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

neat

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

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

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

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

2:10 AM
@Semiclassical Oh, it's a multiindex

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

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

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

Why? A thought a distribution was basically defined by how it behaves under integration
and that's what the Fourier transform is

2:15 AM
distributions really have nothing to do with integration
they're just abstract linear operators on $C_c^\infty$

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

and the convolution of distributions is some strange shit
although FT does still take a convolution of distributions to the product

right

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

2:19 AM
@Semiclassical I mean really, wtf is the FT of a Gaussian supposed to represent

Another Gaussian.

I said represent, not equal
morally what is it

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.

@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

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

2:28 AM

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

@Semiclassical =0?

sooooo not sure i'm the right one to ask
oh. hm
stupid zero point energy, making me look bad

yeah, whatever it is

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 $a=\frac{1}{\sqrt{2}}(x+ip)$

2:34 AM
@BernardoMeurer how do I Skype on linux

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

yeah I remember that from QM

which leads to a bunch of fun stuff

never understood the buzz

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

2:35 AM
maximal?

$\sigma_x \sigma_p=\hbar/2$

so...minimal?

durrrp

@0ßelö7 yaourt -Syu skypeforlinux-bin

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

2:37 AM
I actually did some work with so-called spin coherent states, though it was more formal than anything
ugh, integrals

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

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

wtf is that notation

:: Synchronizing package databases...
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2:39 AM
$$\frac{dx}{x\log x}=\frac{dx/x}{\log x}=\frac{d(\log x)}{\log x}=d\log\log x$$

$d\log\log x$
I know what that's supposed to mean but it's still a crime

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

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

@Jasper so?

Nvm, lol.

2:41 AM
ethan is thicc
everyone wants to look like him

I don't even know who he is.

I wonder who added the red lines.

some memer like @BalarkaSen

I see. He must be a youtuber then.

2:46 AM
Lol

@BernardoMeurer help

3:16 AM
0

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 ...

4:11 AM

4 hours later…
8:16 AM
@BernardoMeurer "foo fazz bar bazz" such beautiful lyrical poetry
@0ßelö7 The Fibonacci spiral edit is gold

1 hour later…
Anonymous
9:35 AM
@JohnRennie Do you know any software for playing videos downloaded with the .mlv extension?

@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

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.

9:54 AM
@JohnRennie Magic Lantern Vormat? :P

VLC is great.

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

@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?

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

@JohnRennie Whoa.

10:02 AM
*Woah

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

I was quoting the Crash Bandicoot

@BalarkaSen Never played that

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

10:08 AM
was he red?

hm? what does that mean?

nvm

@BalarkaSen Aha ;)

@ACuriousMind Yeah I watch it. It is quite good

@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.

10:19 AM
@PrathyushPoduval Did you watch any other Trek before this one?

@ACuriousMind TOS, and currently watching TNG
I love this confused look that kirk gives at the start of every episode :P

@PrathyushPoduval That's just his face ;)

"What am I doing with my life?"
"Is space where I am going to die?"
"What came first? The chicken or egg?" :P

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

It was quite calm at TOS though
picard is just awesome

10:22 AM
As I recall Kirk used to get beaten up fairly regularly in TOS ...

@JohnRennie and loose his shirt

Oh yes :-)

I remember him with a torn shirt quite a many times

Very, erm, tasteful :-)

@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

10:24 AM
^

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

Wait, picard was there in a movie?

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

I though the movies were only with shatner-Kirk

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

10:26 AM
SAvE thE WhaLEs
I like the fact that discovery is no longer about the captain of the ship

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

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

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

I started off with the new movies
It was how, I came to know of star trek

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

Anonymous
Probably it is a printing mistake

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

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 $E=\pi k T$ ?

iunno what the context is

Anonymous
10:57 AM

Anonymous
One min

2

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 ...

^ This is why this site is awesome

Anonymous
It's taking eternity :/

Anonymous

Anonymous
@BalarkaSen There ^

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

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.

