I have never, ever, got maths. Even thinking back to my earliest school memories I get a sinking feeling when I recall those pink covered maths books. It’s the process which bothered me, the fact that there was only one way of getting from question to answer, from A to B. If you didn’t know it or understand it – and I didn’t – that journey was a challenge. And if you did slip up you were screwed, because there was only ever one concrete answer. I hated than there was seemingly a million ways to be wrong, and only ever one to be right.
I understand that some people find satisfaction, even beauty, in the systems of numbers and their logic, though I’ve never been able to see it. That’s not me disputing its existence, but acknowledging that I recognise this limitation to my perception. It’s almost ethereal to me, even now; there are moments when somebody’s explaining it to me and I get a sense that it’s almost within my grasp, but this never lasts. The deep fog around my understanding never fully clears, just momentarily and patchily retreats to a gentler haze.
But I’m also aware aware of how deeply maths is embedded as an influence and device within some of my favourite arts. Music basically is maths – trust the numeric patterns and you’ll get a right answer. In visual art, too, it’s had a significant role. Being a natural law rather an invention of man – despite what the Renaissance might have had you believe – maths can be found working within artistic traditions from around the world.
Though I can never find a satisfying answer to the question of why we find certain ratios and patterns aesthetically pleasing which goes beyond familiarity, that their frequency in nature has got us used to them as being ‘the way things should be’. Maybe it’s because of this that many of the images I’ve been looking at for this week have a kind of divine leaning. The rules of maths being used as proof of teleological arguments, evidence of God’s hand in the design of the world. Whether you go with that or not, its resulted in some beautiful things being made.
Leonardo da Vinci “Vitruvian Man”, circa 1490. More a technical drawing than an ‘artwork’, created to prove a mathematical point. It’s based on the writings of Vitruvius, a Roman architect who related human & architectural proportion. The text is an explanation of the proportions of man in the kind of list where maths loses me. Despite this relatively mundane purpose, I had to include it here because it’s become THE symbol in Western culture for the ‘rationality’ of man.
Katsushika Hokusai “The Great Wave off Kanagawa”, circa 1830. If you Google “Hokusai Fibonacci” you’ll find a whole series of images imposing spirals onto the shape of the wave. A Fibonacci Spiral is one which follows the Fibonacci sequence – which even a maths dunce like me can follow. At its centre are two “1×1” tiles, then as the line moves up and around it moves into a “2×2”, a “3×3”, a “5×5”, “8×8” and so on. Yet the final image doesn’t feel forced into a style, but like a real wave. The Fibonacci sequence apparently has a lot of influence in nature – who’s to say that doesn’t last for the split second of a wave’s lifetime, like this, in real life?
Sandro Botticelli “The Birth of Venus”, circa 1482. Another work that’s believed to specifically use maths to make itself pleasing to the eye. The “golden ratio” is 1 to 1.618 and analysis of this work has show that it uses it everywhere. Venus’ body follow this ratio above & below her navel; the left & right sides of the composition – even the dimensions of the canvas itself have been found to follow these proportions.
A traditional Javanese batik print, of the Solo type. I’m not going to pretend that I understood very any of the equations in the academic paper I read investigating the occurrence of fractals in batik motifs, but I understood that it found they’re there. The idea of fractals kind of makes my brain melt at the best of times: structures which are infinitely reoccurring, symmetrical at the deepest points, formed out of what maths calls ‘chaos’ – and in nature potentially between dimensions. OK. Well, turns out that it’s possible to find at least the potential for these qualities in a range of traditional Javanese batik patterns. I don’t really know what that means – is it because the art borrows from nature or has been formalised in its own way? But the results are pretty nice, aren’t they?
‘Zellige’ tiles from the Place El-Hedine, Meknes, Morocco. Zellige is just one form of Islamic architecture, particularly associated with Morocco. The geometric pattern is immediately obvious and geometry has an important role in Islamic art in general, as figurative images aren’t common in sacred contexts. What you see here in this pattern is intricate craftmanship – each coloured piece is an individually shaped tile, the total of which create a complex and beautiful mosaic of shapes and overall patterns.
Albrecht Dürer, “Melencolia I”, 1514. What we’re looking at is the personification of melancholy – and isn’t her face a spectacular depiction of dark brooding? Notice that she’s holding a compass, and there’s other mathematical tools around which imply that what’s plaguing her soul is the quest for knowledge. It was during the Renaissance that the idea of gloominess- perhaps what we’d not recognise as depression, but certainly all the way up to insanity – became seen as a possible driver of artistic creativity. So what we have here is possibly the first, certainly the first significant – visual representation of the ‘tortured genius’ trope.
M.C. Escher, “Day & Night”, 1938. I hate Escher. I associate his drawings with the covers of those dreaded maths textbooks, and the opening slides of imcomprehensible powerpoints. But this means that he’s the first artist who came to mind when I chose the ‘Maths’ theme, so here he is. And “Day & Night” certainly has its mathematical basis, with its tesselating birds and almost-not-quite symmetry. It feels closely related to Surrealism – but I’m afraid as with that movement, I can’t see it as anything other than twee.
