COGNITIVE ROLE OF ILL-STRUCTURED REPRESENTATIONS IN PRELIMINARY DESIGN*

Transcription

1 Cognitive Role of Ill_Structures Representations in Preliminary Design* VINOD GOEL Dept. of Psychology, York University, Toronto, Ont. Canada Abstract. I have previously argued that cognitive processes involved in preliminary design require "lateral" transformations or mental state shifts, and that "ill-structured" mental representations are necessary to support these transformations. I review the argument and provide additional support for it by appealing to some neuropsychological data. 1. Characterizing the Design Problem Space Goel characterizes design problem solving as involving four development phases: problem structuring, preliminary design, refinement, and detail specification; and notes that each phase differs with respect to the type of information dealt with, the degree of commitment to generated ideas, the level of detail attended to, the number and types of transformations engaged in, and the symbol systems needed to support the different types of information and transformations. This is depicted in Figure 1. Here I am interested in the contrast between the preliminary design phase and the refinement and detailing phases. Preliminary design is a classical case of creative, illstructured problem solving. It is a phase where alternatives are generated and explored. This generation and exploration of alternatives is facilitated by the abstract nature of information being considered, a low degree of commitment to generated ideas, the coarseness of detail, and a large number of lateral transformations. A lateral transformation is one where movement is from one idea to a slightly different idea rather than a more detailed version of the same idea. Lateral transformations are necessary for the widening of the problem space and the exploration and development of kernel ideas. Figure 1. The design problem space. The refinement and detailing phases are more constrained and structured. They are phases where commitments are made to a particular solution and propagated through the problem Seite 1 von 11

2 space. They are characterized by the concrete nature of information being considered, a high degree of commitment to generated ideas, attention to detail, and a large number of vertical transformations. A vertical transformation is one where movement is from one idea to a more detailed version of the same idea. It results in a deepening of the problem space. Figure 1 also notes that preliminary design phases are accompanied by "ill-structured" representations (in this case belonging to the symbol system of sketching), while the refinement and detail phases are accompanied by more "well-structured" representations, belonging to the system of drafting. Intuitively one might understand "well-structured" mental states as being precise, distinct, determinate, and unambiguous. "Ill-structured" mental states, on the other hand are imprecise, ambiguous, fluid, amorphous, indeterminate, vague, etc. A central claim of this theory is that the structure of mental representations facilitates cognitive transformations. In particular, ill-structured representations are necessary to facilitate lateral transformations while well-structured representations are necessary for vertical transformations. Section 2 offers a formal definition of ill- and well-structured representations (these were referred to as nonnotational and notational representations respectively in Goel (1995)). Section 3 specifies the cognitive role of ill-structured representations. All this is a review of previously discussed material. Section 4 reviews some neuropsychological data from Goel and Grafman that provides additional empirical support for the theory. Section 5 provides some concluding remarks. 2.Structure of Representations By way of an example of a well-structured representation consider the diagrammatic representation in Figure 2. It depicts two states and a transformation in a game of chess. The representation and the symbol system it belongs to have the following seven properties: (p1) Syntactic Disjointness: Each token belongs to at most one symbol type. Thus for example, no chess piece of the type 'rook' belongs to the type 'queen'. (p2) Syntactic Differentiation: It is possible to tell which symbol type a given token belongs to. So given the types 'queen' and 'rook' and a token of the type 'rook', it is possible to tell which type the token does and does not belong to. (p3) Unambiguity: Every symbol type has the same referent in each and every context in which it appears. Thus no 'bishop' refers to a knight regardless of context. (p4) Semantic Disjointness: The classes of referents are disjoint; i.e., each object referred to belongs to at most one reference-class. So, for example, no pawn belongs to the class of rooks. (p5) Semantic Differentiation: It is possible to tell which class a particular object belongs to. Thus, given a king and two classes of objects, one could determine which class, if any, the king belongs to. Seite 2 von 11

