A different geometry

One of the challenges of the kind of painting I do is avoiding arbitrary decisions, or at least minimizing them. Representational painters don’t have that problem to the same degree, because the need to maintain a likeness puts some constraints on the sorts of liberties they can take. (Which is not to minimize the problems of representational painters, by the way, just to say they don’t experience this particular problem as much.)

Not that I feel a need to have a fully articulated rationale for every element of my compositions. Sometimes “it just feels right” is acceptable. But too much of that and my paintings could easily devolve into sheer caprice, so I’m always pleased when I can draw what I hope is an interesting composition out of the geometry of the rectangle.

I’ve written about geometry several times before in this blog, with a heavy emphasis on the Golden Section, a ratio beloved of early modern painters. However that’s not to say there aren’t other compositional geometries, and in fact a quick perusal of Bouleau’s The Painter’s Secret Geometry reveals that the Golden Section occupies a minority position in the history of the discipline. All of which serves to provide some context for the topic of this post, wherein I draw back the curtain and reveal the geometric underpinnings for one of my latest paintings, which represents something of a departure from my usual approach.

As I’ve noted before, my paintings typically begin with a thumbnail sketch, usually executed with a black fountain pen. Sometimes they go through several versions, other times they get translated into paintings right away. Geometry usually gets applied in the intermediate stage, while the sketch is being transferred to the canvas. I’ve described that whole process in a previous post, so I won’t go into any more detail here. What was different this time is that the geometry and the composition kind of arose organically as the sketch was evolving, rather than being applied after the sketch was done. And as I’ve already implied, the Golden Section wasn’t the framework I used this time.

Instead the fundamental lines of the composition were derived from another well known compositional strategy, which Bouleau calls ‘rabatment’, creating  a square within the larger rectangle by mapping the short side onto the long side. The strategy is so well known that Wikipedia has it covered if you need a better description.

When you’ve got a composition as simple as this one, the main challenge is to keep it from being boring. One of the best ways to add interest is to avoid putting everything on the midline. But then you run into a different problem: once you leave behind the obvious central placement of objects where do you put them? The options are literally infinite.


The diagonals of the larger rectangle and the internal square provided the solution. Their intersection with each other provides the off-centre centre point of the circle that is the focal point of the composition, and their intersection with the rabatment line provides the basis for the framing rectangle. I was particularly pleased that I could also use the centre point of the larger rectangle to derive one of the points on the circle’s circumference, and the diagonal of the larger rectangle could be used to derive the bottom of the internal frame.

You couldn’t do this with just any rectangle, of course. If you used a square everything would be back at the midline, and if the rectangle was too long you’d get other kinds of distortions. Interestingly, the size that seemed to work best was in the 16″x20″ ballpark, an aspect ratio I use quite frequently.

Of course, once the composition had been worked out I still had to paint the thing. There were a couple of considerations there. Compositionally the main issue was painting it in such a way that diagonal balance was maintained even though the compositional weight skewed a bit to the left. I leave it to you to determine how well that was achieved.

The other consideration was that I was determined to make it work with cerulean blue, a colour I love but have had problems working with in the past. Hey, as noted above, I don’t need to have a fully worked-out rationale for everything.


The Golden Ratio: Fast Company misses the point

Golden spiral in rectangles

Golden spiral in rectangles“. Licensed under CC BY-SA 3.0 via Wikimedia Commons

I’ve been meaning to do a post on this one since last month, when I followed the link from the Art Newspaper to the Fast Company article “The Golden Ratio: Design’s Biggest Myth.” It’s a great article but not for its insight into its topic, of which there is little. It’s great because it consolidates several common spurious arguments about the golden ratio in one place. Nice to have all of that together.

I’ve written about the Golden Ratio, aka the Golden Section here before, in a series of three posts I did back in 2013:

It’s not essential to (re)read them but you might want to as they do provide some context for this post, as well as an explanation of what the golden ratio actually is. This page (which isn’t one of mine) might be helpful too.

