The h Bar

Semiclassical

5:02 PM

hi-yo

vzn

...afterthought: makes one wonder about astrology some )( o_O :P

0celo7

@Semiclassical do you know how to do derivative estimates using the Schwarz lemma

Semiclassical

I suspect I should, but no

like, estimates using Schwarz + Cauchy integral formula?

(which it's amusing to note would be very different than Cauchy-Schwarz)

0celo7

No, the Schwarz lemma

Semiclassical

I guess not, then. I was thinking you'd write down the nth derivative of $f(z)$ as an integral around the unit circle

though come to think of it I don't know how one would then use Schwarz, so I dunno

vzn

5:17 PM

doesnt seem to directly relate to derivatives/ integrals, that would probably be some application/ special case...? en.wikipedia.org/wiki/Schwarz_lemma

0celo7

I know what the Schwarz lemma is, obviously

Emilio Pisanty

@vzn don't know about "spking terms" - I continue to be annoyed when you disregard others in this chatroom for your own comfort, but they are all pointwise annoyances and I don't hold them going forward. If you've got me blocked then it's you that's not on 'speaking terms', really.

Semiclassical

well, it gives an estimate on f'(0)

0celo7

see the math chat for more details

vzn

← not a mindreader

Semiclassical

5:20 PM

oh, nice

Emilio Pisanty

@Semiclassical How's tricks?

Semiclassical

so you use a conformal mapping to turn the estimate on f' at z=0 into one on any |z|<1

@EmilioPisanty hmm?

Emilio Pisanty

@Semiclassical how's life?

Semiclassical

eh.

Emilio Pisanty

ah, fair enough

Semiclassical

5:21 PM

still behind on writing, still don't know how I'll catch up

vzn

@Semiclassical stop chatting :P

Emilio Pisanty

@vzn doesn't always help ;-)

Semiclassical

I really get tired of people offering advice

the difference between me being here and me not being here is not the difference between me writing and not writing

the difference is me having any ability to talk with other people and not being able to talk

Nat

@Semiclassical You should talk to someone about that.

Semiclassical

Have.

vzn

5:23 PM

← sheesh, was joking

Semiclassical

A lot.

Emilio Pisanty

(as an example, you can quite clearly track my months of thesis writing as a marked increase in the slope of my phys.se rep graph.)

Nat

← was also joking

Semiclassical

the law of sarcasm on the internet applies here, unfortunately

vzn

what was the sarcasm? which law?

Anonymous

5:25 PM

Poe's law

Nat

Works for me. =P The silliness that is the interwebs can be quite relaxing in a stressful life.

Semiclassical

sarcasm is the wrong word, perhaps

But a remark that wasn't meant seriously.

Nat

Tongue-in-cheek?

Semiclassical

this bit from the Wiki page on poe's law is pertinent

Nat

We should ask on SE.English, or whatever it's called.

vzn

5:26 PM

ok. (thx) poes law refers to extremes/ parody. yet dont think its nec applicable. en.wikipedia.org/wiki/Poe%27s_law

Semiclassical

"As early as 1983, Jerry Schwarz, in a post on Usenet, wrote: 'Avoid sarcasm and facetious remarks. Without the voice inflection and body language of personal communication these are easily misinterpreted. A sideways smile, :-), has become widely accepted on the net as an indication that "I'm only kidding". If you submit a satiric item without this symbol, no matter how obvious the satire is to you, do not be surprised if people take it seriously.'"

tbf, you did use ":P"

I tend to stick with /s myself

Nat

Who would avoid sarcasm merely to avoid risk of misinterpretation? Where's the sense of adventure in that?!

vzn

@Semiclassical lol maybe related to the other schwarz

Semiclassical

lol

Nat

Personally I take crafting messages that'll be read different ways by different observers to be an art form.

Emilio Pisanty

5:28 PM

Oh, a failed Detect Sarcasm roll -- got it. Yeah, I'd rather not have to spawn tabs for every "quick look" that I want to take; I spawn tabs when I'm going to need to do something more substantial but don't want to do it right this instant. — Monica Cellio Oct 11 '17 at 17:27

vzn

← likes to learn all guidelines so as to more thoroughly break them :P

Emilio Pisanty

↑ I quite like the "failed Detect Sarcasm roll" formulation

Semiclassical

hah

vzn

@Nat "avoiding sarcasm on the internet"? are you serious? o_O :P

Nat

@vzn Yes, I'm very series about everything I spam.

vzn

5:30 PM

lol all ~~cretins~~ cretans are liars :P

Semiclassical

all cretins are bad liars

0celo7

apparently I can't compute a derivative

1 hour gone

fml

vzn

82

Q: What is a social strategy I can use to respond to "How's your PhD going?"

