The h Bar

Slereah

5:00 PM

But they are both R^n

Obviously the same

0celo7

@Slereah ...what?

Slereah

t. Physicist

ACuriousMind

@0celo7 That's a dinatural transformation.

0celo7

@ACuriousMind What?

AccidentalFourierTransform

@EmilioPisanty at this point, I would buy them on amazon

0celo7

5:01 PM

WHY NOT BUY ON AMAZON FROM THE START

AccidentalFourierTransform

because capitalism

0celo7

What?

Unless the store is half the price, this is a waste of time.

ACuriousMind

A transformation between functors of different variance is not a natural transformation in the strict sense. The notion of a transformation between functors of different variance is more general and not quite as well behaved as that of a natural transformation

AccidentalFourierTransform

its not about the price, its about the trees

stores dont kill trees, amazon does

hence, the name

0celo7

You're a troll

Tell me the real reason

Slereah

5:03 PM

Can we get a trigger warning for category theory

AccidentalFourierTransform

the real reason is that it should be way easier and faster to get out of your house, walk 100 meters, and get the thing at a store

instead of having to wait from one to two days for just paper

0celo7

@ACuriousMind Ok Mr. Algebra. I'm telling you how people in differential geometry define "natural transformation."

ACuriousMind

If you take the dinatural definition, then you have that $\eta_V = f^\ast \circ \eta_W \circ f$ for any $f : V\to W$ in $\mathsf{Vect}_\mathbb{R}$, which does exist, but it is constrained to be the zero map by the case $f=0$. So the statement is that there is no dinatural isomorphism/no non-zero dinatural transformation between the identity functor and the dual.

Emilio Pisanty

^ AFT's point, really. Buying on amazon just makes it harder for corner shops to stick around, which just makes it worse.

Slereah

Thermodynamics question

At the bus stop and I am cold

What do

ACuriousMind

5:12 PM

@Slereah Get the other people waiting into a big warm group hug

Slereah

Friendship is an unknown emotion in France

Emilio Pisanty

@Slereah ah, then cd ~/southern_france/

0celo7

@ACuriousMind Yes, I just proved that

What's your point?

@AccidentalFourierTransform What? Getting out the motorized scooter, shoes, etc. is much harder than pushing a button.

@EmilioPisanty Unless the shop makes shopping far more convenient than Amazon, I see no reason why it should stick around.

Emilio Pisanty

@0celo7 it does

it's just this specific instance

AccidentalFourierTransform

5:28 PM

@0celo7 going to stores is my only chance of human interaction.

ah, the rush of awkwardly smiling at the cashier

Emilio Pisanty

@AccidentalFourierTransform you should move to England, then

AccidentalFourierTransform

@EmilioPisanty or anywhere in Europe above France

0celo7

@AccidentalFourierTransform that's pretty sad

DanielSank

Has the site burned down yet?

Hmmm, chat seems to work.

0celo7

Why would the site burn down?

vzn

5:37 PM

aieee ~~politics~~

DanielSank

@0celo7 Rebellion against the man.

General rioting.

ACuriousMind

@0celo7 That you were using imprecise terminology, I guess. A transformation exists, but it's not an ismorphism.

vzn

Experiment Reaffirms Quantum Weirdness / wolchover, quanta mag

DanielSank

Lots of math chat recently.

Maybe we should offer cookies to attract more experimentalists.

Experimentalists like cookies.

vzn

swag! maybe it will work for guest spkrs too :)

Balarka Sen

5:42 PM

or ban 0celo7 again

i prefer it this way of course

ACuriousMind

@DanielSank Everyone likes cookies!

Except the diabetic, I guess

Emilio Pisanty

@DanielSank sweets in general, really

vzn

@BalarkaSen speaking of math are you getting a degree in it?

Balarka Sen

who knows

Emilio Pisanty

hence Thor Labs sweets boxes

DanielSank

5:44 PM

@EmilioPisanty Those are such a good idea.

Emilio Pisanty

Yo @dmckee are Thorlabs sweets boxes a thing in your field?

DanielSank

Think about it: Some graduate student works in a lab. The lab has a lot of money to spend on equipment. The student, on the other hand, is poor and has no money for candy.

So Thorlabs ships candy with their equipment. The candy costs nothing compared to the equipment cost, but it's a huge win for the student.

