7:01 PM
vOv

If you're asking for what kind of manifold, I think you usually should just think of $\mathbb{R}^n$, with $n$ being the number of variables you use to describe your macrostates
Actually, it's probably a hypersurface in $\mathbb{R}^n$, the one on which the equations of state are fulfilled.
That is, for the standard setting where we use temperature, pressure and volume $T,p,V$, it's the zero locus of some function $f(T,p,V) = 0$ that depends on the system we are considering.

Is is possible to have a degenerate level set?

@0celóñe7 are you a big fan of the internet's busiest music nerd?

Yes

Look at the first comment here.
You'll enjoy it.

Anonymous
7:12 PM
@BalarkaSen I need some good reference with quite a few solved examples on "epsilon-delta formulation of limits". I'm still struggling with it.

@Blue I don't really have a lot of reference other than the textbooks I suggested, honestly.

Anonymous
I need to see Piskunov

Anonymous
hmmm

Piskunov has lots of examples
and exercises

7:15 PM

Anonymous
Looking for epsilon delta in there

Anonymous
@0celóñe7 Why not?

The correct answer is to learn epsilon n proofs first
They are much easier and the skills carry over

Anonymous
@0celóñe7 What type of proofs?

@blue I'm pretty sure it's on the continuity chapter

7:17 PM
@Blue convergence of sequences

Anonymous
We'll start with convergence of sequence next week I think at uni

Anonymous
Okay

@Blue That comment is basically predicated on the idea that the historical order in which ideas were discovered is the important thing in determining what we're going to consider 'fundamental'.
Most pros use a internal decision procedure based on generality and elegance.

Anonymous
@BalarkaSen Can't find the page in the continuity chapter. Could you tell me the page number if you have the book?

Anonymous
Wait.....41

Anonymous
7:21 PM
Oops 35...found it :)

Anonymous
@dmckee agreed

7:39 PM
@BalarkaSen Jesus Christ I can't read a porno in public
Might poke a hole in my chain mail
@ACuriousMind don't read that it's a GoT spoiler

okay so how does $(\epsilon_{ijk}a_jb_k\hat e_i)\cdot (\epsilon_{nlm}c_ld_m\hat e_n)$ equal $\epsilon_{ijk}\epsilon_{nlm}a_jb_kc_ld_m\hat e_i\cdot \hat e_n$
or should I ask it as a proper q?
I feel like there's a simple rule though so no point.

@CooperCape These two things are not equal - where did the $c$ and $d$ come from?

good point
lemme edit

Aside from that, you're just shuffling numbers around - aside from the $\hat{e}$ which are presumably vectors, the dot product doesn't care how you order the factors.

oh really?
that... would be why
yeah the e's are a unit vector
in directions i & j.

7:42 PM
I.e. you're just using $(a\vec v) \cdot (b\vec w) = ab (\vec v \cdot \vec w)$, and all the indices are just distraction ;P

Anonymous
@CooperCape In $i$ and $n$ it seems.

that one

Anonymous
You wrote $\hat{e^n}$

yeah I just realised :p
thanks @ACuriousMind all the greek and indexes overwhelmed me a tad...

Anonymous
@CooperCape I've not seen you around here much. Are you an undergrad? What subject? :)

7:45 PM
Currently doing physics A-level applying to uni this year for physics.
Just like physics I guess

Anonymous
Oh. So you're a high school student!

uk version but yah

Anonymous
Well, you have loads of good unis in uk unlike here. :P Good luck though

thanks

Dammit, I'm stuck in algebraic geometry hell again

7:47 PM
got AS results thursday for maths so...
eek

hi
I got a short question about statistical mechanics(?)

Anonymous
hi

Anonymous

Anonymous

I was typing... They define temperature as $\frac1{k_BT}=\frac{d \ln \Omega}{dE}$

Anonymous
7:50 PM
lol....we were discussing this just sometime back. :P

So it means that if the number of microstates associated with a certain energy, doesn't change locally, we have infinite ttemprature?!
any idea?

Anonymous
You're basically asking if $E$ changes but the microstates remain constant, then the temperature is infinite? I guess: yes.

