Taneli Luotoniemi Hyperspatial Interlace
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 geometry.


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.

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colour images
soft cover with flap, adhesive bound / PDF
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