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Mew
Mew
09:00
huh
Hmm..
Topology is damn hard for me :(
09:40
hey
it obviously takes some time to study
It is funny you say that. I actually came here because I have some clue how to construct hoschild homology but can't figure its significance. What about topology is it saying, the simple construction is somewhat a bit too algebraic. . .
I can't sleep. . . . I will check this again in the morning
0
Q: Do we want chat notifications of potentially low-quality posts?

David ZThere is a chat bot called Smoke Detector, active on several other SE sites, that automatically checks for potentially low-quality posts and writes chat messages to notify people about them. These messages can be posted to a dedicated chat room, as for Mathematics SE, or to the main site chat, as...

 
2 hours later…
11:31
Wait
-1
Q: Why do different color materal differ temperature in the same sunlight?

JenI have a blue, red, and green cup and put a thermometer in each. Of the 3 the blue cup had the coldest temperature inside, then green, then red. I understand there may be differences in the composition of the cups but does color reflect the sun differently? I thought blue being closer to black wo...

waits
This question was posted and then marked as duplicate by the same user and now four people have already voted to reopen it?
No one but the user asking the question closed this question.
And yet people are voting to reopen it. One of the stranger patterns I've seen
But I'd agree it's not really a duplicate
I'm confused
11:46
Goooood morning
8 hours ago, by Secret
user image
@Slereah ^
@Secret 's attempt.
> The category of smooth manifolds is not nice
What does that even mean
@0celo7 It means it doesn't have nice properties. E.g. it doesn't have internal hom and it doesn't have equalizers/fiber products
Non-existence of fiber products, in turn, is indicative that it is pretty hopeless to try to take limits in general
So most of the "powerful" categorical constructions won't work, making a categorical approach to smooth manifolds alone hopeless
If you try to copy

$\mathrm{H}=\frac{p^{2}}{2}+\frac{\omega^{2}}{2}q^{2}=\frac{\omega}{2}(\frac{1}{\omega}p^{2}+\omega q^{2})=\frac{\omega}{2}\frac{1}{2}(\frac{1}{\omega}p^{2}+\omega q^{2}+\frac{1}{\omega}p^{2}+\omega q^{2}) \\ \ \ \ = \frac{\omega}{2}[\frac{1}{\sqrt{2}}(\sqrt{\omega}q+i\frac{1}{\sqrt{\omega}}p)\frac{1}{\sqrt{2}}(\sqrt{\omega}q-i\frac{1}{\sqrt{\omega}}p)+\frac{1}{\sqrt{2}}(\sqrt{\omega}q-i\frac{1}{\sqrt{\omega}}p)\frac{1}{\sqrt{2}}(\sqrt{\omega}q+i\frac{1}{\sqrt{\omega}}p)] \\ \ \ \ = \frac{\omega}{2}(aa^{+}+a^{+}a)$
$H = \int d^3 x (\pi^* \pi + \nabla \psi^* \nabla \psi + m^2 \psi^* \psi) = \int \dfrac{d^3 p}{(2\pi)^3} (\dfrac{\partial \psi^*}{\partial t} \dfrac{\partial \psi}{\partial t} + \vec{p}^2 \psi^* \psi + m^2 \psi^* \psi) \\ \ \ \ = \int \dfrac{d^3 p}{(2\pi)^3} (\dfrac{\partial \psi^*}{\partial t} \dfrac{\partial \psi}{\partial t} + \omega^2 \psi^* \psi) = \int \dfrac{d^3 p}{(2\pi)^3} \dfrac{\omega}{2}(\dfrac{1}{\omega}\dfrac{\partial \psi^*}{\partial t} \dfrac{\partial \psi}{\partial t} + \omega \psi^* \psi + \dfrac{1}{\omega}\dfrac{\partial \psi^*}{\partial t} \dfrac{\partial \psi}{\partial
Jesus
Now of course $a$ is just the fourier coefficient of $\psi$, which I can derive two other ways, but this way is interesting, how do I go from the un-integrated thing to the integrated thing more intuitively?