Anonymous
8

It's the differential relationship between internal energy and entropy: \begin{align} dU &= T\,dS + \cdots \\ \frac{\partial S}{\partial U} &= \frac 1T \end{align} As energy is added to a system, its internal entropy changes. Remember that the (total) entropy is $$S = k \ln\Omega,$$ where $\Ome... Anonymous Read this once ^ hmmm. let me read it... That was useful. Thank you. Anonymous 7:57 PM No problem. :) Anonymous I think we have spoken before Anonymous You're preparing for IPhO iirc ? I'm assuming you don't mean me... Anonymous @CooperCape I meant @AHB. Anonymous BTW are you too? @CooperCape 8:06 PM "Aximos" !!! i only believe in mathematical proofs , — El Mouden 2 mins ago @ACuriousMind See, that's an example of the stupid liberal obvious troll is obvious I don't think algebraic geometry is anything other than a hell Which of this 3 calculations are used to calculate the "fake" frequency of light using the Relativistic Doppler Effect when the observer is moving? $$\beta_v' = \frac{\beta_v + \beta_u}{1 + \beta_v \beta_u} \;.$$ $${\displaystyle f_{o}=f_{s}{\sqrt {\frac {1-v/c}{1+v/c}}}}$$ $$v' = \frac{u + v}{1 + \frac{uv}{c^2}} \;,$$ Latex doesn't work? 8:07 PM @AccidentalFourierTransform Chill top right corner @EnderLook upper right corner Anonymous @EnderLook What is$\beta$? @ACuriousMind make him @Blue That is the greek beta letter. 8:08 PM$v/c$Anonymous @EnderLook What does it stand for? aka,$v$Anonymous I couldn't have typed$\beta$without knowing its name obviously :P @EnderLook What do you mean by "which of this"? The first seems to be for added velocities as a proportion of$c$, the second for the Doppler-shifted frequency, the third for added velocities. What is the question? Anonymous @AccidentalFourierTransform Oh 8:09 PM lol In German orthography, the grapheme ß, called Eszett (IPA: [ɛsˈtsɛt]) or scharfes S (IPA: [ˈʃaɐ̯fəs ˈʔɛs], [ˈʃaːfəs ˈʔɛs]), in English "sharp S", represents the [s] phoneme in Standard German, specifically when following long vowels and diphthongs, while ss is used after short vowels. The name Eszett represents the German pronunciation of the two letters S and Z. It originates as the sz digraph as used in Old High German and Middle High German orthography, represented as a ligature of long s and tailed z in blackletter typography (ſʒ), which became conflated with the ligature for long s and round... wat Anonymous Oh, my goodness. The ß and the$\beta$have nothing to do with each other Apr 20 at 17:14, by AccidentalFourierTransform no, its a fancy beta and I dont want it anywhere near Gauss 8:10 PM @AccidentalFourierTransform ßuck it up :P D: H=T+V =E_toatal ; H=P²/2m+V ; E=i h d/dt and when E=H we get Schrodinger equation My Problem is where E expression came from — El Mouden 4 mins ago the troll is strong with this one mmm... I... I want to make an little "experiment" and I need that. I want to calculate the change of frequency of light when the observer is moving at 99% light speed Anonymous Your second equation is the correct one for Doppler effect (for light). @Blue Thanks! @AccidentalFourierTransform Be nice, please. Anonymous 8:13 PM @AccidentalFourierTransform wow > Troll troll troll lalalala — AccidentalFourierTransform 1 mins ago Using $${\displaystyle f_{o}=f_{s}{\sqrt {\frac {1-v/c}{1+v/c}}}}$$. If the light is travelling ---> at 100% c (like always) and the observer is travelling <--- at 99% c (they would collide), is v = (100% + 99%) * light speed Anonymous rick rolled -_- @EnderLook No,$v$is the velocity of the receiver with respect to the light source So? v = (100% - 99%) * light speed? 