@nbro They just forget the ''free'' in front of energy, as in ''free energy''. This could also be phrased as ''energy of lower entropy than the environment entropy."

This is essentially energy you can do work with

...the one we are interested in.

@Secret But I still want dangerous chemicals to exists!

ok

@G.Bergeron At no point. And sure, language is a part of this because we probably have fewer words than classes of objects, but I still think that "equivalence class" doesn't really work for what happens to "the same object" during a process at the end of which it is no longer the same object.

@ACuriousMind What I meant is that words / concepts designate an equivalence class of qualia. At some point it may well be neither, but that just means we don't have a word or concept for that. Maybe a sentence can describe it, but then isn't it just a newly formed equivalence class?

''what exists between a solid metal bar and the melted pool it created when heated''

I hate it when I find a piece of software that seems great and I want to use it, but then it's proprietary malware

Ah, okay, the "at some point it may well be neither" is what I was after - I probably had a wrong impression of what you were saying

@BernardoMeurer You extended the definition of malware to include almost everything

His notion of "malware" is a proper class :P

@ACuriousMind But if you cannot define an equivalence class of qualia you cannot even create a concept to designate it, since you can't describe it.

@G.Bergeron Well, Malware is software that works against the user

Like Spotify

@ACuriousMind what is the publishing norm for grad students in Germany doing Physics. Do grad students over there leave with like 4 papers published already?

@ACuriousMind And not properly synchronized with everybody else's

@Cows Isn't that the goal of every grad students?

@ACuriousMind Axiom of Choice is bullshit

@G.Bergeron "Of which we cannot speak, we must remain silent." ;)

... Or as much as possible

@ACuriousMind Yes, pretty much!

@BernardoMeurer Why?

@G.Bergeron It just is, it cannot be right

@Cows Not in germany, but I've seen from 0 to 28 (yes!)

@Cows I'm a MSc student, not yet a PhD student.

@G.Bergeron wow!

@BernardoMeurer Invalid argument

@G.Bergeron Axiom of Choice is like P=NP

It's just too good to be true

@BernardoMeurer You do know you've probably used it thousands of time, implicitly?

We saw where that took us with the Halting Problem...

MSc students tend to leave with 0-2 published (usually 0 :P), the PhDs...vary a lot, but of course everyone's goal is to get published, isn't it?

@BernardoMeurer What are you saying?!

@G.Bergeron Yes, and look what that got me

@BernardoMeurer Um, P can be = NP as far as I know

@G.Bergeron Come on, it won't be

It's too good to be true

@ACuriousMind wow.

P=NP would be like halting problem being solvable, it can't be because it's too good to be true

@BernardoMeurer I also think it won't. But it's actually not ''to good to be true''. It would mean the reality kinda sucks

@G.Bergeron What? P = NP would be amazing!

@BernardoMeurer No, the negation of the axiom of choice is P=NP - both are the version the majority disbelieves :P

well my goal is to learn a lot of things first

@BernardoMeurer No, P=NP is NOT like the halting problem

@G.Bergeron In the sense that if the halting problem was solvable it'd be awesome yes

I'm not saying they are the same problem-wise

I used to dream of getting directly into a phd program and publishing mountains of papers

@BernardoMeurer And also, it would mean that mathematics is wrong

@BernardoMeurer Not necessarily or, better, maybe not the way you think. P could also be equal to NP, and things could still not change too much, actually. Imagine P=NP, but all polynomial times solutions to NP-complete problems are actually impractical...

I think I would benefit from an MS first when I get there

someday . . .hehe

@nbro I don't know you, so I will just make the warning: 90% of the time I'm just talking BS

@Cows You get more years of funding doing a MSc first...

In Europe, MSc is usually the prerequisite for doing a PhD (although there are exceptions)

@BernardoMeurer But they are deeply different in the sense that the halting problem is a theorem

It cannot be really be false without throwing all logic out

@G.Bergeron Yes, I do not argue that

P=NP only implies the universe is boring

I'm saying, IFF we could solve the halting problem it'd be neat

of course we all know the ICC 2018 will solve the halting problem

I don't even know what the ICC 2018 is

@nbro Sigh, you don't get it

@BernardoMeurer But my point is that if we could solve the halting problem, i'd drop science right away

WHERE IS CHRIS WHITE TO GET MY COMPILER JOKES

WHERE IS HIM

Chill

@BernardoMeurer Probably not the way you want

@G.Bergeron Yeah, it'd be neat :)

@BernardoMeurer That I'd drop science?

@G.Bergeron Well, not that, but that we could evaluate so much if it was possible to solve the halting problem

@BernardoMeurer You're basically wishing for logic to crumble away... 8|

@G.Bergeron Yes

It's my one true wish

So no evaluation means anything anyway

Only then would I rule the world

@BernardoMeurer It's my one true hell

@G.Bergeron do you have a github page?

@Cows Hum, yes, but I don't think anything is public

why?

just curious.

@G.Bergeron The halting problem is mathematically proven to be unsolvable with Turing machines...unsolvability and complexity classes such as NP-completeness are different areas, somehow though related

@G.Bergeron just wanted to browse your work may be. .

Yeah, most of my stuff is on dropbox, research and hobby data analysis

oh cool

do sklearn or tensorflow

?

pandas?

. . .

I actually want to build something new/different

oh cool

I guess ''am'' building

@nbro Now, leaving my bs aside and talking serious, did you happen to read Aaronson & Yedidia's paper on evaluating ZFC consistency using turing machines?

In python, but I feel like there are no good mathematical tools to deal with high complexity

Do you have your own algorithm, or you want to put together a library

In particular the relations of that and the busy beaver function for the given machine they crafted

@G.Bergeron GMP

I am putting together some npm packages myself

so i can do ml in browser

@Cows It's work in progress, I put together a computer to fiddle with new algorithm

It's probably gonna be based on Theano graphs

I still want to integrate GMP and OpenCL one day

cool, I understand

My brother is a dev for theano so I guess I'm biased :p

@G.Bergeron If you need to hire someone, I don't mind interviewing

Oh, but I'm still doing my phd and not in ml, but in mathematical physics

@G.Bergeron Really? That's nice, Theano is cool

@BernardoMeurer No, I didn't

You should see it as a hobby/plan b

oh cool

@nbro Would you like a link, I think I have it here still

scottaaronson.com/blog/?p=2725

Ta-daa

@BernardoMeurer Yeah, maybe not the best for production, but really flexible for research in ml

it's a 30-page paper, so probably I will download it and put it in the queue of papers to read ;)

@G.Bergeron are you interested in the programming or cs side?

@nbro I have a queue of papers too

it's called the black hole

ahah, nice!

Ok I should get back to reading

@Cows Yes, but mostly for what it can do for me. Also, I'm interested in too many things, not viable...

@BernardoMeurer Really nice paper!

@G.Bergeron It's awesome, really worth the read!

What does "A converts energy into mechanical work" actually mean? Work is actually related to force by the equation w = F*distance

@BernardoMeurer GMP is to handle the actual calculation, I was referring to theoretical tools

@nbro It makes thing move

@G.Bergeron Ah

@G.Bergeron Yes, but does it make sense to talk about a "conversion"?

@nbro Yes because energy is conserved

So only transformed/converted

what does "convert" then mean?

@nbro You convert the potential energy in an elevated bucket of water to the kinetic energy of the water running down when you flip it.

@G.Bergeron Yes, I remember this from high school, but they are two energies...

The potential energy is reduced because the water is lower, but it's kinetic energy increases exactly as much, until something else eats up the kinetic energy

@nbro Yeah well ''everything is energy'' in a sense

That's E = mc^2

except light

@nbro no, including light

@G.Bergeron Does it mean that photons have mass?

...when it's trapped. If you put photons in a cavity, the whole will gain mass

@nbro No

That's the peculiarity of special relativity

No, they have momentum. The full formula is $E = \sqrt{mc^2 + pc}$

what do you mean by cavity?

You can't be in the rest frame of a photon because it doesn't exist

@nbro Two mirrors facing each other

So even at $m=0$, stuff that has momentum has energy.

Ok so to make my statement more precise, that $E = mc^2$ is in the rest frame of the mass, which does not exist for a photon.

@nbro And if you absorb photons, you gain mass, too.

@G.Bergeron Energy is a coordinate system?! :D

@nbro ?

What do you mean?

@G.Bergeron You said that "$E = mc^2$ is the rest frame of the mass"

You're missing an "in" there, read again :P

sorry, my bad

it's a sign I should go to sleep

:D

@ACuriousMind How much sleep deprivation is too much?

What about fasting?

@ACuriousMind Isn't that $E=\sqrt{m^2 c^{4}+ p^{2}c^2}$?

@JaimeGallego lol, you're right, I accidentally...took the root twice? Dunno what happened there

@BernardoMeurer Any deprivation is too much

Just go to sleep if you're tired.

I can't

I'm breaking a record

Also my bed is a mess

and I don't want to clean it

It's been like that for the past couple days

@G.Bergeron but mathematically the energy associated with a photon must be 0, in case it's not in a cavity (which are two mirrors facing each, for whatever it helps)

@BernardoMeurer Just collapse on the floor :P

@ACuriousMind It's super dirty

I haven't cleaned in weeks

smbc-comics.com/index.php?db=comics&id=731

I haven't done anything in weeks in fact

@nbro No, the energy of a photon is $pc$, where $p$ it its momentum $p = \hbar/\lambda$, where $\lambda$ is the wavelength.

so it means that the equation $E = mc^2$ does not really hold for light (at least not in all cases), indeed it would somehow be a "circular" equation, since c is used in the same...

@nbro No, as I said, the full equation for stuff that is moving is $E = \sqrt{m^2c^4 + p^2 c^2}$. It reduces to $E=mc^2$ for stuff with zero momentum and $E=pc$ for stuff with zero mass.

I see

interesting

I never heard about that equation (before)

@ACuriousMind What if "stuff" is not moving at all (i.e. not even linearly)?

I'm not sure what you mean, if it's not moving, then $p=0$, so $E=mc^2$.

@ACuriousMind My bad for not looking up the definition of momentum

thanks a lot, it's been a pleasure to talk with you!

talk to you another day ;)

See ya

Hello all

Question:

@ACuriousMind just another question. momentum is defined as m*v, so when you said "$E=mc^2$ for stuff with zero momentum", then you also said for stuff with zero mass, which would mean that $E = 0$...

@nbro Ah, no, that definition of momentum doesn't work for light (obviously :P)

If I have a monochromatic plane wave incident on a conducting surface at some angle $\theta$ and I need to find the radiation pressure, how does the conducting surface affect the scenario? If I use the equation for radiation pressure, it's $P=\frac{1}{A} \frac{\Delta p}{\Delta t}=\frac{1}{A} \frac{\langle g \rangle Ac \Delta t}{\Delta t}=\langle g \rangle c = \frac{1}{2} \epsilon_0 E_0^2$

@nbro This is a sad commentary on the state of pop-sci relativity discussions.

That relationship can also be written $m^2c^4 = E^2 - (pc)^2$ in which form it is clearly the squared norm of a energy-momentum four-vector. And those things are foundational to geometric understandings of relativity.

And relativity (even the special theory) is best understood in geometric term.

@nbro There are two ways to resolve this: Classically, fields can carry energy and momentum, and the electromagnetic field can do so, too. A "field" does not have "mass", but it does have momentum and energy, and since light is an electromagnetic wave classically, it can have momentum. To understand how one actually computes that momentum we'd have to do field theory

Quantumly, the photon has a momentum associated to its wavelength, i.e. $p = h / \lambda$, which you actually derive from $E=pc$ after noting (e.g. through the photoelectric effect) that $E=\hbar\omega$, where $\omega$ is the frequency of the light and $\lambda$ the wavelength.

@dmckee mm, I've heard about the uses of tensors in special relativity

How does the conducting surface matter at all in this situation?

@ACuriousMind A lot of interesting concepts!

Yes, physics is much richer than the concepts of point particle mechanics :)

No doubt!

@ACuriousMind Can you really follow that advice yourself?

@ACuriousMind still up?

@G.Bergeron Yep - my sleep cycle is just messed up ;) About to go to bed, though

@BernardoMeurer Didn't you need to finish an assignment on an island?

@ACuriousMind What about having work to do?

I'm usually disciplined enough to not have to stay up solely to finish some work

I did it a few times, but I don't work well at all when I'm tired, it's better if I go to sleep and get up a little earlier instead

@ACuriousMind You're good. I know I will probably have around 12-18 hours of sleep between tomorrow and next wednesday... to be arranged as preferred.

@ACuriousMind a little ironic that after all this math I'm back to GR

@ACuriousMind I used to prepare finals the day before in the night, having only 4-5 hours of sleep, and chain 4-5 days like that in a row. It's bad, it's really bad, but it's feasible.

:D

@loltospoon The wave will be reflected, and only the transverse part of the momentum will be transferred (twice the transverse component of the incident wave)

@0celouvsky Heh, well, history repeats itself ;)

Anyway, I'm off, good night/day everyone

me too, good night

Bye

Ughhh wait

aw

The wave will be reflected because the $E$ field cannot penetrate into the conductor, so does that necessarily imply that the magnetic field does not penetrate either? The $E$ and $B$ fields can't split up?

@G.Bergeron I did, yeah

@vzn read your blog. The analogy with solid mechanics caught me by surprise.

@vzn looking around on your blog

@Cows :)

@Cows re solid mechanics analogy with spacetime, and the idea of gravity as an emergent property, its getting major attn lately after promotion by Verlinde. lots of great links on that, planning to blog on that sooner or later.

@Secret lol too many adjectives, check, sometimes happens after editing posts too long living in a solipsistic blog/ cyber world. and how many adjectives have you used in here to describe your dreams over the years? :P ... oh and dont know why everyone seems to be so terrified of dailymail, lol o_O

...

Did the earth move? Einstein does a Night Manager – and exposes the gravity of his depravity: Physicist has a very intimate embrace with his secretary in new TV series Genius / dailymail

@BernardoMeurer interesting discussion re P vs NP/ halting problem some of my fave topics. my feeling is that deep learning is actually "semieffective" against undecidable problems. vzn1.wordpress.com/2016/01/22/…

wow! 't Hooft is the MAN!!

wow, I feel dirty. Been thinking of Moduli space all wrong $M_{k,n}$ for physics stuff. Ok . . fixing this

anyways should clean up within 2 days

for instance dim M{1,2} is 8 with x, rho , g(using paper conv)

yay!!

