The h Bar

Kyle Kanos

4:00 AM

Well that was an interesting touchdown

Who's playing?

Packers at Cardinals

the Murrica Freedoms

Hey @BernardMeurer: github.com/DanielSank/cappy/tree/master

0celo7

@DanielSank Do you want me to give a justification for the usefulness of linear maps in physics

DanielSank

4:03 AM

@0celo7 Uh, no.

0celo7

*multilinear

Hmm, I thought you said something like that earlier

DanielSank

I think it's important to point out that there are lot of coordinate independent objects in physics.

It's good to start there.

Here's an example:

$\ddot{\phi}(t) + 2\beta \dot{\phi}(t) + \omega_0^2 \phi(t) = J(t)$

That's an equation of a forced damped oscillator right?

But we can rewrite it like this:

Slereah

Seems like it

DanielSank

$\langle t | D^2 + 2 \beta D + \omega_0^2 | \phi \rangle = \langle t | J \rangle$

And then:

$(D^2 + 2 \beta D + \omega_0^2) | \phi \rangle = |J \rangle$

0celo7

wat

DanielSank

4:06 AM

What part do you not understand?

Help me help you.

$D$ means time derivative.

Mike Miller

@0celo7: Pick a decomposition into increasing, compact submanifolds with boundary. Progressively define a nonvanishing vector field on each except possibly vanishing on the boundary. At each next stage modify the previous one only near the boundary. Take a limit. Eventually zeroes are "pushed off to infinity".

ACuriousMind

@DanielSank I have no idea what you're trying to tell me/us

0celo7

chat decided to turn the ping noise back on and deafen me

@DanielSank I understand that

DanielSank

@ACuriousMind I'm trying to point out that there are a lot of equations we write down which can be understood in a coordinate independent way.

0celo7

@MikeMiller O...k.

DanielSank

4:08 AM

Once you do that, it's easy to understand that equations like the first one I wrote are special cases expressed in a particular coordinate system.

Mike Miller

You asked for the idea.

Kyle Kanos

But everything's easier with coordinates.

DanielSank

From there it's much easier to understand that what a physicist calls a tensor is really a representation in a particular basis of what a mathematician calls a tensor.

Bernard Meurer

@DanielSank Taking a read on that README and some documentation I found for RPC

ACuriousMind

@DanielSank Uh. How is the first equation "coordinate dependent"?

DanielSank

4:09 AM

@ACuriousMind It's not. The third one is.

0celo7

@MikeMiller I know

ACuriousMind

@DanielSank Well, in the second and the third I'm not sure what $\langle t \vert$ or $\lvert \phi\rangle$ are supposed to be

DanielSank

@ACuriousMind Really?

$|\phi\rangle$ is the state of the oscillator.

$|t\rangle$ is a time basis state.

i.e. $\langle t | \omega \rangle = \exp( i \omega t)$.

ACuriousMind

@DanielSank ??? There is no time operator and no time eigenstates

DanielSank

@ACuriousMind This is not quantum mechanics.

This is linear algebra.

ACuriousMind

4:12 AM

@DanielSank I'm not following you

DanielSank

@ACuriousMind oye

ACuriousMind

What is the vector space?

Kyle Kanos

5

DanielSank

@ACuriousMind The possible trajectories of the oscillator.

$\phi(t)$ is a particular trajectory expressed in the time basis.

ACuriousMind

@DanielSank That's not a vector space. What is the sum of two trajectories?

DanielSank

4:13 AM

Of course it's a vector space.

FenderLesPaul

Twojectories

DanielSank

@ACuriousMind you can add functions together can't you?

Kyle Kanos

@FenderLesPaul well played

ACuriousMind

@DanielSank But that requires a choice of origin.

FenderLesPaul

@KyleKanos takes bow

Kyle Kanos

4:14 AM

@ACuriousMind Hence: coordinates are better

QED

DanielSank

@ACuriousMind I don't understand. The function $\phi(t)=0$ is the zero element.

What are you on about?

$D$ is obviously a linear operator on this vector space.

$\langle t | D |f + g \rangle = f'(t) + g'(t)$.

Kyle Kanos

Hmm. Physics probably should just be taught entirely using bra-ket notation linear algebra

3

DanielSank

@KyleKanos YES!

I actually wrote a book doing this.

It's so close to being ready to release.