8:16 PM So what? @EnderLook No. What is$v$??? youre missing a Thomas rotation @EnderLook The velocity of the receiver with respect to the light source. Since you haven't specified where the light source is or with respect to whom the receiver is moving with 0.99c, this is currently underspecified in your scenario. Any good non-fiction book suggestions? Weinberg's QFT. Next! Anonymous 8:19 PM @macco This I read feynmanns QED which was great, dont know if i'd enjoy a pure textbook curiousmind? pure textbooks are the worst I only like partial textbooks @macco It was sort-of a joke. If you are not interested in learning actual technical QFT, don't read it. these are great 8:21 PM That could be a possible escenario? I just made it with the paint Anonymous Ah, now you're getting into special relativity :) Anonymous Speed of light is independent of reference frame @EnderLook that looks like the omniscient olive sandwich from Cow and Chicken in that episode where they go relativistic I don't know what is that @macco "An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps, and Minimal Graphs" 8:25 PM actually I think it was from I Am Weasel Anonymous @EnderLook Watch professor Ramamurti Shankar's lectures on SR at Yale. I think it is a series of 4 lectures Anonymous You'll get it @EnderLook In that case the$v$you want to plug into the equation is simply -0.99c. The minus is because the observer is moving towards the source. Thanks! tonic water is the best thing ever why some people dont like it Ill never know 8:31 PM @AccidentalFourierTransform You forgot a "with gin" there ;P edit: tonic water is the second best thing ever Best thing ever? @macco the prose is pretty mediocre but it's one of the best physics books I've read in a long time In terms of technical stuff Anonymous Is this your first +--- meme ? @AccidentalFourierTransform :P Anonymous All the previous ones were -+++ 8:35 PM @AccidentalFourierTransform$\mathrm{d}^{-2}k$? Is this from the "Taylor expand the$\delta$" people? :P +--- is the good one, -卐卐卐 is the bad one @ACuriousMind yes. Anonymous Don't get banned XD @ACuriousMind no, it is from the best physicist ever my good friend Bryce Bryce? yes, the best physicist ever 8:37 PM That doesn't sound like Bahoran Jewliger @0celóñe7 thanks. It doesn't have to be physics related. Just looking to extend my booklist. For example I have read "three stones make a wall" (Archeology), QED feynmann, The planet remade (Geoengineering), I contain multitudes (microbiology), life on the edge (quantum biology) recently and enjoyed them. @macco it isn't physics beyond the fact that a physical being wrote it (allegedly) You should still read it @0celóñe7 dr. Bryce DeWitt @macco read The Plague and thank me later @AccidentalFourierTransform macco said non-fiction macco doesnt know what s/he wants 8:41 PM Not sure you'll be able to thank me afterwards Read "The Analysis of Linear Partial Differential Operators" Volumes 1-4 s/he wants to read The Plague @ACuriousMind Can we please have a gender neutral pronoun policy in chat? Anonymous Use (s)he @0celóñe7 What do you mean? @EmilioPisanty Have you ever seen this journal? Is it a respectable journal? 8:43 PM can we omit pronouns as we do in most languages Anonymous I think in English the gender neutral pronoun is "they" Anonymous It sounds awkward though @AccidentalFourierTransform Hm? what do you mean by "omit pronouns"? @ACuriousMind I think it is preferable to call people "ze" or something similar before they state what zeir preferred pronouns are. Anonymous I prefer using "he" unless someone clarifies they are female. "he" is widely accepted as gender neutral. (afaik) 8:45 PM Are you thinking of languages where all relevant information is in the flection of the verb? @Blue That is horribly offensive, you are suggesting a male-female gender dichotomy. I found in [this link](https://en.wikipedia.org/wiki/Radiation_pressure#Radiation_pressure_by_absorption_.28using_classical_electromagnetism:_waves.29) this: $${\displaystyle P_{\text{absorb}}={\frac {\langle S\rangle }{c}}={\frac {E_{f}}{c}}}$$ But I want to calculate the pressure of a single photon, so I don't have **W/m2**, I have **eV**. Is there something that I can do? Anonymous A third-person pronoun is a pronoun that refers to an entity other than the speaker or listener. The English pronouns he and she are gender-specific third-person personal pronouns. The English pronoun they is an epicene (gender-neutral) third-person pronoun that can refer to plural antecedents of any gender and, under certain circumstances, to a singular antecedent that refers to a male or female (but not inanimate) entity. Many of the world's languages do not have gender-specific pronouns. Others, however – particularly those that have a system of grammatical gender (or