So when the student finds two lenses, one from Thorlabs for $100 and one from Acme Lens Co. for $80, what are they going to do? Thorlabs, of course.

Emilio Pisanty

@DanielSank make chatjax friendly, maybe?

and yeah, completely agree

DanielSank

@EmilioPisanty lolwut?

AccidentalFourierTransform

$

Emilio Pisanty

5:46 PM

@DanielSank yer $ signs mangled the stuff in between

DanielSank

@EmilioPisanty Interesting. It looks completely normal to me. Oh, I don't have chatjax on.

How to fix?

welp, too late. Edit period is over.

Emilio Pisanty

@DanielSank backticks

oh well

DanielSank

^ oh yea

Does anyone here have magic?

I mean, fixing frozen chat messages magic?

ACuriousMind

I could offer some quality mod abuse

AccidentalFourierTransform

so, nothing new ;-)

DanielSank

5:49 PM

hahahahaha

rekt

Yo, @ACuriousMind, what's it like to be the community whipping boy?

Balarka Sen

@0celo7 Tell me about holonomy

DanielSank

Feels good, eh?

user228700

@JohnR: Dyou remember the scene in Prisoner of Azkaban in which Harry generates the patronous that saves both him and Sirius?

DanielSank

Oh, hi Cow Smoothie!

user228700

Lol, @DanielSank: Hey :-P

ACuriousMind

5:50 PM

@DanielSank I'm beginning to suspect my masochistic streak is stronger than I thought :)

DanielSank

@ACuriousMind Yah. Well, you asked for it ;-)

John Rennie

@Kaumudi.H Yes ... I was staggered

user228700

@JohnRennie What dyou mean?

DanielSank

As far as I can tell, JR is saying he was in a stunned state:

nethackwiki.com/wiki/Stun

John Rennie

I was stag - gered at Harry's patronus. Oh never mind :-)

DanielSank

5:52 PM

Oh jeez.

user228700

@JohnRennie Sigh, what a wasted attempt :-P

ACuriousMind

::groan::

DanielSank

@JohnRennie do you like board games and such?

user228700

Anyway, dyou remember it?

John Rennie

@Kaumudi.H Vaguely ...

user228700

5:54 PM

I happened to watched the scene in the movie recently (which is presumably not different from that in the book) and realised exactly brilliant Harry is.

John Rennie

@DanielSank No. Some friends tried gallantly to interest me in their favourite board games, but to do avail.

Let me find that scene in the book ...

Balarka Sen

in the book it also saved ron and hermione iirc

it was because of the time turner thing, not particularly because of harry's brilliance

user228700

@BalarkaSen What dyou mean?

John Rennie

The Patronus turned. It was cantering back toward Harry across the still surface of the water. It wasn’t a horse. It wasn’t a unicorn, either. It was a stag. It was shining brightly as the moon above … it was coming back to him. …

Balarka Sen

@Kaumudi he was supposed to make that powerful patronus because it already hapenned before...

time-travel stuff

user228700

5:57 PM

That's not "time-travel stuff". The point is that he was able to conjure it.

Balarka Sen

he was supposed to, because it happened in the past

user228700

So what? I am making the point that he was able to do it.

user228700

The Patronous is an exceptionally difficult spell to conjure. The most important aspect of conjuring it is to think of a happy memory.

Sir Cumference

@BalarkaSen That part didn't make much sense

It's like some weird time loop

user228700

@SirCumference It made sense in that I suppose it gave Harry the confidence to conjure it...because he'd done it before.

John Rennie

5:58 PM

My patronus is a laptop ...

5

Sir Cumference

@Kaumudi.H Yeah, but why had he done it before?

DanielSank

@JohnRennie I wonder if this would change your mind.

Sir Cumference

His previous self would have had to learn it from another previous self, who would have had to learn it from another previous self, etc.

Balarka Sen

@Kaumudi sure, but that's not brilliance, etc (he himself talked about this later in order of phoenix). he never generates such a powerful patronus in the whole series again, ever

user228700

@SirCumference Learn? He already knew how to do it.

Balarka Sen

5:59 PM

also he didn't know it was he who generated it in the past till he actually did it afterwards

It's all in the book

user228700

I know that.

user228700

Sigh, this is not what I was going for.

