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Balarka Sen
Balarka Sen
4:00 PM
"Shooting Sandstorms" and "Never Gonna Shoot Your Stars" are my favorite songs of all time
 
Prathyush Poduval
Prathyush Poduval
Haven't seen those
 
Balarka Sen
Balarka Sen
Check it out
 
Prathyush Poduval
Prathyush Poduval
@BalarkaSen These mashups are extremely out of place and random :P
 
Avantgarde
Avantgarde
grandayy memes are nice
 
Balarka Sen
Balarka Sen
@PrathyushPoduval Well, not if you put them in the context. Shooting Stars was a meme song back in those days
and everybody put up videos of people falling down to spacey backgrounds with that playing on the back
so grandayy decided to do musical remixes with them, and it blew up
 
Prathyush Poduval
Prathyush Poduval
4:05 PM
@BalarkaSen I was ignorant of such wonders back then :(
 
0ßelö7
0ßelö7
4:16 PM
@BalarkaSen he asked about it
 
Balarka Sen
Balarka Sen
well eh writing out the Riemannian length is probably not the best pedagogical technique if you want to teach someone about arclength of curves on Riemannian manifolds
 
Sir Cumference
Sir Cumference
@heather Sad thing is, all those votes on questions already above score 10 are useless. If all of those extra votes were distributed to the other questions, that proposal would be 1 vote away from being in beta...
 
0ßelö7
0ßelö7
@BalarkaSen yeah well I didn't want to talk about Hausdorff measure
 
Sir Cumference
Sir Cumference
Howdy @dmckee
 
Balarka Sen
Balarka Sen
@0ßelö7 lol sigh
 
Sir Cumference
Sir Cumference
4:23 PM
0
Q: What if a white dwarf is less massive than her partner?

YottaEngineerFor example: a system with a 0.2 solar mass white dwarf orbiting a 0.25 solar mass red dwarf. Does the red dwarf steals mass from the white dwarf or vice versa.

astrophysics binary-star star-systems white-dwarf red-dwarf
I guess white dwarfs are female
 
ACuriousMind
ACuriousMind
@SirCumference OP's native language is probably one where 'dwarf' or 'star' are gramatically female.
 
Sir Cumference
Sir Cumference
@ACuriousMind Very true, didn't think about that
 
Physics Meta
Physics Meta
0
Q: Would i make sense of have a rainbow tag?

Mikael FremlingI just posted a rainbow related question and though that a rainbow tag might be useful given that there are a few questions about it. Didn’t want to create one without consulting meta though.

discussion tags
0
Q: Downvoting and Reputation-Loss

Wrichik BasuOn down-voting a question, the person who downvoted, loses 1 reputation point. This is a practice that has been started here to prevent misuse of the option to downvote. However, no reputation is lost on down-voting a question. Why is there an anomaly like this? Shouldn't it be same: either no r...

discussion reputation down-votes
 
dmckee
dmckee
4:57 PM
@DanielSank I saw a (wee, little bit) of perturbation theory in Classical Mechanics at the undergraduate level (but I got buried in the mathematical detail and didn't learn much).
Then I got a little more at the grad level and a little bit stuck but I still had the impression that it was unusually technical and difficult.
It wasn't until I was reviewing to teach Classical that I really began seeing the forest through the trees. It's still mathy in my mind, but no longer so mysterious.
 
Sir Cumference
Sir Cumference
I'm wondering, will we ever know the size of our universe (or if it's infinite)?
 
ACuriousMind
ACuriousMind
@SirCumference It's hard to see how, given that nothing outside the Hubble horizon can influence us as far as we understand.
That is, I think if we ever have evidence either way, we have also discovered new physics first.
 
Sir Cumference
Sir Cumference
@ACuriousMind Er, nothing beyond the event horizon. Things outsize of the Hubble sphere are still visible to us
@ACuriousMind "New physics"?
 
ACuriousMind
ACuriousMind
Pick whatever horizon is the causal one. I don't bother to recall all the different horizons cosmology people invent :P
@SirCumference Something beyond GR + QFT that allows something causally disconnected from us to influence us.
 
Sir Cumference
Sir Cumference
@ACuriousMind Is there nothing that can be predicted from observing our observable universe?
 
ACuriousMind
ACuriousMind
5:11 PM
@SirCumference Not really my area of expertise, but I don't see how such a thing would be consistent with causality.
 
Sir Cumference
Sir Cumference
I mean, we were able to determine the flatness of the Universe beyond our observable universe
 
ACuriousMind
ACuriousMind
@SirCumference Link/reference?
 
Sir Cumference
Sir Cumference
@ACuriousMind The WMAP spacecraft
 
ACuriousMind
ACuriousMind
@SirCumference Can you explain to me how that is supposed to show flatness beyond the observable universe?
Thing is, the FLRW models are of course about an infinite universe with uniform flatness/non-flatness. Fitting an FLRW model to observed data of course predicts an infinite universe with a particular curvature. But that does not mean that the observation data actually implies that the FLRW model actually holds beyond the boundaries of what we have observed.
 
Sir Cumference
Sir Cumference
@ACuriousMind The Lambda CDM model is supposed to apply to the entire Universe. The numbers found from WMAP (by analyzing only the observable universe) strongly match up with those of Lambda-CDM.
 
ACuriousMind
ACuriousMind
5:16 PM
@SirCumference Yeah, so applying the LCDM model to the data gives you that. But the data itself is not evidence for the LCDM model applying beyond the observable universe.
 
Sir Cumference
Sir Cumference
@ACuriousMind I guess not directly, but it seems unlikely that only our observable universe follows LCDM
 
ACuriousMind
ACuriousMind
@SirCumference How did you determine that likelihood?
You have a sample size of 1.
 
