The h Bar

Balarka Sen

18:00

That's why the term "indefinitely integral", even if rather loose, is kinda cute

Phase

@BalarkaSen I dont get that

My maths lecturer called integration the inverse of differentiation

But that would imply $D^{-1} D f = f$ but it isn't

since $D^{-1}$ isn't injective

Balarka Sen

$D^{-1}$ is not really an operator, is the point.

Phase

oh

ok

Balarka Sen

It sends a function to a family of functions

Namely, $D^{-1} f' = f + a$ for any real $a \in \Bbb R$

It's badly multi-valued

Sir Cumference

@BalarkaSen Yup. For many functions, the integral is the difference between two antiderivatives, but the names "definite" and "indefinite" only serve to confuse high school students.

bolbteppa

18:03

For all intents and purposes, $D^{-1}$ is an operator, $D^{-1} = \int$, and this perspective gives a very nice derivation of the Euler-Maclaurin formula, but formally you will run into problems very quick

Sir Cumference

Why even blend the line when the distinction is often noteworthy?

bolbteppa

I've been meaning to look into the problems you run into, there is weird link to Laurent series

Section 3 here is good phys.uconn.edu/phys2400/downloads/euler-maclaurin-summation.pdf

Balarka Sen

@SirCumference It does confuse everyone in high school, yes. Ask any high schooler who hasn't learnt beyond their texts (in particular, they have to be in the complement of the various kidlets in hbar and Mathematics (uh...)), and they will fail to explain the relation between area-under-curve and antiderivative.

It's become a blackbox in calculus education at this point

The terminology just propagates this blackboxing memorization thing more and more

instead of clarifying it

Sir Cumference

@BalarkaSen I remember my Calc II prof emphasized "Unlike the derivative, the antiderivative by itself is not useful, due to the constant (it could be any number). Rather, the use lies in comparing antiderivatives."

At the very least, that gave me a clear realization that the two were different concepts, which cleared a huge chunk of my prior confusion with calculus.

Balarka Sen

Quite

Semiclassical

18:13

It reminds me a little of how people often solve simple ODEs by separation vs. how I prefer to do it.

bolbteppa

How do you do it

Semiclassical

As an example, take $x'(t)=-x(t)$ with $x(0)=1$.

I think the usual approach would be to write that as $\frac{dx}{x}=-dt\implies \ln x = -t+C$

bolbteppa

Yeah

Semiclassical

and then obtain $C=\ln x_0$ upon evaluating at $t=0$

whereas I prefer to do it as $\int_{x_0}^{x(t)}\frac{dx}{x} = \ln x(t)-\ln x_0 = -\int_0^t dt=-t$

Balarka Sen

better yet, write d/dt(log x(t)) = -1

and integrate

Semiclassical

18:16

yeah, same idea

Balarka Sen

well, no, I am not writing out the differentials

Semiclassical

hmm

Balarka Sen

That's important because it's a standard policy to handwave about the differentials

In Calc I you integrate functions

In Calc III you integrate forms

Semiclassical

mostly I mean that I prefer to write it as a definite integral rather than an indefinite one

Balarka Sen

and learn to know integrating forms is the only thing that makes sense

(eg otherwise change of variables goes to shit)

@Semiclassical Ah

OK, I see

Semiclassical

18:17

it's a little thing, of course

Balarka Sen

That's a good point actually\

Semiclassical

but i like being able to say that i'm integrating from $x_0$ to $x(t)$, rather than have the limits be indefinite

Balarka Sen

the bike meme is awesome

CooperCape

So I just spent like 30mins answering this guy with shitty matrices full of nasties and after I answered he deleted the question... smh.

Semiclassical

ugh

that's always shitty

CooperCape

18:21

meh.

Phase

Discussion: _Is Engineering intrinsically a science_
My opinion: _No_

Huh. Why isn't it italicised

CooperCape

denied?

o wow

truly denied

No

ACuriousMind

@Phase Multiline messages break formatting.

bolbteppa

"In a brilliant series of six papers Elie Cartan answered the questions left open by Lie for transformation groups in an arbitrary number of dimensions" thoughts?

Phase

@ACuriousMind aw :(

CooperCape

18:25

It's always fun to have a good diss at biology for no reason...

Sir Cumference

@Phase Use single asterisks on both ends for italicizing, double asterisks for bolding

bolbteppa

I wish I knew biology :(

Phase

underscores work too tho

ACuriousMind

@SirCumference That's not the issue, underscores work, too.

