My gawd so many stars

holy stars

lol

who's the second person starring?

@enumaris who's the first

I would image gateprep himself

oh you can't star your own

so I guess it's who's the first lol

@enumaris he can't star his own messages

no idea then

Must be the great lurkers of chat

And so amazon is having some problems. You'd think that they'd have that covered

One dude has remkved

How to calculate vol of the liquid when required

One dude has removed

@gateprep density has been given

Delivered version 1 of code. Picked up moola. Going to eat like a boss.

@Cows what does a boss eat

@gateprep the vol of liquid is given by the following expression: $$\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty‌​^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^‌​{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{‌​\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty^{\infty}}}‌​}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$$

@gateprep This kind of demanding people tell you how to solve a problem is not welcome here. You're free to ask a question, but please do not push other people to answer you like that.

@gateprep The typesetting of that thing is appalling.

Even Microsoft Write had italics.

and spaces

@Secret one of the infinities is not in heirarchy with the rest

meh, don't expect me to be able to read tons of braces in latex

That one's just a special $\infty^2$

I think if you fix the braces issue, the answer is correct though

so it might be worth looking into

@Loong There are those who care about appearance and those who...don't.

u sure the second set isn't just the empty set?

There are also those who care and eventually give up...tikz

oh my

@ACuriousMind Yeah, you should see our shift log. :-(

ohhh myyyyy

hmmmmm

Evening guys, I'm learning about the node voltage method and I was wondering (because I'm having difficulties) what is the easiest/best way to solve for the node voltages for example here:

Well, that's a linear system of equations, so just do Gaußian elimination?

It's a bit tedious, but it's not difficult :P

We don't have this in Bulgaria but I'll learn it, thanks. :-)

(The website recommends this method as well)

3 equations and 4 unknowns though?

oh wait

there's no V2

lol ok then

It's the ground referrence :D (Meaning 0V)

Just plug that into mathematica or something

@enumaris That's for the lazy ones :D

in the words of Jackson, it's "tedious but straightforward algebra"

and tbh when it comes to linear algebra I don't see much point in being high-minded about it

hmmm

I was always a fan of solving by inversion, though I may have been the only one

If it's simple, do it by hand. If not, hand it off to a computer.

Gaussian Elimination is part of linear algebra, right?

yeah

(there are times when one does have to be high-minded, but this isn't one of them)

Though if you've never solved something like that, you should probably do a few simple ones by hand. After that, just plug it into a computer whenever

What we do in Bulgaria is something called 'a system'. We just align the equations next to a big line, then solve for V1 for example, then plug V1 in the second equation, then solve for V3, then plug V3 into V4... blaaah, complicated. I might impress my teacher by showing her Gaussian Elimination ;D

the usual parlance for that is "solve by elimination and back-substitution"

for simple systems, it's sensible enough.

Anyone hyped for Avengers 4?

it ain't out yet

@NovaliumCompany Well, that's not special to Bulgaria, that's how everyone learns to solve these systems at first ;)

@ACuriousMind Cool, at least now I'll now 2 methods :--)

@enumaris I'm still hyped ;D

@enumaris You saw inf war?

yeah

Ant-Man and the wasp?

yep

Is the sequel to inf war sup war? :P

Aleph-1 War

I haven't watched Ant-Man yet, but I spoiled the credit scene today. :P

insert 'continuum war' joke here

$\aleph$

$\aleph_\infty$-war

I'd watch a math parody of any movie

eh, a proof of the existence of such a parody is enough for me

crud

I have no idea how to perform this union I need on tableau...

union(a, b) :D

well a is a joined table

and so is b

and a and b field names don't match up

lol

hmmm

sharing the poking-fun-at-the-US-job-market fun, here's a listing for a local adjunct faculty position: indeed.com/rc/…

have fun spotting where it takes a turn

jesus

yes, literally

And my actual reaction

I do admit I'm curious of how they include Christianity in engineering/CS courses

> 3. * Have you placed your faith in Jesus Christ for personal salvation?

"Who?"

Is that legal?

followed by "Please describe the circumstances surrounding your becoming a follower of Christ" and " I have read the Declaration of Christian Community and believe myself to be in agreement with it."

it's a christian school?

