Archive for Piero della Francesca

After Piero

Posted in Art, Education, Politics, The Universe and Stuff with tags , , , on October 31, 2010 by telescoper

I don’t often blog about things inspired from TV programmes. I don’t watch that many, and those I do see are rarely inspirational. However, last night, I caught the last of the series Renaissance Revolution, presented by Matthew Collings. It was on the subject of a major obsession of mine, the art of Piero della Francesca, and I thought it was wonderful. I regret having missed the previous programmes in the series, but I’m sure I’ll get a chance to see them sometime.

Collings focused on one particular painting by Piero, The Baptism of Christ, which hangs in the National Gallery in London, and which is illustrated below:

The political and religious backround to this painting are almost as fascinating as its composition, based on the offset superposition of a circle (representing heaven) and a square (representing the Earth). The use of perspective was very new around 1450 when this painting was finished, but that’s not the only geometrical aspect to note. There’s a striking use of symmetry (e.g. in the angles of John the Baptist’s arm and leg), and the central vertical axis defined by the dove, John’s hand and Christ’s hands.

Given the mathematical rigour of his compositional techniques, it should come as no surprise to learn that in his lifetime Piero was just as famous as a mathematician as he was as an artist. In other words he was the archetypal renaissance man. Unfortunately, most of his art doesn’t survive; the vast majority of his works were frescoes in various churches, few of which have withstood the test of time. Regrettably, little also is known about Piero the man, except that he lived into his 80s.

A while ago I mentioned another work by Piero which is the origin of my obsession with his paintings. The Flagellation of Christ is a work that has burrowed so far into my psyche that I quite often dream that I’m in the strange building depicted therein:

In fact I also use this painting in talks about science – I did so in my talk on Wednesday, in fact. The reason I use it in that context is that it is a bit like the standard model of cosmology. On one level it makes sense: the flat Euclidean geometry mapped out by the precise linear perspective allows us to understand the properties of the space extremely well, including the scale (the vanishing point indicates a front-to-back distance of about 250 ft). This is what our standard cosmology says too:- the universe also has a flat geometry. On the other hand, the more you think about the contents, the more confusing the picture gets. The main subject matter of the painting is to the left, in the background, playing an apparently minor part in the whole thing. Who are the characters surrounding the Christ figure? And who are the three figures in the foreground, dominating the whole composition, but seemingly indifferent to what is going on behind? Do they represent dark energy? Do the other characters represent the dark matter?

That’s not meant to be taken seriously, of course, and nobody actually knows what is really going on in this painting. It’s undoubtedly beautiful, but also an enigma, and that combination is what makes it a great work of art. It’s not easy to understand. It makes you wonder.That’s what science is like too. We have our theories, we have data, but there always remains a great deal we don’t understand. And sometimes the more we think about it, the more confused we get. Just as it is with that painting.

As Mark Collings put it brilliantly in the programme last night

When you’re looking at the picture, analysis isn’t exactly what is going on. You’re seeing and you’re getting pleasure from seeing. Partly the picture is telling you how pleasure is constructed, how it’s created, and partly you’re just lost in it. So when you’re lost in the light of Piero, you’re experiencing when you’ve forgotten how to experience. And you’re suddenly curious when you’ve forgotten how to be curious. And what you’re experiencing and being curious about is .. the world.

It doesn’t matter whether you’re a scientist or an artist (or a poet or a philosopher or a historian or whatever). The need to be curious about the world – or some aspect of it – is surely what it’s all about. During the Renaissance it wasn’t unusual for great minds to embrace science, mathematics and art – just think of Leonardo da Vinci. However, over the centuries we’ve become increasingly specialised and compartmentalised and more focused on making money than on making ideas. We’re losing what above all else is what makes us human, our curiosity.

Our society increasingly sees education simply as a means to develop skilled workers, smart enough to do technically complicated jobs, but not clever enough to ask too many questions about the materialistic treadmill they will spend their life upon. The UK government’s plan to withdraw funding for arts and humanities departments in universities is just another step along this path.

It shouldn’t be like this. Universities should be about learning for learning’s sake; not about teaching facts or skills, but about teaching people to ask questions and figure out their own answers. In other words, they should be about curiosity.



