unfixing design fixation: from cause to computer simulation

Journal of Creative Behavior

147

A N D Y D O N GS O M W R I T A S A R K A R

Unfixing Design Fixation:From Cause to Computer Simulation

ABSTRACTThis paper argues that design fixation, in part, entails fixation at the level of

meta-representation, the representation of the relation between a representationand its reference. In this paper, we present a mathematical model that mimics theidea of how fixation can occur at the meta-representation level. In this model, newabstract concepts derived from the meta-representation are not simple combina-tions of the design ideas expressed in the primary representation. Instead, theprocess of meta-representation corresponds to the abstraction of new features ata higher, hierarchically separated level of representation from an existing one.We show a computational process of pattern extraction from existing designrepresentations that results in the crystallization of design ideas or ‘chunks’ atan abstract level. The relation between the representation and its referent isexplicitly described in these ‘chunks’, yet the ‘chunks’ have different propertiesfrom the properties of the original representation.

THE FAÇADE OF FIXATIONIn Maier’s classic study on functional fixation (Maier, 1931), subjects are placed

in a room with two cords hanging from the ceiling, one near a wall and one in thecenter of the room, and with a number of objects including a tool (pliers). Thesubject’s challenge is to tie the two cords together; however, the cords are suffi-ciently far apart that it is not possible for the subject to outstretch arms to reachthe two cords. Most subjects are unable to complete the task and never utilize thepliers as a weight for a pendulum. The claim is that the subjects are functionallyfixated on representing the pliers as a tool for forcefully grabbing an object, ratherthan as a weight for a pendulum to swing one cord toward the other, the preferredsolution to the problem. They remain fixated on each tool as a tool for its gener-ally intended use rather than any other use, and are thus unable to solve theproblem (Duncker, 1945). Other explanations for this type of fixation include an

Volume 45 Number 2 Second Quarter 2011

45-2-2011.p65 6/17/2011, 3:39 PM75

Black

148

Unfixing Design Fixation

incorrect representation of the problem or responding to this problem by follow-ing a past experience (i.e., using outstretched arms to grab to distally separatedobjects).

Fixation produced by responding to a problem in a manner based on priorexperience may be further illustrated in the following simple example. The aim isto connect the grid of three by three points (that is, 9 points) with four straightlines without lifting the pencil/pen from the paper. Many people struggle with thisproblem, unable to recognize that the solution to the problem results from relax-ing a self-imposed rule (probably learned in primary school) of not drawing anylines outside the boundary of the grid. Rather than being functionally fixated,they appear to be fixated upon a rule that they have transferred from experiencelikely ‘gained’ a long time ago.

TABLE 1. Draw 4 straight lines through each of the 9 dots without lifting yourpencil (left). Did you think of drawing lines outside the border (right)?

Fixation is thus an inability to overcome a bias in the interpretation of asituation by transferring knowledge from prior experiences in an inappropriatemanner.

Because interpretations of situations require a representation, what kind ofrepresentation are we talking about? In other words, what is the content in therepresentation that is fixed?

In this paper, we dicuss the kind of representation that may be problematic indesign fixation. We will first start with a discussion of representation, mostly basedon Perner’s three-stage model (Perner, 1991). We will then use the model to dis-cuss how fixation with meta-representations is likely to blame in design fixation.We conclude with a computational model that allows us to simulate the fixingand unfixing of meta-representations.

FROM PRIMARY TO META-REPRESENTATIONWhen we speak of a representation, we presume a mind that has symbolic,

representational abilities. What do we mean though by representational abilities?Research in the cognitive development of representational abilities suggests thathumans progress through at least three stages of representational ability (Perner,

31

24

n

nn

n

45-2-2011.p65 6/17/2011, 3:39 PM76

Black


149

1991). In the earliest stage of cognitive development, toddlers possess a capa-bility for primary representation, a representation that has a direct semanticrelation to the world around them. Primary representations have parsimonybetween the representation of the world and the external world. Thus, if theperson represents that there are a pair of pliers in the room, the pliers shouldactually be present. This does not mean that the person must represent the plierswith an external representation such as with a drawing. The person could, forexample, have a mental map of the room with the pliers in a specific location sothat the person can walk across the room to retrieve the pliers without necessar-ily gazing upon the pliers to direct the person toward the pliers. We do not needto have an external representation of the goal to pick up the pliers; rather we onlyneed to have an internal representation of ‘the represented’ based on currentinformation that we have (Perner & Doherty, 2005).