11:53 AM
did Schrödinger have a cat

0

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...

12:10 PM
@JohnRennie in my household Star Trek is viewed as an inferior tv show and I haven't watched a single one

@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

Bonjour

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

why tho

12:31 PM
any book that uses logical quantifiers/shortcuts like that is trash

in a sense even words are shortcuts

1:02 PM
Example of something that is abstract but figurative

1:13 PM
@Kenshin counterexample: ncatlab.org/nlab/show/HomePage

what's that

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

why is that tho

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

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

1:16 PM
"Definition 5.3. A supermanifold is a functor $X:SuperPointop→SmoothMfd$ equipped with an equivalence class of supersmooth atlases."

I standby my statement that abstraction leads to efficiency
but this is long term efficiency, not necessarily for a specific problem

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

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

The following is abstract:

so @BalarkaSen your "evidence" is a website?

1:18 PM
$$\Omega_{V}^{\circ P}(E)$$

yes it is.

invalid evidence is as good as no evidence at all

The following is NOT abstract

1:19 PM

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

$1+1=2$

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

you won, let it be

The following is neither abstract nor not abstract

1:20 PM
don't you know that words themselves are abstractions of concepts
surely words make communicating quite efficient

And the following is both abstract and not abstract:

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

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

do you have a 5K monitor?

1:22 PM
nope
I just zoom out the browser

@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

1:23 PM
Sir I"m very well educated on this topic

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

Sir can you prove that statement?
or is this your way of thinking?
by induction and dogma?

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

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

wut is this conversation

1:24 PM
but otherwise what you talk is trash

so neither of us takes the other seriously
why are you wasting your time
go learn some arithmetic

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

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

@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

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

1:28 PM
@BalarkaSen intermediate value theorem

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

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

define theorem for me

lmgtfy

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

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

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

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

you are purposefully misunderstanding the argument, ma'am

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

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

and that had nothing to do with abstraction

The therefore symbol is an abstraction of the word therefore

7 mins ago, by Balarka Sen
wut is this conversation

which in itself is an abstraction of an underlying concept
Human minds always abstract to understand

@Semiclassical One that lives under a bridge.

1:32 PM
Deep learning neural networks are all about abstraction, that's what perceptrons are

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

and humans think in a very similar way

and you're arguing about that? lels

Top keq

I frankly have no idea what is being argued here.

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

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

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

a stylistic error

yes but this is an inaccurate assumption on your part

1:35 PM
as my argument is that it is a stylistic improvement
but I'm happy to be proven wrong

ok you win

but dogma isn't proof

I will now kill myself

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

no, you win

1:35 PM
thankyou sir
I'm glad you see the light

fighting irrationality bit by bit

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

dude I like Western philosophy
far superior to eastern philosophy

that's racist

lol

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

most human conversation is my friend

1:38 PM
@Semiclassical let's talk about something that isn't garbage
how about regularity theory for quasilinear elliptic PDE?

@Semiclassical relevant once again

I could talk about coherent states :3
@BalarkaSen yuuup

@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

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)

@Semiclassical I have been thinking a lot about induction lately

@BalarkaSen so I came across transfinite induction the other day

it seems like nonsense

yeah electromagnetic induction
@0ßelö7 dunno that stuff

1:41 PM
lol

damn
I guess I am a mathematician

I didn't even consider EM

o and it gets a bit (insert word)

1:43 PM
@Semiclassical Self-induction and mutual inductions are interesting phenomenons

yeah

I mean, the nonlinearity is just a source term, it doesn't have a derivative
it should really be trivial

@Avantgarde Have you listened to Godspeed You! Black Emperor's new album?

@BalarkaSen that's an interesting band name

They are one of the notable experimental post-rock bands out there
Lift Yr Skinny Fists Like Antennas To Heaven is a great album
also a great meme :P

1:57 PM
yikes
sounds scary