I was surprised when starting my PhD as to how much I get asked this question and how much I fail at answering it. Whenever I attempt an answer, I fumble around and the subject immediately changes after. If I state exactly how it's going, the stress of publishing and intensity of the program come...

social-skills

Semiclassical

I haaate that question

Nat

Hah it's cool. Derivatives are for computers anyway.

vzn

5:34 PM

phdcomics.com/comics/archive.php?comicid=47

Emilio Pisanty

@vzn ah, a classic's classic

does that one have a date?

Nat

@EmilioPisanty It's not polite to ask it for its age!

Emilio Pisanty

@Nat =P

Semiclassical

haaah

Emilio Pisanty

> (Received in final form 27 February 1998)

apparently

so... PhD Comics just turned 20 years old?

goodness

Semiclassical

5:36 PM

man, and I thought my phd was taking a while :P

Emilio Pisanty

first one's dated 27 October 1997

at least if you believe the tagline in the Emergency Button version

0celo7

oh

there's two squares

"pop that ***** up in church" what the hell am I listening to

"get some chicken guac guac"

wtf

Nat

Sadly, 1060nm appears to be down.

There should be a law that, in order to get a PhD in Physics, students must also post a reasonable attempt at a web comic.

Dunno how much it'd help anything, but I just want more nerdy comics.

Emilio Pisanty

@Nat well, there's Lego Grad Student

vzn

@nat so have you started an online degree? (the universe contracts just a little bit every time a comic dies) :'(

Nat

5:40 PM

@EmilioPisanty Ohh I'll have to check that out!

0celo7

Cardi B's album is as preposterous as expected. Amazing

Emilio Pisanty

@Nat it's pretty much PhD-Comics-grade stuff

Nat

@vzn Naw, I've got a stupid number of degrees already. Just had someone I knew asking about going back to school for a CS degree.

Emilio Pisanty

with the benefit that he's fresh and still publishes regularly =P

but with the downside that it's dark.

Nat

(Assuming you were asking about my questions in other chats earlier. Disregard if that made no sense. =P)

Semiclassical

5:42 PM

yeah, I haven't looked at LGS much simply because i want to avoid any more existential crisis than I already have

vzn

← recommends phd comics movie(s) for fans, 1 of few whos seen it, defn hardcore fan among other mere amateurs

@Nat lol what stupid degrees? have heard rumors about online degrees & theres a lot of hype last few yrs but have never seen/ heard anyone actually pull it off. wonder if some are nearly trump-university level o_O

Anonymous

I've never heard of anyone successfully completing an online degree, either (like the masters program offered by Coursera, etc). It's incredibly hard to maintain the motivation to get through.

vzn

@Nat lol reminds me of this one that rob/ mod used to cite sometimes. very, very weird and surreal. (can relate!) :P see what you think webcomicname.com

@Blue think youre right and yet think this shows something fundamentally irrational about human psychology. or maybe that humans have a lot of trouble doing anything "alone". even though thats what degrees nearly essentially amt to in a lot of cases (after taking away all the "trappings")...

Nat

@EmilioPisanty I don't know what this is yet, but I already want to play Minecraft.

vzn

@Nat lol never played minecraft? notch is worth $1.3B so you know its gotta be good :P

Emilio Pisanty

5:48 PM

@Nat this?

Nat

@EmilioPisanty Hah yup.

Emilio Pisanty

also available via other social-media outlets

Nat

@vzn I did! It came pre-installed on a Raspberry Pi 3, so I messed around with it a bit... ended up building a glass enclosure for water falls under a lake. Such silly nonsensical fun. =D

Anonymous

@vzn I have this personal theory that some amount of competition, whether healthy or unhealthy is essential for people to progress. One of the reasons home-schooled kids are usually a bit less (socially and perhaps mentally) less matured compared to the school going kids. I had seen a study regarding this somewhere, but have forgotten the source now. Obviously there exist exceptions.

Nat

@vzn First thought on that one's Hyperbole and a Half. =P Ohh I lost my link to that, I wonder if there's a new one...

hyperboleandahalf.blogspot.com/2010/11/…

@Blue I guess folks have all different sorts of motivations. Competition's definitely one.