have historically had such... @Blue There are gender neutral pronouns, (s)he is not one of them. Anonymous 8:46 PM (s)he was just a joke Anonymous :P Anonymous I just use "he" the problem Im having with my books recently is that a lot of the popular science books explain some concepts again and again with tedious analogies, however textbooks are usually far to dry for me to enjoy reading. There should be more middleground. I propose we use$\nu$e as a gender neutral pronoun. Anonymous -+++e 8:48 PM @0celóñe7 You're welcome to ask people to use that. I personally much prefer the singular they, possibly because German has no comparable option. It's me or Latex doesn't work on chat? It's you. oh... Damn, trying to pirate books on hotel internet isn't working Anonymous 18 It's still considered acceptable. If you really want to cover your bases, include a definition at the front that reference to one gender imports all other genders, unless the context requires otherwise, and explain that you'll be using "he" for the sake of simplicity. Edit: As per below discussi... 8:49 PM wonder if libgen is blocked @EnderLook Sure, you need to compute the energy flux - for which you need to know how many of your photons are hitting your target per unit area per unit time. Anonymous @0celóñe7 nope Anonymous It's working here Anonymous Maybe in US.... @Blue I mean on the hotel internet Anonymous 8:49 PM hmm...use proxy :P oh no, the download is just so slow that OSX won't estimate how long it's taking @EnderLook Did you activate ChatJax with one of the methods linked in the upper right corner? @0celóñe7 Would you prefer it displayed "ETA: After the heat death of the universe"? TIL OSX is Java @AccidentalFourierTransform For the last time, I deleted my Java. @ACuriousMind It worked, great! Thanks! 8:52 PM$\phantom{you cant see me now}$Anonymous now i c u I.C. Weiner @ACuriousMind I want a new keyboard @EmilioPisanty Hmm, according to this, looks like it is; as its editorial board are all well-known researchers in the field. Never had seen any paper from it before :/ ;'( why is this taking so long ... Anonymous 8:59 PM @0celóñe7 ........ that sucks... try again in an incognito window @AccidentalFourierTransform Download again? Maybe I should try a diff mirror no load it again on incognito mode Anonymous Internet Explorer comes in handy in such situations Nah, the Mac PDF reader won't open it Nor Chrome Anonymous 9:01 PM Opera mini too Gonna download from a different source @Blue Apologies I never got back to you an hour ago. No, I'm not preparing for IPhO... that's why I assumed it wasn't me :p Anonymous @CooperCape oh, no probs hmm this is very suspicious Anonymous start praying 9:05 PM hate it when the document loses 200 KB between downloads... that download failed too screw it well I hate world hunger, poverty, child deaths and capitalism shallow much? stop using a computer you commie I hate commies too I just hate people. figures all commies hate people 9:16 PM o wow what's wrong with a lil' bit of communism guys... @CooperCape people die okay okay so there's a fewwww flaws It inherently violates human rights major No one has fun 9:17 PM yeah but ignoring that... Great, it only took me four hours to find a comparatively simple formula these authors were using implicitly! @ACuriousMind boohoo It once took me a week to find a formula "$(a+b)^2=a^2+2ab+b^2$" @0celóñe7 I'm pretty mad they didn't write it down since without knowing it what they were doing just looked like black magic :P 9:21 PM @AccidentalFourierTransform can you show me the proof for that... I'm a bit confuzzled. first, assume$1+1\neq 0$... Anonymous What are$1$and$0$and$\neq\$ ?

Anonymous
=P

@ACuriousMind the author did not mention the formula from do carmo here math.stackexchange.com/questions/1887646/…

Peano is inconsistent.

9:23 PM
"from this, we deduce that" required at least two formulae not mentioned anywhere

9:58 PM
Hey
Could one argue that there are some phenomena in the universe where causality doesn't apply / is a lot messier than cause ---> effect

Rarita-Schwinger coupled to an electromagnetic field
but no, causality (in its technical manifestation) always holds, as far as we know