Painting: A Space Drawn in Ratio (2013)

Using the term painting draws an imaginary line around a set of practices. Where that line falls depends on the art historical moment, on diverging and converging ideas of what might qualify a work within the category painting. The imaginary line encloses a space and immediately puts into play other spaces that border or overlap or run parallel to a space that might be considered painting. How one approaches thinking about painting is worth examining. My visualisation of a line enclosing a space functions like a diagram of painting. As it attempts to describe what painting is like, it is also like a painting. The space it describes is conceived on a plane surface and the devices used: line, border, overlap, edge, are those of composition. As a starting point for an analysis of painting it discloses a flaw in the method by creating a self-referential loop; it presumes the qualities of the answer even as it asks the question.



But a line-enclosed space is firmly lodged in my head. I imagine a rectangle or a square or then again both, and a space with internal divisions and external edges. What I begin to realise is that this rough schema references a specific diagram that has been art historically relevant to painting. A rectangle that encloses a square and a further rectangle in specific ratio; a rectangle cut into two unequal parts, an outline of the golden section. The standard diagram of the golden section or golden ratio is of a square and a rectangle of the same height, side by side, or described differently it is of a rectangle divided into a square and rectangle. The enclosed and enclosing rectangles retain the same format, the same ratio of height and width. Each enclosing rectangle is able to produce a new square, which in partnership makes another rectangle and so on. The first written record of this ratio is by Euclid (1), "A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less." So the width of the square (a) is in the same ratio to the width of the rectangle (b) as the width of the square (a) is in ratio to the width of the square and rectangle together (a + b). Or a + b is to a as a is to b. Visually the width of the rectangle reads as just over half the width of the square. Mathematically ‘a’ is about 1.618 times ‘b’ and ‘a’ + ‘b’ is about 1.618 times ‘a’. The ‘about’ is key – the number built into this ratio never resolves itself to a fixed set of decimal places, but it is consistent, occurring again and again in a variety of circumstances in geometry. The mathematical complexity of this is something I find challenging to access, but the spatial relation it generates is understandable and discoverable through drawing with a ruler and compass (2), and it is a ratio that has been compositionally influential in painting, sculpture and architecture. The cut rectangle diagram has affected my visualisation of painting, of a complex space bounded and divided. Noting again some of its characteristics helps me think why that is: it is at all times a whole shape (rectangle) and a divided shape (rectangle and square); the ratio of just over half is hard to place and so sets up a matching or mismatching of one to the other which is never totally resolvable or knowable while still being definitely and unarguably there; it generates new iterations inside and outside each rectangle that it draws, moving up and down in terms of scale ad infinitum; the confined space it describes is never in isolation, but sets in motion a system of comparison, one space to another.



The works in Limber operate within such a system of comparison, and within and without a negotiation of limit. They present themselves as provisional, as schemas, keeping open their making as a thought process. This diagrammatic quality means they can demonstrate their own possibilities to themselves. Elements or attributes of painting are tested in space, composition is mostly acted out through assemblage. Two dimensions are not a defining characteristic, but three dimensions operate with restrictions - the works retain a front face even as they project into space, and they specifically engage the wall as support and echo of a pictorial structure. The constructed, the processed, the poetic are all inferred as points of likeness and points of comparison. Comparison is inbuilt into the art historical method. I suppose it is inbuilt into any discipline which deals with categories, one thing understood and defined in relation to another. In art history the functions and outcomes of comparison have been considered in very different ways at different moments: comparison leading to inclusive assimilation of the attributes of another art form and comparison leading to exclusion. The basis for inclusion and exclusion are identical, that they strengthen the art form under consideration, but of course they take opposing routes to the same end. Both can be thought to represent a position of extreme confidence or extreme defensiveness. With painting the consequences of comparison have been various, but what is interesting is that comparison is often based on likeness; likeness not just in the sense of depiction, but in the ability to imitate aspects of other practices. The Renaissance method of paragone gives some context to this. Meaning comparison in Italian, paragone describes debates about the relative qualities of one art form to another, most often painting in relation to sculpture but also to literature, theatre, music and architecture, or it describes debates within painting, for example the relative merits of line over colour (3). Notions of uniqueness were less relevant than the potential for a practice to claim a larger proportion of the artistic space. So for painting to imitate the 3 dimensional qualities of sculpture consolidated its position, for it to achieve the expression of poetry enhanced it. Though paragone was often competitive in intent, the jostling for position involved a creative interchange between art forms and the criteria by which they were assessed. It was a context of positive mimicry, taking on the characteristics of other disciplines in order to argue more convincingly the value of one’s own (4).


This has of course been described differently – that painting is liable to illusion and emulation in a way that takes it outside of itself, that the tendency to the quality of likeness needs to be dropped in order to secure painting as itself. Painting as ‘infinitely susceptible to the temptation to emulate the effects, not only of illusion, but of other arts’ is then suggested as painting’s weakness and fuelled a modernist effort to exclude any attributes associated with or shared with other art forms (5). This shedding process was considered progressive, but within it a version of likeness is still in play – likeness to a constantly updating ideal model of painting (6). Likeness can be cited negatively and positively as painting’s most resilient characteristic. But the emulation or assimilation of something outside itself is arguably painting most specifically being itself. The works in Limber are like painting. They are like painting because of and not despite their emulation of sculpture, architecture, music or poetry. Attributes are understood as shared with other art forms and other experiences. Likeness motivates imitation, and motivates comparison. Through the process of emulation does it become clearer what painting is? Is it found in what is left over, when the attributes of one art form are matched against the attributes of another? Or in being like painting, does that then demonstrate what painting is like? (7)


