Looking back: Working with mathematical surfaces (2012- )

The Luminous Envelope #3 (Unravelled octahedron) | 2015 | Digital photograph 59.4 x 84.1 cm

One of the ways I’ve been using the time in lockdown for Covid-19 is to reflect on past work. Although I find advanced mathematics utterly bewildering, I notice there is a common thread in a lot of my digital work that relates to surfaces. I don’t mean surfaces in the usual artistic sense of touch and texture but abstract entities of infinite scale (but no volume) described by points and lines. Mathematicians talk about them using symbols and numbers and, more recently, model and view them using 3D visualisation software.

My first encounter with mathematical surfaces was when I tried to use 3-D printing (laser sintering) to create objects from GPS flight data generated by gliders and birds. It’s relatively easy to plot successive points in space in a computer program and to link them into a screen-based ‘surface’ that you can manipulate in virtual space, but turning those points into a scaled, real-world object with physical volume is a whole other matter.

I encountered a similar issue when in 2015 I was invited to work with a range of 19th century teaching aids held at Oxford University Mathematical Institute. These rendered mathematical formulae as plaster models (ie represented abstract entities as tangible objects you could sit on a shelf). I was particularly fascinated by the claim that such objects were locked away in the 1940s "to protect students from the dangers of intuition". In fact, the constant refrain from Professor Sam Howison, who patiently guided a group of artists through engagement with the collection, was that we were dealing with “surfaces not solids”, even as we held the heavy plaster objects in our hands.

The image above shows one of the photographs I made in response to a model of Fresnel's Wave Surface. The original model represents light waves emanating from a crystal as a solid object. The photographs make use of polarisation to dissolve sculptural objects into zones of colour. (Polarisation, incidentally, is a technique frequently used in the study of crystals.)  It was commissioned by Metron in collaboration with Oxford University Mathematical Institute and shown as part of ‘Illegitimate Objects’ at Oxford University Mathematical Institute (2015).

In this context of things that (imperfectly) co-exist in the infinite abstract and bounded physical realms, I was fascinated to be introduced last year to the myth of Skidbladnir by Anna Heinrich and Leon Palmer. Skidbladnir was the ship of the Norse gods, which was so large that it could hold on board all the gods with all their weapons, arms, and horses, yet could be folded up and put in a pocket like a handkerchief (or possibly, I considered, a memory stick).

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