You bring up an interesting point worth the 3 body problem and randomness.
Classical mechanics is not computable, for exactly the reasons you gave.
The idea that the error grows exponentially with time doesn't make sense exactly in QM because it's grows compared to what? This is where Heisenberg's uncertainty kicks in. There's no underlying ground truth here. In classical mechanics the position and momentum have infinite precision making them not computable. There's is a truth and any computation is an approximation which diverges exponentially. But in QM, the more precisely you know one, the more uncertainty must exist in the other. There's no underlying ground truth that your hypothetical computation diverges from.
Instead you have a probability distribution of position and momentum, and as time grows forwards that distribution expands. At some point it expands exponentially, but nonetheless the distribution itself is computable. The randomness doesn't make it computationally harder, it's what makes it computable at all compared to classical mechanics.
And speaking of computable...
In terms of the brain and complexity, that's not what computable is about. It's not about practicality. It's whether a Turing machine with unlimited tape can compute or in finite time. There's no difference between an ant brain and a human brain there. If you can compute the ant brain, then human might take exponentially more time, and indeed longer than the heat death of the universe. But that's an irrelevant practical consideration mathematically speaking.
Upshot though is Boolean logic is not known to be inadequate for stimulating human brains.