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00:06
I think @heather needs to learn classical Hamiltonian mechanics first.
Just my opinion.
Hey, you started this :P
But I do agree that knowing classical Hamiltonian mechanics makes QM a lot less "weird".
@DanielSank, okay, so: 1. calculus 2. classical mechanics 3. quantum mechanics 4. QED 5. cQED 6. come back to what I'm doing?
@heather I would say 1 through 3 yes, and then re-evaluate.
Your eagerness is admirable, adorable, and a little frightening :D
@ACuriousMind, frightening how? =P
00:08
@heather can you solve basic differential equations?
@heather He means we all feel a bit humbled.
Your enthusiasm and dedication/hard work is admirable.
@DanielSank, no, not yet
@heather Ok, just wondering. To calculus with you!
(::whips out Apostol's calculus::)
@heather let's do one simple little example though.
You know $F = ma$.
Let's think about a particle moving around with some potential energy $U(x)$.
okay
00:11
You know that $F(x) = - (dU/dx)(x)$, right?
now I do
I didn't know that equation until you just said it
Oh, yeah, ok well, if you have potential energy, force is minus the derivative.
Hmmmm
okay
00:13
Hello guys, would someone please help me get some basic, vague understanding behind the way an electric circuit works?
Ok, do you know the kinetic energy of a particle as a function of it's speed or momentum?
sorry, nope
@JohnP Current goes 'round, does stuff on the way. (You'll have to be a bit more specific what you want to know)
ok ok
Let's get back to this after you have your first physics course.
Anonymous
@JohnP Yeah. Just ask the question... BTW it is a big topic and you need to specify where you are facing a problem
00:15
@DanielSank, okay
first question about this calculus book. It says that if we have a region of the plane
Alright, so first - what exactly happens on a "microscopic" level at the part of the side of a battery, which has "too many" electrons?
then when we assign an area to it we can also associate a number with a set $S$ in the plane.
what does that mean "associate a number with a set $S$ in the plane"?
@DanielSank Out of curiosity, were you going to try to show Newton's second law based on the Hamiltonian?
@HDE226868 No
Well, sort of.
then, it says that you can have a function $a$ (an area function) that assigns a real number $a(S)$ (the area of $S$) to each set $S$ in some given collection of sets. At this point, I'm completely lost.
I'd be grateful if someone could explain.
Anonymous
00:17
@JohnP It does'nt have excess electrons. Electrons are usually produced in cells by various methods..see qrg.northwestern.edu/projects/vss/docs/power/…
@heather A "set" is a collection of things.
sure.
If you draw a region in a plane, you have picked a set, i.e. the set of points in that region.
okay, so the first part makes sense.
If you invent a notion of "area" then you have associated a number, i.e. the area, to that set.
00:18
@S007 What? Electrons are almost never "produced", they are just shoved around.
oh...
okay that makes sense.
Then you can declare a function $a$, which takes sets in the plane as inputs, and gives their area as outputs.
def a(region_in_plane):
    return area_of(region_in_plane)
Anonymous
@ACuriousMind Yeah, that was a language problem, but free electrons are produced by ionic reactions..
Anonymous
in electrochemical cells
Anonymous
you are right
00:20
I think there needs to be a lightbulb emoticon specifically for when I chat with people here =D
The article you linked, says "The chemical reactions in the battery causes a build up of electrons at the anode." - would you explain how it's different from what I wrote?
@DanielSank, thank you!
@heather sure
You'll find that it's very useful to think about mathematical functions in terms of what their input and output types are.
This is also true in programming.
It's no accident that we use the word "function" in math and in software.
Anonymous
@JohnP Yes, an electron build up is there after a reaction, but that doesn't mean there are excess electrons initially.
So if the battery is not in a circuit, then there aren't excessively many electrons?
(at the anode)
Anonymous
00:24
@JohnP No, there is just transfer of electrons via ionic reactions in electrochemical cells
Alright, how does the electron flow start, when you make a circuit?