The Fast Company article’s first objection to the ‘science’ of the golden section is that “the golden ratio doesn’t come out to 1.6180. It comes out to 1.6180339887… And the decimal points go on forever.” It seems to me that’s only a problem in design if you think humans can sense or otherwise identify spatial relationships with an absurdly high level of precision, and that we will somehow be troubled by the fact that such relationships are only instantiated approximately. Personally, I think that’s a pretty silly objection. If we couldn’t identify approximate relationships, we’d never identify any relationships. It’s an imperfect world.

The next objection is that some of the claims that have historically been made about the Golden Ratio are preposterous, and the historical source material is of dubious provenance. These claims may be true as far as they go, but they don’t do much to discredit the utility of the Golden Ratio in design. True, Zeisling (who they identify as the premiere apologist for the ratio) does sound like a bit of a loon, seeing the Golden Ratio in places where it’s clearly just a projection on his part. But while the Golden Ratio isn’t quite as ubiquitous as its boosters said it was, it (and its close relation, the Fibonacci sequence) do crop up in some unexpected places, like growth patterns in cacti, sunflowers and pine cones. So perhaps some of the mysticism can be forgiven … but regardless, whether or not you get all mystical about the Golden Section doesn’t really matter either, from the standpoint of whether the Golden Section is a useful compositional framework.

And don’t get me started on the “nobody’s favourite rectangle” nonsense. To me, the fact that most people don’t seem to find golden rectangles more beautiful than other kinds of rectangles is about as meaningful as saying that major scales are useless for composing good music, because most people don’t find C-D-E-F-G-A-B-C to be the most beautiful thing they ever heard. And really, how would you locate any kind of beauty in a simple rectangle? Even Mondrian never went that far.

The argument that contemporary architects and designers tend not to use the Golden Ratio much doesn’t really tell us anything either. For starters, what’s the aesthetic worth of contemporary architecture? A lot of folks tend to think that traditional architecture, such as you’d find in say Venice or Paris, is far more beautiful than the contemporary stuff. Maybe our contemporaries should be using the Golden Section, but aren’t because it’s out of fashion these days. Or maybe they don’t really care about beauty, or if they do, they don’t seek it in harmonious proportions.

To be fair, the article does quote a couple of designers who acknowledge that the Golden Ratio is at least potentially valuable as one of the tools in the designer’s toolbox. And I have to say that approximates my own view as well: it’s not some kind of magic shortcut to effective composition, but used properly it can definitely help.

Interestingly, the article ends with an observation that in a different context could be used to justify the use of the Golden Ratio and other geometries as compositional frameworks: “We’re creatures who are genetically programmed to see patterns and to seek meaning.” True that, and I would go a bit further and argue we are creatures who take pleasure in finding patterns and creating meaning. To the extent that the Golden Ratio can help us to create patterns in our works for others to find, is the extent to which it can help us create works with depth, fascination and, perhaps, beauty.

The right paint for the job

No movements or schools of art began as a result of the discovery of new materials or inventions of new techniques. Rather, when new ideas and aesthetic departures arose, they created a demand for new technical methods that could express them in a more appropriate and fluent manner than was possible with the older methods.
–Ralph Mayer, The Artist’s Handbook of Materials and Techniques, 4th edition

I’ve been trying to remember … it was so long ago … when, exactly did I develop an aversion to polymer paints, aka “acrylics”? I know that I did use them, from time to time, back when I was just starting out. I seem to recall painting a few large, abstract murals in acrylics back in the early 80s.

But I stopped using them altogether sometime in the middle of that decade. I think it had something to do with a growing realization that if I was going to get serious about painting I would have to ground myself more in the craft. Despite having a BFA, or maybe partly because of it, I had begun to chafe at how little I really knew about how paintings were put together. That was when I first apprenticed myself to Ralph Mayer (or more accurately his book, as mentioned in an earlier post), and started delving more seriously into the history of the medium itself.