The star wall is pretty terrible right now.
Unusually terrible.
11:58
Say something funny then
Mister funny man
I'm not funny.
In other words, how is $a$ equal to an integrated thing and to an un-integrated thing
@bolbteppa There is something odd in what you do there. You switch from an x to a p integration in the first step
That doesn't really make sense.
#rektbyACM
Or rather, it means that in the following you have $\psi$ standing for its own Fourier transform, which means that your "unintegrated form" has precisely the "missing" x integration hidden in it
12:02
we have inverse square law in gravitation...But why is the distance raised to the power 2...and not with any random number...like 1.69? Is it coincidence?We had infinite possibilities
That is just what you get after you plug in a Fourier transform right? theory.caltech.edu/~kapustin/Ph205/2013/fall2.pdf It's easier if you don't break it up into two sets of coefficients, skips a lot of algebra
Why is the number had to be so simple
@manshu What do you mean "we had infinite possibilities"? What is your space of events?
Okay I should put Tilde's over the Fourier transforms yes, I think it falls out of the un-integrated thing
@manshu you can derive the inverse square law
12:04
(Probability only makes sense after you define what the space of all possible events is)
@ACuriousMind nonsense
We had infinite possiblities means that there are infinite numbers between any two numbers
the space of possible events is the space of all events
@0celo7 How?
Have you guys ever seen the Dirac Hamiltonian done this way?
12:05
@0celo7 That's not a well-defined space
@bolbteppa Done what way?
The way I just wrote the KG hamiltonian, where you derive the fourier coefficients of the wave function as a by-product through factoring
@manshu Well, but why do you think any other number was possible to begin with?
I just want to skip as much work as possible :p
@ACuriousMind Coz there are infinite numbers...
Think I got canonical/Lorentz EM Hamiltonian looking basically the same
12:06
@manshu I was born with ten fingers - did I have "infinite possiblities" (to have 13248 fingers, for instance)?
@ACuriousMind Never give up on your dreams
There are people with 11 fingers...So you mean that sometimes it doesn't follow inverse square law? it's gibberish
@manshu No I mean that "there were infinite possiblities" is just not substantiated by anything! Not everything that is a number could have been any number.
But, as for why the square in the inverse square law is special, see e.g. this question.
Sure, I could have had 9 or 11 fingers, but 13248 fingers are clearly absurd
12:10
"Not everything that is a number could have been any number."...Sounds like "I am the hero they deserve, not the one they need"
lol
look at the linked question @manshu
yeah.. i was reading it
So, what tells you in the case of physical laws which numbers are "reasonable" and which "absurd"? I think nothing, you can't tell either way, and it is thus meaningless to speak about the "possibility" of laws being different. You can ask whether or not we know any deeper reason that forces the law to be like that, but to speak of "possibilities" for physical laws always has a multiverse-y touch to it that I don't like
In short... you mean to say that "This is how it works"...right?
why is there a 2 in E = mc^2?
12:17
Coz this is how it works
without a 2 it would not be a true equation
More discussion on this topic can lead to severe damages on the way you think about numbers...
@ACuriousMind why not
@skillpatrol dimensional analysis
what is a faithful functor
the opposite of a slutty one?
@0celo7 talking about dimension analysis...Dimensions of E are given by using gravitational force
remember "mgh"?
Kinetic energy will also be affected maybe
damn...I just broke the physics...sorry for that
...what
12:31
never mind
> Trump rescinds pledge to back Republican nominee; Cruz, Kasich refuse to commit support
Damn son
> Trump, who followed Cruz on the town hall stage, said he didn't need a promise of support from Cruz.
lol
trump is trolled
@ACuriousMind People with small heads are so damn smug.
Like physically small skulls.
is he in this room?
ACM?
12:36
I thought ACM blocked me too... :p
He did
how do you know?
He talks in his sleep.
oh...he must be murmuring about me...
cursing me
12:39
cursing you?
13:17
How would you explain the Poincare half-plane model $ds^2 = \dfrac{dx^2 + dy^2}{y^2}$ en.wikipedia.org/wiki/Poincar%C3%A9_half-plane_model I mean wtf is up with this?
