:59 PM
because that's the divergence
not the vector
the vector has one zero
its divergence need not vanish anywhere in there
but it could vanish
 
Hm
True
Is the divergence continuous, at least
 
Yes because $v$ is smooth.
@Slereah Ok let's return to that in a bit...
@Slereah I have a hunch that any smooth vector field defined on $S^n$ is smoothy homotopic to the outward pointing normal vector field
if this does not have a zero of course
 
sounds reasonable
 
Hmm, maybe it only works if the vector field is point outwards
Now what would this homotopy be...
Alright, so let's work with $v$'s unit vector field $\hat v$
Then $\hat v:S^n\to S^n$
And we have the unit normal vector field $\hat n:S^n\to S^n$
Oh no that doesn't work
I was trying to adopt the proof of the hairy gonads theorem but no luck
 
@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ goma saba...
sublime ;-)
 
3:09 PM
Cool @yuggib :D
 
@Slereah Ok, Milnor DOES claim that if $v$ points outward along the boundary, then it's homotopic to the normal vector field.
 
10 messages moved to Trash
 
why are are injective group actions called faithful lol..
so silly
 
@JohnRennie what the hell
>:((((
 
Just keeping the peace
 
3:19 PM
Keeping things peaceful is nice @0celo7
 
WHAT
RANDOM WEBSITE HAS MY FORMER PSE AVATAR
WHAAAAAT
this is for work holy crap
oh my god you can't change the picture
 
better hope your future employers like memes
 
what the hell
 
You're a raider4life now ;-)
 
:(
 
3:26 PM
maybe you can pretend that you're the person in the picture @0celo7
 
Raider fans are not pretenders
we're contenders
 
user116211
@0celo7 Have you googled your name? this avatar pops up first ;/
 
@MAFIA36790 what the fuck
Link?
How is that even possible
 
Google indexes all these chats
No big deal
 
3:42 PM
@Slereah Wait a moment
wait just a gosh darn moment
is a vector field that points some places outwards and some places inwards zero at some point
if it's smooth
it's true in one dimension
Yeah it would have to be
If you project onto the normal direction and take the dot product with the outward normal it follows from the intermediate value theorem
 
You know how the direct product between ordered pairs was defined @0celo7 ? What if it's just $g \times (x,y)$? How is that defined?
fuck i mean a dot
$g \in G$ where $G$ is a group, $(x,y)$ is in a plane
okay apparently it's defined as $(x + gy, y)$
 
4:00 PM
@Slereah I'm so fat I knocked over a chair when trying to sit down :(
 
@0celo7 washes himself with a rag on a stick
 
@Obliv ...what
@Slereah it's true :(
 
like jabba the hut :D
 
Mrs. Lereah is my Leia
It even rhymes :D
 
4:02 PM
inb4 someone takes offense to that meme @slereah
 
good lord why is this so hard
 
Reminds me of
 
damn topology
@Slereah rekt
 
I have printed materials on toroidal wavefunctions
I'll put them in the bathroom to read during the toilet time
 
@Slereah Holy crap finding this homotopy is going to kill me
I cannot find it
 
4:04 PM
@Slereah Are they printed on soft paper?
 
Nah
 
@JohnRennie don't star that, you'll get me banned!
 
why are you talking to yourself
 
@Slereah I need a smooth, position varying $\mathrm{SO}(n)$ transformation
that rotates the vector field into the normal
and them I multiply the parameter by $t$ and boom there's my homotopy
 
@Slereah no-one else will listen
 
4:08 PM
but somewhere I'm sure I need that it's outward pointing ONLY
which means that $v(x)\cdot n(x)\ne 0$
so that should show up in a denominator, I'm sure.
 
One point I'd like to make (and I'm naming no names here) flagging posts attracts stray mods into our cosy little den here, and that's rarely a good thing. I think all the chat room members should think long and hard before raising a flag.
 
@JohnRennie Can room owners see who flagged
 
Indeed they can :-)
 
<- Exhibit A: a stray mod
 
@JohnRennie Well then.
 
