Proportions, Space, Framing

This is a slice through a Nautilus shell. This particular one is in the Zoology Museum in Cambridge, where I photographed it with my iPhone.

I tidied up the reflections and the background, but otherwise, this is a Nautilus shell as the Nautilus made it – except sliced in two.

The Nautilus has ninety tentacles that it waves about in the water to take food that passes. The shell is its home.

It starts out small, and as the Nautilus outgrows the shell it builds a bigger compartment around itself. You can see the little tubes that are its last contact with the compartment it vacates before it seals it off.

The Nautilus builds about 30 compartments during its lifetime. And in doing so it makes this spiral of air-filled compartments.

The compartments that have been sealed off are water tight, which is why a whole Nautilus shell without the creature that lives in it, floats.

I made a joke about the stupidity of Brexit, pointing out that during its life, at no time does the Nautilus abandon its shell in the vague hope that it will find another one as well fitting.

Here though, I just want to talk about the shape of the shell.

There are classical design rules. They are the rules that classical architecture follow. A certain height to a certain width, a certain distance to another certain distance.

Quite the opposite of building economically at the expense of craft and the love the product. That is, building to formula of whatever shape will satisfy the building regulations for the least wastage of plasterboard sheets to line out a room on a housing development…

Some people believe that the reason the classical design rules are as they are is because their appeal is hard-wired into our brains because of the way the world around us is constructed.

Or to put it another way, there is evidence of ‘rules’ of composition throughout nature, and these may explain why an extended form of these rules exists in classical art and design.

The Fibonacci Series in Nature and Classical Design

The Fibonacci mathematical series is simple. Start with the numbers 0 and 1. Add them together. Add the answer to the larger of the two numbers that have just been added. Repeat, and repeat, and repeat. That’s a Fibonacci sequence.

0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8 etc.

And as the series progresses, two things become apparent.

The first is seen if we construct rectangles with sides that are in the ratios of the series (1:1, 1:2, 2:3, 3:5, 5:8 etc) and set them one on another so that sides of the same length are laid on top of one another. If we then draw a line that curves to follow the corners of the rectangles, it forms a spiral.

And that spiral is the spiral that is echoed in nature – in seashells and fruit and flowers and endless features of the natural world.

The second interesting thing we can see as the series progresses is what happens to the ratio of the larger number to the sum of the larger and smaller numbers,.

In the example above I only got as far as 5:8, but if we keep going, the ratio approaches a number, a fixed ratio. It is that described and used in art and architecture throughout history certainly back to the Ancient Greeks, and which is known as the Golden Section.

Another way to express it is Phi (pronounced Fee), which is 1.618.

Take a length, any length. Divide the length by 1.618. The ratio of that part to the whole is what is called the Golden Section.

Here’s a a yellow rod. The red part if the length of the yellow rod divided by Phi.

The Golden Section is the ratio of the red part to the whole length of the rod.

And that relationship is used over and over in the classical tradition of design in art and architecture.

Turn the two parts of the rod at 90º to one another and we have the proportions of a room, or a picture frame.

Perhaps someone could make a digital camera with a sensor in that proportion.