Nancy Reid Hocking
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 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.
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.