Sir Cumference
Sir Cumference
@ACuriousMind This sample is monstrously big. As in, it's literally the biggest thing we can measure
Yet the LCDM model applies to it almost entirely
 
ACuriousMind
ACuriousMind
@SirCumference No, you have a sample size of "1 universe". How are you determining the likelyhood that the LCDM model may only apply to a subregion of a universe?
 
Sir Cumference
Sir Cumference
@ACuriousMind I'm not determining anything. I'm assuming with Occam's razor.
 
ACuriousMind
ACuriousMind
5:21 PM
@SirCumference Imo, the proper application of Occam's razor is "the LCDM model describes the observable universe well".
And being completely agnostic about the state of the universe outside of it.
 
Sir Cumference
Sir Cumference
@ACuriousMind Fair enough.
 
0ßelö7
0ßelö7
@ACuriousMind did you read my poster
 
Sir Cumference
Sir Cumference
@ACuriousMind Though the fact that we've determined, at least, our own observable universe's flatness has let us rule out a lot of potential fates for the entire Universe
 
DanielSank
DanielSank
5:40 PM
@dmckee It's not so bad if it's taught in a not-stupid way.
There is a distressing amount of stupid in physics pedagogy.
 
dmckee
dmckee
I've wondered in idle moments if the problem with classical perturbation theory is in finding an example that is tractable and still relevant enough to be interesting.
Marion and Thornton use the perturbation of stable orbits under $1/r^2$ fields, which is relevant but it takes them three pages to get to the result that perturbed orbit has the same period $\pm \epsilon$ as the original and passes through the point at which the disturbance occurred.
Cool factoid, but a lot of math to get there.
 
Mithrandir24601
Mithrandir24601
@dmckee I vaguely remember being told a thing about the classical equivalent to weak measurements (which is essentially a variant of perturbation theory) on how, when reflecting light (or maybe it was refracting light?) they could see that the position of the light beam had shifted to first order, but when looking at higher orders, they got a kind of splitting of this - it was over a month ago that I heard this, so I've forgotten about it by now...
 
DanielSank
DanielSank
5:56 PM
There are so many "quantum" things that are not quantum.
Avoided crossings: not quantum.
Perturbation theory: not quantum.
Moving poles off of the real axis: not quantum (at all)
Most of that stuff is really just some form of coupled oscillator/mode mathematics.
 
Mithrandir24601
Mithrandir24601
@DanielSank Isn't that most of quantum? :P
 
DanielSank
DanielSank
Grah!
Here's my famous-est post about the pole issue:
21
Q: Complex integration by shifting the contour

user2582713In section 12.11 of Jackson's Classical Electrodynamics, he evaluates an integral involved in the Green function solution to the 4-potential wave equation. Here it is: $$\int_{-\infty}^\infty dk_0 \frac{e^{-ik_0z_0}}{k_0^2-\kappa^2}$$ where $k$ and $z_0$ are real constants. Jackson considers t...

quantum-field-theory mathematical-physics integration complex-numbers
 
ACuriousMind
ACuriousMind
@Mithrandir24601 No, it's most of quantum that we know how to solve. E.g. strongly coupled QCD is not like the oscillators at all but it would be terribly nice to be able to say something about hadrons and stuff without having to rely on lattice simulations that may or may not have the correct continuum limit.
 
DanielSank
DanielSank
@Mithrandir24601 Oh, I misread that message.
@ACuriousMind So solve it. What are you waiting for?
Why is that stuff hard?
 
ACuriousMind
ACuriousMind
@DanielSank the right idea, I guess :P
@DanielSank Slightly flippantly, because we really don't understand interacting QFT all that well.
 
Mithrandir24601
Mithrandir24601
6:01 PM
@ACuriousMind It was a joking reference to that, hence the ':P' :P
 
DanielSank
DanielSank
What's the mechanical problem though? Is there no mathematical model or is the model somehow unammenable to numerical computation?
 
ACuriousMind
ACuriousMind
@DanielSank The model is amenable to "numerical computation" - that's what the lattice simulations do - but to seemingly nothing else. And the numerical computations are themselves plagued by some rather tricky issues.
 
DanielSank
DanielSank
I went to some lectures in grad school about taking math problems and using your brain to reduce them to a form that a computer can deal with. It was amazing and gave me a lot of respect for numerics.
 
Mithrandir24601
Mithrandir24601
@ACuriousMind 'Flippant' - that's the word I was looking for...
 
DanielSank
DanielSank
@ACuriousMind So the problem is really that nobody knows how to numerically compute stuff in a continuum?
That sounds like a solvable problem, i.e. use reciprocal space?
(Clearly QCD isn't that hard and I am going to solve it for everyone)
 
ACuriousMind
ACuriousMind
6:05 PM
@DanielSank Yeah. the major issue is that once you put the theory on a lattice - in either position or momentum space - you cannot really guarantee that the results will converge to the proper continuum theory if you increase the fine-grainedness of the lattice. "Triviality of $\phi^4$ theory" is a buzzword here - I'm still not sure whether we know that the lattice $\phi^4$ are not the continuum, or merely suspect it.
 
georg
georg
I have a brown-black-black-gold resistor

Apparently this is a 10 Ohm 5%
What does the 5% refer to ?
 
DanielSank
DanielSank
@ACuriousMind I'm very, very surprised.
 
ACuriousMind
ACuriousMind
I mean, you can do numerical simulations and sometimes they come out fine, but it's a bit difficult to tell how much of that is because we know what we want to get out of it.
 
DanielSank
DanielSank
@georg It means the resistor value could be anything from 7.5 Ohm to 12.5 Ohm.
 
