Your coworker is a asshole , don't listen to him much
As you should :D
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Really? That's so strange cause Kpop has been so big lately.
@BlueScorpio Not with people my age. But my friends are not mean about it it's more people on the internet that hate Kpop fans but I can't totally blame them cause there are some that are very deranged.
yeah i heard about that. I'm not like a huge kpop fan but there are some band/songs i like. BTS is it and I can see why they became so popular. What other groups you listen to.. i only know about bts, exo, blackpink, and that's about it.. what do you recommend?
@BlueScorpio I reommend 2NE1 and Girls' Generation both older groups but my favorites of all time. NCT is a newer group I really like. Also VIXX, Winner and a ton of girl groups I won't write them all down cause I don't wanna overwhelm you but you can check out some of my mytakes if you want more ^^
How/what does chaos theory have to do with this? How do they relate?
@sensible27 Because like chaotic dynamical system, the tension between police and gangs in Miami is sensitive to initial condition jk it's just a random song in the playlist I chose at the end credits before the QA.
Was it a mathematics class, how are you studying chaos theory at 20? Did your jump classes? Sorry/apologies if I sound naive....
@sensible27 It's a graduate level math class. I'm an undergraduate but I can take it because I fulfilled the prerequisites. You just need to study real analysis and know about ordinary differential equations (ODE) before taking it. Basically chaos is a type of behaviour of a system of ODEs, like this one https://en.wikipedia.org/wiki/Lorenz_systemAt this level there are a lot of crossovers with physics, since physical phenomena are often described by ODEs. For simple objects you have a simple ODE like m x'' = -kx which can be derived from physical laws (just F = ma). For complicated system of many objects such as the weather (imagine how many particles involved lol), you have something like Lorentz system, they are called dynamical system, at this point proper physics is left behind, dynamical systems are typically ad hoc models not derived from fundamental physics but rather from experimental data. We don't care about the physical cause but we still want to solve them. Applying physical ideas such as "equilibrium" on them lead to more general concepts like periodic orbits, limit cycles and attractors in phase space. The attractor of m x'' = - kx in 2 dimension is just a circle.Chaos was discovered when people tried really hard to solve the Lorentz system with computer, aka when they tried to predict the weather, then found it's impossible, because the input to the computer has finite precision, there is always an error and this error grows exponentially (this is what I meant by being sensitive to initial condition). The attractor of Lorentz system looks like thisNobody saw it coming. The best mathematicians thought it's possible to control the weather, they didn't know about chaos.
I mean in hindsight it looks like such an obvious thing. Wasn't it first proposed in 1800s or something that if the initial states couldn't be measured well even determinsitic system wouldn't be predicatable? I think even newton said it... do you think attractors exists for things and situations and conditions but we just haven't found them yet? Or do you think they just don't exist?
@sensible27 No it's something completely different lolIf input to the system has initial error e, then measurement error is bounded by f (e). What Newton and Laplace said was something along the line of: if e = 0, then f (e) = 0. This is causal determinism, which is basically the core of classical physics. Then they just leave it at that. In all known models of physics (back then) when we take the limit: e goes to zero, f (e) goes to some limit. . So the problem is just an issue with limit of precision, you can design things taking the limit of f (e) into account. And science and engineering worked well, so we had no reason to doubt it.Chaos is something they didn't spend time thinking about (ok maybe Poincare had a glimpse of this possibility with his geometric methods), because it kinda makes no sense intuitively in the framework of causal determinism: When e goes to zero (but not completely zero), f (e) does not approaches any number, it could be any number in a huge range. Imagine this happen to a simple system when the rule of evolution is completely known, something like x_(n+1) = 4 x_n (1 - x_n) lol Further more, even though f (e) does not has any limit and it's not predictable, it still has a structure (look at the butterfly shape above)
So the classical situation is, even if e is not knowable, when e is close to something f (e) is close to something else. In that sense it's not disturbing. Chaos is when f (e) is not really approaching anything. And it does not contradict Laplace's view or causal determinism either. This happens to completely deterministic systems. There is nothing obvious about it when you understand it. The issue only surfaces when people look closely enough into large systems with computers (the number of variables in phase space is 3 and above) and all the nonlinearity came out. What are systems with more than 3 variables in phase space? unfortunately most of them 😂 (from structures in civil engineering, electrical engineering to ecosystems to the brain network). Most large systems are chaotic, but they are still predictable within a limited period, like the initial part of the trajectory of the butterfly above, but how long is this period? fortunately for normal systems in daily life it's long enough (so for example it's not super scary if your building doesn't exhibit chaotic behaviour within 100 year). The weather or earthquakes are examples where this limited period is extremely short.An attractor is just a set of points in phase space that if the system gets close to it, it doesn't get out of it. Conservative systems like the ideal pendulum doesn't have attractors, it just swings back and forth. Attractor is a concept people think of when they look closer at reality. It does not entail chaos. An attractor of a realistic pendulum with air resistance is lowest point. The attractor of the earth - ocean - atmosphere system is the climate. When attractor is a weird type of infinite sets like fractals, you have chaos.
Deep hatred 😂
This is just the age and parent child gap, this almost always happens. I actually liked a lot of my parents music but I'm weird :P It's not the same as when someone your age shames you for your music.
@Lynx122 my daughters more than happy with me and all her friends think I’m great and the “cool mum” she’s the cheerleader type. My sons the computer geek and you can see him want to curl up and die embarrassed by me 😂 just odd
I hear you broI love some of the Naruto theme songs like blue bird and silhouette and sign. I absolutely adore unravel in Tokyo Ghoul
Valid my lad, could use less caps lock.
@sensible27 next time
Me I was a big Britney and Christina fan. I was teased by my close friends for listening to them for years. I use to care now that I am older I don’t care
@lsjr16 Haha I think it’s so cool that u listen to them. I’m glad u don’t care anymore. Britney’s reign was everything!
@ strawberry smoothie yea I love them both. Music is music too me and yea it was great. Hopefully she puts out more music
The whole band? What was their name, the Pedles...