The Pagoda Design Space: Extending the Scope of Design - Principia Designae: Pre-Design, Design, and Post-Design - page 58

Fig. 5.1 Solution spaces for differently defined problems (Habraken 1985 , p. 68). Solution
spaces: Sa within explicit problem constraints; Sv virtual - valid for problem solver; Sf forms
acceptable as candidate solutions
which the problem solver decided which operator to apply next. Today operators
are algorithms and they include the constraints. In software design the notions of
problem and solution spaces is still in wide use, and mapping from the problem
space to the solution space is a widely researched topic.
In architectural design the concept of problem space received a wider interpre-
tation and was closely related to the search aspect of the space, sometimes also
termed search space. The concern in architecture was not just efficient problem
solving, but coming up with a creative solution, or design. As such, the issue of the
space's boundary gained importance. Likewise, it was acknowledged that a prob-
lem is often too complex to solve without breaking it up into partial sub-problems.
Unlike the AI notions, the terms problem space and solution space were used
interchangeably in the early design literature, as we shall see in the examples that
follow. At a later stage it was suggested that the two spaces should be conceptual-
ized as a single space within which design problems are searched and solutions are
developed (Dorst and Cross 2001 ; Maher et al. 1996 ). Goldschmidt ( 1997 ) wrote
about a design problem space, but an extended one in which a solution is in fact
sought. I equate this space with the design space.
Let us consider a couple of examples from the design literature that were
concerned with creative design. The first example is from a text by John Habraken
( 1985 ). Habraken distinguished between well and ill-defined problems and
established three types of solution spaces. The widest one Sa, is a space containing
all possible solutions under explicit problem constraints. The second, smaller space
Sv, is virtual and limits the solutions to those valid for the problem-solver. The last
and smallest space Sf, includes only forms that are acceptable as candidate solu-
tions. Figure 5.1 depicts three arrangements of solution spaces, varying according
to the level of definition of the problem.
We note that in the case of well-defined problems the three spaces are concentric
and well aligned one within the other, with no violation of space boundaries. As the
problem becomes less defined, that is, the definition is questioned, the space of
acceptable forms exceeds the realm of the designer's initial valid solutions, as
questioning gives rise to new possibilities. Finally, when the problem is ill-defined