Due to computational overhead, the universe as a whole is unpredictable.
The universe as a simple definition is the biggest thing; to predict it would require a computer bigger than the biggest thing. The computer itself would be unpredictable, as it can't predict itself. It would trivialize prediction for the inner universe, as it is now in control of it. The whole universe has been refashioned into the the computer's guts... However, what the computer would control it to do would itself be unpredictable.
Put another way, to predict the universe means predicting your own prediction, without knowing the prediction in advance. No matter how you phrase it, it's incoherent. E.g, "I am going to add 1 and 1 to get 2, thus I predict I'll get 2 when I add 1 and 1." Either you don't know you'll get 2, and can't make predictions of this kind, or it's not a prediction, it's a postdiction.
Let's talk as little as possible about the numerous insurmountable practical, contingent barriers. The computer would somehow have to be fast despite sending signals from beyond the observable universe to the other side, also beyond the observable universe. You can retrodict the universe, see that you could have computed the future before the future, but there's no point since the future will always come before you finish the calculation. Do it the cheap way and just go look. At the quantum level, stuff is inherently uncontrollable, because there's nothing smaller with which to see it without perturbing it. You can't tell where something is without changing how it's behaving thus rendering your own knowledge moot. This is also true of the instrument you're trying to measure with. The way to find out what will happen is to let it happen.
An unpredictable thing can't be predictable in parts. The unpredictable parts would hit the predictable part, or, equivalently, the predictable parts have to be isolated. Not in fact part of the universe; we found the self-contradiction. Goes double since retrodiction is possible. If an unpredictable part hits a predictable part, you can predict the future path of the unpredictable part. You can work out its past path based on how the predictable part reacted, thus transforming chaos into order. You can predict it in future.
If you can predict one solar system, you can put a computer in every solar system, and predict them all. Run it out long enough that there's time to send all the predictions to a central repository, and bam, you've predicted the entire universe all in one place. You can push out more than a year's worth of planetary evolution in a year, so you can always make it long enough to get to the central repository in time.
If any part is predictable, it's all predictable. But it can't be predictable. Indeed single hydrogen molecules lay waste to the most powerful computers currently conceivable.
Yet, it must be predictable. If you can't predict where to get food, you starve to death. Life does not develop. I mean, like, the planets are right over there.
Prediction is the basis of all control. Can you repeat a motion? Then you can plan to repeat a motion. You can see the past results and predict the future results. If things are themselves, if A=A, then the future with those things will be like the past with those things.
Somehow, unpredictable things add up to predictable. This happens between psychology and sociology, for example. Individuals are chaotic. Sociology is so easy it's boring. Somehow, each totally invisible atom of a children's ball add up to a downright prosaic ball.
Time is impossible, and yet, the future arrives. Time is impossible, and yet, it moves.
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