2:08 AM
what does the following statement mean?
"while the charged fermions are in chiral representations of the full gauge group $SU(3)_C\times SU(2)_L\times U(1)_Y$ , they are in vector-like representations of the $SU(3)_C \times U(1)_{EM}$ group"

2 hours later…
3:45 AM
Good Morning Everyone!
Is it just me or Sounds of Silence sounds gloomy and depressing to everyone?

2 hours later…
5:24 AM
for sure it is depressing

@RewCie the Simon & Garfunkel song?

1 hour later…
6:41 AM
I like it

7:06 AM
As a prog rock/metal fan I shouldn't like Simon & Garfunkel, but I have to confess that my Best of S&G album gets played a lot.

7:52 AM
I saw somewhere that Dynamical symmetry is defined as something which is not a geometrical symmetry..Why do we say that if dynamics is itself so geometrical? What do they exactly mean by the fact that dynamical symmetries aren't geometrical?
For example, just look at the Runge Lenz vector which is a dynamical(non-geometrical) constant of motion...It seems so geometrical to me..It gives you the fact that precession can't occur in the Kepler problem (cz it points in the semi major axis direction), then it gives you an insightful derivation of the fact that momentum vector's tip draws out a circle in the px-py plane...Aren't these "geometrical" enough?
And the celestial mechanics books even call it the eccentricity vector(and for good reasons)! Isn't eccentricity geometrical enough?

@ManasDogra it's not "geometrical" because you can't go to an action-angle coordinate for it
once you've gone to the action-angle coordinates for the "geometric" SO(3) of the system, you have no coordinates left, but the LRL symmetry is still there
@Bohemianrelativist "chiral" means the left-handed part of the fermion transforms in a different representation than the right-handed part

8:34 AM
@ACuriousMind So this seems to be a more correct definition for geometrical constants of motion?
Is there a rigorous definition?

not really; physically there really isn't much of a difference - a symmetry is a symmetry

Thanks...I have another question...I came across a heuristic derivation of the vector triple product rule of vectors(the BAC-CAB one), and it proceeded in the following manner--
The triple product a cross (b cross c) lies in the plane of b and c...so it must be a linear combo of b and c.The LHS is linear in a,b and c so it must be so in RHS...so the coefficients must be a dot c plus a dot b respectively apart from some multipicative constants which are independent of a, b and c. Interchanging b and c shows that the constants must be equal apart from a sign and putting a special case(e.g. principal cartesian basis) reveals the constant to be unity.
My problem is in the line "so the coefficients must be a dot c plus a dot b"---Why can't it be other things such as modulus of a cross c or something like that?

For reference, See from 23:38 if I am not clear enough in the above para.

@ManasDogra the modulus would not be linear in c

8:50 AM
@ACuriousMind Why so? I am just putting modulus of a cross c instead of a dot c infront of the b vector. It's still linear in a, b and c

@ManasDogra the modulus of a cross product with $c$ and $-c$ is the same, i.e. it is not linear w.r.t. multiplication by negative numbers

You are saying |(a cross c)|b is not linear in a,b
And c?
Oh i get it now..the modulus operation is itself not linear! How could i forget that!!!

3 hours later…
11:48 AM
2

I know the decomposition of general rank two tensors $X_{ab}$ \begin{align} X_{ab} &= X_{[ab]} + \frac{1}{n}\delta_{ab}\delta^{cd}X_{cd} + \left(X_{(ab)}-\frac{1}{n} \delta_{ab}\delta^{cd}X_{cd}\right) \\ & = X_{[ab]} + X_{(ab)} \end{align} How about the general rank three tensors?

this had been bugging me for quite a while
it's nice to look it up and set it down in a findable way =)

12:33 PM
@ManasDogra that is a brilliant way to get the result for $\mathbf{a} \times (\mathbf{b} \times \mathbf{c})$ but it's worth spending time just learning how to prove it using the expansion for $\varepsilon_{ijk} \varepsilon_{klm}$ because there's a few of these triple product identities with gradients divergences and curls and they can all be dealt with with no thinking if you can manipulate with the $\varepsilon$'s

@bolbteppa I did that standard thing already before. The trick is to use the reduction of two levi civitas to a bunch of kronecker deltas and then we are done!