Sir Cumference

Oh, huh. TIL

ACuriousMind

18:26

@CooperCape Careful, the biologists might shoot back

CooperCape

(casually adds vpn as libgen blocked in uk smh)

DaAAAAmmmmmmmMMMMMnnnn

Sir Cumference

That sadness when you are on the last day of your bounty but there are no answers...

CooperCape

:c

0celo7

@Semiclassical Congrats, you're doing the mathematically correct thing :)

Semiclassical

lol

0celo7

18:31

@Semiclassical separation of variables, while correct in the end, is a heckshow in the middle

Phase

@ACuriousMind I knew exactly what that link was before clicking

ACuriousMind

@Phase Excellent

CooperCape

xkcd nerds

Semiclassical

@0celo7 ODE separation of variables, or PDE separation of variables

0celo7

@Semiclassical ODE, PDE is also bad for reasons

Semiclassical

18:32

I dislike how PDE separation of variables is usually presented

it comes off as more confusing than it needs to be

I mean, it comes down to: Rather than trying to solve the PDE in general, let's look for some particularly simple solutions.

0celo7

@Semiclassical yeah but when you sum and get a series, who knows if the result converges

that's never addressed

Semiclassical

one usually just assumes completeness, yeah, at least in physics/engineering texts

0celo7

you need some nontrivial facts from Fourier analysis to conclude anything about series solutions

I don't know the relevant results off the top of my head

Semiclassical

which I'm sympathetic about tbh

at the end of the day, the point of doing it in a physics/engineering course is not to entirely understand why it works but to be able to use it in applications

bolbteppa

How do you solve $y' = \frac{1}{2} \frac{x^2+1}{y}, y(0) = 1,$ formally without doing something wrong if SoV is so bad

Semiclassical

18:37

rearrange that to $2yy'=\frac{d}{dx}(y^2)=x^2+1$

then all that's left is integration.

0celo7

@Semiclassical yes!

Semiclassical

to say it differently, if $\frac{dy}{dx}=\frac{f(x)}{g(y)}$ then you can rewrite that as $f(x)=g(y)\frac{dy}{dx}$

0celo7

@Semiclassical Yes!

bolbteppa

Ok, so lets assume we can't use differentials when solving ode's via SoV, what about ode's which require integrating factors to be solved

Semiclassical

then integration gives $$\int_{x_0}^{x}f(x')\,dx'=\int_{x_0}^{x}g(y(x'))\frac{dy}{dx'}dx'=\int_{y_0}^{y‌(x)}\!g(y)\,dy$$

bolbteppa

18:40

I don't understand the problem with using differentials

I am happy breaking the rules, rule-breaker n'all that

I love differential forms but still just feels like you're defining things away

Semiclassical

@0celo7 the above is what i think one should be doing for SoV

Emilio Pisanty

@bolbteppa defining things away does solve problems

Semiclassical

though to an extent the differentials route is just shorthand

Emilio Pisanty

it basically transforms what used to be "how do we do this?" to "what are the key constructs whose definition makes this problem trivial?"

you just need to be damn good at finding those definitions

bolbteppa

There is some famous witty French saying about 'solution by definition' or something, can't remember/find it

Emilio Pisanty

18:46

@bolbteppa ping me if you do

bolbteppa

Cool, was pretty good (aargh memory)

Anonymous

@bolbteppa I guess the problem is $dy$ and $dx$ don't mean anything much mathematically (over here). I was confused about this differential stuff too, till @BalarkaSen pointed it out.

Balarka Sen

They do mean things mathematically

Semiclassical

or they can, at any rate

Balarka Sen

It's just sophisticated to write down the precise meaning

bolbteppa

18:49

My sense is you formalize this by referring to 'exterior differential systems' so you can solve ode's in $n$ dimensions (i.e. total differential equations) but again just attaching definitions to the hand-waving $dy/dx = x/y \to ydy = xdx \to \dots $ (thanks)

Anonymous

@BalarkaSen I mean you said $dy$ is actually $(dy/dx)dx$ (1-form or something)

Balarka Sen

That is correct my man

Semiclassical

i'll say this for the differentials way of doing it: It notationally treats $x,y$ on equal footing

bolbteppa

You get two perspectives if you view ode's as differential forms, a) as curves, b) as a bunch of sheets

Anonymous

@BalarkaSen You gotta teach me differential forms this December :P

Anonymous

18:52

It's also there in Arfken chapter 4. So I'll pre-read from there :)

Balarka Sen

@Blue Sure thing

Anonymous

Yay! :D

Balarka Sen

Pure bliss

0celo7

What’s your motivation to learn them

Anonymous

@0celo7 Me?

