The uncertainty principle usually isn’t the limiting factor that prevents you from being able to reduce complicated systems down to quantum mechanics and make predictions. The biggest obstacle you face is simply that it’s very difficult to do precise quantum mechanical calculations involving large numbers of particles. Even the model of the hydrogen atom, which consists of just one proton and one electron, is fairly elaborate, and each time you add a new particle things get much more complicated.
Fortunately there are often very good approximations you can make to deal with large systems, for example with atoms you can often ignore the interactions within the nucleus and treat it as a single particle (if you’re not interested in things like radioactive decay), and you can use a simplified model of the electron-electron interactions. But the errors that you introduce by using these approximations tend to be vastly larger than the uncertainty that comes from the uncertainty principle. And a lot of the time there aren’t any particularly brilliant approximations available – even some aspects of the behaviour of large nuclei are quite poorly understood, let alone brains.
> This means that I can’t model a human brain through physics
The human brain is extremely complicated and poorly understood even on a large scale. For example, there is a lot of uncertainty about what roles are played by the different large structures in the brain. The uncertainty principle is nowhere near the limiting factor in understanding how brains work.
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