Imagine an isolated planet sized object in space. Modern science can tell a lot about it through mere observation: Its size and surface features, its mass, it if has an atmosphere and magnetic field, the surface temperature, and so on. Now inject another object into its neighborhood, creating something like the Earth-moon system. Newton and other scientists established fairly precisely how those two bodies would interact when initial conditions are known. Einstein further refined those formulas, but Newton’s equations are still the go-to for understanding gravity and tell us how our thought experiment would follow those rules.
When scientists send a probe to Mars, they are using Newton’s equations, which are precise enough to enable the probe to accurately intercept a moving Mars after months at high velocity in interplanetary space -- the two ‘bodies’ being in that case the probe and Mars. Objects in space, it seems, follow very predictable paths once the laws of motion are understood.
But most of that certainty goes out the window if we insert a third object into our thought experiment. Suddenly certainty is replaced by chaos. For instance if another moon sized object intercepted the Earth-moon system, the math formulas cannot always tell us precisely what would happen. Even a predictable direct hit of either the Earth or moon would produce fragments flying in every, essentially random, direction. Scientists and mathematics can scrutinize a single object very well, they can accurately predict the interactions of two objects bound together by gravity, but a third component of comparable size makes precise interaction predictions extremely difficult if not impossible. At least one reason for that is the third object inserts a plethora of new variables into the mix taking a solution out of reach.
Even the most advanced computer cannot make completely accurate predictions in the three-body problem because if even one variable is overlooked or misunderstood or measured in error the entire solution goes wrong, a phenomena sometimes referred to as the Butterfly Effect. Physicists have sought to attack this dilemma by coming up with probabilities of the various outcomes rather than absolutes. But now imagine if there were four or more closely interacting space objects. It is simply not possible to predict with any degree of certainty, even knowing the various variables associated with each, what the final outcome of their interaction would be. It is a chaotic system and becomes much the same as accurately predicting the weather a month out.
One can loosely (very loosely) apply the three-body problem to human interaction. A lot can be ascertained about an individual by careful observation. His physical appearance, his likes and dislikes, his mental state, his habits and idiosyncrasies, his problem solving skills, social skills, the moral code he follows, and so on. Add another person who has also been equally scrutinized and their interactions can be reasonably well predicted. But now add a third person to the group and the compounding list of variables becomes too great to accurately predict what that three-body interaction will be. Chaos becomes amplified and predictability wanes. Two is company; three may be a crowd.
In the human version of the three-body problem additional defining variables are age and intent, characteristics not of general concern for a lump of rock drifting in space. Humans of reproductive age are prone to be the most volatile. Motivations and intent of an additional third ‘body’ may be blatant or at least suspect or completely innocent. The introduction of a third moon-sized body in the Earth-moon system would create instant instability. Similarly the two-body pact in human intimacy (sometimes called marriage) may become unstable with the introduction of a third member. What might have been mere minute cracks in the two-body pact may be torn open by the ‘gravity’ of the third. It can become a test of strength and durability of the two-body bond. Judging by the statistics related to the three-body human problem, it is often as accurate a depiction of chaos as that of the Cosmos.