Creative Search Trajectories and their Implications
Kyle E. Jennings
Department of Psychology
University of California, Davis
Davis, CA 95616 USA
kejennings@ucdavis.edu
Abstract
Creative search trajectories are chronologically organized
intermediate products (such as sketches and
drafts) from the creative process. We discuss what
sorts of conclusions can be made when these trajectories
show non-monotonic progress toward the final creation.
We introduce several key distinctions that are often
overlooked, and argue that two null hypothesis processes
must be rejected before non-monotonicity can be
claimed to support more complex processes. We show
that these null hypotheses are in fact difficult to rule out
definitively using the sorts of evidence that past research
has offered.
The sketches, drafts, revisions, and rejected ideas that creators
leave in their wake on the way toward great masterpieces
offer glimpses of the mental processes that are responsible
for their achievements. Ordered in time, these artifacts
trace a trajectory through a mental space, and may
be the signatures of the specific exploration strategies that
differentiate great thinking from the mundane. Even the differences
in creativity that can be observed among study participants
may be explainable by tracing and analyzing the
detailed steps taken with simple creative problems.
This approach—which we call trajectory analysis—
borrows from the problem solving research of Newell and
Simon (1972) and others. However, whereas most problem
solving research uses problems that are concrete, objective,
and formalizable in terms of specific states, operators, and
goals, the creative problems faced by artists, writers, and scientists
are less easily reduced to symbols, rules, and computational
steps. Though there are examples where researchers
have meticulously examined creative search trajectories using
objective features (Weisberg 2004), most research has
let subjective judgments stand in for complete formal details
(Kozbelt 2006; Simonton 2007; Kozbelt and Serafin 2009;
Damian and Simonton 2011). Despite taking different approaches,
many of these results point to the conclusion
that creative outcomes are not arrived at directly, but rather
through the twists and turns of false starts and retraced steps.
These observations have been taken as evidence that the creative
process is tentative and experimental rather than deliberate
and informed.
Given how complex it would be to devise comprehensive
and objective descriptors of intermediate states in creative
problems, it may not be practical to overcome all of the imperfections
of subjective judgments. However, this does not
mean that conclusions drawn about the creative process on
the basis of these judgments do not need to be rigorously justified.
While it seems intuitively clear that a process that is
tentative, uncertain, or experimental would produce trajectories
that do not move monotonically closer to the final solution
(Simonton 2007; Damian and Simonton 2011) or that do
not show monotonic improvement over time (Kozbelt 2006;
Kozbelt and Serafin 2009), caution must be exercised before
concluding that trajectories with these features could only
have been produced by such processes.
This paper aims to clarify what can and cannot be concluded
about the creative process on the basis of creative
search trajectories. Though we are ultimately optimistic
about the potential of this approach and advocate the view
that creativity requires uncertainty and experimentation, we
will show that existing evidence that creative search trajectories
are non-monotonic is in fact compatible with very
straightforward search processes, and that more care and
precision must be used when analyzing search trajectories.
We begin with a more detailed discussion of existing trajectory
analysis approaches, and then describe in overview
the distinctions that past work has overlooked. We then illustrate
these distinctions by presenting simple but formally
complete examples that demonstrate the need for caution
when drawing the conclusion that non-monotonic search trajectories
necessarily reflect something other than a straightforward
process. We conclude by discussing the burden of
proof placed on researchers who wish to infer the causes
of non-monotonicity and by offering suggestions for future
work.
Background
While there are many approaches that people have taken to
using intermediate products to understand the creative process
(Getzels and Csikszentmihalyi 1976; Finke, Ward, and
Smith 1992; Hennessey 1994; Ruscio, Whitney, and Amabile
1998; Rostan 2010), this paper focuses specifically
on techniques that characterize the nature of the changes
between successive revisions of the work (Kozbelt 2006;
Simonton 2007; Kozbelt and Serafin 2009; Damian and Simonton
2011). Common to these analyses is the prediction
that creativity should be associated with non-monotonicity,
International Conference on Computational Creativity 2012 49
A B C D E F G H
A B C D E F G H
8
7
6
4
2
1
5
3
8
7
6
4
2
1
5
3
What must be
found?
The most desirable
final state
A path between
initial and goal states
What is (non-)
monotonic?
Distances from
intermediate to final state
Quality of
intermediate states
When is quality
judged?
During search After search
How is distance
judged?
Differences in
salient features
Differences in
state representations
Shortest path
between states
Genotypic
distance
Phenotypic
distance
Transformation
distance
Contemporaneous
fitness
Retrospective
fitness
State
monotonicity
Fitness
monotonicity
Path search Place search
External
problem state
What sequence of states
is being analyzed?
