Information Technology Reference
In-Depth Information
Fig. 8.3
The topological
subspace defined by a specific
tool forms a network in the
material space. Each
application of the tool (e.g. a
brush) moves a small step
along the accessible
pathways. Repeated use of
the tool can take us far
with sound or music, the material space consists of all theoretically possible sounds
of a certain maximum length and bandwidth. These spaces are truly huge, with as
many dimensions as there are sound samples or pixel colour values. Musicians or
artists seldom conceive of sounds in these representations, since they are very distant
from the conceptual level of a work, but as theoretical constructs they are convenient
and important, as we shall see.
In other contexts, the material representation could be a three-dimensional form,
a musical score, or a text, the latter two are slightly closer to a structural-conceptual
description of a work, but the mechanisms are similar.
At any specific time, the temporary form of a work is represented by one point
in the material space; one image out of the almost infinitely many possible images.
Through the application of a specific tool, we can reach a number of neighbour
points. In this way, a network of paths is formed, defining a topological subspace:
a network (see Fig.
8.3
). In some contexts that don't allow repeated configurations
to occur (e.g. wood-carving), these networks are structured like trees, while in other
cases periodic trajectories can occur.
Let us look at a simple example. A specific tool, e.g. a paintbrush or a filter
in Photoshop, with some parameters, operates on a particular bitmap and returns
another. That is, it goes from one point in the material space to another. From a
specific image you can travel to a certain number of other images that are within
reach by a single application of this particular tool. With this tool, I can only navigate
the material space along these paths. I can go from an image of a red square to an
image of a red square with a blue line by using the brush to make the line. But I need
two steps to go to an image of a red square with two blue lines. Hence, the vertices
of the topological network of this particular tool are the points in material space
(representing in this case bitmap images), while the edges are connections between
points that can be reached by one application of the particular tool.
The material space may also have an inherent topology, based on the most obvi-
ous neighbour relation—the change of a value of a single pixel colour or a single-
sample. However, this topology is too far removed from the conceptual level of the
human mind to be of particular use, and we cannot even imagine how it would be
to navigate the material space in this way, since such a small part of it contains