Actually, @Blue, aren't you a good bit ahead of your classmates?

Anonymous

5:56 PM

@Nat Ahead in what way? Well, I did pick up a few things here and there out of personal interest/hobby. But I still don't always top class exams or anything.

Nat

@Blue Huh, you seem to get some of the quantum-computing stuff; that's definitely unusual for a first-year student.

Actually, fuzzy on if you're first-year or not, but it's still pretty unusual for undergrads 'til they take the relevant courses, at any rate.

Anonymous

@Nat Uh, well, that's one of my hobbies apart from learning math, CS and physics :P Tbh some of my inspiration is drawn from some of the incredibly motivated kids I see on SE including Balarka, 0celo, heather, etc.

Cows

@BernardoMeurer hehehe, well I ended up sketching out the Java memory model while wrestling a gang kangaroos on the moon hehe. I was a bit confused, as my programmer brain has been fried by JavaScript, but I am making efforts to learn things appropriately. I am trying to understand how things actually work so I can make better performing apps :P

Anonymous

@Nat I actually signed up for some online courses on Coursera, EdX, NPTEL among other places. I love MOOCs! :)

Anonymous

Those resources helped me a lot to pick up new things

Anonymous

6:03 PM

As for QC, Vazirani's lectures were a great resource for me

Nat

@Blue Awesome! I believe the online schools are the future, though I haven't had a chance to actually try any of 'em yet. Good experiences, then?

Cows

@DavidZ yes you are right, Bernardo as said the same thing . tutorials.jenkov.com/java-concurrency/java-memory-model.html

Emilio Pisanty

@Semiclassical seriously though

whatcha reckon are my chances of pulling this off as a lecture demonstration?

Cows

@BernardoMeurer hehe tutorials.jenkov.com/java-concurrency/java-memory-model.html

Emilio Pisanty

6

A: Is it possible to show a diffraction caustic as a home experiment / lecture demonstration?

This may be easier than you think. I took this photo (with my iPhone) of a cusp caustic which I generated by darkening the bathroom, wetting the mirror, and angling the laser pointer so it hit a water drop and then reflected off the mirror onto a convenient spot on the wall: It's extremely clo...

final lecture's on Tuesday, finally getting to the catastrophe integrals

Anonymous

6:06 PM

@Nat Yes, some of them are extremely good. Till now my favourites courses are Vazirani's QC on EdX, UC Berkeley's Data Science Series, Stanford's Algorithm's course and Balakrishnan's QM/CM lectures on NPTEL.

vzn

@Blue (distracted by remarkable nearby M/ F chess game) yes agreed competition and socializing are probably tightly coupled in many ways. but maybe there is a way to increase socialization and still decrease competition. and also non-school students are still competing at large in the economy but its more abstract/ detached.

Anonymous

If you haven't taken any online course yet, you definitely should try them out. Almost all Coursera and EdX courses are for free.

Anonymous

@vzn "increase socialization and still decrease competition". Yes, but I wonder how far that's possible

Nat

Awesome, I'll have to ask ya for links to some of 'em later.

Anonymous

Maybe by involving kids in more group projects rather than just telling them to prepare for tests.

Anonymous

6:10 PM

@Nat Sure :)

vzn

← expecting shortly some home/online/self schooled self-motivated genius to show up, become world famous, win huge awards, havent seen it quite yet

Nat

'night folks!

Anonymous

Goodnight!

Bernardo Meurer

@Cows I honestly could not care less about the Java MM, and I already know the C MM :P

davmac.wordpress.com/2018/01/28/…

Semiclassical

@EmilioPisanty isn't a nephroid a baby example of a caustic? e.g. en.wikipedia.org/wiki/Nephroid#/media/File:Brennlinie.GIF

I guess that's maybe too simplistic for what you want

main thing I like about a nephroid is that you can do it with a coffee cup

as I've actually observed a few times while sitting at a diner under direct lighting

really nice example here: gurneyjourney.blogspot.com/2010/07/nephroid-caustics.html

Balarka Sen

6:24 PM

I want to learn catastrophe theory at some point

Man there's so much classical mathematics I don't know, it's shameful

Semiclassical

Start by understanding the Airy integral :P

(That's not facetious, actually.)