@ACuriousMind so does "vector-like" mean the left-handed and right-handed part of the fermion transforms in the same representation?

yes

1:15 PM
When people talk about is success hard work or luck, what do they mean by luck? Is it the opportunities that come in your way? Some people get more opportunities, others don't? I wanna have a discussion on this topic, but please think as objectively and unbiased as possible, not based on political views or personal experiences (not sure if complete unbiasness is possible tho)
As an aspiring entrepreneur, it's kinda weird to be told that no matter how much work you put in, in the end someone rolls a dice. It makes you feel helpless and hopeless. I'm trying to dig to the core of the idea and create my own opinion on the topic (which I already have)
It's easy to say - yeah, Jeff Bezos just got lucky, but it seems to me that people say that cuz they don't want to consider the possibility of them being lazy and not acting on opportunities.
My opinion on the topic of success so far is - hard work AND luck are necessary, where luck = opportunities coming your way, and action leads to those opportunities, and the more you persist, the more opportunities you encounter.
It's a bit weird to think about this topic, cuz the world is such a complicated place, with so many factors playing in success. My intuition tells me that even if you're not that lucky, through perseverance in time, opportunities accumulate. If 9/10 startups fail, try 10 times. I'm not sure by how much persistence increases chances, and I doubt anyone knows. You can make simplified experiments with agents, calculate probabilities, but the world is much more complicated than that.
If luck is opportunities coming your way, through action, you should be able to put yourself in environments where opportunities are and expense yourself to "luck".

1:32 PM
@JingleBells You can't have discussions about social affairs without being "political" :P Say you inherit the money you use to start your business from a wealthy relative. Is that "luck", is it "hard work" (brown-nosing the relative, perhaps? :P), is it an "example of systemic inequality"? The fact is just that you inherited a bunch of stuff, what you call that is politics.

If your solution to succeeding at business is "Try it ten times", you may not be there thanks to your hard work
Most people do not have the funds to attempt a start up ten times

@Slereah yes, I'll be there thanks to persistence, something I do have control over
@ACuriousMind I'm not talking about fairness, I'm talking about spawning 10 Elon Musks in USA and confabulating over the results. :P

@JingleBells but whether a specific circumstance is "luck" or systemic is about conceptions of fairness

I don't understand

Saying success is hard work + luck is saying - by way of omission - that there is no systemic component to it. Can't be mad at hard work and a bit of random chance, right?

1:41 PM

But what one could be mad at is circumstances that allow some kinds of people to have much greater chances at having "luck" than others
so any discussion about "luck" in the context of economic success is intrinsically tied to your ideas about social (in)equality

Alright, let me make it easier for you - let's talk about academic success
hopefully that'll remove some of the socialistic bias :P
Imagine you're an academic in a communistic/socialistic country
How much control do you have over your academic success. Is it hard work or luck (or both)?

From the perspective of somebody looking back and saying it it probably means things happened that could not have been predicted and without which they couldn't imagine where they'd be to where they are now

I argue that through action and persistence, you increase your exposure to opportunities, and therefore you "create luck".
@bolbteppa can u translate please (what is "it"?) :P

It means you're going to have to roll the dice no matter what

1:54 PM
That's true for everything in the future

@JingleBells Same thing, really. Academic success chances are highly variable across different socio-economic groups (this varies by country, but a pretty common thing is for example that children of academics are more likely to become academics, too). So if you're the child of two academics and become a PhD, is part of that "luck"? Is it genetics? Does the lower success chance mean people from non-academic backgrounds have to put in more "hard work" or does it mean they don't work "as hard"?
"luck", "systemic inequality", "hard work", "genetics" are all things you could use to explain the raw fact that success chances vary
without data with which you can distinguish these, which of these you choose as explanations is a political statement more than a statement of fact

2:11 PM
and that's not even starting on questions of how much of e.g. your work ethic is a product of your environment vs. a genuine choice you can personally make. If you grow up with a social circle telling you you'll never amount to anything it will certainly have a different effect from being surrounded by people who believe in you - is that part of your notion of "luck"?

