Beyond Newton's law

Since Lorenz (1963), physicists came to realize that the predictability of the future state of a deterministic system, that is a system whose dynamical equations are known, was not a trivial matter of computation. For over two centuries, and still a strong belief in the present Western societies, one thought that given the initial and boundary conditions, every deterministic system should be perfectly predictable.
During the 20th century, one started to realize instead that for most systems, except if one is armed with infinite computational power, there will be a time in the future where our prediction will be completely false. Poincaré already noticed that although the two-body problem was a perfectly resolved exercise, in other words a dead problem, the three-body one, however, was not. Predicting the future state of the system Moon, Earth and Sun is still a relatively hot topic.
During the last 50 years, some scientists have started to attempt to overcome this obstacle of unpredictability. This is the science of complexity where one still tries to extract universal patterns from systems which appear chaotic or random. So far, it seems that this science has mostly produced qualitative results, so much so that some have started to doubt its real scientific benefits and have accused it of being at times too philosophical, even mystical. But this science first and foremost does not deny the complexity of natural systems, which is itself a great step forward. By doing so, it attempts to go beyond the predictability problem and to fulfill Newton's dream to comprehend Nature. So much has yet to be learnt, and the science of complexity has so far successfully shaken our stern belief in equilibrium and in linear causal chains of events.

Lorenz, E. N., 1963, "Deterministic nonperiodic flow", Journal of the Atmosphere Sciences, 20, 130-141.