Of course, having come on stream in the 1950s, acrylic paints have very little history, and they had even less back then. I had the sense, whether rightly or wrongly, that the advent of acrylics might have fundamentally changed the nature of painting, and not for the better. Maybe acrylics were responsible for the brash, plasticky look of Pop art, a look I had little desire to emulate. At any rate, Mayer had very little to say about acrylics.

While oils were by then my medium of choice, I also worked in watercolour and gouache, and even dabbled a bit in casein and egg tempera. It definitely didn’t hurt to limit myself to more traditional kinds of paints for a time to get a sense of how their strengths and weaknesses might have conditioned the look of historical painting. But if I was going to be honest, I’d probably have to wonder how much of my aversion to acrylics was grounded in practical considerations like that, and how much was just a kind of snobbishness. Acrylics do have a few unfortunate associations: I mentioned the plasticky look above (which can be overstated), and also they have a whiff of the beginner or the amateur about them, because their immensely practical qualities — quick drying time, no volatile solvents, clean up with soap and water, no “fat over lean” — lend themselves to use by those not willing or yet able to engage with more technically demanding media. Whereas nothing says “old master” like oil paint, the legions of amateur daubers who have worked in that medium notwithstanding.

By Creator:Fernand Léger (Photographed by Zambonia 28 October 2011) [Public domain], via Wikimedia Commons

By Creator:Fernand Léger (Photographed by Zambonia 28 October 2011) [Public domain], via Wikimedia Commons

My current way of thinking is that it’s wrong to get too caught up in what one might call technological symbolism. Yes, the kind of paint you use conditions the look of your end result. And for that reason if you’re seeking to emulate the look of historic styles, as the Classical Realists do, you’d be foolish to try to do that with materials that hadn’t been invented back then. If emulating historic styles isn’t really your goal though it makes sense to use whatever kind of paint will best achieve the result you happen to be shooting for, and not get too wound up about “old master” connotations. If you like working slowly, or delicately blending your colours, then oils are probably the way to go. But if large flat areas of colour, improvisatory techniques with lots of overpainting, or heavy impasto are more your metier, then why not use paints that were developed for those very things?

As per the Mayer quote above, acrylic paints were developed precisely because painters were trying to use oil paint in ways that it was never intended to be used, and that was leading to all kinds of problems. New approaches demanded new technology, and now we have options open to us that earlier painters did not.

So where does that leave me? I’m a bit of a borderline case, I think. My approach derives from styles that date from the first half of the 20th century and so were developed predominantly by painters who worked a lot in oils, like Picasso and Braque. But many of the paintings from that era had more of the characteristics associated with acrylic paintings, like large flat areas of colour and improvisatory technique. Subtlety and fine modeling were often absent from early modernism, as in the Leger above. These styles were in fact some of the transitional ones that led, decades later, to the introduction of acrylics, because oil paint was not optimal for these kinds of uses.

As mentioned before I’m interested in exploring the formal languages of early modernism but more in the way of a commentary than a revival, so I don’t think its necessary for me to cleave to an antiquarian orthodoxy when it comes to the craft. All of which is to say I’ve decided to work a bit in acrylics again, for the first time in something like 30 years. I’ll let you know how that goes.

A trip to the Brera


Why do we think some paintings are good, and others not so much? Why do we like what we like? Is it all just personal preference, or can we legitimately say that one painting is, objectively and for everyone, better than another?

These are hard questions. They were probably somewhat easier back when art was based more in craft, and in fact “art” simply meant craft of surpassing skill. Skill isn’t that hard to recognize, and it’s certainly possible to say that one painting is more skillfully painted than another. But is a skillfully painted picture necessarily better, in some absolute sense, than one of lesser craft? I very much doubt it.

The craft of painting never attained a higher level of perfection than it did in the great painting Academies of the 19th century, but sadly the work of the Academiciens, revered in its day, has not held up so well over time. Much of it seems rather cloying and sentimental to us now. Whereas work painted at around the same period by painters of lesser technique continues to live on and inspire us. Think Cezanne, the Impressionists, Post-Impressionists, and their followers.

