[ted_dunning]

You can get to this conclusion more directly by noting that computational complexity of any Turing simulator of anything more than a trivial system increases very fast as the precision of the initial conditions for the simulation increases. Even the shift map exhibits this phenomenon.

This can be an even more severe boundary for prediction than the actual measurement accuracy.

In the discussion about determinism vs free will, this leaves us with the situation that we can predict what somebody will do even if we assume perfect measurements, but will only be able to produce this prediction after the fact except for very short term predictions.

[dist-epoch]

Stephen Wolfram calls this computational irreducibility.