3 (p6) The rules of transformation of the system are well specified. Thus, for example, there is no question as to what does or does not constitute a legal move for a bishop. (p7) The legal transformations of the system are such that these properties are preserved at each and every state. Figure 2: States and transformation from a game of chess (reproduced from Rich ) The first five of these properties (p1-p5) are adopted from Goodman. The reader is referred to Goodman, and Goel for a more complete discussion. a b Figure 3: States and transformation from early part of a graphic design session In contrast, consider the diagrammatic representations in Figure 3 extracted from the early part of a graphic design problem-solving session. They belong to the symbol system of sketching and differ from the representations in Figure 2 with respect to each of the above seven properties. In fact, they fall on the opposite extreme with respect to each of the seven properties (p1-p7): (p1') Failure of Syntactic Disjointness (i.e Syntactic Overlap): Each token may belong to many symbol types at the same time. That is, in the absence of any agreement as to the constitutive versus contingent properties of tokens, there may be no fact of the matter as to which equivalence-class they belong to. Thus for example, what equivalence-class does token a in Figure 3 belong to? Do tokens a and b belong to the same equivalence-class? There may be no agreed-upon answers to these questions. Seite 3 von 11

4 (p2') Failure of Syntactic Differentiation (i.e Syntactic Density): Because the symbol system of sketching allows for a dense ordering of symbol types (i.e., between any two types there is a third), it is not always possible to tell which type a token belongs to. So, for example, even if we agree that the token a in Figure 3 belongs to only one equivalence-class, it may not be possible to tell which of several classes it does or does not belong to. (p3') Ambiguity: Symbol types do not have the same referent in each and every context in which they appear. For example, the token b in Figure 3 was interpreted as a human head and later reinterpreted as a light bulb. (p4') Failure of Semantic Disjointness (i.e Semantic Overlap): The classes of referents are not disjoint; i.e., each object referred to may belong to many reference-classes. So, for example, the human figure referred to by the symbol-type a may belong to the class of humans and the class of students. (p5') Failure of Semantic Differentiation (i.e Semantic Density): The system of sketching allows for a dense ordering of reference-classes. When this is the case, it is not possible to tell which class a particular object belongs to. For example, in a perspective drawing of a human figure, every height of the figure would correspond to a different class of heights of humans in the world, and these classes of heights are of course densely ordered. In such a case it would not be possible to tell which class a particular human height belongs to. (p6') The system of sketching has no well-specified rules for transforming one state into another. There is no transformation of the token b which would be "incorrect" or "illegal." (p7') As the properties p1-p6 are not present to begin with, they are not preserved in the transformation of the system from one state to the next. It should be obvious that the ill-structured and well-structured distinction is independent of the linguistic and pictorial distinction. The examples that I have illustrated it with are both pictorial. One could use linguistic examples as well. For example, the text of Shelley s Prometheus Unbound would satisfy the semantic criteria for ill-structured representations while a good legal contract would come close to satisfying the syntactic and semantic criteria for well-structured representations. The reader is referred to Goel (1995, chapter 8) for further discussion of this point. 3.Cognitive Role of Ill-structured Representations My claim is that the properties of ill-structured representations facilitate lateral transformations in the following ways (also see Figure 4): 1. Syntactic overlapping gives the marks a degree of coarseness by allowing marks to belong to many different characters. This is a necessary condition for remaining noncommittal about the character. Seite 4 von 11

5 2. Syntactic density gives the marks a degree of fine-grainedness by making every distinction count as a different character. This reduction in distance between characters is necessary to facilitate the transformation from one character to another. 3. Ambiguity of the symbol system insures that the extensions of marks during the early phases of design are indeterminate. Ambiguity is important because one does not want to crystallize ideas too early and freeze design development. 4. Semantic overlap in compliance-classes is needed to remain noncommittal about the exact referent of a character. 5. Semantic density in the ordering of compliance-classes is necessary so as not to exclude possibilities. Figure 4. Role of ill-structured representations in lateral transformation. To date I have provided logical arguments and empirical data from normal controls to support this theory (Goel, 1995). However, recent evidence from neuropsychological studies provide additional data points to evaluate the theory. The Goel and Grafman study of an experienced architect with a right hemisphere lesion is particularly instructive for our purposes and is discussed below. 4.Neuropsychological Evidence Goel and Grafman report the case of patient PF, a right handed 57 year old Caucasian male architect, diagnosed and treated for a right frontal parietal parasagittal meningioma. MRI scans showed a predominantly right hemisphere lesion to the prefrontal cortex, though some minor anterior left frontal damage was also present. At the time of testing, PF had IQ and memory scores in the superior to excellent range, his ability to draw was intact, yet he was unable to design. He was involuntarily retired and lived at home with his mother. To explore the nature of his deficit, Goel and Grafman matched him for age and education with a 54 year old architect and engaged both in a simple architectural design task. Both Seite 5 von 11