Balarka Sen

You know what fuck it. What is it about

Semiclassical

at the most basic level, it's the following contour integral

Slereah

amazon.fr/…

Jesus

300€

are they trying to keep it a secret

Semiclassical

$\text{Ai}(z)=\int_C \exp(t^3/3-zt)\,dt$

Balarka Sen

6:29 PM

Where $C$ is?

Slereah

amazon.com/gp/offer-listing/0883186179/…

WHAT

$10,502.90

Semiclassical

the specific numbers in there are conventional so that it'll satisfy Airy's differential equation $y''(z)=z y$

Slereah

I think it's one of these book with a price set by an algorithm

Semiclassical

to see what the contour is, note how the exponent behaves as $t\to\infty$ along various directions

so $t=|t|e^{i\theta}\implies t^3 =|t|^3 e^{3i\theta}$

0celo7

I'm surprised that ODE doesn't have a simpler solution

Emilio Pisanty

6:32 PM

@Semiclassical oh, no, it's exactly what I want

I just need it to be coherent enough to show the internal interference fringes and the Pearcey lobes at the tip of the caustic

Semiclassical

@EmilioPisanty I just noticed that that's mentioned in the first comment...fail on my part

Emilio Pisanty

and I would like to project it on the same screen as the slides

ideally bright enough to see by the audience?

Semiclassical

right

0celo7

@BalarkaSen can you remind me what a period is in the context of cohomology

Semiclassical

I feel like someone has to have done this before

hmm!

Caustic (optics)

►

that's just an image, alas

but the idea seems simple enough

Balarka Sen

6:35 PM

@0celo7 Integral of the generator 1-forms of $H^1$ over the generating loops of $H_1$, I think. That gives you a matrix of numbers which one calls the "period matrix"

At least, that's what it is for a Riemann surface

Semiclassical

@BalarkaSen which leads to Gauss-Manin / Picard-Fuchs business

0celo7

@BalarkaSen Ah, one can do the same for $p$-forms I guess

Emilio Pisanty

@BalarkaSen I'm not sure full-blown René-Thom-style catastrophe theory is that worthwhile anymore

Balarka Sen

@0celo7 The matrix of the Kronecker pairing $H^p \times H_{n -p} \to \Bbb R$, I suppose, yes

Semiclassical

back to the Airy integral: For the integrand to go to zero as $|t|\to\infty$, we need the real part of $e^{3i\theta}$ to be negative

0celo7

6:37 PM

Kronecker? You mean Poincare?

Semiclassical

if it's positive, it instead blows up

Emilio Pisanty

or at least, many of the initial claims of universality have turned out to be... impractical to realize in the real world

Balarka Sen

@EmilioPisanty I think it is! It came up so often when I was working with h-principles and sphere eversion.

Emilio Pisanty

@BalarkaSen with what?

Balarka Sen

There's a movie of sphere eversions which can be intuited as creating and cancelling singularities

Oh, you know, turning the 2-sphere inside out in R^3.

Semiclassical

6:38 PM

that divides the complex plane into six sectors, each of angular width $2\pi/3$

Emilio Pisanty

@BalarkaSen fair enough

Semiclassical

So for that integral to make any sense, C had better go from one of the "negative real part" wedges to another

Emilio Pisanty

@Semiclassical well, it can stay on the boundary between fringes

Balarka Sen

@EmilioPisanty If it ever excites you, have a look at Scott Carter's text on the sphere eversion.

Semiclassical

eh, fair

Balarka Sen

6:39 PM

@Semiclassical Wait, I have lost you. Ah, so $C$ is a bi-infinite path?

Semiclassical

Right.

In Wikipedia's terms: "where the integral is over a path C starting at the point at infinity with argument $−\pi/3$ and ending at the point at infinity with argument $\pi/3.$"

Emilio Pisanty

@BalarkaSen $$\mathrm{Ai}\left(z\right)=\frac{1}{2\pi i}\int_{\infty e^{-\pi i/3}}^{\infty e^{\pi i/3}}\exp\left(\tfrac{1}{3}t^{3}-zt\right)\mathrm{d}t$$

Balarka Sen

@Semiclassical So an appropriate vertical line

Emilio Pisanty

dlmf.nist.gov/9.5.E4

Balarka Sen

Thanks, @Emilio. I get it now.

