# Margaret Roberts

As a mathematician and an artist I am interested in the construction of projections and transformations between two and three dimensions. Of particular interest is the Möbius strip, a 2-dimensional (2-D) surface that twists in 3-dimensional (3-D) space. Margaret Roberts’s drawing, *TURN*, is a different form of spatial twist. Though always firmly grounded on a 2-D surface, it also spans 3-D space. *TURN* transforms the showroom of Factory 49, making it feel different by providing visitors with the opportunity to physically enter the space of a drawing. As the artist explains, the walls also transform the drawing by breaking it in one corner and causing it to bend back on itself in one direction, while splaying out on the floor in the other. This is the consequence of what she says is the drawing’s attempt to pivot and turn the right-angled wall-structure, and the wall’s inability to turn along with it. Unlike the clever Möbius strip, the success of the yellow drawing emerges out of its failure to achieve this impossible task.

The artist explains that although this makes the architecture appear inert in comparison with the energetic line, its participation frees the line from the responsibility of representation, instead encouraging its inherent eccentricity. *TURN* is thus a process-drawing that uses a system that can be made with any architecture. The starting point is arbitrary, but once begun, the interaction of lines with the 3-dimensionality of its subject and ground has a type of inevitability about it. In Factory 49 the template for the drawing is the two rectangular walls (one short, one long) that are constructed at right angles to each other and that normally provide the ‘hanging space’ of its showroom. The starting point is the centre of the shorter wall where it joins with the floor, and the angle of the turn is about 40 degrees in a clockwise direction. Once these are decided, the line rolls itself out according to the familiar recipe of representational drawing, with the additional ingredient of being life-sized.

Mathematically,* TURN *can be described in terms of transformations, projections and topology. The drawing can be seen as transforming space through the projection from one 3-D space to another 3-D space. In fact, ‘turn’, along with ‘slide’ (translation) and ‘flip’ (reflection), is a nickname for the mathematical transformation of rotation. However, the drawing is not a simple rotation. In terms of topology, the shape of the final drawing contrasts with its template. Topology, or rubber sheet geometry, is a geometry that preserves connectivity and closeness rather than shape and lengths, and the process used in *TURN* emphasises the latter. Though *TURN* follows the architecture of the showroom, the drawing produced is not topologically equivalent to the room as one might expect. This is because the edges that become the lines of the drawing, and that are connected in the original template are not all connected in the final drawing. The yellow line seems to have a mind of its own in the final shape that it generates.

‘The line knows it is in the third dimension here’, the artist is overheard to say in describing the pathway of *disturbed drawing*—the precursor to *TURN—*in which the line slides under a post in the gallery to avoid being deflected. This applied to only one corner of *disturbed drawing*, however, where the artist claims the line needed to be ‘woken up’ to avoid running into the space of other artists in the same show. Otherwise, the artist explains, the line ‘didn’t know it was in 3 dimensions’. This is an approach that is reminiscent of Edwin A. Abbott’s *Flatland*:* A Romance of Many Dimensions* (1884), in which 2-D beings imagine what a world with an extra third dimension might be like. However, most of the time, the line is assuming that the world is flat. It is just that we see its ‘mistakes’ because we see how it bends over 3-dimensionality. The geometrical result is immediately engaging in its unexpected use of Factory 49.