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Notes -
Nitpick, since I don't think it matters for your philosophical point, but the difference can be huge. I know the "butterfly farting in the Mezozoic" thing sounds like a silly metaphor ... but it's not silly, and it's not even a metaphor. Microscopic perturbations changing macroscopic weather (in weeks of time, not just eons) is a straightforward consequence of "chaotic dynamical systems exist" (not in a two dimensional state space or lower, but easy to prove with three dimensions) and "the weather is a chaotic dynamical system" (not actually proven, but Lorenz's first three-dimensional system demonstrating chaos was something of a simplification of the real sextillion-Avogadro's-number-dimensional system, and we're pretty confident the more complicated one actually is more complicated). A butterfly changing the course of a tornado was literally an example Lorenz used in his talks. Chaotic systems can be deterministic (except in the sense that we can never accurately determine their output because the cost of doing so increases exponentially with simulation time), but if you combine a deterministic chaotic system with a stochastic initial perturbation, that perturbation grows exponentially until it's the size of the attractor and the whole macro state depends on it.
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