Emilio Pisanty

6:42 PM

@BalarkaSen it's a weird parametrization, though

0celo7

@BalarkaSen don't assume its orientation please

Semiclassical

0celo7

it's a double pun

Semiclassical

One thing which makes the Airy integral interesting is that, while the basic contour won't change with $z$

Balarka Sen

Oh so it's not a line.

Rather a hyperbolic thing

Semiclassical

6:44 PM

well, you can still make it work as a line.

if you drew straight up/down from the intersection with the real axis

then the curve never crosses the imaginary axis

and as a result it doesn't blow up

Anyways. For integrals like this, the usual scheme is to try to do a steepest descent approximation.

Balarka Sen

I remember that story.

Emilio Pisanty

@Semiclassical and ignore the fact that it fails sometimes ;-P

Balarka Sen

Anyway, why is this integral interesting, classically?

Maybe because of that differential equation

Semiclassical

The main weirdness is that, as $z$ changes, the locations of the saddle points change.

Emilio Pisanty

@BalarkaSen it encodes the passage from oscillatory wave behaviour through to evanescent-wave behaviour

0celo7

6:48 PM

@AccidentalFourierTransform this is not a freakin’ homework question, stop changing the damn tag! — Y2H 2 mins ago

:)

Semiclassical

which ends up having the consequence that the appropriate asymptotic expansion changes as you change the argument of $z$

That's what's known as Stokes phenomenon.

Emilio Pisanty

any phenomenon that has that passage and looks roughly like this

can be mapped onto Ai

Balarka Sen

@EmilioPisanty I see.

Semiclassical

At the level of the differential equation, the important thing is that it has an irregular singular point at infinity

Which means the usual trick of "eh, just look for series solutions" doesn't work.

or at least doesn't work in the way you'd expect

Emilio Pisanty

@Semiclassical well, also "eh, just look for series solutions" gives you somewhere between extremely little and nil understanding

Semiclassical

6:52 PM

right.

Novalium Company

Hi guys! I am reading Quantum Physics for Dummies and I wanted to clear out something. What is that t (for time) in the wavefunction - |Ψ(x, t)|. And another question. The | symbol shows us that we get only the magnitude right?

Balarka Sen

@Semiclassical As in, the solution has an essential singularity at infinity?

blank

Emilio Pisanty

@NovaliumCompany ask a question without context, get an answer that doesn't apply to your context ;-)

(and no, we don't have copies of that book lying around - you'll have to be more specific)

generally, the symbol t in a wavefunction Ψ(x, t) is just time.

Novalium Company

Is it nessesery?

Semiclassical

@BalarkaSen yep

Emilio Pisanty

6:55 PM

there's not much else to say unless you give more context.

@NovaliumCompany if you want a useful answer, yes.

Semiclassical

If you pick a large |z| and vary its angle, you'll alternate between sectors with different asymptotic expansions

as a consequence, it's not too strange that z=infty is very badly behaved

Emilio Pisanty

@Semiclassical ah, that's what that "essential singularity" meant

how do you see that from the ODE?

Semiclassical

it's the irregular singular point

Emilio Pisanty

@NovaliumCompany as for the use of matching pairs of upright bars in QM, they are universally the modulus of the complex number between them. Single bars are almost never used.

@Semiclassical what's that mean in detail?

Balarka Sen

@Semiclassical Yup, pretty much means that the complex analytic function Ai(z) has an essential singularity at z = infty.

I think at least

Emilio Pisanty

6:58 PM

my ODE course was terrible ¬¬

Semiclassical

doesn't have a Laurent series about infinity, basically

Novalium Company

Ok, first question. I've seen videos where they write just this: |Ψ(x)|, without time. What is the point of time, should I use it? For example the book writes it with t, but Professor Dave (youtube.com/watch?v=O6g-7rUgrdg) writes it without time. And also, I don't need to surround the wavefunction with |?

0celo7

@EmilioPisanty is this superior typesetting

Emilio Pisanty

at one point we told the TA that we were upset that the lecturer hadn't done the proof of the ODE existence & uniqueness theorem, and that we thought we were ready for it, so he started doing it

Semiclassical

actually, I think it's something more precise than that since regular singular points allow for log behavior

0celo7

6:58 PM

note the usage of $div$, and the inconsistent $\log$ vs. $log$

Anonymous

@NovaliumCompany That is for time independent wavefunctions (does not change with time)

Emilio Pisanty

and the lecturer told the TA to cut it out and return to mindless examples

¬¬

Semiclassical

ugh