$F=0$

nope, I still see dollar signs lol

can you install chrome and try it with chrome?

I have it working on chrome

I would like to get it to work on here heh

nice!

let me try restarting firefox

$F$

nope -.-

@Cows Depends on what you're talking about, it's a rather vague term

@ACuriousMind ok let me try to clarify

hmmm...

@0celo7 Perhaps, but I think I just like games where global strategy plays a role as well as individual player skill

so given some equation that describes a change of some field or some properties over time, or to be specific, given some equation of motion, there exist a Hamiltonian or lagrangian whose euler lagrange equations give that equation of motion. I think of a duality as some means of starting with different hamiltonials or lagrangians and arriving at the same EOM . While typing this I just realized I probably don't understand what duality is hehe

we could just play BL2 : P

like starcraft II?

I suggested that

Ik

But I’m not paying for another full price game

I declined at first but hey, havent played in aaaaaaaages

SCII just went free to play

Heya

@ACuriousMind do you need the DLC to play online with people who use DLC characters or does gearbox actually have sense

I’m not buying an EA game, and I doubt Joseph “Stalin” ACM will either.

I like Dota because it has a lot of subtle strategical aspects that can override a clear skill advantage, but still a team that's more skilled than their opponents will just stomp them if they're not stupid

@0celo7 down the EA

Let disney kill em

@ACuriousMind I played the shittiest game of Civ in my life yesterday

I just got gangbanged by barbarians

It was weird

@BernardoMeurer not appropriate

@Cows I don't think people call theories with different Lagrangians that lead to the same equations of motion "dual"

They just kept on coming nonstop

I mean, that is a type of equivalence of theories, but it's not what duality is used for

phrasing bro

phrasing

@ACuriousMind i think guage symmetry might be a word they use if you can go from one to another with a transformation? no?

I think duality is more commonly used for theories that look very different on their surface, but whose particle spectrum and correlation functions can nevertheless be mapped to each other bijectively

can't you just trivially add any constant term to the lagrangian and get the same EOM

@enumaris yes

@Cows Generally, a gauge symmetry will not change the action/Lagrangian.

ohai

@ACuriousMind that is true too

That's not duality, it's just gauge symmetry

oh yeah, gauge symmetries too...

lol

I thought you guys were talking about dual vector spaces

@ACuriousMind certainly,

like $\lange \Psi |$ and $|\Psi\rangle$

noooooooooo, it doesn't render for me :(

sad

Dirac notation is probably the least pedagogical thing ever

@enumaris I actually played SC II for quite a while when it came out, was a pretty good Protoss

what league were u in?

Diamond

I never made it out of bronze LOL

Dirac notation is love

$\langle$?

Dirac notation is life

I think you wrote it wrong enum

@ACuriousMind did you ever play LoL?

Is the DOTA community as cancerous? also, why not DOTA2?

I did write it wrong but it didn't render anything for me

mathjax is not working for me...

:c

@Phase No, I've been a Dota player since way back when it was just a WC3 mod

@ACuriousMind so the key is at the level of the particle spectrum one can then identify that they are dual, thus is it that there is a priori no way of finding this out? untill you compute the spectrum and compare ?

Any runescape players? ;)

@ACuriousMind and didnt want to transition to Dota2?

Oh, I did. When I say Dota I mean Dota2 nowadays

And sure, there are some pretty toxic people in there, but if you are nice and consistently report the toxic people most of your games will be fine

o i see

Nice

LoL was beyond toxic

I loved the game but I had to stop playing because the community just took out all the fun the mechanics introduced

I had an obnoxious roommate who played LoL,

i have philosophical issues with it

Has an ult literally named Wukong

Why does every Moba have a monkey king

@Phase Because he's a very cool Chinese mythology figure

mankey nandayo

Dota also has an item called Monkey King Bar, when you purchase it on Monkey King he says: "Why did I pay for this?"

@ACuriousMind so what i get is that, once one compute the spectrum if there is a pattern that hods to go from each element in the spectrum to the other, then we have a duality?

@Cows Yes, pretty much

so this happens at the level of the spectrum

omg yay

Damn Dragon knight's thumbnail looks cool

Most of the Dota2 character thumbnails make them look really edgy tho

It also can happen at the level of the fields, though, e.g. S-duality/Olive-Montonen duality

@Phase I love playing Dk, though he falls off pretty hard late game

[DK ](youtube.com/watch?v=dldJv9yZEp8)

@ACuriousMind so there are two kinds of dualities then? classified based on where they are identified?

The link above is the completely genuine DK rap

@ACuriousMind at the level of spectra or fields?

@0celo7 BL2 then? If so I'll pick up ye olde Max Payne 3

the only one I haven't completed :P quite a fun franchise

@Phase I prefer the original Feel Good Inc.

@Cows Eh, I'm reluctant to say that. Sometimes it's easier to identify the map at the level of spectra, sometimes at the level of fields, but it always leads to the same reuslt: The theories predict the same spectra and correlation functions

man I really need Andrew Ng to finish his sequential models course on coursera....

His courses teach me the most by far of any course in Machine learning I've tried so far...