Anonymous
@JohnP It is big topic. I would advise you to get a introductory idea first. See youtube.com/watch?v=IV4IUsholjg
Alright, thanks I'll be back in 10 mins
Anonymous
@JohnP Sure, it is basically a redox reaction
How are permanent magnets formed again? I vaguely remember something about the orientation of the atoms in the material.
Is there a current in the material?
00:35
@JohnP There are "excessively many electrons", but they can't get to the other side because the electrolyte doesn't transport free electrons. Closing the circuit from outside allows the electrons to go to the other side.
@Obliv Sort-of-but-not-really. Things with spin and charge have a magnetic moment - if the spins of the outer single electrons (the inner ones are all paired spin up/spin down so produce (almost) no field) in a material all align, they can produce a macroscopic magnetic field.
In a Bohr-like model, one could imagine the electrons as a circular current around the nucleus, but that's totally bogus.
What would make the material align? @acuriousmind
Anonymous
@Obliv While Permanent magnets too get magnetized the same way as electromagnets, they are made of special material which have very high retentivity which enable them to retain magnetism long after the magnetizing field is removed.
how do electromagnets form @s007 ?
Anonymous
An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. The magnetic field disappears when the current is turned off. Electromagnets usually consist of a large number of closely spaced turns of wire that create the magnetic field. The wire turns are often wound around a magnetic core made from a ferromagnetic or ferrimagnetic material such as iron; the magnetic core concentrates the magnetic flux and makes a more powerful magnet. The main advantage of an electromagnet over a permanent magnet is that the magnetic field can be quickly changed by controlling...
@Obliv That's...difficult to explain. See, for a start, the explanation of ferromagnetism on Wiki. Some materials just tend to have neighbouring spins align, and then applying an outer magnetic field makes them all align, and then it's "too difficult" for a single spin to flip again so the new magnetized configuration is stable
@S007 What?
The mechanism of permanent magnets and electromagnets is totally different.
Permament magnetism is due to the dipole moment of unpaired electrons and complicated statistical interactions leading to the formation of Weiß domains. Electromagnetism is a straightforward result of sending a macroscopic current through a wire and Maxwell's equations.
Anonymous
00:45
@ACuriousMind Are you talking about naturally obtained permanent magnets ? I was talking about artificially made permanent magnets using magnetic materials. I agree that some materials naturally have a ferromagnetic property due to configuration.
Anonymous
Both electromagnets and permanent magnets need magnetic materials to prepare, there are just some differences in retentivity and coercivity
I bet the 19th century physicists were very frustrated in trying to explain ferromagnetism. Was the idea of magnetic charge ever tried/introduced, do you know @acuriousmind ?
Before Millikan and the discovery of electrons
@S007 I still don't know what you're talking about. When I articially make a permanent magnet, I take a ferromagnetic material and expose it to a strong and preferably uniform magnetic field. If I want to have an electromagnetic I just take any coiled wire and send a current through it. You don't need any "magnetic material" to make an electromagnetic (though a ferromagnetic core makes it much stronger)
@Obliv Sure, people have long searched for "magnetic monopoles", and they are theoretically perfectly possible (if you modify Maxwell's equation a bit). However, there don't seem to be any.
Anonymous
@ACuriousMind Exactly, that is what I am saying. Ferromagnetic materials are needed for strong electromagnets. Like we use a soft core
That a north/south two sided magnet didn't break into a north and a south piece but two smaller north/south magnetis was something physicists could observe perfectly well.
@S007 Okay, but why are you saying that? What has making an electromagnet strong with a ferromagnetic core to do with Obliv's questions about how magnetism works?
I could also make it strong by sending much more current through it. There's nothing necessary about the core, it's just practical.
00:52
Question
Anonymous
@ACuriousMind I just wanted to say that permanent magnets can be produced in the same way, by using a strong current and therby a strong magnetic field, which helps in magnetizing it . Nowadays we do not use naturally obtained permanent magnets as they are very weak (usually)
user218912
@Obliv yo
Can anyone tell me the degenerate radius of a gravitationally held object as a function of mass?
@SirCumference Typing "degenerate radius" into Google gives me a straightfoward answer to that :P
@ACuriousMind Yeah, just realized...
