Dorothea Rockburne: Adventures in Lineland

In some ways, topology—the study of shapes and spaces—is ideal territory for artists. Topology is the study of mathematical functions such as translation and reflection, and it examines the way that spaces align, intersect or separate from one another. Not only are these properties of art itself, these are all concepts with which artists can engage literally, metaphorically, and philosophically as well.

Canadian-born painter Dorothea Rockburne is remarkable for her interest in topology as a set of mathematical concepts, and this has been filtering into her artwork since the 1950s. Introduced to the topic by her math teacher Max Dehn at the legendary Black Mountain College, she was inspired by the idea that ‘nature is written in numbers.’ Since then, Rockburne has engaged with mathematics in a deep way, exploring its consequences in her art, but without any predetermined notion of the ways in which it might unravel.

Indication ofInstallation,Nesting,1973 40”x 52”	(Framed) Carbon	paper	and	carbon lines	on	 paper, Image: Jill Newhouse Gallery

Indication of Installation, Nesting, 1973 40”x 52” (Framed) Carbon paper and carbon lines on
paper, Image: Jill Newhouse Gallery

With an artist’s eye, but a mathematician’s palette of shapes, lines and spaces, Rockburne brings the elements of her work together in complex combinations of parts and units. In a 1972 Artforum interview, she said, “I try not to make useless combinations. After arriving at certain combinations, that will not make themselves into one unit, I join units so that a work is a combination of many parts, units and then larger units. This of course comes from math, which deals with combinations of parts and units.”

These ideas are set out particularly well in the Indication Drawings made for an exhibition of her work at the Bykert Gallery in 1973. According to Rockburne, these drawings “were made during and after the installations so as to retain a memory of the concepts and a way to make actual drawings containing all the principles involved.” However, in this case it was not just the content of the work that followed the ‘rules’ of topology, the literal frame of the drawings explored the concept as well: scaling up and down between entire walls and ‘mere’ 40’’ x 52’’ pieces of paper.

Dorothea Rockburne, Indication ofInstallation,Neighborhoods,1973 40”	x 52”	(Framed) Reversed version of	installation: Transparent	vellum paper, colored pencil and black ink on American etching paper

Dorothea Rockburne, Indication of Installation, Neighborhoods, 1973 40” x 52” (Framed) Reversed version of installation: Transparent vellum paper, colored pencil and black ink on American etching paper, Image: Jill Newhouse Gallery

In a similar way, the drawings documenting Rockburne’s Neighborhood installation refer to the topological concepts of neighborhoods, borders and parameters. But for Rockburne these concepts are not static, but animated by a complex set of ideas, or even inner lives. In her diary entry from 18 April 1973, Rockburne explains it like this:


This subject—of whom the small lines were men and the points women – were alike confined in motion and eye-sight to that single straight line, which was their world. It need scarcely be added that the whole of their horizon was limited to a point; nor
could anyone ever see anything but a point. Man, women, child, thing—each was a point to the eye of a Linelander. Only by the sound of the voice could sex or age be distinguished. Moreover, as each individual occupied the whole of the narrow path, so to speak, which constituted his commerce, and no one could move to the right or left to make way for passers by it followed that no Linelander could ever pass another. Once neighbours, always neighbours. Neighbourhoods with them was like marriage with us. Neighbours remained.


I should note again that Rockburne is not a mathematician: she does not set out to illustrate topology, or to communicate its principles to the naïve viewer. Rather, she uses it as a basis for her own exploration of space and as a set of tools or concepts from which her own art can emerge. This approach can be quite abstract: in Nesting, Rockburne explores the concept of nested functions – in which the scope of one function, concept, or object is constrained by the scope of its containing function, concept, or object – through a dark rectangle rotated within a space of angular lines. In other work, Rockburne explores both well-known mathematical principles, such as the golden ratio beloved of ancient architects, and cutting-edge concepts, such as folding, which helps scientists to understand the origins of some degenerative diseases and which still requires whole rooms full of computers to predict at the molecular level.

More recently, Rockburne has turned to physics and astronomy, but she remains decidedly un-literal in her interpretations of these disciplines. Again, she does not seek to provide a lecture in the natural sciences, but to use it as a foundation in her art. So in much the same way as mathematics underpins the way that nature unfolds around us in everything from Fibonacci-sequence ammonite shells or fractal Romanesque broccoli, from relatively simple origins Rockburne’s work has unfolded into something uniquely elegant and deeply engaging.


Rockburne’s work is on display at the Museum of Modern Art in New York from September 20 2013 – 20 January 2014 in Dorothea Rockburne: Drawing that Makes Itself. An accompanying exhibition, Dorothea Rockburne: Indications of Installation will be on display at the Jill Newhouse Gallery from 1 October – 16 November 2014.

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