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00:26
0
Q: Profile check and number

SAKhanThere is a question I have regarding profile views as shown on my homepage. If a person views a profile twice then will the homepage mentioned it as two profile views or one ?

 
3 hours later…
03:28
Hello,
is anybody available to chat?
04:21
maybe :)
I'm here, but barely
05:01
do you want to talk?
whatsup
hi... I am working on a project, I discussed it with @DavidZ ...
I wanted help... are you available?
here's the conversation:
22 hours ago, by T Abraham
can we talk about path integrals?
i probably wont be able to give useful help , am no expert on calculus.
or QFT
what math level are u studying?
05:16
I am in material science , here only because of my interest :)
doing my masters currently
ok...
well... nice talking to you...
Anyone up for a conversation on the Doppler Effect with light?
ok...
The Doppler Effect makes sense with sound, because if the source moves forward it's physically impacting the medium the waves are moving through. However, light doesn't need a medium. Does this mean that light Doppler shifts are just waves interfering?
grt question... I will try my best at anwsering...
you know... I think that your explanation of Doppler effect is wrong...
Bcos doppler effect is just about frequency.. not bcos it is physically impacting the medium...
quoting wikipedia:
"When the source of the waves is moving toward the observer, each successive wave crest is emitted from a position closer to the observer than the previous wave. Therefore, each wave takes slightly less time to reach the observer than the previous wave. Hence, the time between the arrival of successive wave crests at the observer is reduced, causing an increase in the frequency. "
the key part is "causing an increase in the frequency"
@Arc676 I hope that helps...
05:34
Thanks, I will check that article
In the Wikipedia article it states that the velocity relative to the medium must also be considered with sound. Does this mean that when the wind is traveling in the same direction as the siren the Doppler effect will be reduced?
unfortunately, i am not sure...
however, i think that it doesn't make a difference
@JamalS are you available?
@Arc676 I think the reason you feel that light undergoing doppler shift without a medium is unintuitive is because you are explicitly comparing a purely longitudnal wave (sound) with a purely transverse one (light). Maybe a more apt comparison would be waves on water..
i think wind only affects the intensity of sound received and not the doppler effect of sound or velocity of sound in the medium, and regarding light you should read wiki articles on Relativistic Doppler effect and General Relativity. I think the only answer i can think of is the red/blue shifts is due to the relative velocity between the source and observer ,
i agree w/ @Gowtham
Since sound is a longitudinal wave, where is the amplitude?
The wind could increase the wavelength if it moves in the same direction as the wave but that won't increase intensity
05:48
how does the "wind increase the wavelength if it moves in same direction of wave" happen
I'm not entirely sure it could work. In a longitudinal wave, particles vibrate in the same direction as the wave. If the wind is moving in the same direction as the wave as well, it will push the air further so the air particles already moving "forwards" will be pushed further.
that's why I thought it might not be true...
If it did, maybe the world would be very different!
because changing wavelength of sound, light, etc. could be useful applications...
@Arc676 In longitudnal waves, the amplitude is part of the wavelength itself, and both are related, unlike in transverse waves where amplitude and wavelegth need not be related at all..
06:00
I see. Is there some sort of equation to find the amplitude having the wavelength? With the slinky-style diagram of a longitudinal wave is it possible to label the amplitude?
Thanks
Look for Clausius's answer in this : physicsforums.com/threads/…
07:02
anyone here
Yes
Can anyone explain a question regarding wavelengths?
I can try
me too..
So I got an equation here: y(x, t) = (0.002 m) sin((64.8 m^-1)x + (303 s^-1)t)
07:05
what about them...
To find the wavelength I do 2pi/k = 2pi/64.8
but then apparently it's not the same as the answer
so what are your value for t
Is there something I did wrong that I didn't notice?
t is a variable
@Arc676 how does that matter?
07:07
Well if y is a function with parameters x and t you need to define them right? In a 2D graph x is just the x co-ordinate
Or is there something I'm missing?
@Arc676 This is a 3d graph, describing a wave moving in time
I see
i'm pretty sure it is a mutlivariable fucntion
yea
so 2pi/64.8 is the wavelength right??
I think that you have to convert sin into cos.. or does is not make a difference?