@ACuriousMind even with all the possible data, most of the conclusions will depend on politics/ideology (how you frame the problem, interpret the data etc), as you hint at in the next message

yes, definitely - this is why the "soft" sciences are often much harder to get "right", as it's hard to establish what "right" even means :P

@JingleBells btw the fact that you start talking about "removing socialistic bias" when people are just pointing out that it is not possible to discuss this without it being politic already shows that you don't want to discuss this in good faith

Within the efficient market hypothesis, getting rich on the stock market is just a matter of luck and, of course, initial capital.
Haha, that is, of course, only if success is the same as becoming rich

ah, we're on a roll here, that's another can of worms :P
...where does that phrase come from, actually?

2:23 PM
(sorry for disappearing, trying to fix a bug, be back soon)

@ACuriousMind makes sense

Huh, it's a fishing term? Now I wonder how people sealed the worms in these cans in the first place but I'm not sure I actually want to know that

2:40 PM
Hello World of Physiks..
Hello @ACuriousMind I have question.
Law of conservation of Energy : E = T + V
but sometimes we take T = V , it means E is zero. My question is that when we take E is zero???
@ACuriousMind I have read SE article and at quora but no one give me accurate answer. Pls help me out.

@123 Please don't ping me with questions unless you have a reason to believe I might be interested in them
also, what you've written after "My question is" is not a question, at least not one I could understand

@ACuriousMind One of the reasons I come here is to see ACuriousMind saying this everyday in different ways to newcomers xD :p
8

as eternal work goes, it beats rolling a boulder up a hill :P

@ACuriousMind Ooooops.. Today you are in harsh mood.

xD

2:51 PM
I asked question that's why i pinged you.

@123 you said the exact same thing the last time I asked you not to ping me directly with general questions

@123 how is T=V implying E=0

I'd prefer you'd actually listen to my request instead of ignoring it by ascribing it to a "harsh mood"

How do i know you are interested in my question or not unless i asked... :-)
@satan29 In many numericals/problems we take T = V, i supposed it only possible when E = 0

can you give me an example

2:54 PM
@123 I read most of this chat whether I'm pinged or not, if I see something I want to answer, I'll answer. By pinging me directly you a) give other people the impression it's a question specifically for me when it really isn't and b) trigger notifications (sound, SE inbox) that I don't really care about when it's not something I'm interested in. If you have a general physics question, you can just ask it to the room without any pings - if someone can and wants to answer it, they will

@satan29 A 50gm bullet is fired into a 10kg block that is suspended by a long cord so that it can swing as a pendulum. If the block is displaced so that its center of gravity rises by 10cm, what was the speed of bullet?
In this numerical solution we take $\frac{1}{2}mv^2 = mgh$

So that is $E1=E2$
where $E1=T1+V1$, $E2=T2+V2= 0+V2$

@ACuriousMind Ookay.. I pinged you because you and john sir are mostly given answer to questions. But my question is always for everyone.

Rearranging, we get $T1= V2-V1$
when you claim $T=V$ you need to be precise about what they actually are

@satan29 Yes. But how it is not T = V. Let me share you a picture of solution.

3:02 PM
@123 what is T. and what is V.

T is Kinetic Energy and V is Potential Energy.
Pls see the link W.P 3.11

@123 The link also uses conservation of energy, as I explained.
The General expression is $T_{initial}+V_{initial} = T_{final}+V_{final}$
so it rearranges to $T_{initial}-T_{final}= V_{final}-V_{initial}$

@satan29 Ookay.. Thanks for your input..
@satan29 How it become T = V,

in your case, $T_{final}=0$

Pls also see above link i have same numerical i did not understand the solution they shared.

