Boundary Functions is an exploration of personal space and the relationship
of the individual to society. The piece is realized as a set of lines
projected from overhead onto the floor which divide each person in
the gallery from one another. With one person in the gallery there
is absolutely no response. When two are present, there is a single
line drawn halfway between them segmenting the room into two regions.
As each person moves, this line dynamically changes, maintaining an
even distance between the two. With more than two people, the floor
becomes divided into cellular regions, each with the mathematical
quality that all space within the region is closer to the person inside
than any other.
The regions which surround each person are mathematically referred
to as Voronoi diagrams or Dirichlet tessellations. These diagrams
are widely used in diverse fields, spontaneously occurring at all
scales of nature. In anthropology and geography they are used to describe
patterns of human settlement; in biology, the patterns of animal dominance
and plant competition; in chemistry the packing of atoms into crystalline
structures; in astronomy the influence of gravity on stars and star
clusters; in marketing the strategic placement of chain stores; in
robotics path planning; and in computer science the solution to closest-point
and triangulation problems. The diagrams represent as strong a connection
between mathematics and nature as the constants e or
By projecting the diagram, these invisible relationships between individuals
and the space between them are made visible and dynamic. The intangible
notion of personal space and the line that always exists between you
and another becomes concrete. The installation is non-functioning
with one person, as a physical relation to others must be present.
In this way the piece is a reversal of the often lonely self-reflection
of virtual reality - here we are given a virtual space which can only
exist with more than one person.
The title of the piece, Boundary Functions, refers to Theodore Kaczynski*欄
1967 Phd thesis at the University of Michigan. Better known as the
Unabomber, Kaczynski is a pathological example of the conflict between
the individual and society - the conflict and compromise of engaging
in society versus solitude and individuality uncompromised by the
thoughts or presence of others. The thesis itself is an example of
the implicit antisocial quality of some scientific discourse, mired
in language and symbols impenetrable to the vast majority of society.
In this installation, a mathematical abstraction is made instantly
knowable by dynamic visual representation.
The installation consists of an overhead camera and projector aimed
at the floor through an intermediate mirror. The camera and projector
are connected to a PC computer which performs tracking of the moving
people on the floor below using custom software. The software generates
the Voronoi diagram which is projected back onto the floor.