Fibonacci Unravelled

A galaxy! Trillions of stars whisked into a capricious spiral...

We like to connect the dots, we humans. What does a whole galaxy have in common with a shell on the beach? Or a pine cone? And even more importantly, why is there a link? What does it tell us about the universe?

There is a simple formula. A sequence of numbers built on the simplest arithmetic:
1+1=2, 1+2=3, 2+3=5, etc, so that you get 1,1,2,3,5,8,13,21…etc

Leonardo Fibonacci (1175-1250 AD) discovered this sequence as a solution to uninhibited rabbit population growth. In fairness, the sequence was known to Indian mathematics by the sixth century, but like many things (e.g., Christopher Columbus “discovering” an inhabited America), history is Eurocentric and the sequence bears an Italian’s name.

This sequence is based on the golden ratio (when the ratio is the same as the ratio of their sum to the larger of the two quantities), and the spirals mentioned above are golden spirals.

So, why does that spiral, that ratio, that sequence, appear throughout nature?

The Fibonacci sequence is the optimum growth strategy, a path of least resistance. In the case of leaf arrangement (phyllotaxis), this growth sequence maximises the space for each leaf and the average amount of light it captures. The sequence is also seen in the florets of flowers, pinecones and in pineapple scales. In sunflowers, a golden spiral seed arrangement provides a biological advantage because it maximises the number of seeds packed into a seed head.

The Fibonacci numbers occur again and again:
• 3 petals: lily, iris
• 5 petals: buttercup, wild rose, larkspur, columbine
• 8 petals: delphiniums
• 13 petals: ragwort, corn marigold, cineraria
• 21 petals: aster, black-eyed susan, chicory
• 34 petals: plantain, pytethrum
• 55, 89 petals: michelmas daisies, the asteraceae family

In the animal kingdom, the chambered nautilus is the standard representation with its logarithmic spiral, but it is found in humans too. The cochlea of the inner ear forms a golden spiral.

More importantly, every cell in your body follows the same optimum growth strategy. Here a composite confocal micrograph uses time-lapse microscopy to show a cancer cell undergoing cell division.

You can see it in your fingerprint too:

The by what mechanism does it happen? question is easy enough then: living things, like rabbit populations and cells, grow, and this sequence represents their optimal growth strategy. This strategy maximises energy and materials; lowest input, highest output. A subtler application of this principle applies to a galaxy or a hurricane. In this instance the centre of a spinning mass has less drag acting on it so it rotates at a different rate to its peripheries; a proportional difference in velocities draws the golden spiral. Although this creation of a logarithmic spiral (via fluid dynamics) is by a different mechanism to growth (optimal utilisation of energy resources), a kinship lies in their linking principle: the path of least resistance—nature's preferred pathway.

So back to that big question: what does the underlying pattern of the Fibonacci sequence tell us about the universe?

Here we branch into my own philosophical speculations.

It would be easy to point to what looks like universal design (you can even notate the equation), and proclaim a designer, but I suspect that's a lazy solution. We don't hire a designer to supply us with their lowest-effort solution to our problem. That equates with your architect designing your house as a box with no doors or windows or break-up of living spaces. We require our architect to individualise the product, include utility and special cool features, to add embellishments.

The path of least resistance is what you get when design is unimportant, it maximises your resources and homogenises your product into the same repeated pattern. Ultimate simplicity is a bad look for a designer, but any sensible, naturally arising system will form along just those lines: the lines of maximum economy of resources. Those Indian and Italian mathematicians discovered that pattern because it was everywhere—not an underlying design at all, but a ubiquitous default position.

We all read different meanings into the stars. Some (like me), see solar furnaces, dust and gas clouds, vast cold reaches of space, and marvel at the humbling scale and jaw-dropping beauty of the cosmos. Others see different meaning: a holy void or a precession of equinoxes; or else they read meaning into the patterns of constellations. That's all fine. Meaning is what you impose on what you see. It doesn't mean it's there or that it isn't there.

I'm just thankful that what I see spilling out of that simple mathematical formula is so gorgeous!