Is There a Formula for Everything?

I love movies. Growing up, it was all about westerns. People like Clint Eastwood and John Wayne were my first heroes. There was a pattern to these flicks – an unlikely hero suffers a tragedy at the hands of the villain, he then goes through many trials and tests that ready him for revenge, at the end there is a showdown and, ultimately, the hero gets the girl and saves the day. What's not to like?

Imagine, then, my surprise when I realised that Star Wars was simply a western, set in space. It had all the same ingredients. It plot followed the same formula. This got me wondering if every action movie that I had ever seen followed the same path. As it turns out, Hollywood has long known what appeals to an audience and has catered for us accordingly. Should this come as any surprise? Are we really this predictable? The answer lies in mathematics.

In mathematics, the Fibonacci numbers form a sequence in which each number is the sum of the two preceding ones. The sequence commonly starts from zero and one, and the first few values in the sequence are, therefore:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on.

The sequence was first described in Indian mathematics as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. The sequence was named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci,