The h Bar

1:12 AM

@BalarkaSen from my ancient copy of Spivak 1

2:07 AM

@Semiclassical here is a funny identity. If $u$ is a distribution then $D^\alpha u=(D^\alpha \delta_0)*u$. This of course holds when $u$ is a function $f$...

so differentiation is convolution with some distribution

Semiclassical

neat

0ßelö7

I guess that's something one could "prove" with generous use of Dirac notation

Semiclassical

I'd more expect to prove it by integrating by parts a bunch

0ßelö7

Hmm. $u'(x)=\int \delta(y-x) u'(y)\, dy$

yeah

I mean, that's probably exactly how the proof is supposed to go for functions

Semiclassical

Is alpha an integer here, or is something more subtle involved?

0ßelö7

2:10 AM

@Semiclassical Oh, it's a multiindex

Semiclassical

ahh

0ßelö7

If you don't know what that is I can explain

I'm trying to understand what the convolution with a distribution is actually supposed to be

it's one of those things that's rather mechanical

I'm not sure what it really means though

Semiclassical

could also thing in terms of Fourier transform, since that turns convolution into products

0ßelö7

@Semiclassical hmm

@Semiclassical I understand even less what the Fourier transform of a distribution is supposed to be

Semiclassical

Why? A thought a distribution was basically defined by how it behaves under integration

and that's what the Fourier transform is

0ßelö7

2:15 AM

distributions really have nothing to do with integration

they're just abstract linear operators on $C_c^\infty$

Semiclassical

well, for reference: en.wikipedia.org/wiki/…

0ßelö7

and the convolution of distributions is some strange shit

although FT does still take a convolution of distributions to the product

Semiclassical

right

0ßelö7

@Semiclassical I dunno, FT is a magical thing that I don't really understand either

something something frequencies

Semiclassical

lol

0ßelö7

2:19 AM

@Semiclassical I mean really, wtf is the FT of a Gaussian supposed to represent

Semiclassical

Another Gaussian.

0ßelö7

I said represent, not equal

morally what is it

Semiclassical

tbh, to the extent that I have intuition for the Fourier transform

it's in thinking about stuff like the double slit

where the (amplitude squared of the) Fourier transform of the aperture gives you diffraction pattern

the other approach is to use the fact that the Gaussian is the solution of $-u''(x)+x^2 u(x)=0$

which, once you Fourier transform, is going to be the same equation in different variables.

0ßelö7

@Semiclassical ok that's neat

but what intuition does that give?

from a mathematical perspective I suppose the "justification" is that it turns differentiation into multiplication, but that doesn't give intuition about what the FT is supposed to be

Semiclassical

eh, it's intuitive enough to me: $H=x^2+p^2$.

0ßelö7

2:28 AM

@Semiclassical what about it

Semiclassical

it's quadratic and symmetric in both $x,p$. plus, one has the relation $[\hat{x},\hat{p}]=i\hbar$

which can be accomplished either by taking $\hat{p}$ to be differentiation on $x$, or $\hat{x}$ to be differentiation on $p$.

so the fact that the solution of $\hat{H}|\psi\rangle=0$ looks the same in both position and momentum space seems sorta sensible, tbh

tbf, though, I'm the kinda guy who finds coherent states intuitive/interesting

0ßelö7

@Semiclassical =0?

Semiclassical

sooooo not sure i'm the right one to ask

oh. hm

stupid zero point energy, making me look bad

0ßelö7

yeah, whatever it is

Semiclassical

it's 1/2 in these units

which points to the dirty secret that one is better off thinking of $|\psi\rangle$ as the zero eigenstate of the lowering operator $a=\frac{1}{\sqrt{2}}(x+ip)$

0ßelö7

2:34 AM

@BernardoMeurer how do I Skype on linux

Semiclassical

coherent states takes that and runs with it by considering the eigenvalue equation $a|\alpha\rangle=\alpha |\alpha\rangle.$

0ßelö7

yeah I remember that from QM

Semiclassical

which leads to a bunch of fun stuff

0ßelö7

never understood the buzz

Semiclassical

hey, they all have ~~maximal~~ minimal uncertainly product. that's pretty cool right off the bat

0ßelö7

2:35 AM

maximal?

Semiclassical

$\sigma_x \sigma_p=\hbar/2$

0ßelö7

so...minimal?