ACuriousMind
ACuriousMind
(Also, this is not my primary area of expertise and I might be missing some developments)
 
DanielSank
DanielSank
6:06 PM
The 5% is the tolerance on the resistance value.
 
ACuriousMind
ACuriousMind
@DanielSank That would be 25%, not 5%, no?
 
georg
georg
Ok, tolerance is the percentage of error in the resistor's resistance,
 
DanielSank
DanielSank
@ACuriousMind oops
I mean 9.5 Ohm to 10.5 Ohm.
 
georg
georg
10 ohms \pm 0.5 ohms
right?
 
DanielSank
DanielSank
Right.
@ACuriousMind Hmph.
 
ACuriousMind
ACuriousMind
6:08 PM
You also have really unholy problems in getting fermions to behave properly on the lattice
 
DanielSank
DanielSank
Here's an example of me knowing enough to be dangerous:
 
georg
georg
Is that considered a huge error for resistors?
 
ACuriousMind
ACuriousMind
They don't like to be alone and usually "double" themselves, and while there are methods to fix aspects of that, I don't think we have a method that actually fixes all known problems with fermions on a lattice
 
DanielSank
DanielSank
I learned in a field theory course that you can turn everything in integrals of complex numbers by using coherent states. That tells me that I should be able to write every single thing I ever want to compute as some kind of horrible integral. Can't computers just... do that?
@georg Nah. That's pretty standard.
 
georg
georg
ok. They are available in 5%, 1% and 0.1% tolerances.
 
DanielSank
DanielSank
6:09 PM
Ok...
 
dmckee
dmckee
@DanielSank We had a curriculum re-vamp a couple of years ago at my current school and I tried to rig things so that a significant fraction of students would see classical before quantum. Just so that they'd have seen eigen-problems in a non-quantum context first.
 
DanielSank
DanielSank
@georg You decide which one you want by deciding how much you care about the accuracy of the resistance. The tighter tolerance ones cost more.
@dmckee WHAT THE FUCK?
There's a chance they can do quantum before they ever see classical mechanics?
jpoawsed[o0uaerpoiu aw-98UY AW[4O9UN E9RIJGSFXD
 
dmckee
dmckee
@DanielSank There is a chance they'd see real quantum before doing upper-division classical. Yeah.
 
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@georg depends on your application, and circuit design. Some circuits can be very sensitive to the resistance of a resistor
 
Anonymous
@DanielSank It's pretty standard to learn basic QM before formal Lagrangian and Hamiltonian mechanics (atleast in this part of the world)
 
ACuriousMind
ACuriousMind
6:11 PM
@DanielSank If only field theory was integrals over complex numbers! :P It's path integral, which you can numerically compute via Monte-Carlo lattice methods but for which we do not have the solid numerical mathematical theory of other computations because path integrals are mathematically ill-defined to begin with in most cases...
 
DanielSank
DanielSank
@dmckee EEEK
 
dmckee
dmckee
We typically have 3-6 physics majors per year, so most upper division courses are offered every other year.
 
DanielSank
DanielSank
@dmckee This is why I like Shankar's book so much: he spends the first 100 pages making sure you understand normal modes in classical physics. As @BernardoMeurer would say, papa bless.
 
dmckee
dmckee
They will have take the first year course and modern physics before hitting real quantum.
 
DanielSank
DanielSank
@Blue That's ridiculous.
Well, I suppose it depends on what "basic" quantum mechanics means.
@ACuriousMind I still don't believe that statement that path integrals aren't well defined.
 
ACuriousMind
ACuriousMind
6:13 PM
@Blue I learnt Lagrangian and Hamiltonian mechanics in my second semester (mandatory course, not me being fast!) and quantum mechanics did not really start until the fourth semester. I am continually amazed that that seems to be the exception in the grand scale of things because there's no way in hell I would have understood what's going on in QM without knowing classical mechanics as well as I did.
 
DanielSank
DanielSank
For diffusion problems, they are. You define the measure by requiring the path integral to recover a couple of properties that you know the diffusion equation must have. It's hard to imagine that this doesn't work in QFT.
 
dmckee
dmckee
For values of "basic QM" that just mean 'solve the time-independent Schrödinger equation in a box and for the hydrogen atom', then here too (we do those in Modern) and they haven't had variation mechanics at that point.
 
Anonymous
@DanielSank I agree. I hated when they started with Schrodinger's eqn without teaching us the basics of Hamiltonian mechanics. Anyhow, I did manage to learn it (atleast partially) from some Youtube lectures
 
DanielSank
DanielSank
@dmckee What is this "modern physics" I keep hearing about? Many curricula include such a thing, but I never encountered it.
 
dmckee
dmckee
And, yeah, it's a muddle.
 
DanielSank
DanielSank
6:14 PM
@dmckee That is a crime, IMHO.
Please don't take that as a personal attack though.
 
ACuriousMind
ACuriousMind
@DanielSank They are well-defined in the 0-dimensional case, i.e. ordinary QM and most stochastical problems, which is probably what you are thinking of when you hear "path integral"
 
dmckee
dmckee
@DanielSank At most places it means a quick pass through special relativity (I take 6 weeks) then ad hoc quantumy stuff from 1905-1925, and some level of introdution to wave mechanics.
 
ACuriousMind
ACuriousMind
the problem is not the idea of the path integral. the problem is that "integrating over fields" is simply very difficult to make mathematically precise, as opposed to "integrating over paths".
 
DanielSank
DanielSank
@dmckee Special relativity is good. Waves are good. What is the meaning of ad-hoc quantumy stuff?
 
dmckee
dmckee
Should be called '1900-1930 Physics', but that doesn't flow off the tounge.
 
DanielSank
DanielSank
6:15 PM
@ACuriousMind Hmph.
I say "hmph" to you, sir.
 