In the second year of life, toddlers begin to represent beyond the immediatepresent and entertain secondary representation models of reality. When a childcan imagine that that one thing (say a banana) stands for another (say a tele-phone), the child employs so-called secondary representations, because inaddition to the (primary) representation of what the object truly is, the personrepresents the object as something else (Perner, 1991). As Perner explains, “sec-ondary representations are purposely detached or “decoupled” from reality andare at the root of our ability to think of the past, the possible future, and even thenonexisting and to reason hypothetically.” (1991, p. 7) That is, to make a second-ary representation, a person needs to “jump out” of the current perception stateand conceive of a new one while not mistaking the real object and its pretendidentity. Thus, in Maier’s two-cord problem, the failure of a subject to see the pairof pliers as a dead weight may characterize a fixation with the primary represen-tation of the pliers, and a lack of secondary representation (the pliers as some-thing else). However, a failure of secondary representation does not itself explainwhy the subject could not identify that the solution involves the use of a pendu-lum. At the time that children have secondary representation skills, they cannotappreciate that others might mis-represent the world, in other words, how a repre-sentation represents, how facts about the world can be interpreted in order toproduce a representation. Knowing that there is a relation between a representa-tion and its referent, and that this relation can have its own representation, wouldmake it possible to update the representation when new knowledge about therelation becomes available.

A crucial part of human reasoning is the ability to reason about that which isnot available to the senses, an ability that is made possible by meta-representa-tion (Perner, 1991; Suddendorf, 1999). Meta-representation is a model of the rep-resentational relationship between a model and the actual referent situation, andis illustrated in Figure 1.

Having meta-representation means understanding that representations havean interpretation. Second, because the representation can be purely internal, wecan manipulate the internal representation based on new information and we can

45-2-2011.p65 6/17/2011, 3:39 PM77

Black

150


FIGURE 1. A meta-representation is a representation of the representationalrelation between a referent (the represented) and its model (that whichrepresents) (Perner, 1991).

that whichrepresents

therepresentedrepresentational

relationn

manipulate the represented by changing its behavior to suit the internal represen-tation (Perner & Doherty, 2005) Clearly, in the situation of design, to see the worldonly as it is, with primary representation, is insufficient. If humans were limited tothis representational ability, creative behaviors such as design would never bepossible. Secondary representation is still insufficient for the purposes of design-ing, since we could then only see a rock as something to pound nuts with, or withsome imagination, as a charm. Having meta-representation allows us to see some-thing as something else, which enables hypothetical substitution.

Children do not immediately recognize that the same representation can havemultiple interpretations even though they can entertain multiple representationsof the same situation. The ability for meta-representation develops in childrenafter about 4 years of age, at which time they start to understand the representa-tional mind and to realize that representation is a mental activity (Lillard, 1993).They begin to conceive of alternate interpretations through an understanding ofhow the features of the referent update the representational relation and to en-gage in complex pretend play. It is interesting to note that once children start tolearn about objects based on their intended function, around age 6-7, they startto become susceptible to functional fixation (Defeyter & German, 2003). Defeyterand German show that before this age, they are not yet fully organizing their knowl-edge about artifacts based on a ‘design stance’ (Dennett, 1987), understandingwhat an object is through conventions on the relationships (meta-representation)between the features of an object (the referent) and the purposes for which theobject was designed (representation of an object by function), even though theyhave knowledge of the function of everyday objects. Thus, while the transfer ofknowledge of past experience in an inappropriate way contributes to designfixation, it is the inability to change meta-representations which is likely blockingthe ability to generate new and alternative representations of function.