6 subjects were asked to propose a redesign for a lab space. They were given the following problem statement specifying a set of constraints and encouraged to ask for additional information as necessary. Our lab space is located in Room 5D51. It currently houses three scientists and five research assistants. Another scientist is expected in January. The number of research assistants can increase up to 16 during the summer months. The space is used for reading, writing, computing, telephone conversations, and so on. In fact, we do all of our work in this space except for seeing patients. Some of us spend up to 10 hours per day there. It is a very dismal environment. Your task is to reorganize, redesign, reconfirm the space such as to increase our comfort and productivity. We do not have a budget for the redesign. However, we do have the option of exchanging some of our furniture at the surplus store, and perhaps we can pool personal time and resources to do some painting and cleaning. You have two hours to propose a design. You may spend up to 15 minutes of the first hour in the lab space. While there, you may measure, make notes and sketches, and ask anyone there any questions you think relevant. You may revisit the lab for 10 minutes anytime during the second hour. Please begin. Both subjects had experience designing office spaces and noted that this was a very easy problem for them. The first notable aspect of PF s performance was that his explicit architectural knowledgebase was intact. Both subjects considered issues ranging from information about users (e.g. numbers, categories), their goals (e.g. a quieter environment), behaviors/activities the users need to engage in (e.g. meetings, writing), the functions the artifact/space needs to support (e.g. circulation patterns), and the actual structure of the artifact (e.g. printers, workstations, dimensions). Both the control and patient displayed the sophisticated knowledge base one would expect from experienced architects. Despite this, there were significant differences in the problem solving behavior of the patient and control. In considering the temporal distribution of design-level statements (problem structuring, preliminary design, refinement, and detailing) we find the control s distribution is quite typical of designers. He begins by problem structuring and has it largely completed in the first quarter of problem solving session. The next part of the session is devoted to preliminary design, followed by design refinement and then detailing, each in roughly equal proportion. The whole process is accompanied by some self-monitoring and the phases reoccur as needed throughout the session. The patient's progress through the problem space is quite different. PF spends two-thirds of the session in problem structuring mode. The preliminary design phase, occurs at the tail end of the session. Its duration is short; it is accompanied by much self monitoring and a great many miscellaneous statements; and the patient s movement through this phase is erratic and lacks progression. It is a phase that the patient has enormous difficulty with. At Seite 6 von 11