00:56
Oh man, I'm pretty sure I've just gone down the rabbit hole of having to look up a lot of stuff, to get to understand my initial question hah.
Anonymous
@JohnP Well, so did you get it ?
Well no, because now I'm refreshing on all the stuff. Didn't know what a redox reaction is, so I started googling that. Don't know what a covalent bond is, difference to ionic bond etc. Lots of stuff to look up.
@acuriousmind Why is it that when you spread iron filings about a bar magnet, there exist no filings in b/t the apparent 'field lines'? Also, if you had no friction on a surface with a bar magnet and spread the iron filings, would they maintain their shape of the magnetic field lines as they did before?
@obe guten tag
user218912
@Obliv i'm gonna do a refresher through all of tong's notes want to do it with me?
@obe when will you be doing that?
also, why? I thought you were a math student now ;)
user218912
01:03
physics is too attractive to me
user218912
i'll do both :p
user218912
@Obliv i'm doing it right now
user218912
ugh i have so much to learn in math too
@Obliv Because iron is ferromagnetic so the spins are aligned and each filing has a macroscopic magnetic dipole moment, and on everything with a magnetic dipole moment the magnetic field exerts a force/torque unless the moment is parallel to the field. Friction has nothing to do with this
@obe I don't know what $\nabla \times E$ is yet but that's pretty much the last thing I need to understand before I can start it I think. Was supposed to do gradient theorem & other stuff today but I got so caught up with 19th century EM.. it's just too captivating for me.
user218912
01:06
@Obliv you need to know what div, grad and curl are and also the 3 integral theorems (green's, stokes, divergence)
user218912
then you're all set
@acuriousmind does this mean there is a force/torque acting on the material, itself, if the material is not parallel to the field lines?
is this measurable?
@Obliv Yes.
@Obliv Obviously - the measurement is that the filings align!
Nvm. I imagine the magnetic field is 3D so it would of course affect a 3D volume around the magnet.
@obe I'm afraid I can't join you with your review right away then. Mind if I ask you questions later, when I do start referring to the notes, though?
I have to drive home now. Danke ACM for your guidance as always :)
user218912
@Obliv yes I am doing a full set of notes based off his notes so that I can remember it forever.
01:23
@obe Want to hear a joke?
Anonymous
@SirCumference you may tell me instead :-P
@S007 Forgot it... :/
Anonymous
@SirCumference Good joke :-D
2
@S007 Got one
Just thought it up
What did the chemist say to the atom?
I got my ion you.
Anonymous
@SirCumference XD what a joke... :-P
01:33
lol
Anonymous
I didn't laugh XD
@S007 ;(
Fine, lemme think of a better one...
Hm...
Ok, why did the photon want to lose weight?
Anonymous
It wanted to travel light
@S007 Dammit! I thought I was creative
Wait, photons don't have mass, so...
Anonymous
damn, buddy. you are copying internet jokes :-D...lol
01:35
@S007 Nah, I swear that was off the top of my head
Anonymous
@SirCumference Do you understand Hindi ?
@S007 Huh?
What brought that up?
Anonymous
Oh leave it...I knew a couple of good jokes in hindi :-P
@S007 :/
Ok, lemme think
Here's one I heard on astronomy SE
Anonymous
@SirCumference where are you from ? :)
01:37
A neutrino walks into a bar...and keeps on going...
@S007 'Murica
Anonymous
Murica...merkan ? Hehe :-d
(America, not sure if you get the meme)
Hi @rob
Anonymous
You merken ? I get it man :-D
Have any jokes to share?
Oh! Came up with one
@S007 Why was Newton so smart?
He New tons of stuff
hurr hurr hurr
...Alright, I have to get back to work
Anonymous
That was new :-D ..... okay see you around :)
rob
rob
01:46
@Secret With regard to physics.stackexchange.com/q/289172/44126: By "second anapole moment" I did mean two opposing anapoles. A physical implementation of an anapole current, like the one I developed in response to your question, would have a broken rotational symmetry, even though the "pure" anapole moment doesn't.