3:09 PM
and if we let $V_{final}-V_{initial}$ to be $V$
then your expression reads $T_{initial}=V$

@satan29 Ookay... Hmmm...

y\

@ACuriousMind What's the point you're making that I don't agree with? I've never said that all people have the same starting point (in terms of money, genes, environment, and whatnot).

Pls see quora link and help me out.

@satan29 you probably meant "initial" for the $T$ either there or in the =0 eq., right?

3:10 PM
@ACuriousMind oops yes

@JingleBells my point is that it is a hard (and political!) question which of these differences count as "luck" and which don't

@123 again, this uses the same principle
$T_{initial}-T_{final}= V_{final}-V_{initial}$

I tried myself using same principle but did not find answer.

well then what can I say.... That seems to be the only sensible method of finding the answer...
try again

@fqq Completely un-politically biased, probably not, but less politically biased, maybe, that's why I said "removing some socialistic bias" instead of "removing socialistic bias".

3:15 PM
@satan29 1drv.ms/u/s!AozWlUoG8z4tngkqJYbOvQxpHe0I?e=o89qUY Pls see what i tried to solve but stuck to find answer.

@ACuriousMind What do you mean? The Nova Effect?

@JingleBells I didn't know what that's supposed to be until now, but no. My point is the following: When you ask "How much of success is hard work and how much is luck?", then you already have excluded any other categories of causes for success - your question doesn't even allow for the notion that there might be things that are neither.
Luck carries with it connotations of pure and uniformly random chance, but the people who care about systemic and structural inequalities are concerned about these precisely because while there is "random chance" involved it is not uniform.
The question "hard work or luck?" is malformed - maybe there's something in your education (or even in your genes) that just makes you better at working hard than some others? Is that "hard work", i.e. personal merit? Is it "luck", something we have no control over at all? Or is it systemic, something society as a whole can control even if individuals can't?
Drawing a line between these things - what we've called here merit, luck and systemic or structural issues - is what's hard, and may even require confronting our conceptions of free will and personal autonomy.
(It should be no surprise to you by now that I'm not a fan of easy answers to simple-sounding questions :P)

3:32 PM
@ACuriousMind Yes, I'm not either, but it carries a personal emotional weight to me. The question really doesn't make sense and I guess people consider it because they relate it somehow to - can I make it or not, what are my chances... It's an emotional question.
I've gotten unlucky (or maybe lucky, nova effect) to even be introduced to this question because it's proven that people who believe success is entirely up to them are more likely to put in the work and actually succeed. So I have to find a way to convince myself that luck plays no role.

@JingleBells Do you have a reference to this proof?

@B.Brekke Veritasium video :P

4:02 PM
@JingleBells I may have mentioned this before, but I think you'd enjoy & appreciate:

@PM2Ring probs will watch the documentary, thanks!

4:17 PM
@PM2Ring Thanks for suggesting, but why did u assume I would enjoy it?

@JingleBells I also saw it
But here's a question what does luck mean in a deterministic universe?

@JingleBells Because it's about this topic of the connection between luck and success, although it's focusing on the level of whole societies, rather than individuals

@MoreAnonymous I don't know :P

@JingleBells Damn, was hoping you would tell me :P

I can make up a definition if u want

4:24 PM
@MoreAnonymous For that matter, what does "free will" mean in a deterministic universe? ;)

@PM2Ring I dont believe in free will ..
@JingleBells yes plz

in order to not believe in it you'd first have to define it :P

@ACuriousMind Libertarian free will
:P
Though never understood the compatibilists

@MoreAnonymous Luck in a deterministic universe means for something rare (good or bad) to happen despite it being knowable beforehand
nobel prize now

Interesting ststems tend to be complicated, even systems with relatively simple rules. So it's not often possible to calculate how the system will behave, and we might as well treat it as if it were not deterministic

4:26 PM
@PM2Ring Completely agree Prime Number Theorem is an example of this
@JingleBells Rare? Where are you getting this probability distribution from?

