In physics, the three-body problem describes the complex mechanics of three objects (for example - planets or stars) moving independently under the gravitational pull of each other. Unlike the two-body problem, there is no closed form solution and hence no expectation of the system approaching a steady state. It is an example of a surprisingly chaotic system made from very few simple parts operating under extremely well defined simple laws of motion.
Three is the smallest number of items that can create a pattern. Any three points in space define one circle which intercepts them. Three, as Bob Dorough sang, is the magic number. Compelling stories are told with at least three acts - a beginning, a middle, and an end. Pythagoras claimed that three was the perfect number - symbolising harmony, wisdom and understanding.
Teams of three people have a special magic. Where two people can agree or disagree, positively feedback or negatively feedback, three is always in a state of flux. Teams of three are dynamic, resistant to factionalism, prone to exploration.
Computers operate with three primary systems - compute, memory and storage. Three nodes in a cluster can vote on decisions, elect a leader, and lead to fault tolerant systems.
When facing a decision between two extremes, always look for a third way. Confucian scholars believe that the middle way encapsulates wisdom and impartiality, leading to correct moral outcomes.
I do not fear chaotic systems and change. Rigid formalism and equilibria are found only in idealised thought experiments. When you are designing systems and find yourself with two components, always look for a way to introduce a third. Emergent behaviour comes from groups of three or more. Choose a path that embraces emergence.
The three body problem is not a problem. It is a marvel to which we should aspire.