4:11 PM
@Loong :-)
 
which post was flagged? @johnR
 
@JohnRennie you'd better watch out @JohnRennie
I've got my eye on you
 
I said I'd name no names.
My point is just that if we want this chat room to be just the way we like it then we should not be attracting outside attention to it.
 
I think we all know who flagged.
 
what, are you ASHAMED of us?
 
4:13 PM
Clearly The goblin has a sock puppet
 
God, now you've attracted dmckee :-)
 
@johnR i meant the actual post that was flagged, not the person who flagged.
I have a feeling it was the #slaveleia tweet lol
 
@Obliv no the one about the toilet paper
 
@0celo7 that was not offensive. it had to have been the tweet, no?
 
@Slereah hey is there a good way to add two vectors of length one and get another vector of length one
@Obliv it was offensive
 
4:15 PM
@Slereah For the record I value all the regular contributors to the chat room and the room is a better place for your presence. Yes, that even includes you 0celo7.
 
Divide by norm???
 
@JohnRennie Why would I think you don't value me
You're weird
 
@0celo7 I'm a physicist
 
I'm clearly the reason this chat exists
@JohnRennie no you're a chemist.
 
Physical chemist
 
4:17 PM
And I'm a Student but my name isn't Stu
 
is it dent?
 
No
@Slereah how do I divide by the norm
 
Physical chemists know both physics and chemistry. That makes us clearly superior to people who only know physics.
 
$$\frac{a+b}{\| a + b\|}$$
 
4:20 PM
Indeed, multiple times an abstract concept in physics is often consolidated in my physical chemistry lectures

Chemistry is THE CENTRAL SCIENCE, thus it mixes nicely with some medicine, biology, and physics (even maths and stat when you consider the epxerimental side of things)
You know a bit of everything when you do a chemistry degree
 
My only chemistry book is Henley's formulas for the home and workshop
 
@johnR do you know anything about bohmian mechanics? I didn't really know about this deterministic formulation of QM until recently. Why isn't it more popular if it's just as accurate?
 
and you know enough to self study for other science once you do the more molecular side of physical chemistry
 
Bohm can't do spins and it can't do relativistic theory
 
There's too much memorization in chemistry.
 
4:22 PM
Or with a lot of difficulty
 
@Obliv I don't know much about it. It isn't popular because it's more complicated and gives exactly the same results as regular QM. So why use it?
 
@skillpatrol That's only really true for organic chemistry (as you need to memorise a host of reagent conditions which often has no underlying explanation other than it works), for other chemistry disciplines, usually some guidlign principle will allow you to derive msot things qualitatively and in some cases quantitatively
 
@slereah arxiv.org/abs/1305.1280 is a paper on spin described by bohm mechanics
 
for example, when thinking about chemical reactions, to first order you only need to know about what controls the rate of reaction, orbitals, and thermodynamics
 
oh you said or with a lot of difficulty
 
4:26 PM
But that makes the entire subject's philosophy memory based. @Secret
Just look at BioChemistry.
 
@JohnR I guess for computational reasons, it's easier to use QM. However, for the theoretical side, it makes sense to grapple with different theories that predict the same thing, no?
 
@Obliv yes it does. People grappled with BM when it was first formulated, then rapidly abandoned it when they didn't learn anything useful from it.
 
but you know thermodynamics and rates equations from your physics classes. If that is hard then I will argue physics concepts is a lot of memorisation too

Biochemistry is a subset of mostly organic chemistry and some inorganic and phsyical chemsitry. That one is REALLY a lot of memorisation due to the complexity of proteins (and the myrid metabolism pathways and chemical pathways these components interact
so yes, the bio side of chemistry is heavily memorisation, but the other branches of chemistry is not so. Take physical chemsitry as an example, it is actually quite simmialr to physics
and atmospheric chemstiry you can use 5 basic rules to derive the fate of any molecuule you released into the atmosphere (to first order)
 
Ok, we agree then :-)
 
@JohnRennie btw what's your view on physical chemistry and memorisation, based on your experience?
 