@DavidZ Thanks. Yeah, I considered doing it myself, but I figured it might be better to have a Physics mod do it.
13:59
@bolbteppa it's a hyperbolic plane or something like that
Check Zee's book, he talks about it.
Cool, which book?
hi
@bolbteppa which book would talk about geometry...
Thanks, so "the space at one value of $x$ looks exactly the same as the space at some other value of $x$, but it is not translation invariant in $y$."
Is that from Zee?
I sadly do not have his book memorized any more.
14:09
Yeah, pages 67 to 68, basically just gives an example of how to use this model, no idea what it's about still
@bolbteppa you should refine your question
I don't know what your confusion is
Did you read the wiki article?
What the hell is this model, what is it about, why would anybody think of such madness and why is it obvious you should use it in scenario X
It's not a model, it's a crazy space!
I think it has to do with hyperbolic spaces, but I don't know specifics.
Maybe check do Carmo.
It's a hyperboloid of two sheets~
[Random] Claim: Problem of evil is due to the lack of unlimited resources for all possible worldviews to realise their ideals

For starters, there are no infinite copies of every of us to serve someone, to be tortured by a sociopath, to be protected, to be saved from sociopaths etc. etc etc.
14:16
go back to Philosophy SE
How is it linked to a hyperboloid of two sheets?
PhSE is dead unfortunately, hence why the random stuff end up here (the last stable chat that allow discussion of off topics)
Can't find a direct morphismmorphism
But there is one from hyperboloid to Poincaré disk
In geometry, the Poincaré disk model also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which the points of the geometry are inside the unit disk, and the straight lines consist of all segments of circles contained within that disk that are orthogonal to the boundary of the disk, plus all diameters of the disk. Along with the Klein model and the Poincaré half-space model, it was proposed by Eugenio Beltrami who used these models to show that hyperbolic geometry was equiconsistent with Euclidean geometry. It is named after Henri Poincaré. The Poincaré ball model...
$$(t, x_i) = \frac {\left( 1+\sum{y_i^2},\, 2 y_i \right)} {1-\sum{y_i^2}}$$
$$y_i = \frac{x_i}{1 + t}$$
@Slereah dammit man what is your opinion on the goblin Secret drew
Not ideal
14:20
@bolbteppa Do you understand what a manifold with positive or negative curvature is?
The Poincaré model is a simple example of a 2-manifold with a negative curvature.
Yeah but I still have no feel for this nor idea about why anybody cares, this nonsense about cold rulers seems to sync with Zee though!
https://books.google.ie/books?id=TABicHVMQhMC&lpg=PA258&ots=qXVFhA-916&dq=Hyperbolic%20upper%20half%20plane%20metric&pg=PA63#v=onepage&q=Hyperbolic%20upper%20half%20plane%20metric&f=false
@bolbteppa "...why anybody cares...", do you want to know about its applications?
I mean, how would you motivate the necessity of the upper-half plane model to a mathematical child on a desert island basically
AFAIK there are many applications of the Poincaré disk in string theory and CFT, but you have to ask others about that. Besides its applications, it's often used in basic differential geometry to illustrate the concept of a metric.
You know about metrics, like $g_{\mu\nu}$ in Riemannian geometry?
@bolbteppa You can't eat the upper half plane model
14:35
Yeah, but it looks like you can use it to model frozen food shrinking according to the page I linked to
@bolbteppa Necessity is a poor thing to require in abstract math.
@bolbteppa Yes, because the metric is like a ruler that you use to measure things. Normally, rulers have always the same length, so they are pretty boring metrics. But if temperature changes, the rulers will change their length. That's where Riemannian metrics start to get interesting.