07:09
sin and cos are just shifting the graph to the right by pi/2
yes..
gota go..
so nothing should change
ok
Well I tried graphing it
how did it go
I defined your function as f(x,t)=0.002*sin(64.8x+303t)
then graphed z=f(x,y)
would that be correct for your wave?
07:12
yes
I believe 2pi/64.8 is indeed the correct answer, as I see from various source like hyperphysics.phy-astr.gsu.edu/hbase/waves/wavsol.html
I bet it's the answer key that's incorrect
@Derek朕會功夫 it is correct
just out of curiosity, u realize that graphing z=f(1,y) yields exactly the same result right?
@Arc676 what do you mean by that
you shouldn't get the same result since you are now only looking the x=1
just looking at how one particle in the wave moves in time
it might be a limitation of my graphing app
@hwlau thanks for the conformation
confirmation*
07:18
(Tex math doesn't work)
man I hate these online problem platforms
@skullpatrol it will do the calculations from left to right so I don't think that's a problem
I just realized that :)
@Derek朕會功夫 what is that platform
@hwlau that's smartPhysics, if you are wondering
@Arc676 it does somehow work, people need a script for it to work
07:26
I see
and they use it here often
I would assume so. Math is an essential part of physics
@Derek朕會功夫 Just send the tutor/instructor an email with screenshot to explain it
@hwlau Given that it's already the end of the semester and this is an optional exercise, I don't really have the feeling to report it
:/
@Derek朕會功夫 how stupid do you think of the system, or is it just manual error
07:35
@hwlau I think overall the system is not bad, especially how you can get instant response, but when you get a wrong answer all you get is a "cross" and you don't know where your mistake is at
@Derek朕會功夫 It is how automatic system worked. At best, they will have a sequence of question guiding you with some feedback
If the one who make it is patient to do so
BTW, you name look so strange
@hwlau why is that?
@Derek朕會功夫 Sound strange
@hwlau you mean the chinese text after my name?
:19094284 There is a button to upload/ image
@Derek朕會功夫 yup
07:41
@hwlau I just put that there cause it sounds funny :)
It doesn't really make any sense
@Derek朕會功夫 it does make some sense, but strange "Derek I know kungfu"
@hwlau Looks like you know chinese too
@Derek朕會功夫 yes
usually you will only find it strange if they know it
except the shape
@hwlau Actually I know chinese too, if you take a look at my location in the profile
@Derek朕會功夫 me from HK too
07:47
@Derek朕會功夫 That's clever
@hwlau Seems like I guessed it right, by looking at your last name
@Arc676 What is clever?
The Chinese bit. Especially how its not the most commonly used characters for the meaning you want to express
The first 2 are traditional chinese aren't they?
@Arc676 They are
But 朕 actually has more meaning than just "I"
07:51
@Derek朕會功夫 are you us or hk people or you just stay there?
@hwlau from hk but moved to us quite a long time ago
@Derek朕會功夫 clever move
and you have lots of rep at SO
I do think US is better for programming jobs
@hwlau especially in mountain view
@Derek朕會功夫 where are you living, seattle?
07:57
Nevermind
@hwlau chicago
a great city
heard it has been really cold this winter , is it ?
@Derek朕會功夫 how great is it?
@Gowtham kind of windy like usual
@hwlau It has a great skyline
and people are great there
ic, is it snowy in the winter?
08:02
oh yea it snows every year
very snowy and "wind-chilly" too , hehe
@Derek朕會功夫 so you can ski there? Is the lake frozen in the winter
@hwlau unfortunately there aren't that many place for skiing because there's no hills or mountains in the city, and the lake Michigan isn't frozen either
small lakes are frozen, but I won't walk on them :)
Sound nice
So it is not as cold as Canada
and you do a lot of thing out there
@hwlau like what?
08:09
@Derek朕會功夫 Nevermind. Are there lots of thick snow on the road or not
usually its cleared by local authority i think , but off the road you can see 2 or 3 feet snow or even more depending on the weather
@Gowtham you live in chicago too? 2 or 3 feet is quite a lot
The city government will clear the road for us, but the dirty snow are all shoved onto the side walk which piles up quite high
2 or 3 feet seems normal , i lived at state college pennsylvania ,chicago and my place can be comparable for snow received i guess,
but chicago is far colder due to windchill effect
I would think that the snow is less in the middel part of US because there are not much sea water there
08:16
@hwlau you forgot the lake
ok
see you guys
gotta leave now
see you
@hwlau you might also want to join our group here if you want :)
@Derek朕會功夫 thx, I will take a look
 
2 hours later…
Huy
Huy
10:11
Why the invite, @skullpatrol?
