In the Hot Black Smoke video, how does the asymmetry occur? Is it due to imperfections in the calculations?
I recall that there are algorithms for generating divergence-free random fields, but I'm not particularly familiar with them. In another code I worked with more when I was younger, I recall discussing with a much more senior researcher than myself this issue, and if I recall correctly he said to not worry about the initial condition not satisfying the divergence constraint (the divergence was non-zero but known), as the numerical method will enforce the divergence constraint for all future time steps. Presumably one could modify the algorithm (this was a "pressure projection scheme") to take an arbitrary velocity field along with the desired divergence field and correct the initial velocity field to be divergence free. This may not preserve the desired statistical properties of the noise, however.
In reality, even if you can manage perfectly symmetric initial and boundary conditions, thermal noise would still cause this symmetry breaking.
Since these systems are physically unstable, the source of initial perturbation is unimportant as long as it is small.
To be clear, it absolutely is correct to say that this would lead to symmetry breaking. Depending on the numerical method and the computer, it might take a long time, if I recall correctly.
Would flames not be symmetrical if all of the above plus everything imaginable like quantum physics, solar activity, dark matter, wtv, are all controlled for?
Maybe if you had a perfectly homogeneous air density (which you'd never see, even in a really good vacuum and near absolute zero temperature. You can thank QM for that), that constantly stayed homogeneous. Problem in real world conditions is that nothing is perfectly homogeneous (entropy exists), so things will heat up unevenly, certain parts will gain more velocity than others, and just a small offset can create a large change in outcome. Short answer is that these systems are chaotic in nature, so they are not stable.
But that doesn't have anything to do with simulations (except what you are trying to emulate). As far as simulations, numerical accuracy will play a role, but really what you look for is if it is realistic, because the real world has random events. That's more what I was trying to get at. You want something that represents reality, not an overly simplified example that you can't use in a meaningful way. Even with these inaccuracies you can get representative models (they will reflect what happens in a physical experiment). And I say representative, because you aren't going to account for all those factors in a simulation, but you are accurate enough to make extremely effective conclusions. I'll even note that some people will add random noise into their simulations (I don't know if this author did, but numerics can play that role).
Replace the word random with unpredictable and it shows why some people are bothered.
To say something is fundamentally unpredictable means that it is immeasurable and not merely complex.
No, it just means that the measure cannot be predicted in advance.
OTOH, the observer effect can make measurement problematic.
And just to be clear, you do not think an observer has to be a conscious being, right? I only ask because pop culture science gives this impression. A photon can be an observer.