Hey how does one express the projection operator in matrix or tensor notation?

In other words how does on use it for calculations?

They are talking about relative velocity and $P(u)$ is the projection operator

$|u\rangle\langle u|$

$\mathbf{u}\otimes \mathbf{u}^T$

depending on the notation you are using

thanks

@ACuriousMind Sup, how's it going

@JingleBells fine, you?

@ACuriousMind fine too, you?

let's make a joke where we say "fine, you?" for 2 hours :D

@ACuriousMind Do you have anything cool in mind you wanna share or discuss?

usually when I want to share something here I just post it :P

@ACuriousMind how did you decide to be a metalhead?

assimilation to my peer group, I think :P

@ACuriousMind you found nerds that are metalheads?

I fell in with a bunch of nerds at school that were into metal, and so I got to hear a lot of metal because they liked it and at some point I started liking it, too

Mm nice

I was the only nerd in my class

it was lonely...

but I made it out stronger

My favorite genre is funk

I just like how it sounds

James Brown funk

oh and Jeffery Bezos genre

well, you're perhaps using a narrower definition of "nerd" than I am :P I think the only other things that most people in that group really shared was that we were into video games

@ACuriousMind Oh I need friends to ponder existential questions with, yk and discuss interesting ideas, people that I can learn from, etc.

People I share interests with

There was no one close enough to that in my class, but I still hung around a few people but just because I didn't want to be alone

No real deep connection tho, just memes and talking about school

In my experience the "let's ponder existential questions" phase usually comes around somewhere around 3am and after a few empty bottles :P

@ACuriousMind yeah I used that as an example but you get what I mean, shared interests and people I can learn from

At least I didn't get bullied or anything

@ACuriousMind How did get into socialism? (hopefully that's an okay question to ask)

I don't think I would describe myself as being "into socialism" :P

Aight

anyway, I don't think I arrived at my beliefs today through any particular moment, they just grew over years of listening to what other people had to say

Yeah makes sense

And 16-year-old me who hadn't yet seen anything of the world, really, was definitely a lot more neoliberal than me today. The more people I got to know, the more I realized that the simple idea of what humans are like I carried in my head didn't really match what was out there

@ACuriousMind That's interesting, I'm definitely a free marketer and I'm interested in what you've seen that changed your mind

I don't run away from ideas that oppose my beliefs and views

@ACuriousMind where u went :P

@ACuriousMind for some reason I thought u were neo liberal ... What is ur political ideal?

@MoreAnonymous CuriousMindism

neo-mindism

im starting a political ideal tomorrow

@JingleBells It's not the market I stopped believing in, it's the meritocratic idea that people have to "deserve" benefits (money, healthcare, etc.) that drives a lot of opposition to public goods. I met a lot of people who'd have really needed help they didn't get and I just stood there coasting along in life, and I couldn't figure out what they had done "wrong" to deserve to have it worse than me

@MoreAnonymous somewhere on the nebulous left, but I don't like any of the specific labels well enough to identify with it :P

in site news: If you're seeing messed up favicons, someone probably messed up the sprite sheet

@ACuriousMind ""and I couldn't figure out what they had done "wrong" to deserve to have it worse than me"". It means that you are not a great observer :)

@ACuriousMind I can understand that point of view, some people are born dumber, others are less lucky, some have it easier, others harder, and so on. People aren't born equal and people aren't capable of equal stuff. So facing those facts we have to figure out what's the best way to organize society so everyone is better off.

@Abbas I would like to think I'm just being an empiricist: If I just took counter-evidence as proof I didn't look hard enough to justify my belief, then I would exclude any possibility of my belief ever being wrong

@Abbas ACM if that didn't convince you that you're not a great observer I don't know what will XDDD

@ACuriousMind Do you think giving resource control to people who haven't proven to be able to use it for the benefit of society is a good idea?

@JingleBells What do you mean by "resource control", and how would one prove to do something "for the benefit of society"?

@ACuriousMind resource control is money and you prove to do something for the benefit of society by using that money to make more money (generally)

yeah, that's the part I disagree with

there's lot of unambiguous goods for society that don't make a lot of money for the people doing it

(but that do make a lot of money for the corporations employing the people who do it, e.g. eldercare, cleaning services, etc.)

or, the other way around: tobacco companies made a lot of money by lying to people for decades about the dangers of smoking. Does that prove that lying to people about getting lung cancer was a benefit for society by your logic?

@ACuriousMind I don't exactly understand your point

@JingleBells I'm saying that the equivalence between "making money" and "doing something for the benefit of society" that you claim exists isn't obvious to me :P

@ACuriousMind Agreed

I make money but I don't think I do good for society

@MoreAnonymous The people who gave you the money probably do, unless you're selling drugs or something

I make some dude richer but ... did I really create value? meh ...