7 the 87 minute mark (of a 95 minute session), the beginning of the refinement period, the patient notes "lets start again." Refinement of this proposal occurs during the last few minutes and the session ends abruptly. Throughout the session both subjects make a number of drawings. These drawings depict the generation and development of ideas/concepts and as such, constitute states in the problem space. Figures 5 & 6 show the actual drawings made by the subjects and the type of transformations that lead from one drawing/idea to the other. There are nine states in the control s problem space (Figure 5), a start state (a & b), a goal state (j) and seven intermediate states (c - i). The starting state for the control is drawing (a) of the existing lab space and the accompanying measurement drawing (b). Both drawings were made in the lab space. Three of the intermediate states belong to the preliminary design phase (c - e); four belong to the refinement phase (f - i); and the final state belongs to detailing (j). The preliminary design states are all quite abstract. He begins by considering "circulation patterns" in drawing (c). This pattern constitutes his kernel idea. It is developed and transformed to deal with the issue of and "social organization" (d) and "permanent and transient spaces" (e). The refinement drawings are structural. They depict workstations, tables, doors, windows, and corridors. The subject transforms state (e) into a proposal (drawing f) (half way during the session) that he considers "reasonable". However he thinks the center condition can be improved. He therefore holds the perimeter conditions constant and transforms the center in drawing h. He rejects drawing (h), returns to drawing (f) and transforms it into drawing (g). He is happy with the idea depicted by drawing (g). He now shifts gear and begins to detail and fine-tune the proposal, first in section (drawing i) and then in plan (drawing j). The movement from states (c) to (g) is underwritten by lateral transformations. The transformation of state (g) to (i) and from (i) to (j) is underwritten by vertical transformations. An analysis of the patient s state space tells a very different story. There are five states in the patient s problem space (Figure 6), a start state (a ), a goal state (e) and three intermediate states (b - d). The start state drawing of the existing lab space (a) was completed by the patient from memory in the testing room. It is as detailed and accurate as the control s drawing. The patients final state drawing (e) was completed during the refinement phase. The three intermediate drawings (b - d) were completed during the preliminary design phase. The first of these drawings (c) the kernel idea occurs twothirds way into the session. Unlike the preliminary drawings of the control, the patient is concerned with arranging furniture right from the start. But perhaps the most dramatic difference between the patient and control is that the patient s three preliminary design drawings are fragmentary and unrelated. Seite 7 von 11

8 Figure 5. Control s state space and transformation functions. LT = lateral transformation; VT = vertical transformation. Reproduced from Goel and Grafman. Preliminary design sketches are, almost by definition, fragments of ideas. Designers do not generate several independent fragments and choose between them. They generate a single idea/fragment and develop it through transformations (lateral or vertical) to a point it is complete and can be evaluated. The patient has made several (successful) attempts to generate idea fragments. But he is unable to develop and explore these ideas through the application of lateral transformations. Each of his preliminary drawings must be treated as independent idea/fragments. Indeed, he tries to articulate the difficulty he is experiencing as follows: You see, normally, what I would have, even as a student, I'd be -- there would be sketches on top of sketches. And I could -- it would be progressive. Here I seem to be doing several different thoughts on the same piece of paper in the same place, and it's confusing me. So, instead of the one direction that I had at the beginning, I have three or four contradictory directions with not a kind of anchor to work from... On generating drawing (d) 87 minutes into the session, he says "lets start again". The only idea/drawing transformation he engages in is from (d) to (e). This is a vertical transformation where he fine-tunes the proposal. Seite 8 von 11

9 Figure 6. Patient s state space and transformation functions. LT = lateral transformation; VT = vertical transformation. Drawing (e) is a little misleading. It was executed on transparent tracing paper on top of drawing (d). It includes everything in (d) plus the indicated modifications. Reproduced from Goel and Grafman. Further evidence of the patient s difficulties with the preliminary design phase is provided by analysing the aspects of design development considered by the control and patient during the four phases of design development (problem structuring, preliminary design, refinement, and detailing). During problem structuring and preliminary design the control devotes the majority of his statements to abstract, nonstructural aspects of the design having to do with users, goals, behaviors, and functions. This distribution shifts with the refinement phase, where function and structure dominate, and again in the detailing phase, where structure dominates. For example, during the structuring phase the control considers issues of social hierarchy (research assistants vs. scientists). This is propagated and translated into structural arrangement in terms of giving the scientists more spacious workstations and placing them in corner locations. The level of abstractness of the statements in the patient s problem structuring phase is quite similar to the control s. He solicits and generates much relevant information about people, purpose, and behaviors. The patient s refinement phase distribution is also not unlike the control s. However, the patient s preliminary design phase is dramatically different. Whereas the control carries through the information regarding people, purpose and behaviour through to the preliminary design phase (and in fact through to refinement and detailing) and uses it to guide the emerging design, the patient is unable to carry through this information and use it to guide problem solving. 5.Conclusion Given the above theoretical apparatus and the behavioral deficits observed in the patient, I Seite 9 von 11