So craft skill is out. Note that I don’t think this means craft is completely unimportant – obviously, the painters I just mentioned took it quite seriously indeed – but just that it can’t be the only determinant of what makes one painting better than another. Better craft does not necessarily equal better painting.

Unfortunately this gets us no closer to answering the questions posed above.

Maybe there is no absolute scale of values. Maybe the canon is basically just a random group of historical talents whose apotheosis is sheer convention, and we could substitute another group just as well. Is it possible that our liking for Cezanne, Picasso, Piero, etc, was learned or even conditioned? That is to say, we were told so often during our impressionable years that these were great painters that we simply came to believe it?

Somehow I doubt that too, and I’ll back up my doubt with an anecdote.

Many years ago, in the context of an extended European vacation, I made a day trip to Milan. Since there were several things I wanted to see while I was in the city, I had at most a couple of hours to spend in the Pinacoteca di Brera, the main public gallery there. It was an absurdly short time to spend in a place with so many amazing paintings. (Heck, I could have spent the entire two hours in front of the Piero.) In order to see the small collection of paintings I had previously determined I absolutely could not afford to miss, I had to run past other paintings that, had the circumstances been different, I would have gone out of my way to see. Countless Modern and Renaissance masters … “Next time,” I thought. “Next time.” Not knowing when that next time would be, if ever.

And then I came to a small group of paintings that stopped me dead in my tracks. These paintings weren’t on my must-see list, and in fact I’d never heard of the painter before. There was nothing obviously arresting about them: small paintings of musty-looking bottles and generic Italian landscapes in muted tones. But they had some kind of curious, undefinable power. Ultimately I spent longer looking at those paintings than the ones I had come to see. When I finally did tear myself away I carefully made a note of the painter’s name so I could look him up later: it was, of course, Giorgio Morandi.

The point of the anecdote is of course that no one told me Morandi was important; he wasn’t on the curriculum of any of the art history survey courses I’d taken to that point, or mentioned in any of the books I’d read. So you can’t say in Morandi’s case that I was looking at his works because I’d been told to. Nor can you say I was looking at them because they were on the walls of a prestigious gallery, since there were many other works on the same walls I was regretfully bypassing as I checked off the paintings on my list. You can’t even say I looked at them because they resembled other paintings I’d been taught to like, since a Morandi doesn’t resemble anything but a Morandi. No, I think the only possible explanation is that I was looking at Morandi’s paintings because of some intrinsic quality or qualities they possessed. But that gets us no closer to understanding why I liked them (and still do, to this day).

If you’ve read this far you may be a bit disappointed to learn that I’m not actually going to answer the questions I posed at the beginning. In fact I don’t really think there is a definitive answer, or if there is one it’s probably complicated and far from universal in its application. What I am going to say though is that ultimately I prefer not having an answer. I think it’s a lot more productive to leave open ended the question of why we like what we like. Occasionally we’ll come across something that seems to give us a clue, a part of an explanation. But the full explanation continues to elude us, and so we keep looking.

The Painter’s Secret Geometry

Shortly after I started this blog, a couple of years ago now, I wrote a series of three posts on my approach to using geometry in composing my paintings. In one of them I wrote “For painting, the go-to book is probably Charles Bouleau’s excellent The Painter’s Secret Geometry (sadly out of print, but many libraries have it).”

And it was true – at the time I remember the cheapest copy available on Abe Books was going for something like $200. I can only assume the good folks at Dover Books are reading my blog, because they issued a reprint edition about 6 months ago. Or maybe just a coincidence? … Nah, couldn’t be …

The difference between Bouleau’s book and others of a similar bent is that Bouleau’s geometric analyses of historic paintings are convincing, well thought out and explained with reference to period writings by the artists and their contemporaries. With some other books on composition you get the feeling the overlays are mostly arbitrary lines that could equally well be replaced by different ones. That’s seldom the case here.

Dover deserves a lot of credit for keeping this old stuff in print and available in reasonably priced editions. It’s great to see they’ve added this classic to their repertoire.