I'm sorry I am on mobile and I hit the wrong button @Huy
Huy
Huy
@skullpatrol: And I was already hoping you liked me. =(
I do pal :D
You're cool @Huy
Please accept my apologies.
Huy
Huy
Fine.
 
1 hour later…
11:30
So I recently started a petition to have a second course in GR in my degree, and it turns out there is quite a lot of interest. However, now that the plan has become quite feasible, I'll have to actually come up with what kind of topics I'd be interested in learning about
This has proven to be quite a difficult question. In my degree, there is only one course on GR, but there are courses on 1) Cosmology 2) QFT in curved spacetime 3) "Black holes and instantons" (?)
...so any proposed course should not have too much overlap with any of those pre-existing courses.
@Danu: So, uh, what did you have in mind when you started that petition?
like.... "more advanced GR"
Turns out it's really not obvious what that is.
The three courses you just cited sound to me like they are exactly that
I was thinking of stuff like... (note that I only know these words, not their actual content) ADM formalism, conformal diagrams, maybe singularity theorems...
I also saw this interesting book by Penrose & Rindler on Spinors in curved spacetime
Huy
Huy
That's no good.
11:34
What isn't? :P
Huy
Huy
The book.
Penrose & Rindler? What do you dislike about it?
oh, oh yeah... also Cartan formalism!! @JamalS
Do you already treat GR mathematically by looking at frame bundles, jet bundles, and stuff? If not, I'd say that would be quite fitting for a mathematical physics degree, too
^nope, do you have a reference book?
Our GR course is extremely physical
...it's taught by Prof. Mukhanov! ;D
Huy
Huy
@Danu: Did you use a textbook in your GR course?
11:39
@Danu Not really, but the reference list, for example, on the Wiki article for covariant field theory looks like a starting point
@Huy Not really... Mukhanov seems to freestyle. But take Carroll's book as an approximate equivalent to get some idea
(without the final chapter on QFT in curved spacetime, of course - Mukhanov will teach from his own book for that haha)
Huy
Huy
I've heard good about Carroll's book.
Very good book - I read it about 1.5 years ago as an undergraduate and was able to understand almost everything :)
@Danu I had not heard of him before, but it seems you've got quite a famous lecturer there
He is one of the fathers of inflation, yes :)
And he's epic
Huy
Huy
11:41
@Danu: Our GR course followed Dirac's and Pauli's book. It was rather mathematical, too.
@ACuriousMind Just check this out youtube.com/watch?v=S06-xP4jK6g
We followed Schutz. Ugh.
Lmao
unfortunate
Could his Russian accent be more cliche? :D
@Huy Do you mean Dirac's 'General theory of relativity' or something else?
@ACuriousMind viekter
(vector)
Huy
Huy
11:42
@Danu: Yes. That.
@Huy That seems like literally the worst book to learn GR from as a physicist. 2 pages on the Schwarzschild solution?!
Huy
Huy
@Danu: I'm a mathematician. :P
Yeah... then there's not really any need for 'useful' things ;)
But that does make you a good reference. Any tips on which topics one might want to look into?
Huy
Huy
@Danu: It was a course for physicists though.
@Danu: What have you seen already?
@Huy Carroll minus the appendices
Very little mathematical formalism - quite a lot of physics
...but I'm not interested in purely mathematical things to do - just more advanced things which may (or may not) require more advanced mathematics than basic GR
Huy
Huy
11:46
@Danu: Do you mean Spacetime & Geometry or Lecture Notes on GR?
@Huy The book (although the notes probably cover almost the same material)
Huy
Huy
@Danu: Oh, I've never seen the book before. Just a lot of friends telling me the lecture notes are really outstanding.
The book is an extension/completion of the notes.
Anonymous
@Huy You study Physics?
Huy
Huy
@Ashwin: No, technically, mathematics.
11:48
@ACuriousMind your recommendation about the bundles etc seem a little too superfluously mathematical to me (I don't mind mathematics, but don't want to organize a course on GR just for the sake of mathematics)
@Danu Yeah, right as I read your last comment, I thought it might not be what you want to do
It's also intended for some non-math.phys. students
Anonymous
@Huy Why is that most Thermodynamics books do not cover mass transfer and things?
