Grasping Four-dimensional Geometry Through Crafted Models
Four-dimensional space is a mathematical
thought-experiment involving adding an extra spatial dimension perpendicular to
our three dimensions of length, height and width. Research on the properties of
hyperspace is made possible by generalizing the methods acquired by studying
more familiar spaces of lower dimensions. Originating in philosophy and
mathematically formulated in geometry, the concept has inspired interpretations
in mysticism, in theoretical physics, in fiction and in the visual arts.
Just as three-dimensional objects can be
drawn, unfolded, sliced, photographed or otherwise portrayed onto a planar
medium, these graphical techniques can be generalized to produce
three-dimensional appearances of the 4D structures described by mathematicians.
Hyperspatial Interlace – a doctoral work in the interdisciplinary context of
mathematics and art, studies new possibilities for visualizing hyperspatial
Hyperspatial reasoning offers artistic
research a provokingly counter-intuitive, but nevertheless logically consistent
framework rich with scientific, historical and poetic significance. The sensuous
accessibility provided by physical artifacts and the simple vocabulary of
geometry makes the research easy to share across various disciplines.
The work was granted three-year funding
from the Finnish Cultural Foundation, and the Fulbright Center Finland endorsed
it with a stipend for a semester’s visit to the Department of Mathematics of the
University of Illinois at Urbana-Champaign.
Taneli Luotoniemi conducts visual research in
the Department of Mathematics at Aalto University, designing educational
concepts for manipulable mathematical objects. He holds a Masters of Arts
degree in art education from the Aalto University School of Arts, Design and
Architecture. In his research, he investigates the visual possibilities of
provoking and counter-intuitive conceptions of space described in mathematics
in the context of, for example, topology, projective geometry, and the higher
dimensions. He also lectures on these topics to art, design and engineering
students at his home university.