Kyle Kanos

.....link pls

ACuriousMind

@DanielSank Hm. Okay, I meant that you cannot in general add two trajectories. I didn't realize that part is specific to the oscillator already

DanielSank

4:17 AM

@KyleKanos Not yet.

I need to spend a weekend on it.

It's soooo close.

Kyle Kanos

Well email me when it's ready

DanielSank

@KyleKanos Ok!

Kyle Kanos

Because I will read the shit out of that

Bernard Meurer

@DanielSank so an RPC is like a function call where you delegate the function's processing to another machine over a network? Is it necessarily synchronous?

DanielSank

@KyleKanos I explain the following thigs:

ACuriousMind

4:18 AM

@DanielSank Okay, so your vector space is the space of smooth functions. I could quibble about the $\langle t \rvert$, but I'll leave that be. How is now that notation "less coordinate invariant" than the $\phi(t)$?

0celo7

quibble away

DanielSank

1. A lot of problems can be expressed without a particular choice of basis. This is because integration and derivatives are linear operators.
2. E&M, linear mechanics problems (like the oscillator) and quantum are examples.
3. Matrices are representations of linear operators in particular bases.
4. Change of basis.
5. Greens functions are really simple if you think of things in this way.

@BernardMeurer You're right about the first part, but definitely not synchronous.

Trying to make that look synchronous is why a lot of RPC systems fail.

TanMath

@DanielSank I was confused about what you want me to do...

I agree I should maybe start out simple...

Bernard Meurer

@DanielSank So while the function is being run by the networked PC the client can still continue it's runtime processing and wait for the function return?

DanielSank

@ACuriousMind $(D^2 + 2 \beta D + \omega_0^2)|\phi \rangle = |J\rangle$ is more coordinate independent than $\ddot{\phi}(t) + 2 \beta \dot{\phi}(t) + \omega_0^2 \phi(t) = J(t)$.

Don't you think?

FenderLesPaul

4:21 AM

guys help

DanielSank

@BernardMeurer Yes.

Bernard Meurer

I can definitely see the use of this in quantum computing

FenderLesPaul

I can't stop looking at random threads in biology SE

it's been like two hours

DanielSank

@BernardMeurer It's useful for a lot of things.

TanMath

First, I do not know, apart from figuring out if the qutip package is messed up, how modeling a two level system helps...But I knew that you were trying to help me, so I was going to do it...

DanielSank

4:22 AM

@FenderLesPaul Sounds like you found a new interest!

TanMath

@FenderLesPaul good!

You are entrapped in my community!

FenderLesPaul

this is a trapped horizon I am not familiar with

:p

DanielSank

@TanMath Did you ignore the part where @dmckee specifically told you that n00bs always think they've found a problem with software packages and they're always wrong?

It's like you're not even reading the things people are telling you.

TanMath

@DanielSank I did not...

DanielSank

Ok, then in that case erase from your mind the notion that qtip is messed up.

TanMath

4:23 AM

I know that I couldn't have possibly found an error in the package...

@DanielSank I did not say that it isn't messed up...

DanielSank

@TanMath It's possible, it's just much less likely than there being an error in your code.

ACuriousMind

@DanielSank No. Because you have the space of functions in one variable. Writing them as $\lvert \phi \rangle$ or $\phi(t)$ makes me prefer $\phi(t)$ because I'm trained to think of $\lvert\phi \rangle$ for some abstract vector in a space about which I don't have information such as "functions in one variable".

TanMath

I said that modeling a two level system could show that the qutip package is messed up, but it is not necessarily messed up...

@FenderLesPaul so far, what is your favorite thread?

DanielSank

@ACuriousMind Ok, look, suppose I have an $n$ dimensional space over $\mathbb{R}$.

Kyle Kanos

OOMGOMGOMGOMGOMGOMGOMGOMGOMGOMG

DanielSank

4:26 AM

Actually, @ACuriousMind, here's a great example for you.

Kyle Kanos

Rodgers just scored another Hail Mary TD

DanielSank

Consider the set of arrows in the 2D plane.

These for a vector space, right?

(say "right" and then I'll go on)

ACuriousMind

right

(given an origin)

TanMath

@KyleKanos you certainly love sports...do you realize this is a physics chatroom? :p

DanielSank

Ok, now if I pick two coordinate axes, I can represent these arrows as pairs of numbers.

FenderLesPaul

4:27 AM

@TanMath I found two I've really liked so far

DanielSank

So, you might want to say that this vector space is just $\mathbb{R}^2$.

But it's not quite.

