``Prediction can be difficult, particularly about the future.''
-- Mark Twain
Astrophysical N-body systems are chaotic. In other words, they have sensitive dependence on initial conditions. This means that the phase-space distance between two solutions whose initial conditions differ by an arbitrarily small amount will increase exponentially with time. Since computers constantly make small errors in the computation of such solutions, it is guaranteed (with probability 1) that a computed solution will diverge exponentially from the true solution with the same initial conditions. Thus, it is possible that numerical solutions for chaotic systems are overwhelmed by exponential magnification of small errors, which might mean computed solutions are worthless. This could be the case even if quantities such as energy or momentum are conserved to arbitrary accuracy, because there are infinitely many solutions whose energy is exactly the same, but have vastly different phase space trajectories.