Anonymous

19:01

Being called a hand-wavy physicist is the last thing I want to hear from mathematicians :P That's my primary motivation...lol

Mithrandir24601

@Blue if a mathematician doesn't call you hand-wavy, then doesn't that kind-of make you a mathematician?

0celo7

@Blue physicists abuse differential forms though.

Balarka Sen

There's a wikipedia page on Mozart and scatology. My life is a lie.

Nothing has meaning anymore.

Anonymous

@Mithrandir24601 I don't like to be bounded by the narrow scope of words like: physicist, mathematician, engineer. I have always considered all of these three fields to be mutually dependent.

Anonymous

@BalarkaSen wtf

Anonymous

19:09

Mozart and scatology

Wolfgang Amadeus Mozart displayed scatological humour in his letters and a few recreational compositions. This material has long been a puzzle for Mozart scholarship. One view held by scholars deals with the scatology by seeking an understanding of the role of it in Mozart's family, his society and his times, while another view holds that such humour was the result of an "impressive list" of psychiatric conditions from which Mozart is claimed to have suffered. == Examples == A letter of 5 November 1777 to Mozart's cousin Maria Anna Thekla Mozart is an example of Mozart's use of scatology. The...

Anonymous

WTF

Balarka Sen

I am dead bro. Don't ask me anything.

Anonymous

"such humour was the result of an "impressive list"[2] of psychiatric conditions from which Mozart is claimed to have suffered"

Anonymous

XD

Anonymous

There's even a linked page on Toilet humour

Anonymous

19:11

Wikipedia's standards have just....

Semiclassical

gone down the toilet?

Anonymous

yeah :P

0celo7

Boo.

Bernardo Meurer

Morning

Anonymous

\o/

vzn

19:18

@Mithrandir24601 thx much, mutual feeling, it was very mind expanding for me too, hadnt heard of that key area/ line of investigation, think its rare that pro scientists say/ admit some context where "I dont know" & sometimes very meaningful when they do, to be contd :)

Bernardo Meurer

Goddamit

0celo7

@ACuriousMind is trivial really a German word?

Bernardo Meurer

No deals on noise-cancelling headphones

I thought today would be the year

ACuriousMind

@0celo7 yes

bolbteppa

Mozart was left-handed runs

0celo7

19:32

Left handed people are probably psychopaths. It’s no coincidence the Romans call it sinister.

bolbteppa

sinistra

0celo7

@ACuriousMind do you agree?

@ACuriousMind what’s the German word for rate?

ACuriousMind

@0celo7 No. In fact, the "bad" meaning of sinister comes from ideas that being left-handed is wrong, not the other way around

Bernardo Meurer

Goddammit no sale on stereo amplifiers either

ffs

ACuriousMind

@0celo7 Rate

Bernardo Meurer

19:34

What do I have to do to get a sale on audio equipment

0celo7

@ACuriousMind Are you left handed?

ACuriousMind

@0celo7 yes

Bernardo Meurer

@ACuriousMind You son of the devil

Let's burn him

bolbteppa

@0celo7 the real question is, why are you not left-handed

Bernardo Meurer

Let's burn him right now guys

ACuriousMind

19:36

Feb 3 '16 at 2:20, by 0celo7

(I'm a leftie.)

bolbteppa

ahaha interesting

Bernardo Meurer

@ACuriousMind I thought that was in a political context!

0celo7

@bolbteppa I am :P

bolbteppa

Who here is not left-handed (shame)

Times are a changin', freaks taking over etc

Anonymous

@0celo7 Are you left footed too?

0celo7

19:40

What?

Anonymous

@0celo7 Are you left-footed or right-footed?

Sid

@0celo7 you eat with your left hand?

Anonymous

Usually left handed people are left footed

Bernardo Meurer

I'm right handed, but I pick my nose with my left hand, and I'm left footed

what does that make me

ACuriousMind

@BernardoMeurer broken

Bernardo Meurer

19:42

lol

Sid

@Blue what on Earth?

0celo7

@Sid I eat with both

I have reached such a very high level of intelligence that I am mostly ambidextrous.

Anonymous

I thought you don't like to eat with hands...

0celo7

@Blue He means utensils.

Bernardo Meurer

Lol

Sid

19:45

@0celo7 so, can you write with both hands at the same time?

Bernardo Meurer

@0celo7 Why are you talking about yourself in third person

@0celo7 Can you masturbate with both hands too?

