MATHS BITE: The Beginning of Chaos

In 1887, King Oscar II of Norway and Sweden offered a prize for the solution of the following maths problem:

Say you have a number of celestial bodies with known mass and you know the speed and direction they are moving in at some given point in time. Use Newton’s laws of motion and the universal law of gravitation to calculate the trajectories of the bodies.

After three years, the French mathematician Henri Poincaré, who restricted himself to the case where there are just three bodies, won the prize.

However, after winning the prize, Poincaré noticed a flaw in his solution putting him in an embarrassing position, as his manuscript was to be published for the King’s birthday within a few weeks’ time!

In his attempt to correct his work, Poincaré discovered that even this simple problem suffered from the Butterfly Effect: “sensitive dependence on initial conditions“. This means that the smallest variation in the initial values can build up over time to create massive discrepancies in the trajectories. Hence, you cannot reliably predict the motion of planets over time, as you can’t know the initial values with an infinite degree of accuracy.

With this discovery, Poincaré laid the foundations for Chaos theory.

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