Understanding is a vital thing in abstract math though - Why not spend your time computing integrals in random coordinate systems? Obviously you don't because you want to play with interesting ideas, understanding where the upper-half plane comes from means you don't fall into the trap of treating it like doing a double integral in some random difficult coordinates :p
@Bass Yeah but why change it in this way, why model it on Euclidean lengths, very arbitrary the way you're stating it
@bolbteppa There are two ways of dealing with curved spaces: 1) You embed them into a higher-dimensional Euclidean space and "induce" the Euclidean metric of the surrounding space on them. For example the surface of a ball is a two-dimensional manifold that's embedded in 3-dimensional Euclidean space.
But sometimes this is not possible, or there are other reasons to avoid it. For example, we know that our 4-dimensional spacetime is curved, but we don't know whether or how it is embedded into a higher-dimensional space.
2) But you can calculate many things intrinsically, which means you don't have to embed the space into a higher-dimensional space, you just analyze it using the metric.
@0celo7 yo did you see the talk?
14:49
The Poincaré disk model is an example of a space which looks flat to us if we ignore the metric. After all, it's a flat plane. But when you change the metric, the manifold you get is intrinsically curved.
@Bass the poincare disk does indeed have applications in CFT
but mainly as a computational tool
it's used a lot to conformally map hard problems to easier problems
e.g. path integral calculations on half planes
There is a secret behind this that makes it all obvious
@FenderLesPaul IIRC it also plays a role in AdS spaces, which also have constant negative curvature. But I don't know the details.
@Bass yep
there's a local coordinate system for AdS called the Poincare patch
and the AdS metric can be put in a manifestly Poincare disk form in that patch
15:05
@FenderLesPaul what
Did you
see the talk I posted
I didn't know you posted one
Wow
just wow
I would say I'm sorry, but I'm not
And I don't lie
user54412
Oh look, semi-famous person spotted: physics.stackexchange.com/users/112768/john-baez
3
15:13
Who that is
Oh
Baez
he's Joan Baez's cousin!
@ChrisWhite Would you happen to know how to tell when a book on Springer is being released?
or maybe can you access rd.springer.com/book/10.1007%2F978-3-319-26654-1 already with your Princeton powers
I can't even buy it!
15:34
Peter Petersen
lol
@FenderLesPaul can you access it?
I want to learn some more global Riemannian geometry and my prof recommended Petersen among others
I can't off campus
if you give me 2 weeks then I can
actually week and a half
How much of a heart attack would you have if I wrote

$\mathrm{H} = \int d^3x(\pi \partial_0 \psi - L) = \int d^3x(i\psi^+ \partial_0 \psi) = \int d^3x(\overline{\psi} i \gamma^0 \partial_0 \psi) \\ \ \ \ = \int \dfrac{d^3p}{(2\pi)^3}(\hat{\overline{\psi}} \varepsilon \hat{\psi}) = \int \dfrac{d^3p}{(2\pi)^3}\dfrac{\varepsilon}{2}(\hat{\overline{\psi}} \gamma^0 \gamma^0 \hat{\psi} + \hat{\overline{\psi}} \gamma^0 \gamma^0 \hat{\psi}) \\ \ \ \ = \int \dfrac{d^3p}{(2\pi)^3}\dfrac{\varepsilon}{2}(\hat{\overline{\psi}} \gamma^0 u \overline{u} \gamma^0 \hat{\psi} - \hat{\overline{\psi}} \gamm
that's nothing
you ain't a real man until you've calculated a second variation
16:02
@FenderLesPaul are you around
16:16
@0celo7 sup
what
@FenderLesPaul I hate topology
that is all I have to say
Topology hates you
good
I slapped the shit out of it
It would be weird if it didn't hate me too
domestic violence of the homeomorphic character
oh I homeomorphiced him good
16:25
they*
what?
topology is gender fluid
or should I say
gender homeomorphic
17:02
Hello!
hi
why are you so happy
17:32
@Slereah out of fucking nowhere a wormhole appeared and delivered Visser to me...
hurray
Not in great shape
Corners are messed up
Eh
As long as the pages don't detach
The used book place sent it cross-country in a plastic sleeve
Couldn't be bothered to put it in a box!
Hey check one thing for me
Go to page 195
And tell me the page number that follows
17:36
In connection to yesterday's discussion. publish.csiro.au/?paper=PH920591 Would someone like to discuss this paper?