Or just your ego ;)

Sid

.. Lol

ACuriousMind

::ahem::

Anonymous

@0celo7 Try to increase it to a level that you can do everything with all fours.

bolbteppa

It's called practice (I will leave it up to the reader which sentence this refers to)

Anonymous

19:46

@BernardoMeurer lolol

bolbteppa

I cannot write with my right hand at all

0celo7

@BernardoMeurer Yeah. I like to rotate.

Bernardo Meurer

lol

Anonymous

You triggered our AI

0celo7

@BernardoMeurer I’m kidding :p

@Sid no, that’s one thing I can’t.

@ACuriousMind are you gonna delete it?

@Blue my toes are actually very dexterous. I can pick things up with them

I share that trait with a sister

Anonymous

19:49

@0celo7 Start eating and writing with them too ;)

Bernardo Meurer

@0celo7 That is true

Anonymous

Some people can do that

Bernardo Meurer

I can eat toes

Anonymous

Whose toes?

Bernardo Meurer

If I told you I'd make the FBI's job too easy

Sid

19:51

I can sort of attempt to pick things up with my toes and I succeed for a short duration

Anonymous

Human toes are badly shaped. A little bit of modification would make them more useful

Anonymous

Also, we need a couple of spare hands

0celo7

20:03

Blue thinks he’s smarter than YHWH

Anonymous

@0celo7 Meh

Anonymous

As if i believe in YHWH

0celo7

No blasphemy pls

3.5

20:24

lol

CooperCape

20:43

@Blue Is this the Artin book? It's the only one I could find not on Libgen (which is blocked in UK)...

Anonymous

@CooperCape Give me your mail id

CooperCape

Okay

(It's trashy because it's my spammy one don't judge)

[email protected]

I do believe it's what I signed up to runescape with.

Anonymous

Check your mail

CooperCape

Yeah I got it :), thanks

Time to djvu->pdf

0celo7

Libgen is blocked in the UK?

Anonymous

20:48

@CooperCape Use Sumatra pdf app ;)

CooperCape

Ahh okay, thanks

Anonymous

It can read djvu, epub, pdf, everything

0celo7

You should convert to PDF anyway

CooperCape

@0celo7 Yeah... it gives out an error somewhat like "Blocked by the high court..."

I tried to use vpn but the internet always cut out ~~5Mb downloaded

0celo7

@CooperCape wow, how are academics supposed to function

CooperCape

20:49

Without money?

0celo7

Even if you have money I probably use Libgen five times a day

The library doesn’t have everything

Anonymous

True. Libraries are too old-fashioned. 90% of the books I need are either already in circulation or unavailable. Libgen is the way to go

ACuriousMind

@0celo7 They aren't supposed to.

CooperCape

Isn't it a tad illegal? Idk... All I know is high court people are nonces

ACuriousMind

@CooperCape Yes, it is illegal

CooperCape

20:53

Okay, just checking

So, perhaps, high court people aren't nonces.

ACuriousMind

It's not the court's fault it's illegal, no

CooperCape

I mean technically they could... yano... remove copyright laws... ;p

jk, ofc.

ACuriousMind

The nonces are the people who have created a system of publishing where getting all materials you need is basically unaffordable to the average customer

CooperCape

I swear any academic book is like $$$ wow

Prolly need black friday deals on textbooks

0celo7

ACM is about to sing the Soviet anthem. Textbook prices are always a touchy subject.

Even if they were $15 apiece I would still use libgen. I know hundreds of books, I’m not gonna buy all of them

CooperCape

20:57

It's all about knaawwledge

Anonymous

Russia does it right. I love them for that :P

0celo7

Of course many books are Springer and I have legal PDFs of those

bolbteppa

Spinors are tensor densities, spinors are projective representations, spinors are things which transform under a spin group in a certain way, fun times

Bernardo Meurer

Textbook pricing is ridiculous

CooperCape

Hang on a sec - let's annoy everyone here.

TEXTBOOK PRICES ARE REASONABLE IMO

bolbteppa

20:58

Why can't math or physics be simple

CooperCape

It's simple if you stop at the simple bits.

bolbteppa

Even 'simplicity' in algebra can be incredibly complicated at times

Bernardo Meurer

Fractions are hard

CooperCape

2+2 is 4 minus 1 that's 3 quick maths

Bernardo Meurer

Lol

CooperCape

20:59

(go on, hate me.)

Bernardo Meurer

Big Shaq

CooperCape

Okay putting scissors in your mouth is not a good idea owwwwww

shoot

Semiclassical

...

i probably shouldn't ask why

CooperCape

Yeah let's keep it that way

Let's just say my top lip is not a happy bunny

Semiclassical

oook

CooperCape

21:11

It'll all be good.