We can now apply Perner’s three-stage model to describe how subjects mightbe representing the situation in Maier’s problem. The subject could represent therelation between the referent situation (the represented: the pliers) and the repre-sentation (that which represents: the subject’s mental model of the pliers) throughphysical properties and intended function. The mental model of the pliers nowcontains two structures and a relationship. One structure (A) represents thepliers as an object with mass, geometry, and intended function and the otherstructure (B) represents what the representation depicts (pliers). Finally, the mental

45-2-2011.p65 6/17/2011, 3:39 PM78

Black


151

model must have a model (C) to relate these two together, to represent how therepresentation of an object (A) relates to the actual pliers (B) through its massproperties and geometry. The person could also represent the surface properties(e.g., smoothness) of the pliers, as these are also physical properties, yet therepresentational relation is unchanged, and the result is only a more parsimoni-ous representation of the pliers as a clamping tool. Suppose the subject were toupdate this model C to propose a hypothetical situation wherein the representa-tional relation is modeled by mass only, so that the pliers have no geometry butonly mass (weight) and ignores the intended function. Then, it becomes possibleto have a secondary representation of the pliers as a dead weight, because theperson has modified the underlying representational relation. Attaching other toolscould increase the weight, but adding the other objects would not have theperson represent the pliers plus other objects as some other kind of tool. If wecombine the same line of reasoning to the ropes, the set of changes to themeta-representation could lead the subject to the solution. The subject can repre-sent the set of relations to the referent. This allows us to think of alternatives(Perner, 1991).

Thus, the source of blame in design fixation may be the subject’s meta-repre-sentation of a referent situation. The subject is inappropriately carrying over in-formation because the subject is not altering the underlying representationalrelation, leading the subject to continue producing primary representations ofthe situation. There is a negative transfer of knowledge from prior situations,because the relation between the representation and the referent continues to bebased on what an object is intended for. If this is the case, in the instances ofusing external stimuli to help designers overcome design fixation, rather thanhelping designers to recognize the deficiency in meta-representation, the stimulimay inadvertently cause the designer to lose sight that having (symbolic) insightmeans paying attention more to what the symbol is intended to represent (orcould represent) rather than the properties of the symbol. This problem has beenshown to be exacerbated when subjects are presented with objects that are highlyrealistic rather than those that have generic attributes (DeLoache, 2000; Uttal,O’Doherty, Newland, Hand, & DeLoache, 2009), and, in children learning aboutscientific concepts through visualizations (Linn, Chang, Chiu, Zhang, &McElhaney, 2010). If design fixation is a problem with meta-representation, thatis, the designer both fails to use the representational relation to update ‘that whichrepresents’ and fails to modify the representation relation, the designer may befailing to exploit symbol-referent relations (Sharon & DeLoache, 2003).

In summary, meta-representation means having the ability to change therepresentational relation between that which represents and the represented.In practice, we deal with multiple sets of representations and their meanings(those which refer) with respect to the real world being modeled, or the repre-sented, and meta-representation means having the ability to change the “web” ofrepresentational relations. Most adults can do this, but part of design fixationalready starts here.

45-2-2011.p65 6/17/2011, 3:39 PM79

Black

152


In the next section, we will show an algorithm based on the matrix factorizationtechnique of singular value decomposition. The algorithm has the quality ofbeing able to “jump out” of singular mappings between symbol and meaning.We will illustrate the properties of producing representational relations, updatingthe representational relations from changes in the referent situation, and produc-ing alternative representations of the referent situation based upon desireddegrees of parsimony as one possible way to influence the interpretation ofrepresentations.

ALGORITHM FOR META-REPRESENTATIONWe present an example from the domain of architectural design to demon-

strate an algorithm that mimics meta-representation, which may further help tounderstand the mind’s conceptual apparatus underlying fixation and de-fixation.A common design task regularly performed in architectural design is space lay-out planning. Space topology planning is a process in which a feasible or bestconfiguration has to be found for a set of space components (for example, rooms),given some constraints on connectivity or adjacency. Some very simple examplesare the requirements that a kitchen must connect to the dining area in a house, orthat lifts and staircases must be centrally placed in an apartment complex. Acomplete design for a building may involve tens or hundreds of such require-ments and constraints, depending on the size of the project. The design problemis to work out feasible or optimal space layout configurations that do not violatethese constraints. Often, this crucial task sits at the beginning of every architec-tural design project, and is the basis for generating the conceptual plan uponwhich further development of the project rests. Architects frequently employ“bubble diagrams“ to work out feasible topology configurations, in which spacesare assigned as bubbles of different sizes, depending on their area requirements;connections between the bubbles mark the architect’s topological plan.