@Loong I would guess it is, since it's a college with a faith-based mission

@Semiclassical Actually not unique to the US, there are university-like institutions in Germany that adhere to a particular Christian confession and require their staff to belong to that confession.

I mean, it doesn't surprise me for a Christian school...

@ACuriousMind yeah, true

Guys, a very stupid question, CS stands for Computer Science right?

most of the time

no, Cauchy-Schwarz. (yes, yes it does)

These institutions cannot hand out PhDs but are otherwise equivalent to "true" public universities, ie. can bestow Bachelor's and Master's degrees.

Ok thanks xD

Yeah. It's not really so surprising, it just caught me off-guard

from an article re: private schools and discrimination policies: "Religiously-controlled private schools can discriminate on the basis of religion in hiring decisions. For example, Jewish schools are under no obligation to consider Catholic or Muslim teachers for their faculty."

@ACuriousMind There is a decision of the European Court of Justice that this practice in Germany is not generally permissible.

@Loong Yes, but the German Christian churches do not appear to care.

"they have ruled it so, now let them enforce it"

One should note that this really is a privilege of these churches - it is not something generally tolerated for all groups of faith.

Separation between state and church has never been very strong and I have little hope of that changing soon.

particularly not in the US context

Come take a trip to the US south. I probably have half a dozen churches within walking distance of my house and I'm in a pretty small town

sounds about right

I was talking about Germany, but sure

I was just saying that it was fairly religious here. I have no idea about elsewhere. I do find all the people sending their kids to Christian school then Christian colleges around here to be a bit odd

I mean, for a private institution, I can't see how separation of church and state would apply to them...

@enumaris The institutions I was talking about receive a lot of support from the state.

hmmm

And, of course, the fact that they are permitted to discriminate on the basis of faith while others are not is also a result of lacking separation.

on that note: americamagazine.org/politics-society/2017/06/27/…

Yeah, but that would be an issue of religious discrimination, not necessarily separation of church and state tho

I wasn't talking about separation of church and state in my comment, though the culture here does bleed into politics and government

Although if you do take that idea to the extreme, you might find yourself requiring that e.g. Christian minister positions be open to other religious leaders...o.O

@enumaris It is the state that decides who is or is not allowed to discriminate. When the state allows it for certain churches, that certainly seems to me to imply a breach of separation of church and state, in that the state is explicitly favouring particular churches.

Yeah if they favor particular churches over others

with the implication in the US, at least, being that a religious college may have the right to benefit from govt funding

but if their position is only that all churches can discriminate based on religion for their hiring practices, then I think it's not really a separation of church and state issue

more of a discrimination issue

It's a church-state issue insofar as it's government funding (and therefore govt policy)

@enumaris Yes. When I say "churches", I mean the two main Christian churches in Germany, the Catholic church and the Protestant church. These privileges are not granted to any of the numerous smaller Christian organizations, nor to most other religious groups.

I see

With the German context, it sounds like it's mostly a matter of that being the status quo

i.e. those institutions have always had that deference, so they continue to receive it

I shudder to think of the media outcry if, say, Muslims were explicitly allowed to hire only Muslims.

(To their credit, the Protestant church has mostly relented on hiring restrictions over the last decades, allowing people of arbitrary faiths or none to work in positions not directly related to religious duties)

like a Muslim Church, or generally Muslim business owners?

Are Muslim Mosques in Germany required to e.g. allow a non-Muslim to become an Imam?

@Semiclassical Yes, it is very much the inertia of the status quo

Whereas in the US I feel like it's different insofar as you have a very politically active and influential evangelical contingent

@enumaris Well, no one is required to hire anyone. I'm talking here about e.g. Catholic churches being allowed to require their clerks being Catholic, I'm not talking about positions that involve actual religious duties.

and that's not tied to a historical church in the same way as in the German context

Certainly it is a requirement for the position of a priest of some faith to actually belong to that faith; the thing is that the churches are allowed to require a certain faith even for positions that have no evident relation to the faith

@ACuriousMind which is where you get into the territory of math instructors being required to avow a certain faith

@Semiclassical Yes, exactly, that's the thing I'm talking about. Math instructors, clerks, janitors, you name it.