Phase

@Semiclassical its an english past time

We put scissors in our mouths and sing rule Britannia, first one to slip up and mention regicide gets stabbed

CooperCape

Oh wait

Yeah... was playing with my brothers

Semiclassical

...that's a bit messed up

Phase

Yeah but when you dont have any more logs for the fire and the police confiscate your technology and router so you can't be exposed to dangerous outside information what else is there to do?

There's only enough clothing and food for one child, in a family of five you gotta cut down

CooperCape

Can't wait until I can leave home and go to Uni... get out of the South cut-off

Phase

21:24

m8 born a southerner die a southerner

Also whereabouts in the South? I'm from Devon

CooperCape

Oooh nice... I live near Lymington if you've heard of that but it's 30mins west of Southampton

Mithrandir24601

@CooperCape I was in Southampton just last Sunday :)

CooperCape

@Mithrandir24601 Oooooh any particular reason?

Also... I'll be in Bristol next Wednesday ;p

Mithrandir24601

@CooperCape Being taught Kung Fu by a Shaolin monk :)

CooperCape

Right... Average weekend then?

Mithrandir24601

21:33

@CooperCape Ahh, any particular reason? :P I'll be doing more Kung Fu next Wednesday :)

@CooperCape Well... Normally I only get 2 hours on a Sunday afternoon as opposed to... 6-7 hours requiring waking up before 5.30 am and not getting back until around midnight...

Shaolin monks are insane

CooperCape

@Mithrandir24601 Bristol offer holder visit day I do believe it's called

It is quite a drive

That's quite cool

Mithrandir24601

@CooperCape Ahh, OK - Possibly end up seeing you around then... I'll be the one carrying a sword

(although obviously, not out in the open - it'll be in a bag that goes on my back)

@CooperCape Yeah, I was with friends, so it was a good drive :) Maybe not so much for you though :/

CooperCape

@Mithrandir24601 "Have you got any questions for us?" "Yeah... ummm do you know a guy with a sword that maybe goes by the name of Mithrandir24601... just... out of interest..."

Mithrandir24601

If you actually do see me, the bag is relatively thin and narrow, dark blue and has Chinese on it

CooperCape

lol okay...

I'll look out for it... I guess.

Mithrandir24601

21:38

@CooperCape (my actual name is Ross)

CooperCape

Too socially awkward to say anything and it would probs weird you out but... I'll stare...

Oh, ok...

Mithrandir24601

@CooperCape Nah :P To be honest, chances are that you won't see me around (I'm still in the depths of the engineering department until we get official permission to move to the office in physics)

Phase

is @CooperCape 's real name... Cooper? :thonk emoji:

Mithrandir24601

Although if you do, you're free to talk to me :P

CooperCape

Ewww engineering ;)

3

Mithrandir24601

21:40

@CooperCape We were supposed to be moved out by now, but red tape :/

CooperCape

@Phase Nah it's Jordan... Coopercape->Koopa Kape Mario cart track

Classic red tape...

0celo7

@SirCumference Bernardo is right

Bernardo Meurer

21:53

@0celo7 About what?

0celo7

us being bros

Physics Meta

0

Q: How to building an AOM driver with a DDS board? What is Evaluation Board? Does the community welcome engineering physics question?

How to building an AOM driver with a DDS board? What is an Evaluation Board? Does the community welcome engineering physics question? e.g. use AD9915 chips to build a ~400 MHz AOM driver.

Bernardo Meurer

Ah, yeah, duh

Balarka Sen

I see everyone is announcing their real names

It's time to announce mine

Bernardo Meurer

We will have proof if X ends up happening

0celo7

21:54

@BalarkaSen who is?

Mithrandir24601

@BalarkaSen I 'announced' (rather, someone correctly guessed) my real name months ago :P

Balarka Sen

well it's pretty hard to guess my real name

ACuriousMind

@BalarkaSen It's Salarka Ben, obviously.

CooperCape

Did someone guess your name? Huh...

Balarka Sen

Ben Salarka actually sounds pretty dope

Bernardo Meurer

21:57

@ACuriousMind I was going to guess Enlarkse Baa

Balarka Sen

well none of that are correct

ma nama jeff

0celo7

@BalarkaSen Balarka Sen is your real name.

CooperCape

Jeff vine

Mithrandir24601

@CooperCape Yeah, I gave enough hints in my AMA post

Bernardo Meurer

@Mithrandir24601 Come to CA, let's hang out

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