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, who introduced the sequence to Western European mathematics in his 1202 book, Liber Abaci.

The sequence, it turns out, appears everywhere. It is found in nature, in music, in poetry, in our own bodies. Like every sequence defined by a linear recurrence with constant coefficients, the Fibonacci numbers have a closed form expression. It has become known as Binet's formula, named after French mathematician Jacques Binet. The outcome of Binet's formula, as it happens, is a value. This value has become better known as "the golden mean" – 1.618. Originally, the golden mean was seen as the desirable middle between two extremes, one of excess and the other of deficiency. It appeared in Greek thought at least as early as the Delphic maxim "nothing in excess", and was discussed in Plato's Philebus and, subsequently, Aristotle's Nichomachean Ethics Book II: That Virtues Can Be Described As Means.

The golden mean appears in Eastern philosophy, in Christianity, in Judaism, in Islam, and in Hinduism.

Why, then, is Fibonacci and, by extension, the golden mean so important? It may be that it is the key to unlocking the very mind of our creator. Whether you are looking at the petals of a flower, or the spirals of a galaxy, the design is always consistent with the golden mean. Every building block, every increase or decrease of scale, every design – they all follow this one number sequence. And the fraction is always the same.

Just look at your arm – measure the distance between the tip of your longest finger to where your wrist starts. Now measure the distance between the tip of your longest finger to your elbow. If you place the latter number over the former, you will find the answer being 1.618.

Now, take a look at the image at the top of this piece. The Nautilus shell follows the progressive proportional increase of the Fibonacci sequence. While shells are probably the most famous examples of this because of the fact that their lines are very clean and clear to see, you can see the same patterns if you look at the bands that constitute our Milky Way galaxy, or indeed, the pattern of the neural pathways of the brain.

We are fearfully and wonderfully made. If, before reading this piece, you were still unsure whether or not there was intelligence behind creation, I believe I have gone a long way to illustrate that the odds of creation being without thought or reason is simply ludicrous. God exists, whether you like it or not. He has a plan, he always had a plan, and evidence of his plan is plain for anyone with even the slightest intelligence to see.