@loltospoon The B field is coupled to the E field. It exists in a wave because of the E field. So no, the E and B field can't separate in a wave propagating in vacuum. Now as to why there is a reflection on an (ideal) conductor, this is because the free charge will cancel any fields inside the conductor. Then, one way of seeing how the wave is reflected is by considering that those charges will emit, in turn, the reflected wave.

@loltospoon The proper way to deal with that, though, would be to find the transverse and parallel boundary conditions on the conductor and then separate the incoming field into a transverse and parallel components to be able to use those boundary conditions to match the incoming and reflected waves.

This should be covered in your favorite classical electromagnetic textbook.

@G.Bergeron was I right about the equation though?

@vzn Deep learning is isomorphic to a Turing machine, so no gain to be realized with respect to undecidability. It is important to mention that undecidability is a mathematical theorem and not just a pragmatic result, with far-reaching consequences

It seems that the only thing I need to find is $E_0$...

what is g?

And if I recall, this seems to be the case for the absorption of transverse waves

@G.Bergeron g is the momentum density stored in the fields

the group

Not an exact analogy, but a ball that rebound transversly to a plane transfers twice the momentum as if it sticks to the plane

@Cows :p

@loltospoon And so does not count the re-emitted wave

@loltospoon Also, this equation does not count the incidence angle...

There should be a dot product in your formula to take that into account

@G.Bergeron $\langle \vec{g} \rangle = \frac{1}{2c} \epsilon_0 E_0^2 \hat z$

@G.Bergeron Ohhh yes, I misread this part of my book (Introduction to Electrodynamics by Griffiths). Yea, this equation is for normal incidence on a perfect absorber.

@loltospoon This doted with the normal of the plane would work if not re-emission. Since you said its a conductor and have not given a conductivity, I assume it is an ideal conductor. Thus, there will be total reflection

@G.Bergeron yes, I agree haha, I'll look for the correct equation.... ::facepalm::

@Cows why?

@loltospoon You should look into being able to derive it

@G.Bergeron yes commander!!

I understand the constraints, but it should never be an equation hunting exercise

Don't think I / (we?) remember all those equations by hearth, it's often a mix of dimensional analysis, knowing key elements and the basic conservation laws / symmetry principles.

@G.Bergeron I meant group element

@Cows I know, but I was talking about the g of @loltospoon

oh lol

but I am curious

What paper are you talking about?

@Cows the thing with t'Hooft...

let me get you the arxiv number one sec

@Cows Are you working with moduli spaces in string theory?

actually the 't hooft thing was from a lecture the $\sigma_{n,m}$

I am thinking about yang mills

instantons

ah ok

yeah

cool

I barely just internalized what collective coordinates and moduli spaces are

Did you have some abstract algebra courses?

I mostly just read up on this every other year

and attended some lectures (sat in)

need to go

ok well i enjoyed the convo

aka conversation

:P

@G.Bergeron I would assume that $\pi^{-1} (0)$ and $\pi^{-1}(0^*)$ would be different fibers

"For me, a basic example of the beauty of this function-theoretic approach is the definition of a vector field as a derivation $D:C^\infty(M) \to C^\infty(M)$. The proof that such a derivation defines a vector field hinges upon the fact that $Df$ near a point p only depends on $f$ near the point $p$. To prove this fact you use the fineness of your sheaf $OX$, i.e. the existence of partitions of unity. "

Hm

That could be an issue with the problems I'm having

I'm assuming that the integral is well defined

Since I require it for the pseudometric

Howdy

Howdy doody

hey

did any of you do the science march? I was at home

same

Integrating forms on a manifold indeed depends on the partition of unity

@Slereah what?

Would they not

what is $0$ vs. $0^*$?

Two different zeros for the line with two origins

oh

this skyrim guide I wrote is pretty comprehensive

So I think the issue in Hicks is that he assumes that you can define integrals on non-Hausdorff manifolds

my current character is a lot weaker than the one in guide

Dunno how that's happening

crappy RNG loot I guess

I'm supposed to be level 11 in two missions

I don't think that will happen

eh, grind a little

it's not that hard

I don't think I needed to grind when I wrote the guide

this is actually pretty cringely written

go find some skeletons and grind their bones

I can't post here because I would get b&

Do you try to sound cool with a lot of 2012 lingo

Shiggy diggy

I will send you a thing on skype

I'm off

cheers

Should I learn php

Well

If you need a job badly

It is useful

What's that mean?

There are a lot of people hiring for php skills

is it worth learning for fun?