4:32 PM
Doing a degree requires lots of memorisation whatever course you choose. I don't think physical chemistry is any worse than physics at degree level. When you start postgrad work you specialise and rapidly forget all the stuff you had to learn for your degree.
 
Anybody in here think of 'differential calculus' as living in 'locally-convex topological vector spaces'?
@Secret a book like McQuarrie sets up physical chemistry as an extension of quantum/statistical mechanics pretty nicely with as little memorization as possible
I agree it is a sheer nightmare trying to learn biochemistry
So much memorization it is insane, but it's so cool :p
 
I thought differential will mean it is locally flat instead (since a differential is a linear approximation of the manifold) ?
@bolbteppa yeah, just the names of the proteins and what they do will drive you nuts. But that's nothign when it comes to metabolism networks
 
It has driven me genuinely nuts just trying to remember the 20 amino acids
 
i wish I could just download all the math required for physics into my brain already ;(
 
@Obliv your brain will explode due to overload with too much info in a short time
 
4:36 PM
@Obliv me too, that's why I'm trying to read Bourbaki so I just know everything from the ground up as best I can so I can then ignore it :p
 
@bolbteppa which book?
 
(on pics) To me: Screw that, just tell me the main steps and the important components. The names are JUST labels, they don't matter to me other than identify them
 
All of them, right now trying to understand why they didn't write book 4 after book 5 as the 2nd half :p
In other words, why didn't they explain calculus as an application of 'locally-convex topological vector spaces', even in Dieudonne's treatise he does calculus in Banach spaces which Bourbaki don't even do, even though all their other books are the pinnacle of generality (ignoring categories)
 
Ironically, I like to draw network diagrams
 
4:39 PM
What a surprise :P
 
@bolbteppa are you talking about elements of mathematics? That's a LOT of books.. good luck :D
 
In fact, the main reason why I like organic chemsitry despite the memorisation is because I like to draw mechanisms
http://rowdysites.msudenver.edu/~wiederm/401chp/unit1chp/vonrichterchp/rosenblummech.gif
I am known among my peers to draw mechanisms that fly in all directions
...which kinda reiterate the point that Acuriousmind said I need to learn how to present things linearly and coherently
 
Try to develop your verbal reasoning skills.
It will pay off in the long run.
 
@JohnRennie just browsing back, I disagree with this rather strongly. I think that if the room is in a state where we have major concerns about what reasonable outsiders (mods or otherwise) will see in it, that is a problem.
Or to put it another way, we shouldn't have flag-worthy messages posted in the first place, but if they are posted, the flags are not the problem. It's the messages that are the problem.
 
We don't live in an ideal world.
 
4:52 PM
I'm not suggesting the room should be a den of iniquity, but I sometimes feel those reasonable outsiders aren't that reasonable. I don't think this is malicious, it's just hard to judge a room when you don't know anything about it.
My main point is that if someone doesn't like a post of mine they should say so rather than flag it.
 
you will never find a more wretched hive of scum and villainy
 
We are all basically reasonable people here, and while no-one likes being told they are wrong if you tell me I'm wrong I will listen (then disagree ;-).
I would hope this applies to all room members.
 
@JohnRennie That I agree with. Chat flags shouldn't be cast willy-nilly, to be sure; only for situations where attempts to resolve the problem by just talking aren't working.
 
Then we agree :-)
 
Wars are what happen when words fail.
 
4:56 PM
I guess I take issue with the reasoning that having moderators from elsewhere on the network come into the room is inherently a bad thing, to be avoided, and therefore we should hold back from flagging things that are otherwise worthy of flagging.
 
Having moderators from elsewhere on the network come into the room is inherently a bad thing and is to be avoided. It means we can't keep our own house in order and that reflects badly on us. We should hold back on flagging unless it's really necessary. Then we should flag.
 
See, that's the issue: I think the inherently bad thing is being unable to keep our own house in order. Having moderators come into the room is merely a consequence of that. It's an indicator of a bad thing, but not a bad thing itself.
 

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