Jesus christ what has he done

Sadly there’s no J duality in the future

@ACuriousMind very cool, very cool, looking over the wiki page now

@ACuriousMind I was hoping for a JU duality in the future but you nixed that

Juan duality?

@ACuriousMind this is great stuff, so how do we know if an identified duality means more , and is not just a fluke?

@ACuriousMind this is magic I swear

@Cows What do you mean by "fluke"? Any duality hints at relations between the two theories that are worth investigating

@ACuriousMind do you know what I’m talking about

@0celo7 Nope

JU duality?

Ahhhhhh

Got it :)

@ACuriousMind this is true, so once a duality is identified two things happen? one builds the associated map between the two theories and hard problems between both are traded, then once investigates the meaning of the duality

?

Yeah

@ACuriousMind nice

@0celo7 dont make me burst your door down

Some questions are usually easier to solve in one of the theories, while others are more obvious in the dual theory

@0celo7 To BL2 or not to BL2, a 5.99 game hangs in the balance

@ACuriousMind hi there, is it a bad time for 1-2 questions? :)

@user929304 Nope, ask away

@ACuriousMind so in the case of Montonen-Olive duality, the outcome is the unification of electric and magnetic field. So how likely is this the case for guage /gravity ?

@Phase wait 6 bucks?

I’m out and about, I can’t make that decision now

Is today the last day?

no 6 bucks is a completely unrelated game

you dont own BL2?

Why would I?

Wait

I thought you played it with ACM/

?

What is BL2

anyway its 5 quid so it probably is around 6 bucks

Ohhhh

Borderlands 2..

Yeah I own it

Smh.....

@ACuriousMind awesome! When we say a system s in a definite state, we can measure it without any uncertainty, but when describing the state of a system, we first choose a basis, I can choose one where my system appears to be in a superposition state, and one where it is in an eigenstate/definite. So then, how do we objectively say whether a system is in a definite state or not?

ill keep like 15 leftover just in case, sale ends on 28th btw @0celo7

so you shouldn't miss it

@user929304 We can't. A system is in a "definite state" or not only with respect to an observables, and in that case it means the system is in an eigenstate of that observable.

@Cows I'm afraid I don't understand the question

can u have a system where all the observables commute

@enumaris Yes, but that's a pretty boring system :P

@ACuriousMind let me try again, I made some technical misgivings the previous time around

It has no angular momenta, no position and momentum :P

but then you can define a definite state unambiguously

mmm

@enumaris Ah, well, we call that "classical mechanics" ;)

@ACuriousMind so let me try to parse Montonen-Olive duality at a superficial level

here goes

There's a Hilbert space formulation of classical mechanics where everything commutes, it's called Koopman-von Neumann formulation.

Coopman huh... ;p

It's not very useful except for realizing that the crucial feature of quantum mechanics is really that observables don't commute

@ACuriousMind right, maybe an example, a spin 1/2 system: bob prepared prepares his qubit along the positive direction of S_z, but if Alice doesn't know that, she may choose to describe the system in terms of S_x eigenvectors, but then as a result, she sees a superposition while bob had set the system in a definite one

Bob's system was only definite with respect to his z-axis

if Bob makes measurements on his system along the x or y-axis he will find it to be not in a definite state either

@user929304 Maybe there needs to be a clarification here: you don't "see" a system unless you decide to measure it, and if you make a (strong) measurement, then the outcome will alwas be an eigenstate of the observables you decided to measure

@0celo7 or if you're bored of BL2, another co-op game that springs to mind is SR3/4 but you may have played it to death like I did

In quantum mechanics, there is no "seeing" without measuring

except when you use your mind's eye

through the power of love

dun dun dunnnnn

@ACuriousMind Come strong measure me big boii

@BernardoMeurer Ew.

No, really, I don't know my height and I need it measured

@ACuriousMind so whether the spin state of the system in that example is actually in a definite state or not, is independent of the basis, right?

@CooperCape Heh

@user929304 Yes, although different interpretations may disagree on what "actually" means

@ACuriousMind It was good bant, I promise.

@ACuriousMind sure :), I just mean before measurement

In some interpretations, the quantum state only reflects the knowledge of the observer, while in others, it is an objective feature of reality

(buzzwords: $\psi$-epistemic vs. $\psi$-ontic)

@ACuriousMind ok there is quite a bit of stringyness to this, but essentially this is a case of S duality. So i can't really say what I wanted about it. However, what i wanted to ask is that in this case, if we were not sure that the electric field and magnetic field were in fact unified as one, could investigating a duality like this result

in such a discovery directly. If so, is the same line of reasoning suggestive of a sort of unification between gravity( a type of gravity) and say yang mills(a type of yang mills)

@ACuriousMind is there even in principle a way to find out whether the system is in a def state without measuring it?

@CooperCape God, you're so British :)

@ACuriousMind Can I come live with you and you teach me QM

@ACuriousMind I messaged my gf "It's just a highschool report" today. I was so embarassed at my American terminology (jk...) ;p

@BernardoMeurer Yes, but you'll have to live in the "library", which is a 1.5x1.5 room without windows and a lot of books on the walls

@CooperCape Showing your true ColOrs

@ACuriousMind Is that meter or feet?