I didn't elaborate further in my answer because I was concerned about getting lost in the weeds.
Evening, all
Anonymous
Does magnetic flux change when a iron rod is inserted into a current carrying solenoid ? Can someone answer please ?
Anonymous
I initially thought flux = B.A where B=inA, and as current does not change flux should not change, but I am not sure
Anonymous
@ACuriousMind Any ideas ? :-P
Question
Is there a limit to how massive an electrically neutral object can be before it becomes a black hole? Say it's composed of hydrogen
Anonymous
Sorry, I meant B=mu n I
Anonymous
01:57
@SirCumference yes
@S007 Which is?
Anonymous
Chandrashekar Limit if I remember correctly
Anonymous
Just google the name
Chandrasekhar limit is for collapsing white dwarfs
Beyond the Chandrasekhar limit they become neutron stars or explode as supernovae
@S007 You thinking of the Tolman-Oppenheimer-Volkoff limit?
Anonymous
02:00
that is for neutron stars isn't it ?
Anonymous
that is, the maximum mass a neutron star can have before it collapses
@S007 Yeah
I'm talking about hydrogen objects
Anonymous
yes beyond that it can form black holes
What?
I'm asking if there's a maximum mass for a bunch of hydrogen before it becomes a black hole?
Anonymous
@SirCumference Sorry, I am not an expert on the this topic....I will not be able to answer
02:02
Realize I'm not being specific, actually...
Say a bunch of iron
Hi, I am wondering if diffusion will be enough to ventilate an underground city. I think it would be enough. I mean plants draw CO2 from anywhere they can get it and CO2 will naturally diffuse into the atmosphere if there is a higher concentration underground(which with people living there, there will be). Similar things for the oxygen except that now oxygen is of lower concentration underground than in the atmosphere and plants give off oxygen while animals and people draw oxygen in.
Anonymous
@SirCumference AFAIK black holes are not just created from a random large mass....they are created from neutron stars or white dwarfs or large stars at the end of their life cycle...for neutron stars it is the TOV limit and for white dwarfs it is the Chandrashekhar limit....anyway I think you better ask on Astro SE
Anonymous
@SirCumference Wiki says "The maximum mass of a neutron star is not well known. In 1939, it was estimated at 0.7 solar masses, called the TOV limit. In 1996, a different estimate put this upper mass in a range from 1.5 to 3 solar masses. In the theory of general relativity, a black hole could exist of any mass."
Anonymous
BTW do you know the radius of the Schwarzchild event horizon ? That might be an answer to your question
rob
rob
@Caters Diffusion through some barrier to the surface atmosphere, or diffusion in the still air of the city?
Anonymous
Okay, i just came to know that minimum mass of a black hole can be 22 micrograms (Plank's mass) :-D...but it will disappear almost instantly due to Hawking radiation....
03:03
I mean bidirectional diffusion without a barrier(unless you consider gravity a barrier). Namely the CO2 diffusing into the atmosphere where plants are and the O2 diffusing into the underground city where it is needed.
Anonymous
03:14
@Caters I think you will get good/better answers if you post your question on the main site....
user218912
03:45
@SirCumference hi
user218912
@MAFIA36790 hello
user116211
hey @obe.
@obe Greetings
@obe Question
04:11
Holy crap!
I just realized
if you take any of the products of 9, from 9 to 90, and you add the ones and tens digits
you get 9
Hell, it works for all products of 9 that aren't multiples of 99
I feel so proud of myself...
user218912
@SirCumference hmm?
@obe Don't remember
user218912
lol
user116211
The chat is actually a bit dull when there is no 0celot ._.
I just realized
For any number $n$
$n^2 = (n-1)^2 + (n-1) + n$
So $30^2 = 29^2 + 29 + 30$
Math is cool
user218912
04:26
ummm
user116211
Why are you playing with numbers?
user116211
Do some Maths.
user218912
that's not a special formula or anything @SirCumference
@MAFIA36790 There are subliminal messages
user116211
04:27
^
user218912
you can write a random formula like that for anything
user218912
just write $n^2$ in a more complicated way
@obe sigh ;-;
@MAFIA36790 Isn't it ever cool to you when you discover something like that 9 thing?
