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Isn't the halting problem about knowing all future states and not a future state?

You know the initial conditions, the position function x(t), the velocity function v(t), and acceleration is constant. Why can't we evaluate the state at any point in time without having to calculate previous states?

A deterministic system isn't a necessary or sufficient condition to be able to calculate a particular future state without calculating intermediate states.

It just happens to work for the system you propose, not all systems of that class.

Not everyone understands that problem.

How so?

...unless the input tape also is deterministic.

"deterministic system" is not "deterministic program"