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require extra oxygen. Some points are easier to reach aided by GPS navigation,
others require ropes and harness. Each means of transport provides certain navigable
or facilitated paths, and where the path networks intersect, i.e. where both means are
possible or needed, we can change our way of travelling. All of them bring different
potential and constraints, just like different tools.
So, one idea behind the introduction of a material space is that we can start think-
ing about application of different tools in succession, since they all operate in the
same space—the material space. They all define different topological networks in
the material space, which intersect, and we can switch between tools at any time.
Another reason is that the material representation introduces true open-endedness,
since anything can happen in the material form. I can spill coffee on my score,
or there can be a tool failure. A teacher or collaborator can alter my sketches. All
this of course adds further complications to the process, but these cases still fit the
model.
8.3.2 The Conceptual Representation
The conceptual representation of the work is how it is represented in the mind of the
artist, in terms of abstract or concrete ideas and generative principles. This represen-
tation is vague with respect to the material representation. If my idea is a picture of
ten monkeys forming a pyramid, this conceptual representation corresponds to the
set of all images that can be interpreted as a pyramid of ten monkeys. Since nothing
is said about the colour and species of the monkeys, where they are located, or from
which angle we see them, there are a lot of images that fit this description.
In the course of the creative process, the conceptual representation is changed,
e.g. by being made more specific, which shrinks the subspace, or altered, which
transforms the subspace. The internal structure of the conceptual representation de-
termines which transformations are possible, along the lines of the variable param-
eters of the representation. If my idea, again, is ten monkeys forming a pyramid, the
variables in this representation are the kind of animals, the number of individuals,
their formation, etc. If I decide that it should be specifically ten cotton-top tamarines,
or ten monkeys in a pyramid under a rainbow, the subspace shrinks. If I elaborate my
idea to be ten mammals forming an upside-down pyramid, or a number of monkeys
in any formation, the subspace is restructured or expanded. This relates directly to
the invention of new knobs to turn (Hofstadter
1985
) or Boden's transformation of
spaces, and is one of the challenges of computational creativity.
The conceptual representation can be vague in at least three different ways.
First, there may be many points in the material space that comply with the ideas
expressed—it defines a subspace of many possible results. Second, the conceptual
representation may not yet include the necessary small design decisions that we of-
ten postpone to the implementation stage. Third, because of our limited predictive
capacity, generative works can be exactly defined by concepts, but we don't know
what the outcome will be. Our expectations—what we envision—form a subspace
