How The Game Of ‘Plinko’ Perfectly Illustrates Chaos Theory
“The key takeaway of chaos is this: even when your equations are perfectly deterministic, you cannot know the initial conditions to arbitrary sensitivities. Even placing a Plinko chip on the board and releasing it with down-to-the-atom precision won’t be enough, with a large enough Plinko board, to guarantee that multiple chips would ever take identical paths. In fact, with a sufficiently large board, you can all but guarantee that no matter how many Plinko chips you dropped, you’d never arrive at two truly identical paths. Eventually, they’d all diverge.
Minuscule variations — the presence of air molecules moving from the host’s announcing, temperature variations arising from the contestant’s breath, vibrations from the studio audience propagating into the pegs, etc. — introduce enough uncertainty so that, far enough down the line, these systems are effectively impossible to predict. Along with quantum randomness, this effective classical randomness prevents us from knowing the outcome of a complex system, no matter how much initial information we possess. As physicist Paul Halpern so eloquently put it, “God plays dice in more ways than one.””
Chaos! Physics! Determinism! And The Price Is Right’s greatest game of all-time, Plinko! What a winning combination; enjoy the science outreach today!
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