196
Hm
I guess only my copy is fucked up
My copy is like
You want a pic?
193, 194, 197, 195, 196
And then normal
Holy crap that last problem
17:40
Yeah it's a tough one
I wonder if the goblin could solve it!
I'm sure he already has
I think the GR goblin is really smart
He just smoked too much weed or something and something happened to him
recommend me an algebra book please.
Hey folks
papa bless
17:52
@3075 I don't know any algebra
:'(
If you get frustrated by a lack of stated proofs you're not gonna have a lot of fun with Visser btw :p
Reading is for loosers
just sleep on top of the book
3
it works the same, I swear
learning by osmosis?
17:54
Uhum
but you have to really press against the book
@Slereah does he at least give references
Plenty of references
ok, but no GR today
Do like me
I need to make a blog post
17:55
Bake some potatoes instead
2
artin or hungerford?
I'm going to prove some things on the blog today about vector spaces
@Slereah The best solution to a problem I've seen in this chat so far
I am making a burger and baked potatoes
Tasty eatin'
I want to do a post on vector spaces from the manifold PoV
but I need some stuff about their topology first
@Slereah I wonder who has more GR books now
18:00
Iunno
@Slereah well, count'em!
Purely serious GR books, 9
no QFTCS
did you count Visser?
Not counting quantum gravity, diff geom and QFT on CST
I did
yeah, I have 9 as well
oh that's right you have Stephani
18:03
Visser, Hawking Penrose, Hawking Ellis, Walf, Callahan, Stephani, Carroll, Straumann and that one on scalar fields in GR
Hawking Penrose?
"the nature of space and time"
@DeNiSkA: Teachers said that Krotov is too hard me. What should I think about this?
Zee, Visser, Straumann, Hawking-Ellis, Sachs-Wu, Penrose, Wald, Weinberg, I can't count
only 8
9 if you count BEE I guess
Would you recommend SW, outside of the notation
18:05
but they say at the beginning that they have no interest in physics
@Slereah I haven't spent enough time with it, tbh
I got it because it has some interesting stuff that's not standard
@hubot after doing Resnick-halliday (mainly newton's laws and rotational dynamics) hardness vanishes!!
like photon gasses
"Stuff that is not standard" is good
That's the problem with those books
and they also have rigorous proofs of some common lore
You need a fuckload to have most aspects of the theory
18:07
I'm in 5 chapter forces and dynamics
also SW has a shitload of exercises, which might be fun one day
hard exercises
I'm also doing exercises from 3, 4 and 5 chapter
@hubot brings back memories.
@Slereah basically, SW is rigorous as fuck
they do the whole variation of a curve thing with an induced connection, some fancy stuff there
but I got it last week, only read a few pages here and there
@hubot i have not yet completed krotov completely , asterisked questions REALLy kill me!!!
@BernardMeurer you know C++ , right?(i think i have asked)
18:10
@0celo7 how many of those GR books did you read through? WTF do I have to read through that many books to pass a GR course? :(
@DeNiSkA Yes, I know more C than C++ though
and more Python than C
and more magic than Python
@DeNiSkA Have you finished Feynman exercises? Do you also this?
@hubot not completely but i am doing in order!!
@Obliv around 15
@DeNiSkA Do you know something about programming, Wolfram Alpha, Matlab, QCL, electronics etc.?
18:13
@hubot yup i have started C++ and SQL.
@0celo7 I think I'd turn into a shut-in hermit if I read through 15 GR books in 1 semester.
@0celo7 I'll just start learning it asap before I have to take that course x.x
@BernardMeurer then i think you can answer my question (although C is mother of all C's)
@Obliv I like to think @Slereah and I are beyond first semester GR
@DeNiSkA I'm studying C# and Unity3D (game physics mainly) for two years.
dunno if that's true or not
18:14
@DeNiSkA Go for it, I'll help you if I can
Never ask if you can ask a question :)
I'm beginner in Unity3D.