The problem has an inherently combinatorial, discrete and multi-modalnature, making it very difficult for designers to have a clear view of a definedproblem-space. At the outset of a design problem, designers simply do not knowall the problems that will need to be worked out. They perform something like aprogressive treatment of constraints, mostly guided by the architect’s intuitive“vision” for the project, and allow the problem space and solution space toco-evolve (i.e., the solution-space can expand/contract the problem-space andvice-versa) (Suwa, Gero, & Purcell, 2000). Therefore, there is a danger of becom-ing fixated in a small part of the overall solution space: the existing solution mayrestrict the designer from seeing many other alternative feasible or better solu-tions that may exist for the same set of topological constraints. Visual analogieshave been promoted as a possible intervention to minimize the effects of suchfixation and to improve problem solving in space planning (Casakin &Goldschmidt, 2000). What compounds the problem further is that there may beaesthetic considerations that are not captured directly by these topological con-straints. The only way to jump out of any fixation is to reformulate the existingsolution model into a new one. Usually, this is infeasible and expensive, because

45-2-2011.p65 6/17/2011, 3:39 PM80

Black


153

an architect can only develop a few solutions in parallel, while the combinatorialnumber of possible solutions to the problem may be very large. Therefore, this isan example where an early fixation on a solution may prevent a designer fromadequately exploring the solution space.

While the bubble diagram itself sits at the secondary representation stage (lines,shapes and relationships between them signify real spaces and spatial interac-tions ), whether or not the secondary representation is able to represent the com-plete design solution is a meta-representation question. Referring to Figure 1, themeta-representation question is whether the set of representations chosen (thedrawing) is able to satisfactorily represent the space of potential solutions ratherthan a single solution. Could the re-representation of this relationship (i.e. the“arrow” in the diagram) lead to a better solution?

With this example in mind, we now present an algorithm that develops alter-nate ways of representing, such that the algorithm is able to represent the relationbetween its representation of topology and the actual topology. We consider first,similar to the bubble diagram, an alternative matrix representation of the spatial/ topological constraints and relationships. We note here that this is still just asecondary representation. Suppose that an architect designing an apartment haschosen to consider the following set of requirements, with each of therequirements converted to an arbitrary but consistent numerical score in a ma-trix. The numerical score rewards with positive integer values the highly desirableconnections but penalizes the not desirable ones with negative integer values.

1. The kitchen must be connected to the dining room and may be connected tothe living room.Kitchen-Dining score = 3Kitchen-Living score = 1

2. The living room must be connected to the bathroom.Living-Bath score = 3

3. The kitchen must not be connected to the bathroom.Kitchen-Bath score = –1

4. The bedroom must be connected to the living room, and may be connected tothe dining room.Bedroom-Living score = 3Bedroom-Dining score = 1

This set of requirements produces a matrix as shown in Figure 2. The diagonalentries of the matrix have been given a highest score of 4, with the commonsense interpretation that any space is most connected to its own self. Further, indesign, a common occurrence is that designers work with incomplete informa-tion. The incompleteness may arise from the fact that some information is genu-inely not available, or from the fact that the problem model has simply missedout considering some requirements. For example, a very important constraint,that the bedroom should be connected to the bathroom, is missing from this set.

45-2-2011.p65 6/17/2011, 3:39 PM81

Black

154


FIGURE 2. Matrix representation of topological requirements.

A matrix technique called the Singular Value Decomposition (SVD) is performedon this matrix. SVD enables dependent information in the original data to bedecoupled and then re-coded in an independent way such that the original matrixcan be described in terms of a linear combination of linearly independentorthonormal bases. Mathematically, this is stated as X = USVT. Conceptually, itdiagonalizes the matrix X into a set of independent vectors in two orthonormalbases U and V (the left and right singular vectors), along with a measure (thesingular values S) of how important a particular vector is in capturing theinformation specified in the matrix X. The largest singular value captures themost important pattern of association in the data, and so on in decreasing orderof magnitude. This is a re-representation step only, because these new represen-tations can be combined at any time to reproduce the original information.

Figure 3 shows a conceptual representation of what SVD does. Conceptually,the newly derived left and right singular vectors U and V are attributes of thereferent that are not immediately apparent (perceived) in the original data, andthe singular values S are a measure of the weight of each newly derived represen-tation vector, i.e. how important it is in capturing the representational relationbetween the referent and the representation.

