Lets just say physics is deterministic. You could predict the future by making a copy of the system and simulating it into the future. You could observe what happens. But, there's a catch. If you looked at the result of the simulation, you would need that result near the beginning of the simulation to run it properly. So, it wouldn't work unless you did not observe the result. As long as you don't observe the result, you can create a good simulation that just assumes that you don't know the result. Unfortunately the whole thing is pretty pointless if you can't observe the result of the simulation.
Anyway, the thing about observation reminds me of quantum mechanics - even though this thought experiment has nothing to do with quantum mechanics and assumes the state of the world is measurable and deterministic.
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