@BernardoMeurer Meter

or kilometer

h bar is americanning me

Oh, EZ GAME

Aloooooooooooominuum

Whoa ACM has his own book closet

I've slept in worse spaces

man I'm jealous

@Phase Not my own entirely, it's a shared flat and at every party things happen in that library that shouldn't leave the room...

uhhhhhhhhhhh

@BernardoMeurer maybe bring a plastic sheet to lay on the floor before you sleep there

^seconded

@ACuriousMind Woah, it's a sex hole!

Nice!

Um.

Let's not pursue this conversation further :)

There's a hole in the wall but... To whose room?

Tip: see if there's signs of compactification on the other side

ok I regret that joke

@ACuriousMind I had another question regarding inherent uncertainty in measuring non commuting observables of a system: if I have n exact copies of my system, and the two non commuting obs are A and B, on half of the copies I measure the A observable and record, on the other untouched half I measure the B observable and record. Why do I still end up with a non-zero uncertainty?

@ACuriousMind i guess what i've been try to ask without by too direct, is what a plausible end goal of say the most popular duality right now is?

@user929304 see the no-cloning theorem for why you can't set up this experiment

@user929304 Why wouldn't you? By the axioms of QM, the result of measurements is random, after all

@ACuriousMind Has some pretty cute friends tbh

@Cows I can't really answer that. Dualites are neat because they allow us to approach certain problems from "two sides" at once but I wouldn't say there's a single unifying goal to them

ha maybe gayyyy

@ACuriousMind I never measure the two obs on the same copy,

@user929304 I know.

@enumaris assume the copies are given to u, hypothetically, u don't have to copy the state urself

@ACuriousMind certainly

But the probabilistic nature of QM means that even if you have two identical copies of a system, you cannot be certain that the result of a measurement on them will be the same

@Phase I don't think he means my male friends, but, once again, let's not pursue this avenue of conversation further :P

hypothetically if the person who gives the copies to me can violate the no-clone theorem, I'd hypothetically be very interested in meeting this person

Self-promotion:

@ACuriousMind If Bernardo went to 'live with you' would he have to live in one of the lockers next to the supercomputers in Skynet?

@Phase In the medium to long term, he'd of course have to agree to be uploaded into the cloud.

@Phase They'd probably just get rid of the supercomputer and use ACM as the replacement

@ACuriousMind in time all will be cloud

Except gaming because that just doesn't work and never has

@Mithrandir24601 he is the supercomputer

@Phase exactly

In a way we're all supercomputers

Incredibly poorly optimised supercomputers

@ACuriousMind I'm terrible at expressing this, basically my question arose after reading the second paragraph of page 73, of these lecture notes www3.imperial.ac.uk/pls/portallive/docs/1/613904.PDF

and ACM will deliver us to the next life, via optimisation of our puny human forms

Suck us into his ultimate universe

Maybe it's Stranger Things situation

Is ACM the 'upside down'...

@user929304 Okay, I think that paragraph is actually pretty clear. Can you be more specific what troubles you about it?

@ACuriousMind trying to understand why even in that case \Delta A \Delta B still greater than 0

@CooperCape haven't watched it : p

@user929304 Can you express in your own words what $\Delta A$ means?

There's a fundamental difference between Quantum and Classical mechanics in how they treat identical particles though. Identical particles in quantum are indistinguishable from each other, in classical mechanics, they are still distinguishable when we are counting particles.

@Phase Think you pinged the wrong person

I hate tagging the wrong person

yeah

Awww stranger things is great

@Phase I dunno... Are there quantum effects going on in our brains? - the size of e.g. neurons suggests the answer is quite possibly

@ACuriousMind the standard deviation obtained on the average value of A

@user929304 Yes, but what does that mean?

That is, if I do a measurement, how do I obtain the standard deviation?

I feel that your question dissolves once you answer that

All I remember reading about quantum effects in popsci is that electrons prank transistors hard.

@Mithrandir24601 yeah, that's Penrose's thought

@ACuriousMind after many measurements, I will get a distribution then I can get the variance, and std var from it

I'll say this for it: It proposes that quantum mechanics influences the brain, not that the brain influences quantum mechanics. So that hypothesis doesn't trigger my "gtfo" reaction.

'std var' heh. I'm such a youth...

@user929304 It's crucial to note that "many measurements" in that statement already means "many measurements on identically prepared(="cloned") states". You do not perform these measurements sequentially.

@ACuriousMind he says: "the uncertainties in the measurements of the two observables are not caused by a perturbation of the quantum mechanical system by the measurement as we are measuring the two observables on different systems which are in the same state. "

@ACuriousMind indeed

@user929304 Ah, I think you're misinterpreting what he means by that: He means that these uncertainties will be there no matter how good your measurement apparatus is.

Nothing more and nothing less.

@Semiclassical Well, yeah.. As in (explaining what the question "Are there quantum effects going on in our brains?" is actually asking in more detail), if it is possible to somehow explain the details of how the brain works, would it require quantum physics?