Sir Cumference

@Kaumudi.H He had to see himself do it before he could do it

user228700

Brilliant wizard or not, when I watched the scene, I realised just how brilliant he is as a person. Having been through so much loss and suffering, he was still able to conjure up such a powerful patronous, by thinking about his happiest memory.

dmckee

@EmilioPisanty Never been the guy to order fiber optics kit so I didn't know about this.

Balarka Sen

6:02 PM

he's a good guy

Emilio Pisanty

@dmckee fair enough

user228700

It took me back to what Dumbledore said at the beginning of the book--"Happiness can be found even in the darkest of times, if only one remembers to switch on the light"

Emilio Pisanty

any other manufacturers send goody bags as standard over on that side of equipment-space?

dmckee

That said, my wife is a avid knitter and gets her supplies off the internet. One vendor sends a few pieces of candy with each order.

user228700

(Or something along those lines)

dmckee

6:03 PM

I'm fairly sure she picks them when all else is equal, so I've seen the same strategy in action.

Then she gives the candy to me.

user228700

Oh well, I just thought that it was a good reminder.

user228700

@DanielS: Did somebody mention board games? :--

user228700

kickstarter.com/projects/1018340123/wizard-school

Balarka Sen

HP (both books and movies) is a good fantasy fiction series. But I think there are better fantasy fictions :)

user228700

I haven't read anything better since.

Balarka Sen

6:06 PM

Have you read The Hobbit?

user228700

Yep.

Balarka Sen

Well, I think it's brilliant (along with LoTR)

But tastes do vary

0celo7

@BalarkaSen I know embarrassingly little about holonomy. I know de Rham's theorem and the Berger classification, but that's it :/

user228700

It is great, but I like a good fantasy book that is also metaphorically resonant.

DanielSank

@Kaumudi.H Yes. It was me.

0celo7

6:08 PM

Symmetric/homogenous spaces are on my long list of things to learn about

But I need to bolster my algebraic topology first

DanielSank

@Kaumudi.H There's an octopus!

0celo7

My algebra for sure

user228700

@DanielSank Why, yes there is!

DanielSank

@dmckee Try it. You get gummies.

dmckee

I find that, like many books intended for youth and adolescents, peoples reaction to Harry Potter depends a little on where they were in their lives when they read it.

Balarka Sen

6:09 PM

@0celo7 Fair enough. I've been learning a thing or two about holonomy of foliations.

dmckee

A lot of people who grew up with the characters are deeply emotionally involved with the people in the book.

Bernardo Meurer

@0celo7 Today I watched someone show Poincaré-Hopf, it was cool

Now I want to read more about topology

0celo7

@BernardoMeurer On the sphere?

dmckee

I was old enough that I never made that kind of connection so its just a pretty good fantasy series.

DanielSank

@dmckee Indeed. I picked it up after having read the Redwall series for my entire childhood, so after about five pages of Harry Potter I thought "Meh, I've read this before" and stopped.

Bernardo Meurer

6:10 PM

@0celo7 No, not hairy ball theorem, the generalisation of it, the actual poincaré-hopf

user228700

I didn't grow up reading it but I do believe that I haven't read anything better ever since because of JKR's exceptional skill of world-building and the abundance of metaphors in a book "for children".

DanielSank

@BernardoMeurer Remember what I told you about the Samurai theorem?

Balarka Sen

@Kaumudi I like LOTR because of the realism, not of the fantasy. But then, I haven't really read a lot of fantasy.

Bernardo Meurer

Also my algebra prof told me to read introduction to lattice theory, according to her "It sounds like your kind of stuff"

DanielSank

There's some really cool topology attached to that.

0celo7

6:11 PM

@DanielSank Samurai theorem?

Bernardo Meurer

@DanielSank Yes, Green's theorem right?

Green or Stokes

DanielSank

@0celo7 Generalized Stokes. I call it the "Samurai" theorem when talking to Bernardo.

He and I have a certain way of communicating.

Balarka Sen

My tastes have changed since I read my last fantasy fictions. Haven't meddled with that genre for a while

DanielSank

@BernardoMeurer <3

Bernardo Meurer

@DanielSank <3

DanielSank

6:12 PM

I could use a good scifi/fantasy but so many of them are crap.

0celo7

@BalarkaSen My plan right now is to finish Hall's QM, then read Wald's QFT, then some Yosida, in particular Bochner integration, then GMT from Morgan

After that, who knows.