@MoreAnonymous from data

@JingleBells An infinite universe?
There might be some convergence issues :p
in calculating a probability distribution
(semi - joking)

Diamond is arguing against the idea that Eurasian hegemony is due to any form of Eurasian intellectual, moral, or inherent genetic superiority. Diamond argues that the gaps in power and technology between human societies originate primarily in environmental differences. So basically the whole premise is that it's environment that gives the strong advantage?

@JingleBells Also when you say from data. You might be assuming all outcomes are equally probable?

@MoreAnonymous Right. The primes are totally determined, and we can find as many as we want using the sieve of Eratosthenes. But they sure look messy when you have large numbers of them. ;)
A couple of days ago, an OP on Math.SE announced that he'd discovered a pattern in the distribution of the primes, but he gave no details. Eventually, after a couple of days of pestering him in the comments to improve his question, he finally revealed his pattern. It boiled down to: all primes >3 are of the form 6n+1 or 6n+5. :D

4:34 PM
Exactly but when we come in topics like this. Prime Number Theorem gives the probability of a number being prime in a particular range. Thus if I choose a random number then I get the probability.

But the catch to remember is in a deterministic universe I cannot choose a random number :P ...
@PM2Ring That's funny ... I found a pattern between geometry and number theory
managed to get a formula out of it

@PM2Ring If I and my friends spawn in different places in Minecraft, it's the geographical location that mostly determines who develops an advantage? Supposedly we all start with the same skill.

@JingleBells It's time for Game theory and Nash equilibrium :P

In conclusion, Diamond argues, the differences between different peoples and societies of the world are largely attributable to geographic differences between different regions of the world. In certain parts of the world, humans began pursuing agriculture because the fertile soil and temperate climate made agriculture a good use of time and resources.
Agricultural societies then gained tremendous advantages over non-agricultural societies, because the increase in leisure time enabled people to develop technologies and centralized political structures, and the proximity to animals gave people immunities to deadly diseases. As a result, some societies were able to conquer others.

@JingleBells can you spot where the political angle is there? ;P

@ACuriousMind unfairness = socialism :P

4:39 PM
Socialism is system that holds the human to standard he's not at and fails
(everytime)

I first thought socialism was about socializing lol
I guess that's why I don't like it :P
(jk - discomfort = growth)

@JingleBells This is why you weren't given the Nobel Prize :P

@JingleBells I'm not sure what that's supposed to mean, but if you don't actually want to talk about it, that's fine

@ACuriousMind I want to talk about it.
Socialism sees the world as unfair, that's why I assumed it's socialism

So, that quote is very curious - it ends with "Some societies were able to conquer others", but it doesn't tell us why they conquered others

4:42 PM
When an object is thrown upward. It rises to height h. How high is the object, in term of h. When it has lost one-third of its original kinetic energy?

it's another implication by omission - it is the assumed natural state of human societies to conquer one another, and so, if they can do so, they will, requiring no further elaboration

Pls help me answer is h/3.

@ACuriousMind But it does tell us why, it's due to unfair environments

@JingleBells Yes, but it's a little more subtle & complex than that. The book goes into much more detail than the doco, with supporting evidence. In a richer society, the average citizen has more scope to prosper. If you're poor, it's tough everywhere, but a poor person in a rich country probably has a better life (by some measures) than a poor person in a poor country. OTOH, they might be happier than the poor person in the rich country, because they have lower expectations.

@JingleBells uh, people could just have chosen not to go ahead and invade other societies
if I have better gear in minecraft than you do, nothing about that obliges me to kill you

4:44 PM
@ACuriousMind But what about as an optimal strategy ?
brb

@ACuriousMind I don't understand your point. How does the inherent nature of humans to kill have any relation to a political side?