...no?
user116211
@SirCumference Well, I'm not saying that's bad; but frankly speaking, it's not those Aha moments that you get while you do some real maths.
user218912
did you discover it yourself? @SirCumference
04:28
@obe Yeah
9,18,27,36,45,54,63,72,81,90

9n=10m+p=(9+1)m+p=9m+m+p

18=10*1+8=(9+1)*1+8=9+(1+8)
27=10*2+7=(9+1)*2+7=9*2+(2+7)
36=10*3+6=(9+1)*3+6=9*3+(3+6)
...
9n=10m+p=(9+1)m+p=9m+(m+p)
Therefore m+p=9

Therefore there exists recursion relation:
$$9n=10m+p=9(n-1)+(m+p)$$

Therefore
9=10*0+9=(9+1)*0+9=9*0+9
90=10*9+0=(9+1)*9+0=9*9+(9+0)
99=10*10+(-1)=(9+1)*10+(-1)=9*10+(10-1)
etc.
user218912
@SirCumference ok then maybe it's cool
user116211
@Secret ooooo....
@obe Ikr :D
@Secret Dude...
Wall of text?
user116211
How do you do this @Secret?
04:29
I wonder if there are similar recursions for other number bases...?
@MAFIA36790 My maths class taught me to always keep an eye for patterns formed by a complicated expression
@MAFIA36790 Sometimes numbers themselves are a bit fun
user116211
ahh.
As a kid, were you never impressed by huge numbers?
I don't see numbers as numbers (because then I never understood it), but when looked at them in the eye of abstract algebra, then suddenly the rules become clear.

The same idea underlies on why people tries to find the TOE in physics
Well come on, don't you remember pondering math tricks in middle school?
Even if they were useless, they were cool?
04:33
You might argue one possible motivation of me become so interested in abstract algebra is to understand numbers
user218912
I was writing a latex document where I store all my notes for everything I learn and I called it "independent study in science". I only realized what a bad name that was when I wanted to name the file with the acronym.
Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares. p = a 0 2 + a 1 2 + a 2 2 + a 3 ...
Another little thing I like
user218912
though I like that title, idk if I should keep it
Perhaps I should call my "discovery", Pies' nine theorem
(old name)
Sir Cumference's nine theorem is too long
user218912
someone probably discovered it before somewhere
user218912
04:39
but then again
user218912
stigler's law
user218912
yea it's boring here without 0celo7
user218912
gtg bye
user228700
Ello everyone :-)
user228700
For anybody interested in the story of that poor crow of mine: the crow had been climbing up a small water can now and again, all day yesterday. Today, we placed a taller cardboard box near the ledge of the balcony and huzzah, using the support of the box, it was able to stand on the ledge. Then, it took off, but it fell down into another garden. Thanfully, nothing happened to it. This is him/her now: (The one on the right)
user228700
04:53
@obe It's already been 11 days
Just 79 to go
Wonder why he doesn't bring it up on meta
user228700
I've absolutely no idea how it to managed to get up there but this means progress so yay! :-)
@Kaumudi I thought you said you lived in a big city?
That looks like suburbs
user228700
@SirCumference Yes, I do. Our cities are still relatively green :-)
@Kaumudi Lucky...
We get sunlight almost three times a year
gtg
user228700
04:56
Yes :-)
user228700
Oh, wut? :-|
user228700
Bye!
Anonymous
05:09
@Kaumudi Hey, thank you for talking care of the crow :) I hope it gets well soon :) Birds have an inclination to fly even when they are injured!
is the phrase "flow of current" correct?
current is flow of something
flow of flow of something?
Anonymous
@YashasSamaga Current by itself means the flow of something. So you know in colloquial terms that is acceptable but not in technical writings. (Just my opinion)
user116211
05:26
@YashasSamaga This is wrong literally; flow of flow of...; but it doesn't really matter now; what matters is the maths and the physics; any book even like the big Jackson is indifferent to its literal meaning; after all it is not a big issue.
user116211
@SirCumference I don't disagree at all.