Kyle Kanos

@TanMath Yes, I'm just like many other normal Americans

FenderLesPaul

This one: biology.stackexchange.com/questions/17077/…

and this one: biology.stackexchange.com/questions/30116/…

DanielSank

I can choose a different set of axes, and when I do that the same arrow gets a different pair of real numbers.

Kyle Kanos

And while this is a physics chat room, there is absolutely no requirement that every line actually be about physics

Bernard Meurer

4:27 AM

@DanielSank Remote function calls sounds awesome, never touched this before; exciting!

ACuriousMind

@DanielSank I'm familiar with that :P

DanielSank

The number pairs are representations in a particular basis of the more abstract vector space of arrows.

@ACuriousMind Right, so the functions $\phi(t)$ are representations of something more general.

TanMath

@FenderLesPaul I like this one too...

DanielSank

For example, I can express $|\phi\rangle$ in a different basis.

@ACuriousMind observe:

ACuriousMind

Don't go Fourier transform on me

TanMath

4:29 AM

lol

DanielSank

$\langle \omega | \phi \rangle = \int dt \, \langle \omega | t \rangle \langle t | \phi \rangle = \int dt \, e^{-i \omega t} \phi(t)$.

@ACuriousMind Why not?

It's exactly the right way to think about Fourier transforms.

Kyle Kanos

Hmm, I wonder if those should be \equiv's there

DanielSank

Of course, $\int dt \, | t \rangle \langle t |$ is the identity, as you expect.

TanMath

What are you talking about?

DanielSank

@BernardMeurer Oh yeah, it's actually rather fascinating.

Bernard Meurer

4:30 AM

@DanielSank reading this article on it

0celo7

@DanielSank Did you get that from Shankar

dmckee

I spent hours convinced I'd found a problem in GNU's implementation of atan2. Turns out I was (a) supplying the arguments in the wrong order and (b) supplying them in degrees rather than radians at the same time.

DanielSank

You have to think about how to take a sequence of bytes from the network, which is totally without type information, and turn that into a well typed object in your language of choice.

@dmckee hahahahahaha nice

0celo7

@DanielSank how is that defined

Kyle Kanos

@dmckee (a) is the worst

DanielSank

4:31 AM

@0celo7 No.

ACuriousMind

@DanielSank Because that's not a coordinate change. "Momentum" is not a coordinate on space time, while position is.

TanMath

@FenderLesPaul I had this question in my mind so I asked a biology.SE question:

24

Q: Hot water and bacteria

I know that it is common to say, "use hot water when washing your hands" or when you've got a cut, "wash your hands with warm water," etc. I was wondering, why is this the case? Since bacteria grow in warm environments, you would think that it might be beneficial for bacteria. Is this just anothe...

DanielSank

@ACuriousMind wtf

Who said anything about relativity?

TanMath

@dmckee lol

DanielSank

Why the hell do you guys always complicate simple stuff by going straight to relativity?

dmckee

4:32 AM

@KyleKanos Yep. I must have looked at the prototype twenty or thrity times, but I kep seeing what I expected instead of what was there.

DanielSank

It's so frustrating.

Bernard Meurer

I have a feeling we can't have a discussion for five minutes until someone throws in the relativity card and the other party in the conversation gets sad

TanMath

@DanielSank relativity is complicated...

ACuriousMind

@DanielSank ...what has momentum being the Fourier transform of position to do with relativity?

DanielSank

@ACuriousMind You said spacetime.

TanMath

4:32 AM

What is the discussion about? Fourier transform?

DanielSank

Why did you say space time?

ACuriousMind

Uh...habit?

DanielSank

@TanMath Read the chat log for heaven's sake.

FenderLesPaul

@TanMath yeah I saw that

Kyle Kanos

Well relativity is wrong, so we probably should just drop it from curricula

DanielSank

4:33 AM

@KyleKanos wat?

FenderLesPaul

I liked your answer to the question about why yellow/black

Bernard Meurer

Oh god @KyleKanos don't go there

FenderLesPaul

is used for danger signs

TanMath

@FenderLesPaul thanks..

ACuriousMind

Anyway, "spacetime" was not essential there, just replace it by "space"

Kyle Kanos

4:33 AM

Mmmm, curly fries

FenderLesPaul

sweet potato fries > all

DanielSank

@ACuriousMind Ok whatever. How can you possibly not think a Fourier transform is a basis change?