Internal
search state
(Solution)
path
Search
trajectory
Figure 1: Depiction of the key questions, answers (italicized), and terms (bolded) that impact how search trajectories are
analyzed.
which is perhaps best understood as the opposite of direct,
incremental progress toward the final creation (other theories
predict this, too, e.g., Perkins 2000). Beyond this
commonality, the theories differ in their reasons that nonmonotonicity
should be expected, and indeed in how they
operationalize monotonicity.
One approach to characterizing monotonicity is that taken
by Kozbelt (2006) in his analysis of the sketches preceding
Matisse’s Large Reclining Nude. His approach focuses on
the evaluation of each sketch, and in particular on whether
the sketches become monotonically better with time. Given
that Matisse’s own evaluations are not available, Kozbelt has
both artists and non-artists rate each sketch (presented in a
random order) on 26 items, which are then analyzed in order
to extract a latent quality dimension. The artists’ ratings
are found to be maximal at the final image, but beyond this
they show non-monotonic variations over time (the contour
of which is replicated in the non-artist sample). Similarly,
Kozbelt and Serafin (2009) analyze intermediate sketches
from drawings by non-eminent artists, and find that artwork
that had been previously rated as more creative resulted from
less monotonic trajectories. This is suggested to be due to an
“interactive, hypothesis-testing dynamic” (Kozbelt and Serafin
2009, p. 358), though the specifics of this process are
not articulated.
The other approach taken to characterizing monotonicity
involves looking at the structure of the sketches themselves.
The preponderance of this evidence stems from
sketches Picasso left of Guernica. After an informal suggestion
by Simonton (1999) that these sketches showed “false
starts and wild experiments” (p. 197), Weisberg (2004) undertook
a detailed analysis of the features shared between
sketches and concluded that they were elaborations on a
basic idea that itself had precedent in other work, including
Picasso’s own Minotauromachy. In response, Simonton
(2007) undertook an alternative analysis in which various
raters arranged the sketches in the order they would
most logically have been generated, which reliably resulted
in an order that did not match the actual temporal order.
Later, Damian and Simonton (2011) had raters judge the
similarity of the components from Minotauromachy to their
counterparts in the Guernica sketches, and again found
that the Guernica work did not get monotonically closer
(or further) from the prototypes. Simonton claims this
as evidence in support of the Blind Variation and Selective
Retention (BVSR) theory of creativity (Simonton 2003;
2010), which holds that both desirable and undesirable variations
will be generated during the creative process.
The Simonton work, in particular, has generated a great
deal of recent controversy (Dasgupta 2011; Gabora 2011),
much of it focused on the computational and algorithmic
specifics of BVSR theory. In fact, neither Kozbelt’s nor
Simonton’s analyses offered precise and detailed accounts
of the processes that would lead to non-monotonicity, with
Gabora (2011) suggesting that BVSR wouldn’t even predict
non-monotonicity. While Simonton has begun better
formalizing BVSR theory (Simonton 2011; 2012), the fact
is that there are basic problems for the trajectory analyInternational
Conference on Computational Creativity 2012 50
sis approach that any theory of the creative process must
overcome. Therefore, rather than specifically addressing
the claims by Kozbelt and Simonton, this paper will instead
try to address some basic inconsistencies regarding
how monotonicity is conceptualized and operationalized,
and will demonstrate that non-monotonicity can result from
processes that are more straightforward than most theories
suggest.
Overview of Distinctions
In this paper we introduce several distinctions that are essential
when analyzing search trajectories. As depicted in
Figure 1, these distinctions revolve around questions about
what the search must find, what aspect of trajectory monotonicity
is of interest, and how monotonicity is measured.
Throughout the paper we will define and illustrate the terms
that these questions delineate, using the coordinates in the
margins to reference to the relevant portions of the figure.
The first and most important question is what the search
must find (Figure 1, D1). Problem solving research describes
problems by the set of states and the operators that
move between them. The problem solver’s goal is to find a
sequence of operator applications that transforms the initial
state into (one of) the goal state(s). Because the goal state is
already known, the thing being searched for is the path itself,
which is why we refer to these as path searches (Figure 1,
AB23). (See also Jennings, Simonton, and Palmer 2011.)
Because the goal states are well known in path search,
solution quality depends more on the quality of the path
than on the specific goal state reached, with shorter (or less
costly) paths being better. Though this situation aptly describes
many problems (e.g., proving a theorem, inventing
a process for synthesizing a given protein) there are other
problems where the end points are not known in advance.