The diagram I imagined at a remove from painting in order to simplify thoughts about painting turned out to be like painting or like a painting, while painting is also like a visualisation of something outside of itself. Proposing a diagrammatic consideration of painting is already thinking within the framework of painting. Visualising a ratio, one that is art historically embedded, as a short hand for the shifting edges and limits of painting may be suspect as a method. It draws on analogy, association, and likeness to propose a connection – that this is like that, but not actually that. It is of course a form of picturing. A diagram can schematise a relation between painting and something which is not painting, but also between certain opportunities for painting and other opportunities for painting: ‘…painting as, let’s say, all edges, everywhere hinged, both to itself and to what it adjoins, making itself out of such relation’(8). A space drawn in ratio implies an internal division, a cut that allows for extremities of position while still remaining inclusive; what is without the line is also within as the next version gets drawn (9). It does reflect, I think, the mind-set of the studio that can find new logics for new work, balancing and countering and negotiating one thing against another.


Moyra Derby July 2013


(1) Euclid’s Elements Book VI Definition 3 (Sante Fe, New Mexico: Green Lion Press, 2002) pp123

(2) The instructions to draw a square and rectangle in golden section demonstrate how the ratio is discoverable in geometry: Draw a square Draw a line from the midpoint of one side of the square to an opposite corner Use that line as the radius to draw a circle The circle defines the height of an adjoining rectangle The square and rectangle are in golden ratio

(3) ‘Image and Text: The Paragone’ in The Intellectual Life of the Early Renaissance Artist, Francis Ames-Lewis (New Haven: Yale University Press, 2000). pp 141 – 162. Also see the chapter ‘Pictures and Categories’ in Painting and Experience in Fifteenth Century Italy, Michael Baxandall (Oxford University Press,1972) pp109 – 153 on the development of a descriptive and conceptual method for considering painting during the Renaissance.

(4) An example of paragone at work in painting is the response to sculpture’s ability to depict a full form, in the round. The motivation then for painting was to offer multiple views, often using groups of figures with various changes to pose and position, or using the device of a reflection, so that the front and the back of a form can be seen simultaneously in a mirror. A specific example is found in Vasari’s Lives of the Artists, taken from the ‘Life of Giorgione da Castelfranco’ ‘there could be shown in a painted scene, without any necessity for walking round, at one single glance, all the various aspects that a man can present in many gestures a thing which sculpture cannot do without a change of position and point of view, so that in her case the points of view are many, and not one.’ Giorgio Vasari, Lives of the Artists (Oxford University Press, 1991) pp299- 304

(5) ‘Towards a Newer Laocoon’, Clement Greenberg, Partisan Review 7, 1940 pp 296-310. The text as a whole opens up a long tradition of arguing the merits of one art form over another, and the value of exclusive rather than shared criteria. The extended extract published in Art in Theory 1900-1990: An Anthology of Changing Ideas ed. Charles Harrison, Paul J Wood (London: Blackwell Press, 1993) pp554–560 usefully points out the wider context of related texts in the introduction.

(6) Rosalind Krauss’s picturing of a series of closed rooms and doors clearly visualises a forward only trajectory of modernism, ‘Within each room the individual artist explored, to the limits of his experience and his formal intelligence, the separate constituents of his medium. The effects of his pictorial act was to open simultaneously the door to the next space and close out access to the one behind him’ ‘A View of Modernism’ Rosalind Krauss, Art Forum, Sept 1972 pp. 48-51

(7) Lucy Lippard, writing in 1967 discusses a shifting demarcation between painting and sculpture. ‘As Painting is to Sculpture: A Changing Ratio’ marks an exchange between two art forms that had sought to guarantee their exclusivity, but now move into a mode of assimilation. The title proposes the idea of ratio, a measuring of two quantities and their relative value one to the other, though in fact the word ratio only appears in the title and isn’t discussed directly in the text. But the space it implies informs an understanding of shared characteristics. Lippard states, ‘three interacting points seem particularly pertinent: the relationship of painting and sculpture as physical objects, as vehicles for formal or sensuous advance, and as vehicles for color’. ‘As Painting is to Sculpture: A Changing Ratio’, Lucy Lippard in American Sculpture of the Sixties, (Los Angeles County Museum of Art, 1967) pp 31- 34

(8) Stephen Melville in ‘Counting /As/ Painting,’ from As Painting: Division and Displacement, eds. Phillip Armstrong, Laura Lisbon, Stephen Melville (Cambridge: The Mit Press, 2001) pp 1 – 26

(9) Mel Bochner uses the analogy of brackets to visualise how at certain times certain aspects of practice can be activated or deactivated, ‘when you bracket you set something aside, you don’t eliminate it’. ‘How Can You Defend Making Paintings Now? A Conversation between Mel Bochner and James Meyer’, 1993 published in As Painting: Division and Displacement, eds. Phillip Armstrong, Laura Lisbon, Stephen Melville (Cambridge: The Mit Press, 2001) pp 199-204


ISBN 978 0 9570797 8 6 Catalogue contribution for Limber: Spatial Painting Practices, curated by Jost Münster & Cherry Smyth at Herbert Read Gallery, Canterbury Sept 13 - Oct 12 2013 and Grandes Galleries de L’Erba, Rouen