Semiclassical

durrrp

Bernardo Meurer

@0ßelö7 yaourt -Syu skypeforlinux-bin

0ßelö7

lol if it makes you feel better I was doing a practice math GRE with my advisor and I couldn't integrate $1/(x\log x)$

Semiclassical

2:37 AM

I actually did some work with so-called spin coherent states, though it was more formal than anything

ugh, integrals

0ßelö7

the math GRE is a mix of tedious calculus, stupid algebra and some clever problems

I have to start practicing and I'm not happy

Semiclassical

actually, that one isn't bad if you note that $dx/(x\log x)=(dx/x)/(\log x)=d(\log x)/\log x=d\log\log x$

0ßelö7

wtf is that notation

Semiclassical

lol

0ßelö7

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core 125.7 KiB 6.14M/s 00:00 [######################] 100%
extra 1654.3 KiB 5.21M/s 00:00 [######################] 100%
community 4.0 MiB 7.16M/s 00:01 [######################] 100%
multilib 173.0 KiB 8.45M/s 00:00 [######################] 100%
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Password:

Semiclassical

2:39 AM

$$\frac{dx}{x\log x}=\frac{dx/x}{\log x}=\frac{d(\log x)}{\log x}=d\log\log x$$

0ßelö7

$d\log\log x$

I know what that's supposed to mean but it's still a crime

Semiclassical

pff

if you understand it, then I don't really care

Jasper

@0ßelö7 People might mistake the guy in the pic for you.

0ßelö7

@Jasper so?

Jasper

Nvm, lol.

0ßelö7

2:41 AM

ethan is thicc

everyone wants to look like him

Jasper

I don't even know who he is.

0ßelö7

Jasper

I wonder who added the red lines.

0ßelö7

some memer like @BalarkaSen

Jasper

I see. He must be a youtuber then.

Bernardo Meurer

2:46 AM

Lol

0ßelö7

@BernardoMeurer help

Abcd

3:16 AM

0

Q: What does "energy required to make room for the system mean"?

I read the answers to What does enthalpy mean? and both answerers mentioned that it's the energy required to "make room for the system". What does this mean? How do we provide that energy and how does it succeed in "making room"? Does this also involve the building up of matter as the gas didn't ...

vzn

4:11 AM

Balarka Sen

8:16 AM

@BernardoMeurer "foo fazz bar bazz" such beautiful lyrical poetry

@0ßelö7 The Fibonacci spiral edit is gold

Anonymous

9:35 AM

@JohnRennie Do you know any software for playing videos downloaded with the .mlv extension?

John Rennie

@Blue Have you tried VLC? That plays pretty much everything.

Anonymous

@JohnRennie Oh, I don't have VLC on my PC. I'll download it and try. Thanks

John Rennie

MLV is Magic Lantern format, and the FFMPEG library introduced support for it about three years ago. Since VLC uses the FFMPEG library it seems very likely that VLC will play those files.

ACuriousMind

9:54 AM

@JohnRennie Magic Lantern Vormat? :P

Balarka Sen

VLC is great.

John Rennie

Video :-)

Magic Lantern Voles - it's a technology operated by voles

ACuriousMind

@JohnRennie Heh. Voles are more known for destroying technology (or at least the Cardassian voles on DS9 were), though ;)

Speaking of Trek, do there exist people who a) watched Discovery and b) liked it?

John Rennie

I'm ashamed to say the last Star Trek I saw was The Search for Spock (the first being TOS of course)

ACuriousMind

@JohnRennie Whoa.

Balarka Sen

10:02 AM

*Woah

user685252

^

ACuriousMind

@BalarkaSen Awoh

(Awo, with a long, drawn out 'o', being a sound of dismissal in some German dialects)

Balarka Sen

I was quoting the Crash Bandicoot

ACuriousMind

@BalarkaSen Never played that

Balarka Sen

@ACuriousMind This reminded me of a character from Dostoyevsky screaming "Jawohl" out loud to a German baron.

user685252

10:08 AM

was he red?

Balarka Sen

hm? what does that mean?

user685252

nvm

neat graph

ACuriousMind

@BalarkaSen Aha ;)

Prathyush Poduval

@ACuriousMind Yeah I watch it. It is quite good

John Rennie

@BalarkaSen the Crash Bandicoot character is wonderful, but the games weren't especially innovative. I've never felt any great urge to go back and start replaying them.

ACuriousMind

10:19 AM

@PrathyushPoduval Did you watch any other Trek before this one?

Prathyush Poduval

@ACuriousMind TOS, and currently watching TNG

I love this confused look that kirk gives at the start of every episode :P

ACuriousMind

@PrathyushPoduval That's just his face ;)

Prathyush Poduval

"What am I doing with my life?"