Living Dining Kitchen Bedroom Bathroom

Living 4 1 1 3 3

Dining 1 4 3 1 0

Kitchen 1 3 4 0 –1

Bedroom 3 1 0 4 0

Bathroom 3 0 –1 0 4

FIGURE 3. Deriving meta-level vectors and weight values to enable creation ofmultiple secondary representations.

Performing the SVD is the first re-representation task that changes a second-ary representation — a matrix with dependent information is converted into threematrices that have the same information in an independent manner. Now, eachspace can be represented as a point in space, and the mathematical distancebetween them is a measure of how close or far apart they should be in terms of the

Map of concept Newly Values to Newlyspace to concept derived capture the derivedspace independent weight or independent

concept importance of conceptvectors each vector vectors

= * *

X U S VT

45-2-2011.p65 6/17/2011, 3:39 PM82

Black


155

constraints. Because the SVD allows us to calculate a distributed map of associa-tions derived from perceived information about the referent, it can be used tocompute a meta-representational relation. It allows us to form many possible sec-ondary representations starting from the primary representation. Further, any newinformation or changes to X will change the distributed relations calculated by Uand V even if those changes do not fundamentally alter what X represents. In thisexample, these changes could be weakening or strengthening a rule.

The next crucial re-representation step is a dimensionality reduction step thatenables us to extract alternative “bubble diagrams” from the same information.Recall that the original design task is to generate new representations or mapsbetween the represented (design) and representation (matrix of associations orthe bubble diagram). Taking lower dimensional approximations of the originalmatrix is a crucial way in which the original information can be represented bymeasuring varying degrees of possible associations between the spaces. For ex-ample, the original matrix size is 5 × 5, i.e. there are 5 dimensions. However,taking a 2-dimensional approximation of the matrix using the SVD decomposi-tion allows us to use the two most important singular values and vectors in pro-ducing a new set of derived vectors, i.e. new points in space. In re-representingthe referent in a lower-dimensional space, it pulls the strongly connected pointscloser together and pushes the weakly connected points farther apart in space.Now, taking distances between spaces produces a new representation of the space.Due to special mathematical considerations, discussed elsewhere (Sarkar, Dong,& Gero, 2009, 2010), we choose a cosine angle measurement between the vec-tors to decide how close or far apart they are. The higher the cosine value be-tween a pair of vectors, the higher is the desirability of connection between thespaces they represent. The lower the cosine, the lower the desirability of the con-nection. In a sense, the choice of the cosine measure flexibly allows us to re-represent the original representation in whatever lower dimensional space anddistance away from the original representation without completely departing froma plausible representation of the referent. Figure 4 shows the results of the illus-trative example at a 2D approximation of the 5 dimensional matrix. The numbersrepresent the cosines between the vector representations of the two pairs of spaceswhen computed after the SVD and dimensionality reduction steps.

Living Dining Kitchen Bedroom Bathroom

Living 1.0000 0.4704 0.2563 0.9911 0.8483

Dining 0.4704 1.0000 0.9736 0.5835 –0.0683

Kitchen 0.2563 0.9736 1.0000 0.3826 –0.2944

Bedroom 0.9911 0.5835 0.3826 1.0000 0.7703

Bathroom 0.8483 –0.0683 –0.2944 0.7703 1.0000

FIGURE 4. Results of applying SVD and dimensionality reduction, re-representingthe representational relation.

45-2-2011.p65 6/17/2011, 3:39 PM83

Black

156


Note the mathematical consistency — the cosine between a space and itself is1, the highest possible value. The other numbers show the relative strengths ofthe desirability of the connection between a pair of spaces. The results show thatthis algorithm is able to generate an implicit set of constraints derived from theexplicit ones, so that even in cases where the model is under or over constraineda topology may be generated. For example, recall that no explicit relationshipwas specified between the bedroom and the bathroom in the original set ofconstraints. This is an example of a more general occurrence in design problems.Complete information is either unavailable or the designer may miss out on someinformation in the modelling process. The relationship between bathroom anddining was also undefined. From a general understanding that arises from havinglived in a house, one may expect that the bathroom should be close to the bed-room, but no such preference exists between the bathroom and the dining room(assuming that a sink in the kitchen or a wash area exists).

