[Filligree]

> Chaotic activity

Well yes, the brain is demonstrably chaotic.

Why does this matter? If you run a simulation of the brain, you'll soon get different output than the original would output, but does that mean the simulation isn't working?

It'll still be intelligent behaviour, even if it isn't the exact same behaviour. It'll still be the same person; if such behavioural differences mattered, then turning up the temperature slightly would make you a different person. Thermal noise bubbles up to the macroscopic level all the time.