10 postulate that PF's lesion has resulted in a selective impairment of the neural system that supports "ill-structured" representations and computations (see Figure 1). The theory allows that the "well-structured" representation and computation system may be largely intact and predicts that the patient may be competent at the detailing (well-structured) phase of problem solving where such a system is required. But because his preliminary design phase is unsuccessful, it is hard to make much of later phases. However, his exceptional performance during problem structuring and on the well-structured neuropsychological tests suggests that the computational system used for well-structured tasks may be intact. This anatomical dissociation provides additional support for both, the distinction between ill- and well-structured mental representations and their respective cognitive roles. There is an interesting mapping between the theoretical apparatus I have introduced and the literature on cerebral lateralization. For many decades there has been experimental and anecdotal evidence to suggest that the left hemisphere is specialized for "logicomathematical" thinking while the right hemisphere is specialized for "visuo-spatial" thinking. There is evidence for hemispheric specialization from lesion data and neuroimaging data, however, the exact dimension along which this breakdown occurs has been difficult to articulate. Proposals have included verbal vs. visuo-spatial, sequential/temporal/ digital vs simultaneous/spatial/analog, logical/analytic vs Gestalt/synthetic, rational vs intuitive, etc.. I want to propose that the well-structured representations and computations may map onto left hemisphere processes while the ill-structured representations and computations map onto right hemisphere processes. That is, the right hemisphere is necessary to support illstructured mental representations and computations and these mental representations and computations are necessary to support cognitive processes that are visual-spatial, simultaneous, analog, intuitive, and synthetic. PF s predominately right hemisphere lesion disrupts this system, and this in turn prevents him from successfully completing the illstructured phases of the task. His verbal-logical/analytic skills and his ability to engage in well-structured tasks (as measured by neuropsychological tests reported earlier) are intact. Lastly, my claim about ill- and well-structured representational and computational systems is a general claim about the structural and computational properties of mental states. The formal properties differentiating ill-structured and well-structured representations do not break down along linguistic and pictorial lines. So there is no reason to expect that the explanation I offer is specific to design or drawing domains, though the system is particularly well developed in designers and they can provide an external trace of it. One would expect to find ill-structured representations and computations used in many illstructured problem solving domains. Acknowledgments This work was supported in part by a York University Faculty of Arts Fellowship and NSERC and SSHRC grants. References Seite 10 von 11

11 Deglin, V. L., and Kinsbourne, M. (1996) Divergent thinking styles of the hemispheres: How syllogisms are solved during transitory hemisphere suppression, Brain and Cognition, 31(3): Gazzaniga, M. S. (1985) Goel, V. (1995) The Social Brain, NY, Basic Books. Sketches of Thought, Cambridge, MA, MIT Press. Goel, V., Gold., B., Kapur, S. and Houle, S. (1997a) The seats of reason: A localization study of deductive and inductive reasoning using PET (O15) blood flow technique, NeuroReport, 8(5): Goel, V., Gold., B., Kapur, S. and Houle, S. (1998) Neuroanatomical correlates of human reasoning. Journal of Cognitive Neuroscience, 10(3): Goel, V., and Grafman, J. (submitted) The Role of the Right Prefrontal Cortex in Ill-structured Problem Solving. Goel, V., Grafman, J., Tajik, J., Gana, S. and Danto, D. (1997) A study of the performance of patients with frontal lobe lesions in a financial Planning Task, Brain, 120: Goodman, N. (1976) Languages of Art: An Approach to a Theory of Symbols (second edition), Indianapolis, IN, Hackett Publishing. Nass, R. D. and Gazzaniga, M. S. (1987) Cerebral lateralization and specialization in human central nervous system. in V. B. Mountcastle, F. Plum, & S. R. Geiger (eds), Handbook of Physiology: The Nervous System Vol. 5 Higher Functions of the Brain, Part 2 Washington, D.C, American Physiological Society, pp Read, D. E. (1981) Solving deductive-reasoning problems after unilateral temporal lobectomy, Brain and Language, 12: Rich, E. (1983) Artificial Intelligence, N.Y, McGraw-Hill Book Company. Springer, S. P. and Deutsch, G. (1981) Left Brain, Right Brain, San Francisco, CA,W. H. Freeman. Seite 11 von 11