I find it interesting because it shows the similarity to gauge theories, and thus other forces, but it is really not needed for anything physical
Huy
Huy
@Ashwin: I don't know, I haven't studied Thermodynamics.
11:50
@Ashwin In the grand canonical ensemble, particle number is not constant, and particle transfer is mass transfer, no?
@KyleKanos Please don't solve this user's homework for him/her (I had quite a long talk before, and it became clear he/she is really missing a lot of basic knowledge of ODE's)
Anonymous
@ACuriousMind Actually not much of Thermodynamics I have done.
@Huy So, do you have any ideas about what could be interesting?
Then "most thermodynamics does not cover mass transfer" is a bold statement ;)
As I understand it, the grand canonical ensemble does/is able to do precisely that.
Huy
Huy
@Danu: I can't think of anything off the top of my head, but I'll let you know if something comes to mind.
Anonymous
11:52
Actually I am doing Engineering and my thermodynimics book (Blundell) does not cover it!
Anonymous
Does the one by Greiner have it?
::shrugs:: I don't know many books
Especially not on thermodynamics, I rather dislike that subject
(which may just be due to the abysmal courses I had on it)
12:06
Merry winter bash everyone ! :D
Huy
Huy
12:22
Did any of you guys use the feynmf package before to create Feynman diagrams? I have troubles using it.
Yes
I learned how to do it last week - it's all fresh! :P
I'm using feynmp though
(slightly different command in cmd.exe)
Huy
Huy
@Danu: Are you on Windows?
Yes
Huy
Huy
@Danu: I'm using TeXnic Center with MikTeX. I just included the package feynmf and tried the code I found here: de.sharelatex.com/learn/Feynman_diagrams However, I get an error of the form "I can't find file 'diagram' <*> \mode:=cx;nonstopmode;input diagram".
it's pretty complicated
Huy
Huy
12:27
Can you guide me through it?
so you put that in - that's okay
then you run Latex -> DviPS -> PS2PDF
one time
it should not give errors
then you have to go to the command prompt (strange, I know)
Huy
Huy
I don't have that option, I only have LaTeX -> DVI -> PDF.
No postscript.
ehm... you should be able to change it
there's usually compile options
Huy
Huy
In the dropdown menu, where currently LaTeX => PDF selected, I don't have PS, anywhere.
The nearest option to the one you said is LaTeX -> DVI -> PDF
For this one usually has to go to the settings
there, hopefully, you'll find it
Huy
Huy
12:32
No, but I could add it.
These are all available profiles.
Hmm, okay. I'm not an expert but my friend who taught me to use feynmp always said to use the full chain
Also, other editors do have this as a standard option most of the time
e.g. TeXMaker, TeXStudio
Huy
Huy
It apparently isn't, but I'm trying this: tex.stackexchange.com/questions/58729/latex-dvips-ps2pdf @Danu. I'll tell you if it works then.
Hi guys, since many of you here are active researchers and theorists, I wanted to get an insiders view as to the recognition scientists get for the work they do.
People tell me the pay scale is miserable and the recognition too. I tell them that as long as my passion for physics keeps burning, I'm okay to put up with it.
Then they tell me that I won't understand some things until I start earning. So I wanted to get an insider's view as to whether this is actually true or not..
And btw, Merry Winter bash everyone !
I'm not a professional physicist (yet), but you defiinitely shouldn't be in this for the money.
The effort-to-economic payoff ratio is very high
...but you do get the bragging rights (in certain circles, at least)
Huy
Huy
@Danu: I get the same error if I run Latex -> DviPS -> PS2PDF
12:42
@Huy Okay.
Well, let's just proceed with my method
maybe it'll work
Now, you go to the command prompt
are you familiar with how to use it?
Huy
Huy
@Danu: I think so.
Okay. Go to the folder that your files are in
(go to as in inside the command prompt)
Huy
Huy
ok
actually, you can also check the actual folder: is there another file in there with the name of your diagram?
Huy
Huy
yes
12:45
Good
Huy
Huy
there is diagram.mf and diagram.mp
Ok, now that you're in your folder in the command prompt
run: mpost diagram
@Danu I've heard it's a popular fact among researchers that these days since research work is carried out by large organisations, induvidual effort is no longer valued as in the earlier days..