Those things will probably take months anyway

Balarka Sen

More physics than math :(

Bernardo Meurer

@0celo7 She also told me to read on operator theory. What's up with that?

0celo7

@BalarkaSen Bochner integration and geometric measure theory are hardly physics?

DanielSank

@BernardoMeurer I have no idea what that means.

Bernardo Meurer

6:13 PM

but I know she does operator theory so maybe she just wants to convert me

DanielSank

"Operator theory"? Isn't that linear algebra?

Bernardo Meurer

@DanielSank I think so

0celo7

@DanielSank Jesus christ

No, she means functional analysis

DanielSank

@0celo7 Oh

Bernardo Meurer

@0celo7 yeah

0celo7

6:14 PM

That's hardly up his alley and not within reach

Bernardo Meurer

@DanielSank She told me to transfer to maths, she's trying to ruin my life :P

DanielSank

^ yes

Balarka Sen

Not familiar with Bochner integration

0celo7

@BalarkaSen integration of functions with values in Banach spaces

Bernardo Meurer

@0celo7 I like algebra stuff so far

@0celo7 What about lattice theory?

0celo7

6:15 PM

never heard of it

@BalarkaSen It's used in parabolic PDE

Bernardo Meurer

Lattice (order)

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every two elements have a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the natural numbers, partially ordered by divisibility, for which the unique supremum is the least common multiple and the unique infimum is the greatest common divisor. Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities...

Ah

0celo7

@BalarkaSen You should have said "more analysis than geometry"

Bernardo Meurer

amazon.com/Introduction-Lattices-Order-B-Davey/dp/0521784514/…

If anyone is looking to give me a book

My birthday is april 30th

0celo7

@BernardoMeurer This doesn't look like a proof of Poincare-Hopf to me

DanielSank

@BernardoMeurer look up Lattice Green functions. That stuff is amazing.

You can solve the problem of finding the resistance between two nodes in a grid of resistors.

It's very cool.

Bernardo Meurer

6:17 PM

@0celo7 That pic ain't the proof, I didn't copy that

DanielSank

I first saw this problem on the Google Labs Aptitude Test. A professor and I filled a blackboard without getting anywhere. Have fun.

Bernardo Meurer

@DanielSank I WAS ABOUT TO REFERENCE THAT

<3 <3 <3

DanielSank

U R 2 SLOW

0celo7

@BernardoMeurer what is wrong with your professors that they insist you do stuff like Poincare-Hopf before you even know what a manifold is

Bernardo Meurer

@0celo7 We did Hilbert spaces too

user228700

6:21 PM

Byee.

Bernardo Meurer

It's a series of mini courses they do during vacation

It's to show us cool stuff I guess

DanielSank

@0celo7 That's not even the worst of it. His chemistry prof was doing hydrogen atom wave functions before anyone in the course had taken even basic quantum.

rob

@DanielSank That cartoon was published a day after my PhD advisor and I spent an entire afternoon distracted by that exact problem.

0celo7

@DanielSank yes, I know

DanielSank

@rob It's a good problem. Did you guys reduce the answer to Fourier transforms?

I don't think you can do much better than that.

At least, not without some kind of approximation setup.

Bernardo Meurer

6:22 PM

I get triggered when I think of chemistry

@mods can we ban all Chemistry?

DanielSank

^ yes

rob

@DanielSank It was new to both of us and we didn't get that far.

DanielSank

@rob You a grad student?

Chemistry is offensive. Let's ban it. In fact, let's actually outlaw it at the natural level. In other words, anything chemical is hereby forbidden to occur in this chat room.

Loong

:-(

DanielSank

Don't even think about catalysis!

AccidentalFourierTransform

6:24 PM

$\log_{10}$

DanielSank

^ ?

0celo7

@DanielSank To prove PH, you need homology, cohomology, Morse theory, or intersection theory. (@BalarkaSen probably knows another way.) What is @BernardoMeurer supposed to get out of seeing a proof, he doesn't even know multivariable calculus?

rob

@DanielSank Not for quite a while now ... xkcd has been running a long time.

DanielSank

@rob Indeed.

user228700

AccidentalFourierTransform

6:24 PM

@DanielSank a thing only chemists use

DanielSank

@AccidentalFourierTransform Not true! I've been using it much the last few days!