"Is space where I am going to die?"

"What came first? The chicken or egg?" :P

ACuriousMind

Eh, compared to what happens to Picard, Kirk had a pretty good life :P

Prathyush Poduval

It was quite calm at TOS though

just simple adventures

picard is just awesome

John Rennie

10:22 AM

As I recall Kirk used to get beaten up fairly regularly in TOS ...

Prathyush Poduval

@JohnRennie and loose his shirt

John Rennie

Oh yes :-)

Prathyush Poduval

I remember him with a torn shirt quite a many times

John Rennie

Very, erm, tasteful :-)

ACuriousMind

@JohnRennie Yeah, but getting beaten up and then sleeping with random aliens is pretty good compared to what Picard has to endure in some of the TNG episodes and the movies

Prathyush Poduval

10:24 AM

^

John Rennie

I can't comment, not having seen any of the later series

Prathyush Poduval

Wait, picard was there in a movie?

ACuriousMind

@PrathyushPoduval Sure, in several

There even is a cheesy crossover between TNG and TOS in the...fifth or sixth Trek movie, I think

Prathyush Poduval

I though the movies were only with shatner-Kirk

ACuriousMind

Not as cheesy as the save-teh-whales one, but still

Prathyush Poduval

10:26 AM

SAvE thE WhaLEs

I like the fact that discovery is no longer about the captain of the ship

ACuriousMind

I may just be a grumpy old fan, but it didn't feel like Trek to me at all. Far too action-y and I didn't like most of the cast. Then again, I couldn't stand DS9's Sisko for the first two seasons, either

Prathyush Poduval

Haven't seen DS9 yet. But then, didn't the new movies have a lot of action too?

Did you like the new movies?

ACuriousMind

I didn't like the new Trek movies as Trek either, though they weren't bad movies as such

Prathyush Poduval

I started off with the new movies

It was how, I came to know of star trek

Slereah

10:46 AM

Are we talking about the Star Track

Let me put my fake vulcan ears and Federation PJs

Also you may recall that Kirk's son died

Not the funnest life

and he died fighting an old man before being buried in the desert

Anonymous

I'm surely missing something. How is the de-broglie wavelength of a MB particle $\lambda=\sqrt{\frac{h}{\sqrt{2\pi m k T}}}$ ? For that the momentum must turn out to be $p=m(2\pi kT)$. But, $kT$ has the dimension energy and not velocity. I'm not sure how they got it

Anonymous

Source: books.google.co.in/books/about/…

Anonymous

Probably it is a printing mistake

Balarka Sen

10:53 AM

I remember $\lambda = h/\sqrt{2mE}$

Anonymous

Wrong edit

Anonymous

Sorry, got it

Anonymous

@BalarkaSen Yea, I missed the sqrt there

Anonymous

Got it

Anonymous

:P

Anonymous

10:54 AM

I'm being silly

Balarka Sen

kk

Anonymous

But wait, $\lambda=\frac{h}{\sqrt{2\pi m k T}} \implies E=\pi kT$, right?

Anonymous

After comparing with your equation $\lambda = h/\sqrt{2mE}$

Anonymous

Why should $E=\pi k T$ ?

Balarka Sen

iunno what the context is

Anonymous

10:57 AM

I'm uploading a screenshot

Anonymous

One min

Emilio Pisanty

2

Q: Number of photons required for communication

On one hand, the amount of information I can transmit is proportional to the bandwidth. The higher the frequency, the more information I can transmit. On the other hand, the number of photons is reverse proportional to the frequency. I cannot possibly transmit more information than the number of ...

quantum-mechanics photons quantization telescopes noise

^ This is why this site is awesome

Anonymous

It's taking eternity :/

Anonymous

@BalarkaSen There ^

Balarka Sen

11:08 AM

Probably not going to be able to help you on this one

You should ask the actual physicists

Anonymous

No problem. If anyone can decipher what's written do let me know

Anonymous

@BalarkaSen Was that a joke? We don't have any actual physicist over here :P

Prathyush Poduval

11:24 AM

Find the average energy by integrating over the boltzmann distribution

That will give you a factor of pi

@BalarkaSen ^

Anonymous

@PrathyushPoduval +1 👍

Anonymous

11:41 AM

BTW we're using Maxwell Boltzmann distribution to derive the distribution in that case. Something is wrong with that.

Slereah

11:53 AM

did Schrödinger have a cat

Physics Meta

0

Q: How can we add mathematical symbols in our posts?