Perception, Piero and Pollock

Posted in Art, The Universe and Stuff with tags , , , , , on April 15, 2009 by telescoper

For some unknown reason I’ve just received an invitation to a private view at a small art gallery that’s about ten minutes’ walk from my house. Cocktails included. I shall definitely go and will blog about it next week. I’m looking forward to it already.

This invitation put me in an artistic frame of mind so, to follow up my post on randomness (and the corresponding parallel version on cosmic variance), I thought I’d develop some thoughts about the nature of perception and the perception of nature.

This famous painting is The Flagellation of Christ, by Piero della Francesca. I actually saw it many years ago on one of my many trips to Italy; it’s in an art gallery in Urbino. The first thing that strikes you when you see it is actually that the painting is surprisingly small (about 60cm by 80cm). However, that superficial reaction aside, the painting draws you into it in a way which few other works of art can. The composition is complicated and mathematically precise, but the use of linear perspective is sufficiently straightforward that your eye can quickly understand the geometry of the space depicted and locate the figures and actions within it. The Christ figure is clearly in the room to the left rear and the scene is then easily recognized as part of the story leading up to the crucifixion.

That’s what your eye always seems to do first when presented with a figurative representation: sort out what’s going on and fill in any details it can from memory and other knowledge.

But once you have made sense of the overall form, your brain immediately bombards you with questions. Who are the three characters in the right foreground? Why aren’t they paying attention to what’s going on indoors? Who is the figure with his back to us? Why is the principal subject so far in the background? Why does everyone look so detached? Why is the light coming from two different directions (from the left for the three men in the foreground but from the right for those in the interior)? Why is it all staged in such a peculiar way? And so on.

These unresolved questions lead you to question whether this is the straightforward depiction first sight led you to think it was. It’s clearly much more than that. Deeply symbolic, even cryptic, it’s effect on the viewer is eery and disconcerting. It has a dream-like quality. The individual elements of the painting add up to something, but the full meaning remains elusive. You feel there must be something you’re missing, but can’t find it.

This is such an enigmatic picture that it has sparked some extremely controversial interpretations, some of which are described in an article in the scientific journal Nature. I’m not going to pretend to know enough to comment on the theories, escept to say that some of them at least must be wrong. They are, however, natural consequences of our brain’s need to impose order on what it sees. The greatest artists know this, of course. Although it sometimes seems like they might be playing tricks on us just for fun, part of what makes art great is the way it gets inside the process of perception.

Here’s another example from quite a different artist.

This one is called Lavender Mist. It’s one of the “action paintings” made by the influential American artist Jackson Pollock. This, and many of the other paintings of its type, also get inside your head in quite a disconcerting way but it’s quite a different effect to that achieved by Piero della Francesca.

This is an abstract painting, but that doesn’t stop your eyes seeking within it some sort of point of reference to make geometrical sense of it. There’s no perspective to draw you into it so you look for clues to the depth in the layers of paint. Standing in front of one of these very large works – I find they don’t work at all in reduced form like on the screen in front of you now – you find your eyes constantly shifting around, following lines here and there, trying to find recognizable shapes and to understand what is there in terms of other things you have experienced either in the painting itself or elsewhere. Any order you can find, however, soon becomes lost. Small-scale patterns dissolve away into sea of apparent confusion. Your brain tries harder, but is doomed. One of the biggest problems is that your eyes keep focussing and unfocussing to look for depth and structure. It’s almost impossible to stop yourself doing it. You end up dizzy.

I don’t know how Pollock came to understand exactly how to make his compositions maximally disorienting, but he seems to have done so. Perhaps he had a deep instinctive understanding of how the eye copes with the interaction of structures on different physical scales. I find you can see this to some extent even in the small version of the picture on this page. Deliberately blurring your vision makes different elements stand out and then retreat, particularly the large darkish streak that lies to the left of centre at a slight angle to the vertical.

This artist has also been the subject of interest by mathematicians and physicists because his work seems to display some of the characteristic properties of fractal sets. I remember going to a very interesting talk a few years ago by Richard Taylor of the University of Oregon who claimed that fractal dimensions could be used to authenticate (or otherwise) genuine works by Pollock as he seemed to have his own unique signature.

I suppose what I’m trying to suggest is that there’s a deeper connection than you might think between the appreciation of art and the quest for scientific understanding.