Why do they all electronics.stackexchange.com "Electrical Engineering"?
They aren't the same obviously
user116211
@ACuriousMind, you are early riser, I see.
Sigh...noticed mistake in old answer, hunted for the correct solution for about an hour
user116211
ahh.
05:29
@MAFIA36790 Ahahaha...no, I'm just very late to bed :P I wanted to go...too long ago but then things kept me awake (and I wasn't really tired anyway)
Anonymous
@YashasSamaga "Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. " :-P There is a problem with the name, I agree :-D
people care about physics more than their well being lol
user116211
@ACuriousMind okay; have a sleep then at least for an hour. Night.
Binary
$$1_2=2*0+2^0*1=(1+1)*0+2^0*1=0+(0+2^0*1)=0_2+(0_2+1_2)=1_2*0_{10}+(0_2+1_2)$$
$$10_2=10_2*1_2+1_2*0_2=2*1+2^0*0=(1+1)*1+2^0*0=1+(1+2^0*0)=1_2*1_{10}+(1_2+0_2)$$
$$11_2=10_2*1_2+1_2*1_2=2*1+2^0*1=(1+1)*1+2^0*1=1+1+2^0*1=10_2+1_2=1_2*2_{10}+(0_2+1_2)$$


Therefore suspect recursion relation:
$$1_2*n_{10}=1_2*(n-1)_{10}+(m_2+p_2)$$
where $m_2+p_2=1_2$

I suspect the same thing will happen for all bases, but I am not sure. In fact, I have not checked all the binary cases yet and it seems clear there is a crack in the pattern...
user116211
@YashasSamaga Sometimes you can't just sleep without clearing the problem; that happens to me many times.
05:32
I know that :D
I sometimes find profs wandering around the campus at 2AM
sometimes I go and have a chat with them
Anonymous
@YashasSamaga Really? Where do you study? Which university ? :)
Indian Institute of Science
user116211
@YashasSamaga WoW :)
Anonymous
IISC Bangalore ?
:/
there is only one IISc unlike IITs :P
Anonymous
05:36
That's a great place :). You got in via JEE or KVPY ?
Anonymous
Ow..lucky guy :-D
user116211
I can't study other things when there is a problem looming over; unless I get the insight, it will try to collapse my conscious state; it's thrilling though.
I get sleepless nights when I am working something on the computer
user116211
see? same trait.
user228700
05:41
@S007 :-)
Anonymous
@Kaumudi Good Morn :-D
Still got work
Gon be up for a while
user116211
What are you studying @SirC? Number Theory?
@MAFIA36790 Psychology for the credits
user116211
oh.
05:53
Test tomorrow
user116211
OMG.
@MAFIA36790 Surprisingly, psychology does not let me read your mind :/
I feel cheated
user116211
@SirCumference You are not Xavier; sorry.
@MAFIA36790 Jewish, don't get the joke... :(
user116211
Not a joke.
05:55
Nevermind, I'm an idiot
user116211
._.
Somehow, I thought you were talking about religion since you mentioned a Jesuit
user116211
WTH ;/
Okay, look, I'm tired
It's almost 1:00am
user116211
I don't like religion talks.
05:56
D:
I'm really tired, but gotta keep reading
user116211
@SirCumference good.
@JohnRennie Howdy
user116211
My great revelations occur while studying for exam in the exam eve midnight.
@MAFIA36790 Do you ever think dogs know more than us?
But they can't talk?
@SirCumference Morning. Still troubled by the insomnia?
05:58
What the hell am I saying?
user116211
@JohnRennie Exam prep.
@JohnRennie I guess it's nice because I need to study all night
user116211
Morning @JohnRennie, btw.
Anonymous
@JohnRennie Good morning :)
Hmm, I'm unconvinced that working all night is a good way to prepare for exams, but each to their own.
05:59
@JohnRennie Your teachings on degenerate gases helped me in astronomy :D

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