@JingleBells ah, so you think this point so obvious that it isn't even political to you :D some people might think it is not, in fact, "inherent nature" of humans to kill one another - we are foremost pro-social animals, cooperating rather than competing for survival

A central theme in GGS (Guns, Germs, and Steel) is the clash of cultures between nomadic peoples vs those engaged in settled agriculture. Nomads tend to get pushed into the margins by those who want to farm the land.

@ACuriousMind People kill, animals kill, evolution kills. These are facts. Does socialism think humans are angels?

Answering "Why do humans kill each other?"with "because they can" is a philosophical/political standpoint (traditionally expressed by Hobbes' homo homini lupus)

4:48 PM
@ACuriousMind Yes, understood

@JingleBells I'm not sure why you continually think I'm talking about (or promoting) "socialism", I'm currently just trying to promote recognizing political attitudes that are disguised as statements of fact

@ACuriousMind Understood, won't mention socialism then

If 2 groups of nomads both want to operate in a region, they may clash, but generally they just figure out how to avoid each other. OTOH, if a bunch of farmers run out of land due to population pressure, they tend to go to war with their neighbours to get more land.

ah, good old Malthus

So what are the two sides of argument here?

4:51 PM
Diamond points out that population growth tends to be lower in nomads. So the farmers can out-compete the nomads in sheer numbers.

Our fonts have just changed!

@JohnRennie Depending on your device / OS
161

Update - These changes are now live! TL;DR We’re shipping system fonts as our default font stack. We plan to do this on May 10th, 2021. What? We’re planning on specifying system fonts on Stack Overflow and the Stack Exchange Network. On macOS and iOS, you’ll see things set in San Francisco. On Wi...

Different fonts. Meh.

I'm not very font of fonts.
nobel prize now
someone got the joke right :P

@JohnRennie These guys do a great version of Baby Driver youtu.be/0OxP5nrI6u8

4:57 PM
Baby Shark next pls

Changing fonts seems like yet another case of bikeshedding...

@PM2Ring they've more or less straight-up said they didn't do this because it was the most important thing but because it was rather easy :P

@JingleBells If you insist... youtu.be/E1LJrKlK8iY

@ACuriousMind Wanna continue the discussion?

I have to go run a D&D session now, so likely another time, sorry

4:59 PM
@ACuriousMind No worries

@ACuriousMind True. I'd be annoyed if they spent a lot of energy on it.
@ACuriousMind Have fun.

@PM2Ring If you spawn a bunch of equally skilled NPCs in Minecraft randomly on different geographical regions, you can observe what the book talks about directly I guess :P
As long as the NPCs were at least reasonably smart AI

@JingleBells FWIW, the keyboard player on that track is Jack Conte, the founder & CEO of Patreon. The singer, Nataly, is Jack's wife.
@JingleBells Ok. I've never played Minecraft, but I guess that makes sense, from the little that I know about it.

Anyone plays piano/has midi? I can play boogie woogie we can jam
Nevermind, gotta go

@JingleBells One really simple effect from geography is that the Americas have a huge north-south span, whereas Eurasia has a huge east-west span. That had a huge impact on the rate of spread of various agricultural developments.
In Eurasia, if you discover eg some improvement in how to grow wheat, that technology can potentially spread a long way east or west to regions with similar climate & growing seasons. Going north or south, the seasons change. So agricultural innovations took a lot longer to spread in the Americas than they did in Eurasia.

5:15 PM
@PM2Ring Is the book you are referring to controversial are generally accepted by other historians?

5:43 PM
@B.Brekke It got a generally good reception, although it did get some criticism. See the Wikipedia article. Jared Diamond was originally an ornithologist, but he got interested in anthropology after several field trips deep in the highlands of New Guinea. So although he's scientifically educated, he is a bit of an outsider.

2 hours later…
7:37 PM
@bolbteppa Yesterday I asked you a similar thing now this guy is up with a video on the Hilbert hotel just today itself!