Bernard Meurer

That looks like octopus

0celo7

@DanielSank cause he's a boss ass bitch

son

FenderLesPaul

daughter

Kyle Kanos

4:34 AM

FenderLesPaul

let's not be gender exclusive

Kyle Kanos

That's fried octopus

DanielSank

Ok @ACuriousMind, what if we work with a finite discrete set of time samples, and then use a discrete Fourier transform to produce a new set of samples? I can represent that as a matrix acting on a set of numbers. Would you consider that a basis change?

TanMath

@KyleKanos ew...

0celo7

@FenderLesPaul I exclude whatver crappy genders I want

Kyle Kanos

4:35 AM

@TanMath Don't knock it without trying it

DanielSank

@KyleKanos :( :( :( :(

ACuriousMind

@DanielSank Oh, it's a basis change alright. Just not a coordinate change, but I get now that you didn't mean with "coordinate change" what I had in mind.

Bernard Meurer

@DanielSank I think @KyleKanos is threatning

0celo7

I thought we were talking about shit on manifolds

DanielSank

@ACuriousMind Sheesh ok I meant basis change.

TanMath

4:35 AM

@0celo7 you discriminator!

DanielSank

@0celo7 We're getting to that.

0celo7

@TanMath guilty as charged

Abuse

::spanks::

^ for you!

4:36 AM

I was doing something

DanielSank

Anyway, we've established that there are coodinate independent things in very simple situations, and we've even shown a nice notation for it, and we showed an example of a basis transformation.

0celo7

then I was interrupted by Battlefield 4

Kyle Kanos

@DanielSank They offered octopus at the Greek restaurant I went to tonight...I'm curious about my son's will to try it

He really loves octopuses

ACuriousMind

@DanielSank I'm sorry I wasted some of your nice explanations :)

0celo7

now I can't remember what I was doing

Kyle Kanos

4:37 AM

(octopi?)

DanielSank

@KyleKanos Like, he likes them alive?

Kyle Kanos

@DanielSank Yes

TanMath

Well then, there is no reason for me to stay here... @DanielSank anything else you want to say? Are you busy talking to @ACuriousMind?

Kyle Kanos

But he also loves eating

Dude, he's 6

DanielSank

@KyleKanos How old is he? I have a book about them of which I came into possession of a duplicate copy. I'll send it to you if you want it.

Bernard Meurer

4:37 AM

Oh god @0celo7

ACuriousMind

@KyleKanos octopi is common (from the Latin version), but the original Greek has octopodes

DanielSank

@TanMath Try a 2 level system.

@ACuriousMind Yes, and in modern Greek it's more like octopodia.

FenderLesPaul

heck try a 1 level system

TanMath

@DanielSank like I just model a two level system? that is it?

DanielSank

^ LOL

Bernard Meurer

4:38 AM

@KyleKanos amazon.com/Quantum-Physics-Babies-Volume-1/dp/1492309532

DanielSank

@TanMath Yeah, try Rabi oscillations or something to convince yourself you're using qutip right.

ACuriousMind

@FenderLesPaul Never heard of that before! You might have inspired a new research area

DanielSank

Then add dissipation or something.

Bernard Meurer

I just love this

Kyle Kanos

Well, Cardinals just won in overtime, so I'm going to head to bed now

TanMath

4:39 AM

@DanielSank I am convinced I am using it right...I will do a two level system then...then I come back to you? what is the next step?

@KyleKanos they did?

score?

Kyle Kanos

Yes, that's why I wrote it...26-20

DanielSank

@TanMath Just do that.

TanMath

Oh...

Ok...I will tell you when I will done... I will probably get it done late night today...

FenderLesPaul

@KyleKanos night brewski

TanMath

@KyleKanos gud night!

DanielSank

4:41 AM

Anyway @0celo7 @ACuriousMind my point here is that you can show some object to have meaning independent of it's representation via components. The curvature tensor, for example, has a very simple meaning which can be expressed without components.

0celo7

@BernardMeurer What?

FenderLesPaul

@TanMath so are you a student in the US or...?

0celo7

You're never too young

for that kind of stuff

Bernard Meurer

My goodness

DanielSank

One can then introduce what you guys call "algebraic tensors", again without components.

0celo7

4:41 AM

What meaning does the curvature tensor have

DanielSank

Finally, one chooses a coordinate system and shows that the tensor can be expressed in terms of various basis tensors, i.e. with components. Then you show that these components have various transformation properties. Sets of numbers obeying those transformation properties are, sadly, what physicists call a "tensor".