Now, note from Figure 4 that even though both relationships were 0 in theoccurrence matrix, the cosine measurement between bedroom and bathroom ishigh at 0.7703 in the dimensionally reduced approximation, while the cosinemeasurement between the bathroom and dining space is negative at –0.0683.This is not surprising because the algorithm uncovers implicit constraints andrelationships from explicit ones in the problem representation. While both bed-room and bathroom share a high explicit relationship with the living space,

FIGURE 5. A possible design solution.

45-2-2011.p65 6/17/2011, 3:39 PM84

Black


157

causing their mutual cosine values to increase, the bathroom and dining spacedo not share common high relationships with any other common spaces. Thiscauses their mutual cosine value to decrease. Figure 5 shows a bubble diagramgenerated by using the cosine values in Figure 4. The line thicknesses show thedesirability of the spatial connection.

What is mathematically evident is that the algorithm operates not on singularrelationships ascribed between a secondary representation and what it represents,but instead it operates on a collective map of such relationships at a meta-level.Thus, it mimics the exploration of multiple secondary representations as a solu-tion to the same design problem with the same set of constraints by modifyingmeta-level parameters.

While this algorithm mimics meta-representation, it may also assist designersin becoming unfixed. The designer could choose to modify the requirementor constraint set, i.e. the entries in the original matrix, to identify an altered repre-sentation as a solution. If only a single constraint is altered, it shows up as achange in the corresponding numerical entry in the matrix. Changing this singleconstraint may very well result in changing the entire map of distributed relation-ships. Contrast this with the usual method: changing a single constraint wouldimply that the designer handle this locally, within the bounds set by the existingsolution being developed manually.

Second, the designer could apply the dimensionality reduction step parametri-cally, where the number of dimensions is chosen as the meta-level parameterto produce different approximations and thus observe different solutions. Forexample, a designer in the above problem may consider 5 different dimensionalapproximations. Not all the approximations may show useful design solutions,but usually we have found that the using the first few approximations yield goodsolutions. We have shown elsewhere that the mathematical construction is suchthat it will never violate the set of original constraints shown in the matrix, but willallow a designer to see the results of considering different solutions by consider-ing varying degrees of strength of relationships specified by the constraints (Sarkar,et al., 2009).

Third, the designer could fix different cosine values as thresholds, and pro-duce different solutions. For example, Figure 5 shows a solution where the cosinethreshold is set at 0.4. All the connections that have cosine values more than 0.4are considered to be valid physical connections: a corresponding possible layoutis shown. If this cosine threshold is changed to say 0.6, then a direct connectionbetween the bedroom and the dining will disappear (not shown in the figure).

In working only with a single bubble diagram that treats constraints pro-gressively, a designer may become fixated on the immediate relationship betweena representation (the bubble diagram or drawing) and what it represents (thedesign solution). By allowing an algorithm to work on a meta-level map of therelationships between the representation and its referent, it becomes possibleto see a family of possible solutions, some of which may not have arisen fromconsidering only the singular requirement relationships.

45-2-2011.p65 6/17/2011, 3:39 PM85

Black

158


We note here that unlike the illustrative example chosen here for the purposeof demonstration, real design problems run into hundreds and thousands of suchvariables, requirements and constraints, and a designer frequently has to resortto complex mathematical modeling and design tools to generate possible solu-tions. We have presented a computational mechanism here that allows a pur-poseful exploration of a family of secondary representations by parametricallyexploring a meta-representation level parameter that collectively operates ona map or network of relationships. Previously, we have shown the successfulapplication of this method onto much larger design problems in the engineeringdesign domain (Sarkar, et al., 2010).

CONCLUSIONSThis paper presented a case for the failure to meta-represent as a cause for

design fixation, and presented an algorithm that exhibits an ability to meta-repre-sent. Meta-representation fits into the larger scheme of cognitive processing thatproduces concepts from sensations. In this process, the brain combines percep-tual information with knowledge from memory to construct a meaningful repre-sentation (concept) of the perceptual information. While there is a great deal ofregularity in this construction, i.e., when we perceive a pair of pliers, we generallyproduce the concept of pliers as a specific type of tool, the architecture of thebrain allows for a great deal of freedom in available concepts. The ability to gen-erate different concepts of the same stimuli based on the prevailing context iscentral to the behavioral flexibility of humans and many other species, particu-larly the great apes. Thus, representations are not static for given stimuli becausethe brain’s encoding processes can be variable. Yet, there is a problem of regular-ity in design fixation, because there is a failure to conceive of stimuli as ‘some-thing else’ than what it normally is. The real question is, thus, what type ofintervention in the representation-making process may be most useful in over-coming design fixation? Our results would predict that providing designers withexplicit support for meta-representation can help them ‘abandon’ flawed lines ofthinking and thereby recover from design fixation. Recent experimental resultsby Zahner on rerepresentation as a way to overcome fixation (Zahner, Nickerson,Tversky, Corter, & Ma, 2010) support exactly our prediction that helping design-ers to recognize and represent the relation between a representation and thatwhich is represented and then to flexibly modify this relation may assist thedesigner in producing alternative and possibly more productive representations.