ACuriousMind
ACuriousMind
As long as we integrate over paths, we have the Wiener measure and stuff and all is fine and dandy. But once the thing we integrate over is allowed to depend on more than one dimension, things get awry fast
 
DanielSank
DanielSank
@ACuriousMind I don't like it, and I'm terrified that I'm about to be nerd-sniped.
@dmckee Why don't physics curricula teach linear response theory?
 
dmckee
dmckee
@DanielSank I mean blackbody spectra and Plank, photoelectric effect, Rutherford and Bohr and de Broglie.
 
DanielSank
DanielSank
You get so much for free if you spend a semester (or half a semester) teaching people grownup linear algebra, yet it never happens.
 
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@georg Generally, a good circuit design is one that is not that sensitive to the $R$ of the resistors. when designing a circuit you usually don't come up with standard resistances for the resistors in the circuit and have to choose the nearest one, which usually leads to a larger difference that the 5% tolerance.
 
DanielSank
DanielSank
6:17 PM
@dmckee Interesting. I had no such course.
My freshman year physics course was one semester of newtonian mechanics from Kleppner and Kolenkow (including oscillations), and then one semester of E&M from Purcell, with some amount of special relativity at the end.
Sophomore year first semester was Hamilton and Lagrange mechanics.
Second semester was quantum using Griffiths (do not like) and what you'd call "upper division" E&M using Griffiths (do like).
First semester junior year was when you got to start doing what you want. I took the second part of quantum, statistical mechanics, biological physics (basically more stat mech), Russian, and complex analysis.
 
Anonymous
@ACuriousMind Well, most students here don't understand! But well, one can always pretend to understand. I don't know if this method of teaching followed in only engineering colleges or even in pure science colleges. We officially don't have Lagrangian and Hamiltonian mechanics in our course plan (perhaps it being an EE course and not a physics course). Anyway, I intend to learn it myself.
 
DanielSank
DanielSank
I liked that this curriculum really didn't waste much time.
However, I disliked that so much math was sort of expected to be magically understood while taking physics courses.
That said, I did skip the math methods course (because it was terrible).
 
ACuriousMind
ACuriousMind
@Blue What do you mean by "they don't understand"?
 
DanielSank
DanielSank
You know what really bugs me @dmckee? It wasn't until part way through graduate school that I understood Lagrange multipliers and therefore understood Lagrangian mechanics.
 
Anonymous
@ACuriousMind They don't understand QM. They pretend to understand it.
 
Anonymous
6:23 PM
I'm talking about the Electronics engineering students who are taught about application of QM in Solid State in first semester
 
DanielSank
DanielSank
I should write Linear Algebra for Real: How to understand almost everything you don't understand in physics.
 
ııııııııııııııııııııııı
ııııııııııııııııııııııı
@Blue That's the most disgusting course ever
 
ACuriousMind
ACuriousMind
@Blue Sure! how could they understand it if they haven't been taught the proper prerequisites?
 
DanielSank
DanielSank
@Blue That's silly.
 
Mithrandir24601
Mithrandir24601
@DanielSank My first term was dynamics and oscillating systems, then the rest of the year was waves (classical & quantum), rotational mechanics, SR & gravitational and EM fields
 
DanielSank
DanielSank
6:24 PM
That's like @BernardoMeurer's chemistry course that went into the Schrodinger equation in spherical coordinates before anyone in that course had even taken a basic quantum course.
 
ACuriousMind
ACuriousMind
@DanielSank I had an excellent linear algebra course in my first semester that prepared me very well, but which was also decried by many as being really, really hard.
 
Anonymous
@ııııııııııııııııııııııı Yeah. I totally agree. So I have to learn the basics myself. I'm glad to have people like Balarka and you guys on PSE who are always willing to help me out. :)
 
DanielSank
DanielSank
@ACuriousMind Did you learn about Green functions etc?
Fourier transform?
Those things seem to be shoved down physics students' throats in their physics courses, but I think they belong in linear algebra.
 
Mithrandir24601
Mithrandir24601
@DanielSank Blimey, we learned about Green functions all right... They have a glass window representing them in hall where we ate
 
ııııııııııııııııııııııı
ııııııııııııııııııııııı
@DanielSank I think a serious advantage of EE majors over physics majors is the signal processing course
 
ACuriousMind
ACuriousMind
6:27 PM
@DanielSank They do not. A firm grasp of linear algebra is very advantageous to understand them, but they are not linear algebra, they are what is called functional analysis (which one could flippantly call "infinite-dimensional linear algebra").
But when Fourier transforms and Green's functions did appear, the connection to linear algebra was made
 
DanielSank
DanielSank
@Mithrandir24601 good
@ııııııııııııııııııııııı YES. YES. ALL THE YES.
The Dyson series makes intuitive sense if you've ever looked at a feedback control system.
 
ACuriousMind
ACuriousMind
I don't think it's the task of the linear algebra course to teach about these things - it's the responsibility of the person who wants to teach Fourier transforms how that fits in with vector spaces and basis changes, not of the person teaching basis changes in a general setting.
 
DanielSank
DanielSank
I was astounded as I learned some basic signal processing how much of QFT would be familiar to an EE student who was paying attention.
Let me show you something...
@ACuriousMind I respectfully disagree.
If you're sitting in a course thinking about basis change, you are primed to learn about Fourier transforms and Fourier transforms are so useful that you really should just do it then and there.
I'm a practical guy.
 