This order of development makes it waaaaaaay easier to reason about tensors and do physics.

@0celo7 Ok let's go through this slowly.

How many "slots" does the curvature tensor have?

0celo7

I probably know what you're going to say, but let's do it anyway

DanielSank

@0celo7 If you know then why ask?

0celo7

@DanielSank How are you defining it

DanielSank

@0celo7 Like, what rank tensor is it?

0celo7

4:44 AM

4

DanielSank

Correct.

0celo7

woo

DanielSank

That means that if I feed it three vectors (or covectors, I won't distinguish for now) I get back what?

0celo7

looks like multiple books on diff geo have served me well

FenderLesPaul

@0celo7 you seem like the kind of guy that would frequent 4chan

0celo7

4:44 AM

@FenderLesPaul Uh, I do.

DanielSank

@FenderLesPaul Yikes.

0celo7

I don't make that a secret.

FenderLesPaul

can't argue with that

DanielSank

@0celo7 come on I ain't got all day.

0celo7

@DanielSank a vector

DanielSank

4:45 AM

@0celo7 Correct.

The curvature tensor takes three inputs:

0celo7

ok that's a little condescending

DanielSank

First you give it a vector $v$.

0celo7

I know what the curvature tensor is

DanielSank

oh, but you asked...

0celo7

get to the point

DanielSank

4:46 AM

Don't be like that, I'm aswering your question.

0celo7

@FenderLesPaul Although I've been significantly cutting back lately. I have to make an extra effort to remember to browse.

DanielSank

You give it a vector $v$ and then you pick an infinitesimally small parallelogram. That parallelogram is specified by two more vectors which define two of the sides if you see what I mean.

You feed these three things into the curvature tensor.

The output vector is the result of parallel transporting $v$ around that parallelogram.

FenderLesPaul

@0celo7 can't cut back man

DanielSank

@0celo7 ok?

FenderLesPaul

/b is good for your mental health, or so I've been told

0celo7

4:48 AM

@DanielSank ok, I knew exactly what you were going to say

That's literally in every GR book.

DanielSank

@0celo7 ok....

Yeah...

But you asked for a geometric picture... if you knew it why ask?

0celo7

Although the better answer is that the Riemann curvature is really the unique generalization of the Gaussian curvature to more than 2 dimensions.

DanielSank

@0celo7 Riiiight that's so much better that I have no idea what it means.

0celo7

@DanielSank Use the Gauss theorem for an isometric immersion $M^2\to\mathbb{R}^3$

You can see that the Riemann curvature reduces to Gauss in this case

And the Riemann tensor is the unique tensor of second order in the metric derivatives

@DanielSank (sadly I don't get what the point of that was)

I would NEVER advocate for defining the Riemann tensor as $R^i{}_{jkl}=\partial_j\Gamma^i{}_{kl}\cdots$

user54412

I don't suppose anyone from this chat will be in the bay area next week?

user54412

5:00 AM

I have this bizarre goal of meeting as many internet people as possible in real life.

Bernard Meurer

@ChrisWhite not next week sadly

I'm getting to SF on around the 12th of February

FenderLesPaul

5:31 AM

@ChrisWhite come to Ithaca!

DanielSank

@BernardMeurer Still around?

FenderLesPaul

@ChrisWhite I've actually made it a mission to go to all the astro lunches this coming semester

as someone interested in GR research I've realized I know next to nothing about actual theoretical astrophysics

so I'm trying to ameliorate that

damn there are so many things in science I know nothing about

le sigh

0celo7

all they do is look at stars

FenderLesPaul

goes back to biology SE

stars are dope

DanielSank

If you're interested in this whole RPC thingy I'd be happy to learn with you. I'd like to get something written in Scala and python (if you understand how to do it in both a statically and dynamically typed language, you understand it, eh?), and then use it in some projects.

Actually, in the end I may just write code to implement cap'nProto's RPC system (not the encoding) in Scala (it's already done in python) but learning the basics first is usually a good idea.

FenderLesPaul

5:35 AM

@0celo7 also I've noticed that lunches for almost every physics subfield are more interesting than the ones in the department I work in

i.e. particle physics

especially since particle physics lunches are almost always pheno talks

which are sooo boring

DanielSank

@ChrisWhite Awww I thought I was your only one.

Such a player.

FenderLesPaul

"Fraternal twin higgs model with adopted sibling particles and a dad particle who was left at an early age"

by dude from IAS