The Double Pendulum Experiment: Is It Possible to Predict Chance?

The double pendulum is an object that every person interested in doing home experiments should have at their disposal. When we see it in action, its movements seem random; however, the correct definition for the double pendulum is "chaotic". Why? Because it is extremely sensitive to its initial conditions. The pendulum's motion seems random due to our absolute ignorance of the initial conditions, but if it were possible to record and reproduce them perfectly... we could predict its motion, or better said, obtain order from chaos.

The Butterfly Effect

In 1961, Edward Lorenz wrote a program to simulate the climate. While studying the dozen parameters that represented atmospheric conditions, he decided to round one of them, reducing its value from .506127 to .506. That small modification threw his long-term predictions out the window, and established the basis of what we now call the "butterfly effect".

The smallest alteration in the initial conditions leads to very different results, notably limiting our potential for predictability. In other words, we lack information. However, let us imagine for a moment that it is not so, and that we know perfectly the initial conditions of that system, without alterations or deviations. What would happen?

Can We Predict Chaos?

Well... we could predict chaos, of course. One of the best examples (and one we can reproduce at home without being meteorology experts) is the double pendulum. A standard pendulum is relatively predictable, but if you add an extra pendulum... pure disorder. Worse, if you use two double pendulums and activate them simultaneously from a virtually identical position, both will lose synchronization within just a couple of movements.

Now, if those two pendulums shared equal initial conditions, their movement would be the same. The problem is that those initial conditions are much, much, MUCH more complex than we can visualize. The pendulums not only need to start from the same position and the same angle, but they need to be two clones. Mass, friction between parts, energy loss... the list goes on.

Determinism vs. Randomness

The double pendulum is deterministic. Its future behavior is completely tied to its initial conditions, and if our knowledge were absolute, we could predict it... though actually not. Lorenz himself said it masterfully: "Chaos... when the present determines the future, but the approximate present does not approximately determine the future." In contrast, randomness is truly unpredictable, and the best examples are under the domain of quantum mechanics, but that... is another story.