When you write a post you have to use mathematical symbols ( maximum times) but you are stuck. How to do that? In some older posts ( 2-3 months ago) i wrote the whole mathematical term in English words ( literally) which soon turned into symbols when posted Example : whole square root of mu into...

support mathjax tex formatting

0ßelö7

12:10 PM

@JohnRennie in my household Star Trek is viewed as an inferior tv show and I haven't watched a single one

Prathyush Poduval

@Blue No you're not deriving it

you derive the boltzmann dist, find the energy, use it to find the case it is not applicable

Kenshin

Bonjour

0ßelö7

@Blue abandon any book that writes the "therefore" symbol

Kenshin

why tho

0ßelö7

12:31 PM

any book that uses logical quantifiers/shortcuts like that is trash

Kenshin

in a sense even words are shortcuts

abstraction leads to efficiency

Secret

1:02 PM

Example of something that is abstract but figurative

in Mathematics, 2 hours ago, by Secret

Balarka Sen

1:13 PM

@Kenshin counterexample: ncatlab.org/nlab/show/HomePage

Kenshin

what's that

0ßelö7

it might be harsh but if you don't know then you shouldn't talk about abstraction

Kenshin

why is that tho

0ßelö7

it is the most comprehensive encyclopedia of abstract nonsense in the world

Balarka Sen

the point being there are millions of examples in mathematics where abstraction is the absolute 180 degree opposite of efficiency in solving a specific, concrete problem

0ßelö7

1:16 PM

"Definition 5.3. A supermanifold is a functor $X:SuperPointop→SmoothMfd$ equipped with an equivalence class of supersmooth atlases."

Kenshin

I standby my statement that abstraction leads to efficiency

but this is long term efficiency, not necessarily for a specific problem

Balarka Sen

well we standby with our statement, backed with evidence which you don't have, that your statement is the reincarnation of absolute garbage

Kenshin

you can solve one problem now without abstraction, or 100 problems in the future with abstraction

Secret

The following is abstract:

Kenshin

so @BalarkaSen your "evidence" is a website?

is that your thought process

Secret

1:18 PM

$$\Omega_{V}^{\circ P}(E)$$

Balarka Sen

yes it is.

Kenshin

well your evidence isn't valid

0ßelö7

trol alert

Kenshin

invalid evidence is as good as no evidence at all

Secret

The following is NOT abstract

Kenshin

1:19 PM

you must show the logical link between your evidence and your conclusion

Balarka Sen

well you clearly have no knowledge of the mathematics that is presented in the website so your opinion is invalid

Secret

$1+1=2$

Kenshin

you cannot just say evidence implies conclusion without going through the reasoning

0ßelö7

@BalarkaSen why are you arguing with some kid about this

you won, let it be

Secret

The following is neither abstract nor not abstract

Kenshin

1:20 PM

don't you know that words themselves are abstractions of concepts

surely words make communicating quite efficient

Secret

And the following is both abstract and not abstract:

Kenshin

The specific problem we were referring to was the use of the therefore symbol in texts

Balarka Sen

@Kenshin yeah unfortunately everything you're saying is armchair philosophy

Secret

0ßelö7

do you have a 5K monitor?

Secret

1:22 PM

nope

I just zoom out the browser

Kenshin

@BalarkaSen it's not philosophy, it's optimisation

@Kenshin just stop

@0ßelö7 why sir?

lol

because ma'am, you don't know what you're talking about

Kenshin

1:23 PM

Sir I"m very well educated on this topic

0ßelö7

if you don't know nLab then you have no clue about mathematics

Kenshin

Sir can you prove that statement?

or is this your way of thinking?

by induction and dogma?

0ßelö7

Ma'am I don't see any reason to continue here

Kenshin

if you can prove that everyone who doesn't know nLab has no clue about mathematics than I will take you seriously

Balarka Sen

wut is this conversation

Kenshin

1:24 PM

but otherwise what you talk is trash

0ßelö7

so neither of us takes the other seriously

why are you wasting your time

go learn some arithmetic

Kenshin

indeed it seems to be the case that we dont' take each other seriously

But whether I"m wasting my time or not depends on my personal utility function doesn't it

0ßelö7

if you think this is productive then I'm inclined to urge you to look up healthcare near you

Balarka Sen

@Kenshin give me 10 good examples of mathematical theorems of importance which are more illuminating to prove "abstractly" aka, a proof which involves mathematical objects with lesser and more general structures than objects in question already are.

not much, just 10

Kenshin

@0ßelö7 productivity and utility aren't synonymous. Productivity is for the working class mate.

