““The three-body problem illustrates how easy it is to run into computational irreducibility. It is a problem that borders on the trivial, yet it seems that it cannot be solved analytically. There is no apparent shortcut, no mathematical equation that can tell you the trajectory.5 In general, if you want to know where the planets will end up at some time down the road, you have to ride along with them as they trace their paths, either in practice or in simulation. If we want to know whether the planets crash, whether one of them will fly off into space, whether they will be periodic or chaotic, we have to follow them over the course of their travels. We can’t plug coordinates or a time period into a formula and crank out the answer.””