AccidentalFourierTransform

@DanielSank ew

get out

user228700

^^^@DanielSank

0celo7

@AccidentalFourierTransform log base 10 is used in nuclear physics

AccidentalFourierTransform

nuclear physics is almost chemistry

DanielSank

6:26 PM

@Kaumudi.H :-(

Many, there is no love for experimentalists around here.

Ever heard of the Decibel?

0celo7

no, what is that?

AccidentalFourierTransform

WHAT IS THAT

$\Huge\text{WHAT IS THAT}$

DanielSank

Given a number, the value in decibels is $$N_\text{dB} \equiv 10 \log_{10}(N) \, .$$

0celo7

"a number"

DanielSank

It's incredibly common in engineering, particularly in microwave circuits, radar, etc.

It's a convenient logarithmic scale.

0celo7

6:27 PM

ew, engineering

DanielSank

Yes.

@AccidentalFourierTransform Uh, why so big?

Balarka Sen

@0celo7 One can actually understand it simplicially.

AccidentalFourierTransform

because I couldn't hear you

Balarka Sen

But that's not quite "a proof"

Also, agree, I should have said analysis vs geometry

Emilio Pisanty

@DanielSank "a number"

0celo7

6:30 PM

chrome keeps doing that

Emilio Pisanty

except engineers will happily do that with stuff that has units

0celo7

@EmilioPisanty you normalize by some $N_0$...

for sound it's the human threshold

AccidentalFourierTransform

$N_0=1$

0celo7

@BalarkaSen elsevier.com/books/geometric-measure-theory/morgan/…

ACuriousMind

@EmilioPisanty Physicists will too, $\ln(\mu)$ for $\mu$ with non-zero mass dimension is common in QFT...

DanielSank

6:31 PM

@EmilioPisanty What?

Emilio Pisanty

@DanielSank sound being the most common example

0celo7

@EmilioPisanty Wrong

AccidentalFourierTransform

or anything in astrophysics

0celo7

you always normalize the intensity

DanielSank

We have things like dBm which work like this: $$\text{Power}_\text{dBm} \equiv 10 \log_{10}(\text{Power} / 1 \, \text{milliWatt})$$

ACuriousMind

6:32 PM

They really mean $\mu/\mu_0$ but the number of them who forget to mention that at some point is non-neglegible

AccidentalFourierTransform

$\log T$

DanielSank

@EmilioPisanty Oh yeah, the notation there is super lazy.

0celo7

@ACuriousMind does Weinberg make the distinction?

Emilio Pisanty

@DanielSank in a word

ACuriousMind

@0celo7 No idea off the top of my head. Given his fetish for complete notation, I'd bet he does, though

0celo7

6:34 PM

Fetish? How is that any better than phone sex?

Bernardo Meurer

ZFC is wrong

0celo7

oh my god

no one cares about ZFC

Balarka Sen

except the C

0celo7

axiom of choice is wrong

Bernardo Meurer

@0celo7 You use the axiom of choice to justify drinking water ffs

0celo7

6:35 PM

but the worse thing is classical logic

@BernardoMeurer that's perhaps the most nonsensical thing you've ever said

ACuriousMind

@0celo7 Fetish does not necessarily carry a sexual connotation, it can simply be "an object of irrational reverence or obsessive devotion "

Bernardo Meurer

@0celo7 I'm all about going hard or going home

0celo7

@ACuriousMind Phone sex doesn't either.

ACuriousMind

Sex need not carry a sexual connotation?

Balarka Sen

lol

ACuriousMind

6:36 PM

That opens whole new possibilities

Bernardo Meurer

@ACuriousMind You have a narrow view of phone sex

0celo7

Not if done for the sole purpose of procreation.

Bernardo Meurer

all phone sexes matter

0celo7

@BalarkaSen Did you see the GMT book?

DanielSank

How is this conversation not being deleted?

I'm so confused about the chat rules.

0celo7

6:38 PM

Because ACM is a good mod.

@ACuriousMind Good AI.

ACuriousMind

@DanielSank Because it does not violate the Be Nice policy and my impression is that we left off yesterday that no policy except that will be enforced in the future.

Bernardo Meurer

@0celo7 Greme meanwitch tien?

ACuriousMind

(The meta post will be updated shortly to reflect that)

DanielSank

@ACuriousMind Groovy.

0celo7

@BernardoMeurer What?

Bernardo Meurer

6:41 PM

@ACuriousMind God bless

ACuriousMind