## Three Body Problem

The Three Body Problem was first described some 250 years ago by two Frenchmen, Jean d'Alembert and Alexis Clairaut. They presented papers describing how the motion of three planets or celestial bodies all conforming to strict Newtonian determinism (i.e., you can exactly predict the location of a projectile knowing its mass and momentum) can end up exhibiting completely unpredictable motions when considered jointly. If the gravity of planet A interacts with B, and B interacts with C, and C interacts with A, then the sum combination of the various interactions results in each showing chaotic motions (note: not random, rather so-called fractal motions). Small variations in the starting conditions of one or more of the three bodies quickly gives rise to very large differences in their subsequent trajectories. Hence we see frequent course correction maneuvers on long term space voyages.

Work on the three-body+ problem was greatly advanced in the late 1800's by the French mathematician Poincaire who laid the foundations of modern chaos theory. This was later popularized in a book by Edward Lorenz (i.e., a butterfly flapping its wings in South America gives rise to a hurricane in North America). Since we can never measure the starting conditions of any complex system with enough accuracy, the downstream behavior of such a system becomes essentially unpredictable even though each of its components follow essentially deterministic rules.

From the field of ecology a recent study measured how far the red flour beetle would spread (invade) over 13 generations (why 13, why not 14?). The same experiment was repeated 30 times and ended up showing spreads that ranged from 10 units distance to 30 units. This study used an identical stock of beetles and the same experimental setup each time. So it's not nature or nurture. You get a 3x difference in spread (which according to the authors is quite a significant difference for this well-studied bug) simply due to immeasurably small differences in the starting conditions of each study.

Analogously you can get quite different research outcomes with only slight changes in the initial assumptions. See here for an  illustration of this concept, which is one of the 49 ways that we use to develop alternate competing hypotheses+.

Note: In 1772, the Italian-French mathematician Joseph Louis Lagrange, working on the three-body problem, found there were five points of equilibrium within the system where the motion was essentially predictable. These are named in his honor, the Lagrangian Points. Although the quantitative modeling of complex systems is inherently chaotic, there is always hope of finding stability in amongst the flux.

References:

Highly Variable Spread Rates in Replicated Biological Invasions: Fundamental Limits to Predictability

Three Body Problem - Wikipedia

Mathematics and the Unexpected (Poincaré discussion)