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ııııııııııııııııııııııı
@DanielSank we learned this in the linear control systems course
 
ACuriousMind
ACuriousMind
@DanielSank Point is, "Fourier transforms as basis change" require much more difficult mathematical prerequisites than ordinary finite-dimensional linear algebra if taught rigorously. Your version only works if you are not requiring the "linear algebra" course to be mathematically rigorous to begin with.
I mean, you can do that. But you need to be upfront about it - it's not that the mathematicians are stupid or anything, they have their reasons to separate linear algebra and "infinite-dimensional linear algebra".
 
DanielSank
DanielSank
6:35 PM
@ACuriousMind "if taught rigorously"
@ACuriousMind, education is not about adhering to some Platonic ideal of what "should be". The point is to help people learn stuff.
If you spend two lectures connecting Fourier transforms to the basis change stuff you already discussed in finite dimensions, you are doing your students a huge service in terms of what they understand and will be able to then learn on their own time.
Restricting that out of an obligation to rigor is like not building a house to shelter yourself against the rain because you saw a castle one time and see houses as inferior.
You will never teach your students all they need to know in order to function as researchers, or even as engineers. Never.
Your job as an educational institution is to get them to be as self-sufficient as possible by the time they leave.
Gotta go, but this is an important issue and I'd like to hear everyone's thoughts.
 
Mithrandir24601
Mithrandir24601
I completely and utterly agree with what @DanielSank ^
Rigour is fine for subjects where rigour is the point of the subject, but that's *not* the point of (at least monumentally huge chunks of) physics
 
ACuriousMind
ACuriousMind
@DanielSank I'm not saying you shouldn't teach student about Fourier transforms as basis change. I'm saying a "linear algebra" course typically has different goals than making people understand Fourier transforms. If you do a "linear algebra for physicists" course that would be sort-of appropriate, but I also think that it is kind of limiting only teaching physicists "math as applied to physics".
 
Mithrandir24601
Mithrandir24601
I accept that it's there and am happy that's it good and useful and all, but I want to learn physics, not spend ages getting bogged down in technical details that ultimately only change small, extremely niche cases, if anything at all
 
ACuriousMind
ACuriousMind
So I'd still put the burden on teaching people the "linear algebra" perspective on Fourier transforms on the physicist teaching Fourier transforms, not the guy teaching linear algebra.
 
Mithrandir24601
Mithrandir24601
@ACuriousMind There are certain aspects of maths that are useful to know, like "this is what a rigourous proof actually looks like" and "here's how to properly prove something"
 
0ßelö7
0ßelö7
6:55 PM
@DanielSank he also explains that FT can be viewed as a change of basis. The reason you'd never see that in a linear algebra class is because not everyone teaching LA knows/cares about FT and it's not usually viewed as a change of basis anyway
@ACuriousMind completely agree
I don't think algebraists should cater to the way (some) physicists think about Fourier transforms
 
DanielSank
DanielSank
@ACuriousMind this argument is essentially "that's not right because that's not how it's typically done".
 
nasil
nasil
I want to learn python and I have some projects in mind such as (grapher, physics simulator, nazi enigma machine, chess bot...)Can anyone recommend a book?
 
0ßelö7
0ßelö7
@DanielSank Changing what bases?
 
ACuriousMind
ACuriousMind
7:11 PM
@DanielSank No, it's "I think (this aspect of) how it's typically done is right". I wouldn't trade the rigorous and excellent linear algebra course I had for any other "more practical" course. I see how it would be more efficient if all we want to do is prepare physicists for doing typical physics problems but I think it is important that physicists are exposed to the mathematically rigorous versions of basic math to realize how different physics really is.
 
heather
heather
@ACuriousMind, that paper you linked too yesterday is focused on type II spdc instead of type I =/
unfortunately.
 
0ßelö7
0ßelö7
@ACuriousMind Halp
 
nasil
nasil
I want to learn python and I have some projects in mind such as (grapher, physics simulator, nazi enigma machine, chess bot...)Can anyone recommend a book?
 
heather
heather
@nasil no need to repost your question.
how much python do you know?
 
nasil
nasil
@heather none
 
heather
heather
7:21 PM
try starting with something like codecademy's free online course to get some basic knowledge of the language.
you can then use stack overflow/google to help you get set up and work through some of your projects.
if you want to get experience solving problems using python, try the euler problems (also online).
 
DanielSank
DanielSank
@ACuriousMind you really can't think of one thing you'd trade from your linear algebra course for some exposure to Fourier transforms and Green functions?
@nasil learn by example and ask questions.
 
heather
heather
^
 
DanielSank
DanielSank
@0ßelö7 it's not just physicists.
 
0ßelö7
0ßelö7
@DanielSank To accept that FT is a change of basis, you have to completely destroy the notion of basis that is taught in linear algebra.
And how are you going to talk about Green's functions to a bunch of kids who've never seen a PDE or know what boundary conditions are?
 
Balarka Sen
Balarka Sen
What level of linear algebra course we are speaking of here?
 
0ßelö7
0ßelö7
7:32 PM
@BalarkaSen Is there more than one?
 
Mithrandir24601
Mithrandir24601
When it came to maths, we didn't have any particular 'linear algebra' or any specifically named courses, but "Maths for the Natural Sciences", which covered the maths we needed - we needed to do PDEs before Green's functions? Well then, let's cover PDEs first. Problem solved!
 
Balarka Sen
Balarka Sen
Ted spends a lecture on absolute basic Fourier theory in his freshman multivariable slash linear algebra course mashup
 
0ßelö7
0ßelö7
@Mithrandir24601 That's probably how it should be.
 
Balarka Sen
Balarka Sen
Not anything super technical, but I loved it
I thought it was very useful
 
0ßelö7
0ßelö7
@BalarkaSen Does he call it a change of basis?
 