Yeah I suppose a lot of churches in parts of Europe may have been around longer than the US as a whole and have a lot more backing. No clue how that is in Germany since it's a lot younger though

@Semiclassical Yeah, I believe the historical background is very different

as is the resulting contemporary influence

@danielunderwood Germany as a country is young but the smaller parts it consists of are old, too, and the churches have long had influential relationships with the local rulers.

@ACuriousMind I see

@ACuriousMind Out of curiosity, when do you generally conceive of "the start of the German State" happening?

by contrast, the Christian college mentioned earlier was founded in 1902

Like here in the U.S. we generally count starting from 1776 - the date of the signing of the Declaration of Independence

in China, they count from the Shang dynasty or perhaps even the Xia dynasty and a general thought would be "China is 5000 years old" (Even though 5000 years is well in the realm of pre-Xia dynasty)

@enumaris A rather uncontroversial point would be 1871 with the founding of the German Empire

and prior to 2013 it was specifically a "bible and missionary training school"

@ACuriousMind I see

Yeah I'm curious about the early German history as well. I don't think I was ever taught about it in school and only recently found out that it was founded fairly recently

I'm mostly curious at not like a "scientifically accurate date", but more in what's in the consciousness of the German people generally speaking

Like if I asked "How old is Germany" to a typical German, what would he/she say?

Count starting from 1871?

However, all the smaller states that conceive of themselves as "German" are much older, and the idea of "Germany" goes back at least to the days the Holy Roman Empire, which came to be called "of German Nation" sometime in the late Middle Ages

hmmm

@enumaris I think most would start from '45, if not '89

So there's no one unified answer?

I see

with the US context it's a bit different, since we started as a british colony

So counting from end of WWII?

so the transition from 'british subject' to 'american citizen' is a bit more precise

@Semiclassical yes certainly, the context in diff countries will all be different

In my perception, we do not really identify ourselves as being in an unbroken line with Hitler's Third Reich, and for many, Germany only really became "Germany" with the end of the GDR

but I'm just interested in what "the average Joe" would think

@enumaris It's...not something we talk about much

In other words, I'm not so much interested in precise History with this question as a general Sociological question

@ACuriousMind I see

Due to historical circumstances, any pronounced interest in the notion of what's "truly German" is...viewed with suspicion

Fair enough

I suspect there's an interesting contrast to be made with the American Civil War

At least among many people I know. Certainly, there are others.

and how southerners view the Confederacy

I guess a few Americans might view "The U.S." as tracing lineage back only to the end of the Civil War with the restoration of the Union...but I suspect that is a minority.

1776 is the date I am most exposed to

@enumaris I think one data point for "we don't talk about it much" is that there's no holiday for something like "foundation of Germany". However, unification day - the day when West and East Germany became a single country again- is a rather important holiday.

@enumaris I doubt there’s a lot. The difference between “reunification” and winning a civil war is a pretty big one

@ACuriousMind makes sense :D

Yeah I don't know that I've heard of anything other than 1776. Still a lot of people around here flying Confederate flags though

Though I have heard people describe the difference before/after the Civil War as being: people saying “The United States are...” (ie plural) to “The United Stated is...”

yeah

@danielunderwood yeah, and I suspect that’s the crucial difference

There’s a notion of Confederate heritage

It's hard for me to really understand that one

I’m a northerner, so I don’t really comprehend it either

@enumaris Keep in mind though that I was born after unification, and that I generally move in circles that are far from any notion of nationalism. There may well be Germans with a wholly different take on the issue, and especially in recent times, I'm not exceptionally confident in what's the dominant take.

By contrast, “Nazi heritage” is definitely not socially acceptable

I've always been from the south and I don't really understand it either. Though I suppose NC isn't really the deep south

I could imagine there are some people with fondness for east Germany

Maybe just remnants from being on the losing side

But not anywhere near how it is here with the Confederacy

@Semiclassical Some, but they are few and far between - keep in mind that East Germany ended with thousands and thousands of people in the street protesting against it.

And the fact that there weren't large changes in the south even for a long time after the Civil War was over

@ACuriousMind yeah

Again, it’s the difference between reunification and the suppression of a rebellion

With the former, you have a notion of a new nation built from the old

Convince me that quantum mechanics should have operators.

Planck found that electromagnetic modes hold discrete amounts of energy.

We know that a spark in a hydrogen gas makes spectral lines instead of a broad spectrum.