@hubot cool, i will also try unity (for games)
Oh man
Burger and potatoes
I am stoked
@DeNiSkA Do you parents afraid FPS and horror games? My mum is trying control what I'm creating games in Unity3D.
dude topology proofs are long chains of theorems
I hate topology
18:17
@0celo7 Oh thought you guys were taking the course as of right now.
@Obliv no
I have no interest in taking a course on GR, at least from the physics department
@hubot nope and i am not that expert who can start coding a game :-)
@0celo7 You're weird man.
@Obliv what
no one has ever said that to me before
@0celo7 Owns 9 GR books but doesn't take the course at school.
18:20
@Obliv from the physics department
@0celo7 where else can you take a GR course at a school o_o
I do not need someone to tell me what the equivalence principle is or how to calculate the orbit of mercury
@Obliv my advisor in the math department has been known to teach a course on geometric analysis with applications to GR
he's also taught a straight GR course before, too
using Hawking-Ellis and O'Neil
@BernardMeurer ^
Does Qmechanic ever drop by here?
Why did you make a const int instead of a preprocessor directive #define for that value?
18:23
@0celo7 to each his own I guess. As long as you enjoy learning it, the angle you take doesn't make much of a difference.
What's the third line supposed to do?
and the fourth
@Obliv I'm interested in the math of GR, not the physics
an intro physics course will stress, well, physics
why ++ptr and not ptr++?
and the "advanced" course here is just cosmology
ignore third line because it's use is inside for loop and my confusion is on fourth line!
18:24
Those are some good potatoes
@DeNiSkA What error are you getting?
Again, what do you hope to accomplish with the fourth line?
@0celo7 What's so interesting about the math of GR? I have a vague picture of it as something to do with diff geometry and topology.
@BernardMeurer code for counting vowels in word mollie
@DeNiSkA Your switches have no break statement, they are falling through
18:28
@Obliv I'm also interested in Riemannian geometry
and GR is modified Riemannian geometry
yup, because if the letter is one among "a, e ,i ,o ,u"
vowel has to get incremented
Still, fallthroughs are ugly
18:30
@BernardMeurer ;)
because there's no way for the second person to know they were intentionally done by the first
@0celo7 what the heck Riemann'
true
@0celo7 his math is used in GR? this guy is the mvp of the 19th century i swear.
@DeNiSkA is that supposed to run against user-inputted data?
18:31
@TylerH no! only for word "Mollie"
Also, why aren't you using std::string
It's so much better than c-style strings
363
Q: How to convert std::string to lower case?

KonradI want to convert a std::string to lowercase. I am aware of the function tolower(), however in the past I have had issues with this function and it is hardly ideal anyway as use with a string would require iterating over each character. Is there an alternative which works 100% of the time?

because you can call it's objects
vzn
vzn
guys talking about code? need a favor =D
@BernardMeurer yup, but i am having practice on pointer and arrays so i preffered C-style string !!
@DeNiSkA I just hate c-style strings :p
Null terminated monsters they are
18:34
@BernardMeurer haha!
vzn
vzn
@BernardMeurer what kind of stuff do you code
Now my major question:
in fourth line " *ptr=name " this statement makes "ptr=M", right?
my question not yet over...
this is how I'd do this
Note how I organized the if statement by usage of the vowels in the english language
The frequency of letters in text has been studied for use in cryptanalysis, and frequency analysis in particular, dating back to the Iraqi mathematician Al-Kindi (c. 801–873 CE), who formally developed the method (the ciphers breakable by this technique go back at least to the Caesar cipher invented by Julius Caesar, so this method could have been explored in classical times). Letter frequency analysis gained additional importance with the development of movable type in Asia in 1040 CE and in Europe in 1450 CE, where one must estimate the amount of type required for each letterform, as evidenced...
This was the code is more likely to run a little faster
because the if will end first
having done less comparisons
@BernardMeurer hmmm, code looks quite better!
18:54
Help
I ate too many potatoes
@Slereah WHAT?
@Slereah lol
I paid for my potato hubris
@BernardMeurer What's the use off this app you have sent me?
@hubot App? I haven't sent you a thing

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