Mithrandir24601
Mithrandir24601
7:33 PM
@0ßelö7 It was hard as it jumped around a lot, but then, the whole degree was hard, so that was nothing new :P
 
Balarka Sen
Balarka Sen
Well, uh, no. He spends time on Fourier series than Fourier transforms, mostly
He does it in the context of Gram-Schmidt orthonormalization
 
0ßelö7
0ßelö7
@BalarkaSen Good. Daniel wants to teach it as a change of basis between the bases of position and momentum eigenstates.
1/10 mathematicians know what those are, and they also know that neither of those are bases, and none of those vectors are even in the vector space
To make it even a little precise you need tempered distributions, and no one wants that.
 
Balarka Sen
Balarka Sen
I have to admit I don't quite know what it means when you say "Fourier transform is change of basis". I think of it as an operator between various L^p spaces
 
0ßelö7
0ßelö7
@BalarkaSen It takes things in the position basis and represents them in the momentum basis.
 
Balarka Sen
Balarka Sen
I think I see what you mean
 
0ßelö7
0ßelö7
7:39 PM
@BalarkaSen It's the reason why HUP is "essentially" a statement about FTs.
 
Balarka Sen
Balarka Sen
Right
 
Mithrandir24601
Mithrandir24601
@BalarkaSen "Fourier transform as change of basis" makes sense. "operator between various L^p spaces" sounds like a mathematician went "in my rigourous definition of 'change of basis', this doesn't work, so I'll call it this instead". After teaching the physicists this, they went "Meh. Makes no difference to how we actually think of it, so we'll not take up this new term"
 
0ßelö7
0ßelö7
@Mithrandir24601 No, the mathematician will say that $| x\rangle$ is not even in $L^2$, so stop saying they form a basis
 
Mithrandir24601
Mithrandir24601
@0ßelö7 Fine, so they say "this doesn't form a basis as it doesn't fit any rigourous definition of basis, so I'll call it this instead" and repeat as above
Does something like "change of vector space" make you happier?
 
Balarka Sen
Balarka Sen
@Mithrandir24601 Well, that it's an operator between various L^p spaces is almost definitional. I honestly didn't know the physicist interpretation of Fourier transforms until today.
I do think I see what you mean.
Typically I think Fourier transforms are like continuous versions of Fourier coefficients of a Fourier expansion of a given function.
 
0ßelö7
0ßelö7
7:42 PM
@Mithrandir24601 FT is an isometry of $L^2$ onto itself. That makes me happy.
 
Balarka Sen
Balarka Sen
^ True, that's a neat fact.
 
0ßelö7
0ßelö7
@BalarkaSen Yeah. So the weights $e^{\pm ikx}$ in the integral are like the "basis vectors" and the integral is the "sum"
 
Balarka Sen
Balarka Sen
Got it, yup
 
0ßelö7
0ßelö7
But $e^{\pm ikx}$ isn't in $L^2$, so it's not a basis
 
Balarka Sen
Balarka Sen
Right, I don't know how to make that precise.
 
Mithrandir24601
Mithrandir24601
7:44 PM
@0ßelö7 Then call it that if you want. It doesn't affect me in any way. I have some vague idea of what you mean, so am happy with you calling it that and it's nice to know, but it doesn't change how I think of what a FT is, even if it has now got a different name
 
0ßelö7
0ßelö7
@BalarkaSen You can extend FT to the dual of the Frechet space of rapidly decreasing smooth functions. I think delta functions/plane waves form a basis of that space.
where "basis" means...something
 
Balarka Sen
Balarka Sen
@Mithrandir I understand and acknowledge that's how physicsts think of these things, but the same is true for us mathematical minded persons
Word by word what you wrote
 
0ßelö7
0ßelö7
My interests in QM don't extend to that stuff. Google "rigged Hilbert space"
 
Balarka Sen
Balarka Sen
Hm I see
 
0ßelö7
0ßelö7
@Mithrandir24601 Exactly, but Daniel is talking about making math people teach your point of view. What Balarka said.
@Blue I have no idea what you're talking about.
 
Balarka Sen
Balarka Sen
7:57 PM
Honestly so many people have so many different intuition about various mathematical tidbits that it's hard to impose a uniformly specific point of view for everyone. You don't have to go as far as the physics vs math dispute to see this; even within math some people think naturally in terms of pictures, and some think in terms of symbols.
 
skullpatrol
skullpatrol
Good point^
 
Balarka Sen
Balarka Sen
For example in topology there's a group of people who consistently draw commutative diagrams to prove pretty much literally whatever. I can never understand why.
 
skullpatrol
skullpatrol
...and some prefer to think in terms of words.
 
Anonymous
@BalarkaSen Sounds like me...;) I used to draw (or atleast try to) graphs for literally every function that I came across in single variable calculus
 
Balarka Sen
Balarka Sen
Well, that's geometric intuition, not algebraic
An approach I personally advocate
 
Mithrandir24601
Mithrandir24601
8:07 PM
So many of my least favourite differential geometry moments come from things like "so... What do all these symbols mean?.." several minutes later: "Ah. I'm just mapping from Euclidean to spherical co-ordinates... Why didn't you say so in the first place?" -_-
 
skullpatrol
skullpatrol
One should try to be equally skilled in as many approaches as time permits.
 
Balarka Sen
Balarka Sen
@Mithrandir I absolutely abhor coordinate calculations in differential geometry. Indices, Christoffel symbols, etc. I had the impression that you physicists love them.
 
Mithrandir24601
Mithrandir24601
@BalarkaSen Not when something so straightforward as going "OK, replace x with ..." is hidden behind layers of symbols and definitions...
 
Balarka Sen
Balarka Sen
Gotcha, me neither.
 