@DanielSank Counterchallenge: Newton found stuff moves in a straight line if no force acts on it. Now get me to Lagrangians and the principle of extremal action.

@ACuriousMind Action principle comes from optics. If you want to figure out how a lens works, you can get right answer by minimizing the optical path length.

@ACuriousMind understood :D

Not sure how to get from there to more general action principles. Thinking...

@DanielSank Right. And if you want to figure out how Stern-Gerlach works, you need non-commuting notions of measuring something.

Note that neither optics nor Stern-Gerlach are in our lists of things we demanded to start from.

I don't find stern-gerlach convincing.

This is something I've believed for a rather long time: Classical physics is often as mysterious and strange in its leaps of logic to more general theories as quantum physics. But because it can be translated more easily into language matching our intuitions, and because our intuitions are shaped by first learning classical physics, we tend to view quantum physics as more mysterious.

Can't we interpret Stern-Gerlach as exposing an unstable behavior of the electron beams?

@ACuriousMind I never said otherwise.

I do not think quantum mechanics is weirder than classical.

I simply asked how to logically recover some parts of it from things that come before it.

It is as interesting to ask about where Lagrangian mechanics come from, but that's not what I happen to care about just this moment.

Also, QM is weird

@DanielSank are you referring only to logically how things came about or also historically how things came about?

since QM was developed by a huge number of different people, I'm not sure its historical development is actually logical

@DanielSank I still think the analogy is helpful. You first had Newton's laws and basic mechanics, and then someone noticed these equations of motion could also be attained from extremizing an action. Similarily, you first had old quantum theory, with its weird quantized orbits of electrons that somehow don't fall into the nuclei and whatnot, and then someone (Heisenberg) noticed how such discrete orbits could be obtained as the eigenvectors of operators.

And you also had the double-slit and Schrödinger's wave mechanics, and all this was - in a leap of faith - synthesized into a more general theory of operators (=matrices) and states that could superpose much like waves.

@DanielSank @BernardoMeurer (?) this is why we can't have nice things

@DanielSank you are weird

QM is definitely weirder than classical mechanics

@EmilioPisanty What's not nice about tea time?

I'm in full agreement that "ooooohhhh, loooook at the myyyyysteryyyy of QM" is often best met with "yeah, CM does that too"

but try to CM the measurement problem

@EmilioPisanty Try to QM Norton's dome.

@ACuriousMind you probably can

it'll be right at home on the quantum/classical illnesses/symptoms paper

lemme find it

@EmilioPisanty Unitary time evolution is unitary - no chance for non-unique solutions there

aapt.scitation.org/doi/10.1119/1.17221

@enumaris I don't really care about the history right this moment.

@ACuriousMind well, as in, you'll get equally pathological behaviour

@EmilioPisanty No access, the pearly gates of knowledge are closed to us who have forsaken sacrificing our lives to it.

@DanielSank alright, so, where, logically would you like to start? Because the use of "operators" can be a starting framework itself.

I mean, CM gets weird already at the level of $V(x) = -\lambda x^4$

@EmilioPisanty That is amusing.

@EmilioPisanty Bah. Newton's law is very unintuitive.

@EmilioPisanty That's the only weird thing about quantum though.

basically, for $V(x)=-x^4$, you get to infinity too fast

i.e. in finite time

easily seen from quadratures

@enumaris Suppose I know classical Hamiltonian and Lagrangian mechanics.

Now get me to operators.

which then means that you cannot extend EOM solutions to all times $t$

@ACuriousMind that's right in the same ballpark of pathology as trying to climb Norton's dome

@DanielSank agreed

but it's enough weird to keep us busy eight decades and counting

@DanielSank that's a tall order

so, given Classical Mechanics as formulated by Hamilton and Lagrange, and given quantum experimental results (e.g. electron diffraction, Hydrogen spectra, etc.), get QM as formulated with Operators in a Hilbert Space?

I feel like that's not doable because there isn't a single unique framework with which you can explain a set of physics phenomena...

you might equally end up with Feynman's path integral formulation for example...

@EmilioPisanty Not sure what I'm looking at, nothing in that image seems pathological except for the "partially complex" in the middle, perhaps :P

or de-Broglie-Bohm mechanics

@ACuriousMind solutions not defined for all times (CM) and momentum without a unique self-adjoint extension (QM)

@enumaris Well ok fine. I don't mind a biased story ;-)

This can't be that hard.

