As Poincaré’s work shows, this simple premise can produce examples so complex and random that they are literally called chaotic.Īn elegant way to understand Poincaré’s conclusion, and bring some order to chaos, came some 70 years later. This allows us to repeatedly plug the outputs of the function back in, allowing for evolving behavior. So began the field of dynamical systems.įor our purposes, a dynamical system is simply a function whose possible outputs can also be inputs. He now saw that even a system with only three bodies could behave too unpredictably - too chaotically - to be modeled. A month later, he submitted a corrected version. Poincaré admitted his error and paid to have the copies of his solution destroyed (which cost more than the prize money). Poincaré’s solution - which indicated that at least some systems, like the sun, Earth and moon, were stable - won the prestigious prize, and an accompanying article was printed for distribution in 1889. Unfortunately, his solution was incorrect. Will our solar system continue its clocklike motion indefinitely, will the planets fly off into the void, or will they collapse into a fiery solar death? The French polymath Henri Poincaré focused on one related to the motion of celestial bodies, the so-called n-body problem. In 1885, King Oscar II of Sweden announced a public challenge consisting of four mathematical problems.
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