There’s no limit to predicting the weather that I’m aware of for an infinitely advanced intelligence, what do you mean exactly?

Let me try and be very precise: We know that weather is a chaotic system, which means it has a positive Lyapunov exponent, which measures how the uncertainty of a chaotic system evolves as a function of uncertainty in initial conditions.

Usually this just means that our weather models will fail if our initial data input isn’t precise enough. But even if we imagine a perfect weather model, perfect data input and a perfect intelligence to model future weather, the input data is still limited in precision by the Heisenberg uncertainty. As far as we know, something like the position of an atom cannot be known with infinite precision, and a future theory which is more precise (aka a “hidden variable theory”) has been consistently shown to be impossible through the “Bell tests” or “nonlocality experiments”.

So, if we assume that the perfect intelligence still only knows the position of each atom down to say, a precision of one Angstrom, 10^(-10) meters, and we assume a Lyapunov exponent of about 0.5/day, see e.g. this paper, then we can calculate that after two months the uncertainty is approximately

1 Å (ångström) exp(60 days×0.5/day) = 1 km

So even with perfect data, perfect model, perfect intelligence, the location of each atom in your weather model would have an uncertainty of one kilometer after predicting just two months into the future. In other words, there is a fundamental limit to prediction of complex physical systems.

Define “awareness” in an empirically testable manner first and then we can start applying it.

One criterion we could apply is the ability to respond to stimuli beyond Newtonian mechanics. All living humans and animals have this ability, no rock has this ability. It can be empirically tested.

Does the ability to react to stimuli mean that you are aware? Not necessarily. But if you cannot react to stimuli, then you cannot be aware.

By the way, thanks for sticking with the conversation, this is super interesting stuff!