Anonymous
@Mithrandir24601 Probably the symbols are too obvious for people who have been using them for years. That's one of the reasons why all good physicists/mathematicians are not good teachers. Being able to boil things down to a newbie's level is an underrated skill.
 
skullpatrol
skullpatrol
8:13 PM
Another good point^
 
Mithrandir24601
Mithrandir24601
@Blue You say that, yet those differential geometry notes were better than any textbook we found (for a beginner anyway - they're actually online somewhere) and the lecturer was really good at explaining everything. The guy that wrote the lecture notes also happened to be an extremely good lecturer and explained things astonishingly well and in clear terms :)
@Blue Personally, I view this as an extremely important skill :)
 
Anonymous
@Mithrandir24601 That's good, then :)
 
Anonymous
It's hard to find good teachers
 
Mithrandir24601
Mithrandir24601
although you're absolutely right - I've had some apparently phenomenal researchers as lecturers and they just can't teach the stuff
(not all of them, of course - some of the best researchers make the best lecturers. They sadly can also make the worst lecturers :/)
 
Sir Cumference
Sir Cumference
8:34 PM
@Blue Sad truth
A poor teacher can destroy someone's grasp or interest in a subject
 
0ßelö7
0ßelö7
@BalarkaSen lmao
@Mithrandir24601 I've never had a professor who was legitimately trying and couldn't explain well. I think those researchers put teaching on the back burner.
 
Mithrandir24601
Mithrandir24601
@0ßelö7 It's very possible...
 
Anonymous
Well, the money they get from teaching uni students will be constant anyway. Doing research pays more. :P
 
Mithrandir24601
Mithrandir24601
8:52 PM
@Blue Actually...
OK, I suppose for the top profs, research probably pays more...
 
ACuriousMind
ACuriousMind
@Blue Huh? Since when are academic scientists actually paid for their research? :P
 
Mithrandir24601
Mithrandir24601
@ACuriousMind I think he just means their regular salary
 
ACuriousMind
ACuriousMind
@Mithrandir24601 Then I still don't understand the statement
 
Anonymous
@ACuriousMind I suppose they are paid over and above the salary which they get for teaching. Publishing papers and making patents keeps the government funds flowing in
 
Mithrandir24601
Mithrandir24601
@ACuriousMind A number of places (maybe not all) will pay more for people who lecture/demonstrate etc.
 
ACuriousMind
ACuriousMind
8:57 PM
@Blue You don't get a single penny from publishing papers and physicists are generally not known for producing a large amount of patents.
@Mithrandir24601 That's be the exact opposite of what Blue is saying.
 
heather
heather
"don't get a single penny from publishing papers" - ::sighs:: you actually have to pay money to publish, right?
 
Anonymous
@ACuriousMind I'm talking about government funds which are given to researchers so that they can pursue their research
 
Mithrandir24601
Mithrandir24601
@ACuriousMind Depends if they count the lecturing as extra work hours or not
 
Anonymous
Atleast here the government provides monthly or yearly grants to researchers
 
ACuriousMind
ACuriousMind
@Blue But...they don't get any of that money themselves, grants are for funding the research group, not the prof. If you're trying to say "doing research is more beneficial for getting research grants than teaching", then I agree with you, but that's a very different thing from "Doing research pays more".
 
ZeroTheHero
ZeroTheHero
8:59 PM
@Blue My experience conforms to the 20/80 rule. If you take the top 20% of researchers at an institution, you will find that 80% of them are great teachers. The informal basis of the rule is that if you care enough to prepare great classes, you'll likely care enough about your research. In addition, good research requires clarity of thought and breath of knowledge that are essential to good teaching.
There is a "genius clause".
Some people - like Lars Onsager - are true genius but just incapable of teaching.
 
Anonymous
@ACuriousMind I see your point. Yes, I agree
 
0ßelö7
0ßelö7
@ACuriousMind Halp!?
 
ZeroTheHero
ZeroTheHero
@ACuriousMind They are implicitly paid more as promotion and tenure, along with merit bonuses, are strongly skewed towards research output, at least at many institutions where faculty are expected to have a research program.
 
Anonymous
Oh yes, that too ^
 
ZeroTheHero
ZeroTheHero
There is no survival for a mediocre instructor in a teaching-oriented college.
 
ACuriousMind
ACuriousMind
9:04 PM
@ZeroTheHero True enough, but also not an immediate effect. I just want to nip the impression that research immediately earns any physicist money in the bud. It's "doing great research improves your career trajectory" not "great research pays the big bucks".
 
Anonymous
@ZeroTheHero Perhaps that's true for the developed countries. Over here in teaching-oriented colleges the teachers are literally awful :P Even in research-oriented colleges only say 20-30% are good teachers. Probably the reason is that professorship is not a well-paying job over here.
 
0ßelö7
0ßelö7
@ACuriousMind Are you implicitly granting permission
 
ACuriousMind
ACuriousMind
@0ßelö7 I have no idea what you're talking about
 
ZeroTheHero
ZeroTheHero
@ACuriousMind Fair enough. Beyond bonuses or pay increased linked to the granting of a spectacular amount of $$, a good institution will recognize a good long term research program and reward accordingly. Of course short term there is always the "danger" that some rich competitor will try to poach your budding star.
 
dmckee
dmckee
At least in the US, professors at major research universities get their jobs and promotion for a combination of things that is weighted rather heavily towards research. They also get paid rather more than professors at teaching oriented schools.
 
0ßelö7
0ßelö7
9:09 PM
@ACuriousMind I have no idea how to compute $P_2-P_1$. Can't use Bernoulli
 
dmckee
dmckee
SO you can argue that research pays for professors.
 