(or other name if you renamed the diagram)
Huy
Huy
@Danu: Done.
12:46
does it give you some sensible-looking messages?
Huy
Huy
yea
Huy
Huy
metapost did something
now go back to your latex
Huy
Huy
and 1 output file was written
12:46
and run the full chain
good, that sounds perfect
should work now
Huy
Huy
still the same error
ah crap
Huy
Huy
+1
is there a .log file in your folder now?
Huy
Huy
yes, for both the diagram as well as the .tex file
12:47
yeah, okay
the one for the diagram is the one you need
I'm honestly not enough of an expert on latex to help you out much more than this... It's something with your LaTeX
some setting probably has to be adjusted...
to get this chain to work properly
Huy
Huy
@Danu: This is MetaPost, version 1.803 (MiKTeX 2.9 64-bit) 16 DEC 2014 13:46
**diagram
(mpost.mp (D:/Program Files (x86)/MiKTeX/metapost/base/plain.mp
Preloading the plain mem file, version 1.004) )
(C:/Users/***/2nd derivative/diagram.mp
(D:/Program Files (x86)/MiKTeX/metapost/feynmf/feynmp.mp) [1] )

Here is how much of MetaPost's memory you used:
301 strings using 4436 characters
1534584 bytes of node memory
922 symbolic tokens
14i,77n,28p,105b,3f stack positions out of 16i,96n,32p,200b,4f
1 output file written: diagram.1
But at least this is the general idea
@Huy Yeah, this is how it should be
Huy
Huy
I'll try rebooting. Works wonders sometimes.
Latex -> cmd.exe mpost [name] -> Latex
good luck
Huy
Huy
Nope, still exactly the same error message. @Danu
12:54
I'd suggest goin to the TeX chat - they're pretty helpful
Sorry I wasn't able to solve your problem!
13:10
@Danu I see you specialize in mathematical physics and are also pretty active as a science historian. I wanted your views as to whether the origin of math as a tool in physics was purely accidental or not.
I've heard many such an argument. I don't find it to be true, however, since math is clearly the most efficient way of dealing with science since time immemorial..
But when did scientists exactly begin to realise it ? Was it after the emergence of calculus, or much before it ?
13:32
@Danu It definitely seemed like he/she was missing a lot of basic knowledge of calculus really
14:07
@Simha Well, there was Zeno's paradoxes that required a bit of math (e.g., halving distances) to describe something physical (Aristotle's rebuttals also show signs of calculus).
Consider a 10000 kg weighing body is placed on a weak small table. Naturally the table will break and the body will accelerate through it. In that case for the body we can write mg-N = ma , where a is accel of the body. And thus we can find the normal force N by table on the body .
Jim
Jim
@AnjumSKhan what was this in response to?
"However, it is important to point out that the mathematical formulation of the physicist's often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena. This shows that the mathematical language has more to commend it than being the only language which we can speak; it shows that it is, in a very real sense, the correct language."
@Jim I asked a question in the forum and now I am asking my doubt here.
@Jim It is related to Newton's 3rd law.
@AnjumSKhan We ain't a forum. Also, I don't understand your question
14:17
Your question was answered though?
@ACuriousMind We say the table exerts a forceequal and opposite to that applied by book on the table and so book remains at rest.
@ACuriousMind I was wondering then , why a massive book will break through the table.
@AnjumSKhan Because the table cannot withstand so strong a force?
@AnjumSKhan Obviously the answer is the force due to the book is greater than the force the table can withstand
@ACuriousMind thats what I am asking, then where is the 3rd law ?
Newton's laws say that forces in equlibrium are equal and opposite and produce no net acceleration
The breaking table is not in equilibrium with the book
14:20
@AnjumSKhan when it falls there wont be any normal force if thats what you are asking
it is "free fall" once the table breaks
Jim
Jim
when the table breaks, the book is not exerting its entire weight on the table. only enough force to make the table accelerate with the book is applied and that is reacted upon the book. But it does not cancel the weight of the book, so both table and book fall
@Gowtham So normal reaction on the Book by the table can be found using mg-N=ma ?
Jim
Jim
if the table is massless, yes
@Gowtham m = mass of book, a = accel of book after breaking the table
when the table breaks there is no "normal" i think . and the book has a=g
Jim
Jim
14:22
when the table breaks, a is not g
But still when we keep a book on table, so N must be there ?