REFERENCES

CASAKIN, H. P., & GOLDSCHMIDT, G. (2000). Reasoning by visual analogy in design problem-solving:the role of guidance. Environment and Planning B: Planning and Design, 27(1), 105-119.

DEFEYTER, M. A., & GERMAN, T. P. (2003). Acquiring an understanding of design: evidence fromchildren’s insight problem solving. Cognition, 89(2), 133-155.

DELOACHE, J. S. (2000). Dual Representation and Young Children’s Use of Scale Models. ChildDevelopment, 71(2), 329-338.

45-2-2011.p65 6/17/2011, 3:39 PM86

Black


159

DENNETT, D. C. (1987). The intentional stance. Cambridge, MA: MIT Press.

DUNCKER, K. (1945). On Problem Solving. Psychological Monographs, 58, 113.

LILLARD, A. S. (1993). Pretend Play Skills and the Child’s Theory of Mind. Child Development, 64(2),348-371.

LINN, M. C., CHANG, H.-Y., CHIU, J., ZHANG, H., & MCELHANEY, K. (2010). Can desirable difficultiesovercome deceptive clarity in scientific visualizations. In A. S. Benjamin (Ed.), Successfulremembering and successful forgetting: a Festschrift in honor of Robert A. Bjork. London:Psychology Press.

MAIER, N. R. F. (1931). Reasoning in humans. II. The solution of a problem and its appearance inconsciousness. Journal of Comparative Psychology, 12(2), 181-194.

PERNER, J. (1991). Understanding the Representational Mind. Cambridge: The MIT Press.

PERNER, J., & DOHERTY, M. (2005). Do infants understand that external goals are internally represented?Behavioral and Brain Sciences, 28(5), 710-711.

SARKAR, S., DONG, A., & GERO, J. S. (2009). Design optimization problem (re)-formulation using singularvalue decomposition. Journal of Mechanical Design, 131(8), 10.

SARKAR, S., DONG, A., & GERO, J. S. (2010). Learning Symbolic Formulations in Design: Syntax,Semantics, Knowledge Reification. Artificial Intelligence Engineering Design Analysis andManufacturing, 24(1), 63-85.

SHARON, T., & DELOACHE, J. S. (2003). The role of perseveration in children’s symbolic understandingand skill. Developmental Science, 6(3), 289-296.

SUDDENDORF, T. (1999). The rise of the metamind. In M. C. Corballis & S. E. G. Lea (Eds.), The descentof mind: psychological perspectives on hominid evolution (pp. 218-260). Oxford: Oxford UniversityPress.

SUWA, M., GERO, J., & PURCELL, T. (2000). Unexpected discoveries and S-invention of designrequirements: important vehicles for a design process. Design Studies, 21(6), 539-567.

UTTAL, D. H., O’DOHERTY, K., NEWLAND, R., HAND, L. L., & DELOACHE, J. (2009). Dual Representationand the Linking of Concrete and Symbolic Representations. Child Development Perspectives, 3(3),156-159.

ZAHNER, D., NICKERSON, J. V., TVERSKY, B., CORTER, J. E., & MA, J. (2010). A fix for fixation?Rerepresenting and abstracting as creative processes in the design of information systems. ArtificialIntelligence for Engineering Design, Analysis and Manufacturing, 24(Special Issue 02),231-244.

Andy Dong and Somwrita Sarkar, Design Lab, The University of Sydney, Faculty of Architecture, Designand Planning, Wilkinson Building (G04), Sydney NSW 2006 Australia; [email protected];[email protected]

45-2-2011.p65 6/17/2011, 3:39 PM87

Black

unfixing design fixation: from cause to computer simulation

Documents