Nancy Reid Hocking

Independent artist
London, UK

I find grace and beauty in the folding, twisting and turning depths of topological surfaces. Their use of a spacial 4th dimension is deeply fascinating. Despite it being just the addition of another vector for an unromantic mathematician it has a delicate intangibility for me. The strange concept of homeomorphism is visually powerful and very sculptural. The tension between the strict parameters of topology and it's sensual visual potential is a wonderful creative stimulus.

I have recently joined forces with Scott Carter, professor emeritus of the University of South Alabama. We both explore topological surfaces from the artist’s perspective. Happily with Scott I have a ringside seat to the strange and beautiful world of topology.

Conversations in a Foreign Language, Three Solid Arguments
Conversations in a Foreign Language, Three Solid Arguments
40 x 60 cm
HB, 4B and 9B pencil on Saunders 120lb paper

Conversations in a Foreign Language; Three Solid Arguments depicts the Hopf link, (two linked circles) in three iterations with five views of each. I wanted to set a task for myself of turning the 'objects' in my mind's eye, as if holding small sculptures in my two hands.There are five views of each of the three arguments. I was asking the question; With the rubber like stretchiness that topology allows can these apparently 3-D objects on this 2-D paper be considered the same, I.E. can they be considered homeomorphisms? I have 'seen' them from all angles and to me their origins are the same two linked rings.
The drawing is part of a series, Conversations in a Foreign Language with topology being the foreign language.

Two-Twist Spun Trefoil Knot, Art for Math's Sake
Two-Twist Spun Trefoil Knot, Art for Math's Sake
40 x 90 cm
HB, 4B AND 9B pencil on heavy cartridge paper

With topological input from Dr. Carter my most recent endeavour has taken me to the heart of a 2-twist spun trefoil knot. Two-Twist Spun Trefoil Knot, Art for Math’s Sake represents 3 dimensional cross sections depicting the moves and the folds progressing through the core of the knot as it twists and un-twists, dipping in and out of invisible 4-space, resolving in the opposite orientation.
Because I work with folds and curves the visual metaphor for 4-space as defined by the hypercube doesn't fit. Happily the struggle to depict the intangible is the artist's home territory!
The names across the bottom of the drawing are those of the mathematicians who, over the decades have worked on developing the understanding of this surface.