Jim
Jim
the acceleration of the book is less than g because some of the force is used to complete the breaking of the table. Once the table is fully free to fall, then the table and the book will have acceleration of g.
depends on how slow or fast you actually place it on the table i think , when the force exerted by the book on the table reaches the critical or breaking point the table is gonna break and book is gonna fall through . but once the table breaks and when there is no contact b/w book and table, there is no normal and the book should be in free fall
Then how 3rd law is acting here in the entire scenario ?
Jim
Jim
If I had a video camera and silly putty, I could make such a demonstration to explain this. The point is, the table will only provide as much normal force as it can withstand. Any additional force applied makes it move. The book will make the table move with it, but it will not apply the entirety of its weight to do so. Only as much force as is required to make the table move with it is applied to the table. This force is opposed by the table, which slows the book's acceleration.
The excess force is not applied to the table and is used to make the book accelerate through the table
14:34
@Jim lot of confusion, will do more reasearch on this. thankx.
@AnjumSKhan as Kyle Kanos said when two bodies are in EQULIBRIUM , then newton laws are valid. So till the breaking point its valid . after that if the configuration of the table is awkwardly such that it can maybe hold the book then we can talk about normal forces. but if it breaks in my knowledge the book should just be free falling without at g
@KyleKanos Yeah... and didn't seem willing to learn to do some basic stuff before jumping into more difficult matters... an all-too-common problems, especially amongst those who haven't been studying all that long yet :P
@Simha Purely accidental? What do you even mean by that
Jim
Jim
@Gowtham Newton's laws are always valid in classical problems. Not just equilibrium. They are easier to see in equilibrium, but in every case an applied force is still opposed by a force of equal magnitude. In non-equilibrium cases one must remember that the entire force on one object is not fully applied to the other
@Danu There are people who believe (or pretend to believe) that science and math are not intrinsically connected - that it is a mere historical accident that today's science is so heavily relying on mathematics
@ACuriousMind I'd venture to guess that these are not mathematicians... nor physicists or otherwise mathematically educated scientists
14:39
You're not wrong
I'm reading the AMS paper (finally) and the following made me laugh: Figure 4 shows the behavior of the positron fraction at low energies, from 1 to 35 GeV.
A few GeV is "low energy."
@Jim ok my statement was wrong. All i can say to @AnjumSKhan when there is action there is equal and opposite reaction . When the table breaks, the action i.e the weight of the body wont act on the table anymore. so there is no reaction . i dont know how to explain in a more simple way .Sorry
@KyleKanos Of course, on cosmological scales! :D
If the sub-site like chemistry.SE is in beta , does that mean not much moderating is done ? all i am seeing is lots and lots of homework type problems O.o
@Gowtham Are homework type problems even off-topic there?
14:48
well its not mostly off-topic but blatantly and openly asking for direct solutions without any prior attempt
he is asking for equations :D like sometimes i think people dont even use google and just blindly use the site like an answering machine :P
It seems that the moderators/3k users are lazy, then :P
@Gowtham History of Science and Math is in beta, and I am one of its moderators. I certainly try to maintain high standards (though homework is not really a problem on HSM)
@Danu ok. when i first visited this site i was also clueless but still somone posted that common thing about the site
this "Hi and welcome to the site! Since this is a site that encourages learning, you will get much more help if you show us what you have already done. Could you edit your question with your thoughts and ideas?" and i tried to do solve first and only post after that :)
@ACuriousMind i noticed yesterday you were discussing dota 2 with one of the users , you like the game ?
@KyleKanos Good point. I was thinking science's real breakthrough was clearly Newton's era, which saw the emergence of calculus, and thus it resonates with the fact that math is indispensable to physics.
Jim
Jim
@Gowtham Physics.SE tends to be stricter than most about homework-like problems. If we didn't do that, we'd become AppliedMath.SE
14:57
@Gowtham I played DotA years ago, and @Phonon is trying to get me to come back and play DotA2, but I haven't played it yet.
@Jim ::shudder::
Though, physics is "just" applied math, of course ;) (I won't link the infamous xkcd again)
Jim
Jim
@ACuriousMind sixteen times is probably enough
00:00 - 15:0015:00 - 23:00

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