@DanielSank Have you read physics.stackexchange.com/q/46015/50583 and its answers?

wall of texts

@EmilioPisanty The expectation that every classical system have a unique quantization is misguided, and I don't see why the failure of such a quantization to exist should be pathological.

@ACuriousMind read the paper ;-)

I can email a copy if necessary

@ACuriousMind Jeezus that's a lot of words I don't know.

@EmilioPisanty I can probably get it if I want, if not I'll get back to you. It's probably gonna be a few days before I've got the leisure to read it, though

@ACuriousMind fair

hmmmmm

@DanielSank I'm not saying Urs' answer is the one true path to QM, but I am saying that "get me from Hamiltonian mechanics to operators" may look very different than you expect it to, depending on who's answering :)

posted an answer at 7pm utc and it's now riding the HNQ train

the question is

will it ride it fast enough to make the rep-cap?

one hour and 65 rep to go

@Blue V.I. Arnol'd

amazon.com/…

@ACuriousMind ok...

@Blue Abraham/Marsden

Look, I can analyze a classical harmonic oscillator in terms of $a$ and $a^*$ variables defined in terms of $q$ and $p$ exactly how you expect, i.e. $a = q - i p$.

at least for Hamiltonian reduction

That can't be an accident.

@DanielSank have some ideas on that but youd have to unblock me to hear them :| :P

Those variables are particularly useful as they are eigenvectors of the Hamilton equations of motion written as a matrix:

$$\frac{d}{dt} |\Psi \rangle = H |\Psi \rangle$$

where everything there is classical.

I'm sure somebody in the early 1900's knew that.

@Blue it'll teach you all you need to know

it can be tough going

it's very mathsy

I learned stuff from Arnold.

but it's a wonderful book

@DanielSank We've been here before, haven't we? The classical $\{H, -\}$ (the Poisson bracket) is getting mapped to the quantum $[H,-]$ (the commutator). This is what one calls "naive quantization".

@ACuriousMind what's jaded quantization then?

@ACuriousMind yes we've been here before, but we've never actually motivated the introduction of operators.

@EmilioPisanty :-P

@EmilioPisanty "shut up and calculate"

Jaded quantization is what you study toward the end of your PhD.

@ACuriousMind ah, yes

I forgot

@DanielSank speaking of, the end-of-my-PhD work finally got published

arXiv:1606 and published may '18

damn near an absolute age to the finish line

(admittedly a large part of which was caused by the paper just sitting on my desk with me unable to face dealing with it =P)

@DanielSank Stern-Gerlach and the double slit suggest some sort of linear superposition of states, and the archetypal incarnation of things being able to be combined linearly is vectors. Knowing that the fundamental object of Hamiltonian mechanics is the algebra of phase space functions, the "natural" way to apply an algebra to vectors is to seek a representation of the algebra on the vector space.

hmmmmm

Ok that's something to chew on. Thanks.

It's still a giant leap of faith, don't get me wrong. But it's, in a way I can't quite describe, the smallest leap of faith that turned out to match very well with experiment.

@Blue tbh, I haven't read it - but I've read bits and pieces of it when referred to it by other things

the longer you chew

the less it makes sense maybe

@enumaris the more cow you become

yes

For me the most elemental example is Stern-Gerlach

and hence things make less sense

@Blue My second semester theory lecture was Hamiltonian and Lagrangian mechanics, and the lecturer was brilliant.

Also, my focus on QFT meant that I revisited a lot of these concepts again and again when trying to understand something in quantum field theory. Read Hennaux/Teitelboim for (Hamiltonian) gauge theory, but I mostly picked up bits and pieces from wherever I found them whenever I needed them

I've never been a very structured learner :P

I am very thankful for the many excellent lectures I had

@Blue Sure, try it! I'm just saying don't give too much on my recommendations ;)

@Blue I was actually watching that course a couple weeks ago. It was pretty heavy on the math side imo

He also has problem sheets for them though

Then I started the CM here, which seems less mathy but less rigorous. Though I guess that's a normal tradeoff

But he kept referencing problem sessions in that second one, which aren't online. And the camera operators sometimes weren't the best