Fibonarty

Do you know what I'm bored of?

I'm bored of people justifying how great a piece of artwork is by plonking a Fibonacci spiral on it and saying, "Look! Some features of this canvas appear to coincide with some of the curves and lines on this complicated geometrical figure. Isn't that meaningful?"

People have done it with that picture of Scarlett Johannson with a Pearl Earring, for example.

OK, so her eyes fit into a hole each and the spiral vaguely follows the line of her turban but what does this prove? There are many remarkable things about Vermeer's painting; the girl's winsome glance, the startling contrast between her pallid flesh and painted lips, the dramatic lighting. I wouldn't, however, consider of great relevance the possibility that there might exist the limit of a converging spiral on her left eyebrow.

Does the addition of the spiral here indicate a particularly elegant posture? Does it, in any way, increase our appreciation for the artist's composition?

Well I've undertaken a little experiment and selected some pictures on which to superimpose this ubiquitous curve. For a start, see if it helps you to appreciate the artistry of the following poster.

The artist of this image, compelling all ten year-olds to join the Hitler Youth, is unknown. You probably wouldn't own up to it either. Nevertheless, the Fibonacci spiral fits exquisitely. It centres on the Führer's right eye, tracing the outline of his scowling forehead, and plunging to the base of the composition shadowing the back of the obedient Arian's head. The tangent parallel to the peak of the spiral appears to underline the propagandist heading faultlessly. I would argue that the spiral fits this picture more convincingly than it does The Girl with the Pearl Earring.

It's very easy to add a Fibonacci spiral to a picture. You just download the two separately and manipulate the curve until it seems to fit. It seems to fit in a remarkable number of situations.

Here's the Fibonacci spiral fitting the GapKids advert that has been withdrawn today because of complaints it is racist. Reinstate it! It's a work of artistic genius!

And if you're reading this thinking, "Well the Nazi propaganda and controversial clothing advert are actually very well-conceived from an aesthetic perspective", then stop it! Stop it now! The Fibonacci curve also appears to fit the handiwork of a certain Cecilia Gimenez of Zaragoza:

Part of the problem is the number of degrees of freedom one has when positioning the spiral. One can place its centre anywhere in the picture, enlarge it, reflect it, and rotate it full-circle. Is it any wonder that at some point it might be positioned in a satisfactory way? The unscientific nature of this process can be demonstrated by some spiralled Mona Lisas that I found online. There doesn't appear to be a definitive position to put the maths.

There are, in my opinion, two ways to interpret this. Either the more ways there are to fit a Fibonacci spiral to a painting, the more impressive it is. Or, the whole idea that spiral equals beauty is beginning to look a little unsound. If the former were true then the following striking fractal, from the tumblr feed Chaosophia218, would be hanging in the Tate Modern.

Last time I went, it wasn't.

So how did we get into this mess? At what stage did people start haphazardly slapping spirals on Leonardo's masterpiece? Well, ironically, da Vinci appears to carry a fair proportion of the blame. In 1509, a book was printed containing scores of his exquisite geometric illustrations. The author was Luca Pacioli of Milan and the book was called De Divina Proportione. You can leaf through a copy by clicking this link.

da Vinci's diagram of an icosahedron from De Divina Proporione.

The first section of the book explores the maths of the eponymous Divine Proportion, or golden ratio. Pacioli certainly investigates relationships between proportion and perspective but there is not a Fibonacci spiral in sight. I am rather taken by the idea that a maths textbook might be illustrated by an eminent artist of the day, though. I think I'd choose Grayson Perry. That would be extraordinary.

In the centuries that have followed Pacioli's publication, the appealing idea that there is some magic golden ratio appearing everywhere in art appears to have seeped into the consciousness of the proletariat and become common knowledge. It is certainly true that it crops up frequently in nature but this is a different matter and we have a sound understanding of the biological reasons for it. I refer you to a superlative series of videos explaining why this is so by US mathemusician, Vi Hart.

Art, however, is a different matter. Certainly, some artists will have conscientiously incorporated hints of the golden ratio into their work, whether they be painters, sculptors, choreographers, or composers. But that doesn't mean you can take an accidental photo of, say, Manchester on New Year's Eve, and whack a spiral on it in order for a national newspaper to claim, "It's just like a Michelangelo".

Photograph by Roland Hughes

I think, however, my favourite misuse of this hallowed curl I found on a blog that shall remain nameless. The following picture unwittingly sums up everything that is wrong with Fibonacci Fever.