0ßelö7

1:28 PM

@BalarkaSen intermediate value theorem

Kenshin

@BalarkaSen ok, how about 1 + 1 = 2? This is more efficient than always saying 1 cat plus another cat gives 2 cats etc.

Balarka Sen

"1 + 1 = 2" is not a theorem...

Kenshin

define theorem for me

0ßelö7

@Semiclassical please send this guy to the shadow realm

Balarka Sen

lmgtfy

Kenshin

1:29 PM

and in addiiton, explain why you;re restricting the analysis to theorems only

when I've given an example where abstraction clearly has benefit

Semiclassical

Life's too short to bother listening to people who don't respect mathematics.

Balarka Sen

I am not saying abstraction has no benefit. Just that it's most of the time not efficient to actually do anything

Coming up with axioms is not one of the things which are actually worth doing

Kenshin

@BalarkaSen and I just gave you an example of where abstraction does have benefit

0ßelö7

you are purposefully misunderstanding the argument, ma'am

Balarka Sen

yet you have failed to produce an answer to my question about 10 examples up there

Kenshin

1:31 PM

This all started when 0celo claimed that using the therefore symbol in a text means the text is rubbish

obviously 0celo was using his irrational way of thinking (e.g. everyone who doesn't know nlab doesn't know maths) etc. but this was what raised the abstraction argument

0ßelö7

and that had nothing to do with abstraction

Kenshin

The therefore symbol is an abstraction of the word therefore

Semiclassical

7 mins ago, by Balarka Sen

wut is this conversation

Kenshin

which in itself is an abstraction of an underlying concept

Human minds always abstract to understand

0ßelö7

@Semiclassical One that lives under a bridge.

Kenshin

1:32 PM

Deep learning neural networks are all about abstraction, that's what perceptrons are

Balarka Sen

believe me, coming up with terminology is the most trivial kind of abstraction a human being is capable of doing

Kenshin

and humans think in a very similar way

Balarka Sen

and you're arguing about that? lels

0ßelö7

Top keq

Semiclassical

I frankly have no idea what is being argued here.

Kenshin

1:33 PM

terminology is a great example of the benefits of abstraction

@Semiclassical whether thinking and using abstract concepts is more efficient

than just thhinking about the concrete issue

0ßelö7

what the hell does that have to do with someone too lazy to format a proof correctly

Kenshin

@0ßelö7 you are assuming the therefore symbol is an error tho

0ßelö7

a stylistic error

Kenshin

yes but this is an inaccurate assumption on your part

Semiclassical

this conversation: youtube.com/watch?v=gxW4p2Uuhhs

Kenshin

1:35 PM

as my argument is that it is a stylistic improvement

but I'm happy to be proven wrong

0ßelö7

ok you win

Kenshin

but dogma isn't proof

0ßelö7

I will now kill myself

Kenshin

and if you can't prove me wrong, then your opinion is subjective

0ßelö7

no, you win

Kenshin

1:35 PM

thankyou sir

I'm glad you see the light

Semiclassical

...

Kenshin

fighting irrationality bit by bit

Balarka Sen

kenshin reminds me of our old dude Zee

@BalarkaSen A. Zee?

1:36 PM

Zee used to come to the math chat

and troll about how all the western philosophy is junk

he got banned

Kenshin

dude I like Western philosophy

far superior to eastern philosophy

0ßelö7

that's racist

Kenshin

lol

Semiclassical

ugh

i'm-a pull a balarka and say this conversation is all garbage

Kenshin

most human conversation is my friend

0ßelö7

1:38 PM

@Semiclassical let's talk about something that isn't garbage

how about regularity theory for quasilinear elliptic PDE?

Semiclassical

ugh

Balarka Sen

@Semiclassical relevant once again

Semiclassical

I could talk about coherent states :3

@BalarkaSen yuuup

0ßelö7

@Semiclassical I'm stuck on a proof where the guy references a paper for a regularity result, but it would be much easier to just reference back to an earlier chapter

So I'm worried I'm missing a subtlety

Semiclassical

ok

0ßelö7

1:40 PM

(the issue might be that for nonlinear PDE you can't break it up into a bunch of smaller parts using a partition of unity)

Balarka Sen

@Semiclassical I have been thinking a lot about induction lately

0ßelö7

@BalarkaSen so I came across transfinite induction the other day

Semiclassical

Faraday's law or...?