>Some, like the double pendulum or the three-body problem, are deterministic but chaotic. In other words, their dynamics are predictable but we can’t know their state at some time in the future without simulating all the intervening states.
Literal nonsense. Everything in the second sentence is false.
Deterministic means that the state at some point in time fixes the state at all future points in time. Nevertheless in a deterministic system you can know a future state without calculating intermediary states.
Chaotic means that future states are discontinuous in regards to the initial state. Nevertheless a chaotic system can be known at future states without calculating intermediary states, you can even have an analytic solution to a chaotic system. Furthermore chaotic can mean that you can't calculate future states from initial states. Numerical ODE solvers in particularly have errors which grow exponential in time. So simulating intermediate states does not give you the solution to the problem.
>Some, like the double pendulum or the three-body problem, are deterministic but chaotic. In other words, their dynamics are predictable but we can’t know their state at some time in the future without simulating all the intervening states.
Literal nonsense. Everything in the second sentence is false.
Deterministic means that the state at some point in time fixes the state at all future points in time. Nevertheless in a deterministic system you can know a future state without calculating intermediary states.
Chaotic means that future states are discontinuous in regards to the initial state. Nevertheless a chaotic system can be known at future states without calculating intermediary states, you can even have an analytic solution to a chaotic system. Furthermore chaotic can mean that you can't calculate future states from initial states. Numerical ODE solvers in particularly have errors which grow exponential in time. So simulating intermediate states does not give you the solution to the problem.