@JingleBells well consider Uber ... One way Uber has made money is by being dicks to its workforce

@ACuriousMind Well how would you measure the benefit? If something is beneficial to me (a toothbrush), I buy it with money, so generally whoever has more money has created more benefits, no?

They don't pay for car damages, etc and taxi drivers hate them ...

Its a similar story here :/

@JingleBells That's a very naive view of how the capitalist economy works

@ACuriousMind I'm happy to consider any opposing views, beliefs, and data to mine

E.g. someone has inherited a house and rents it out for a lot of money. They have a lot of money, but what benefit for society have they actually created?

or, again, my tobacco company example - they'd have made a lot less money if they'd been honest

but the only thing their dishonesty has arguably done is killed people, so how does the profit they made reflect a benefit?

@ACuriousMind I agree with that point, you shouldn't get to have resource control just because your parents or grandparents did something beneficial. But on the other hand, maybe your parents and grandparents did something beneficial so you can be better off, kind of like an incentive?

@ACuriousMind I agree with that too, stuff like smoking, and tobacco, are generally grey areas and should be disincentivized thru high taxation (maybe some government regulation)

@JingleBells An incentive for what? An incentive to be born as the child of wealthy people?

@ACuriousMind An incentive for the wealthy people to become wealthy, so their child can be spoiled

@JingleBells but so what is your basis for believing that these are outliers? what if most large wealth is like this, i.e. not based in a directly created benefit?

@ACuriousMind I highly doubt the majority concentration of resource control is in tobacco, drugs, etc.

And tbf tobacco and some drugs do help and create benefits to some people

no, but why should these problems be limited to these examples?

@ACuriousMind Because in reality they are?

I think money shall be equally distributed . There will be more entropy :) and hence a greater equilibrium:)

@JingleBells Okay, three more: 1. Health- and elder- caregivers in my country are notoriously overworked, but the corporations that run the care facilities rake in a lot of profit. What is the societal benefit here compared to making less profit but having less stressed workers? 2. What societal benefit do day traders generate? 3. If money represents societal benefit, why do salaries often correlate with amount of qualification needed and scarcity of applicants?

@ACuriousMind Can we take it one by one cuz my brain is pretty tired (about to go to sleep in 2 hours)? There are a lot of buzzwords here like what does "notoriously overworked" mean, what does "profit" mean, what does "societal benefit" mean, etc. Can we pick one thing to debate on and stick to it, like take it thing by thing so I don't debate like 3 things simultaneously XD?

@JingleBells I'm just sticking to the single claim you brought up: You said that someone having a lot of money is a sign that they do a lot to benefit society

so asking me to define what "societal benefit" means is a bit strange :P

everything I've said after that is intended as a counterexample to that claim: Either cases where people doing something I clearly view as a benefit to society but not getting a lot of money, or cases where people have a lot of money without a lot of apparent benefit

@ACuriousMind In the caregivers example, what made you think that laboring is more beneficial than what the corporation does?

@JingleBells The corporation is not a person; the profit goes either to its owners or shareholders depending on the model

@ACuriousMind Yes

Howdy folks, been a while

I had a bit of gravitational lensing code I was trying to understand but I actually never got to do more than special relativity so I was wondering if someone could help me break down what's going on and a bit of relevant reading (especially to help me figure out if this is an approximation)

def lensImage(img, src, lens, xs, ys):
    """Useage: lensImage(img,src,lens,xs,ys)
    lens a 2d numpy array in place using a given source distance src and
    black hole coordinate (xs,ys).
  Parameters
  ----------
  img : 2d array of floats.
    Image data from cv2 capture
  src : float
    Distance to source (pixels)
  lens : float
    GR lens parameters
  xs,ys : int
    pixel coordinates of black hold location
  Returns
  ----------
  None"""
    # edits image in place
    if (lens >= src):

no codeblock support =(

there is, but not with that markup

there :)

hmm, youre right mathjax hadsomething right

I don't really know a lot about gravitational lensing but I find it somewhat suspicious I don't see the mass of the lensing object anywhere in that code

"might put a mass term in here" is a very suspicious comment :P

I think this code doesn't actually simulate any physics

the visual effect seems reasonably approximate but it definitely doesnt scream physical to me either

I'm also confused about the comments claiming the function returns nothing and edits the image in place, and then it ends with return imageCopy :P

not that comments lying is unusual, it's still irritating

@ACuriousMind oh that was actually my only edit to actually make their code a little easier to mess around with

just swapped overwriting img with imagecopy to return the copy

i expect that's technically done to allow for it to be better performance on video