0ßelö7
0ßelö7
 
ACuriousMind
ACuriousMind
Sorry, I don't do hydrodynamics.
Or hydrostatics, for that matter :P
 
Anonymous
0ßelö7 is doing physics....aaaaahhhhhh! :P
 
0ßelö7
0ßelö7
@dmckee ?
 
dmckee
dmckee
9:11 PM
However the salaries at university are generally not as high as those in industry, so you can also argue that they give up some earning potential for the freedom to chose their own research lines rather than doing that which pays.
 
0ßelö7
0ßelö7
@dmckee I already found $V_2$ from conservation of mass
it's just the average of $V_s$ and $V_j$ according to the surface area
so I can't use that average velocity in Bernoulli's law
But I don't really know of any other way to calculate pressure
 
CooperCape
CooperCape
@0ßelö7 Sorry for disturbing you but do you if there's solutions to Carroll's Space-time and Geometry book?
 
ZeroTheHero
ZeroTheHero
@Blue Too bad. If you look at many of the very good newer textbooks, many are written by outstanding researchers. Think Weinberg, Peskin etc. in field theory as prime examples.
 
dmckee
dmckee
Poiseulle's (sp?) law might be an angle of attach.
 
0ßelö7
0ßelö7
@CooperCape You're not disturbing me, and I don't know. Have you googled?
 
CooperCape
CooperCape
9:15 PM
Yeah I have and Sean said himself there were no solutions however I was wondering if you knew of any unofficial answers :p
He did link to an alternative question book with solutions online, however
 
0ßelö7
0ßelö7
@dmckee Google says that's for laminar flow
 
Anonymous
I think it can be done by using basic work-energy theorem ....i.e. using the method in which Bernoulli's theorem is originally derived
 
0ßelö7
0ßelö7
@Blue Right, but when I tried that I got the wrong answer
 
Anonymous
It's an interesting problem
 
0ßelö7
0ßelö7
Off by roughly a factor of two
er, factor of 1.6
 
ZeroTheHero
ZeroTheHero
9:17 PM
@Blue When you get a faculty position you can reverse the trend. ;)
 
Anonymous
@0ßelö7 That's strange....could you show your method?
 
Anonymous
I would actually do it on pen and paper...but it's late night now and I need to go to bed :/ Perhaps I'll try it tomorrow morning :)
 
0ßelö7
0ßelö7
@Blue Aha
I put in 0.008 instead of 0.08
I used the Reynolds transport theorem
 
Anonymous
@0ßelö7 wow...never heard of that
 
DanielSank
DanielSank
@0ßelö7 false
@0ßelö7 uh, with an ordinary linear equation like a forced harmonic oscillator. The fact that you think Green functions are only for PDE's is a perfect example of the pedagogical failure I keep talking about.
 
0ßelö7
0ßelö7
9:30 PM
@Blue total force on the control volume is the difference of momentums of the back and front, roughly.
The total force in this case is the pressure difference, modulo a factor of area
@ACuriousMind are there no arxiv updates on weekends?
 
Anonymous
@ZeroTheHero I'll probably never get into an academia job; it doesn't really suit me. (No, it's not because of the salary)
 
ACuriousMind
ACuriousMind
@0ßelö7 nope
 
0ßelö7
0ßelö7
@DanielSank I'm sure one can define green's functions for ODEs, but I can't ever say I've had a use for that.
 
CooperCape
CooperCape
If a book is online in flash is there a way to put it in a less horrible format? :/
 
ACuriousMind
ACuriousMind
How is a book online "in flash"?
Is it a flash application that displays the pages of the book?
Then I'd wager they made it that way specifically to prevent people from easily downloading it ;)
 
0ßelö7
0ßelö7
9:38 PM
@CooperCape did you not use libgen
 
CooperCape
CooperCape
Yeah it is... index.html
Yeah I did
for the S Carroll book
 
0ßelö7
0ßelö7
Did it not give you a .djvu
 
CooperCape
CooperCape
yeah I ocnverted that to pdf
 
0ßelö7
0ßelö7
So what's the issue?
 
CooperCape
CooperCape
but the questions book he recommends is in flash...
might be on libgen tho
I'll check
 
DanielSank
DanielSank
9:40 PM
@0ßelö7 Somehow you have been tricked into thinking that Green functions are only for complicated multidimensional problems.
That is absolutely not the case. At all.
 
CooperCape
CooperCape
ahh yes it is :D
 
0ßelö7
0ßelö7
@DanielSank did you not read what I said? I said I haven't had use for them. It's not common in math, so why should it be in a math course?
That's my point here. You want to drop stuff from a math course to benefit physicists
Maybe we should talk about tensors in linear algebra too. What about group representations?
 
Mithrandir24601
Mithrandir24601
@0ßelö7 I'm slightly confused now - do most places put physicists in the exact same maths lectures as mathematicians?
 
ACuriousMind
ACuriousMind
@Mithrandir24601 In Heidelberg, we all get the same linear algebra "for mathematicians" lecture and physicists have a choice between standard math analysis and "math for physicists", which is basically the three semester analysis course haphazardly crammed into two semesters (yeah, it's crap :P).
 
0ßelö7
0ßelö7
@Mithrandir24601 yes
 
Mithrandir24601
Mithrandir24601
9:50 PM
@ACuriousMind :o
@0ßelö7 :o :o
OK... That's a problem...
You 2 just put my undergrad in a whole new perspective...
The way we did it was so blatantly obviously sensible, that I've clearly assumed everywhere did the blatantly obviously sensible thing. Turns out I was wrong
 
DanielSank
DanielSank
@0ßelö7 the fraction of math students that use math in a way that you're interested in it is tiny.
 
0ßelö7
0ßelö7
@DanielSank To clarify -- what do you think I'm interested in?
 
CooperCape
CooperCape
@Mithrandir24601 You graduate at Bristol or...?
 
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