For instance, in painting the artist seeks to depict a certain
scene, theme, or emotion using brush and paint. In most
cases we compare paintings not by the set of brushstrokes
that led from an empty canvas to the completed image, but
rather by that image itself. Thinking of these final images as
places in a solution space, we refer to this as a place search
(Figure 1, EF23).
Creativity is possible with both path and place search,
and most real problems involve some element of each (e.g.,
choosing a place and then finding the path to it). Though
we’ll speak of these as distinct kinds of searches in this paper,
we recognize that understanding joint path-place search
is an essential task for future work.
Monotonicity in Path Searches
Our discussion begins with path search. For simplicity we’ll
consider the classical Towers of Hanoi problem. (Though
this problem leaves little room for creativity, it nicely illustrate
our key points.) As depicted in Figure 2, there are three
disks of decreasing size that are initially stacked on the leftmost
of three pegs. The problem is to move the disks to the
rightmost peg by moving one disk at a time without placing
larger disks on top of smaller disks. The figure shows the
shortest sequence of states that solves the problem, which
together constitute the path found in this path search.
The Towers of Hanoi is often used to illustrate the failure
of an heuristic called difference reduction, which entails
iteratively applying the operator that most reduces the discrepancy
between the current state and the goal state (Anderson
1993). In fact, solving this problem requires selecting
operators that temporarily make the current state less
similar to the goal state, and for this reason it could be argued
that even a simple problem like the Towers of Hanoi
has a non-monotonic solution. By this logic, there is no
controversy behind claiming that creative problems exhibit
non-monotonicity. However, we will see that the Towers of
Hanoi isn’t inherently non-monotonic, at least in sense that
matters when making inferences about the search process.
Let’s begin by looking at the monotonicity of the sequence
of states forming the shortest path in Figure 2.
Though we’ll ultimately conclude that these are not necessarily
the states that we should be analyzing when making
inferences about the search process, they conveniently illustrate
the different ways that monotonicity can be judged.
The difference reduction heuristic works by economically
comparing the current and goal states. For example, we
could compare states by looking directly at their representations.
Each state in Figure 2 can be described as an ordered
triple indicating which pegs the smallest, middle, and largest
disks are on. (This is sufficiently descriptive since larger
disks cannot be on top of smaller disks.) Thus, the starting
state is (1, 1, 1), the final state is (3, 3, 3), and the intermediate
states are (3, 1, 1), (3, 2, 1), etc. By analogy to genetics,
we can think of the state encoding as being a genotype.
We’ll define genotypic distance to be the dissimilarity between
the encodings of two states, which here we can define
as the sum of absolute differences in state representations
(Figure 1, C78). For instance, the third state, (3, 2, 1) differs
from the final state, (3, 3, 3), by |3!3|+|3!2|+|3!1| = 3.
We could also compare states by looking at their salient
features, which may or may not be directly related to the
state encoding. Again by analogy to genetics, we’ll call
this phenotypic distance (Figure 1, D78). For the Towers
problem, let’s calculate phenotypic distance by counting the
number of disks that are on different pegs. Thus, the first
and final states differ by three, the second and final by two,
and so on.
As Figure 2 shows, the best solution to the Towers problem
is indeed non-monotonic in genotypic distance (DG)
and phenotypic distance (DP ), with the solution becoming
less similar to the goal at various points, and difference reduction
would indeed fail with either of these methods for
choosing operators. However, the fact remains that the sequence
of moves shown is minimal (the path is the shortest
path possible). Defining the transformation distance (DT )
as the length of the shortest path between two states (Figure
1, E78), then we can see in Figure 2 that the path does
get monotonically closer to the final state. On the one hand
this is a useless insight since performing difference reduction
with DT just pushes the work of finding the solution
into calculating DT . On the other hand this reveals that the
solution really isn’t non-monotonic, in the sense that there
International Conference on Computational Creativity 2012 51
DP
DT
t
0 1 2 3 4 5 6 7
DG
Figure 2: Illustration of non-monotonicity in genotypic distance, DG, and phenotypic distance, DP , but monotonicity in
transformation distance, DT , with the Towers of Hanoi problem. Distances are between the current state and the goal state, and
have been normalized. The sequences of moves shown is optimal.
is no point when the path takes steps leading away from the
goal state.
Having defined the various distance metrics that can apply
to states, we need to ask whether we’re in fact looking at
the states that are relevant when making process inferences.
Recall that in path search the solution is itself a sequence
of states connected by operators. Thus, the states at the bottom
of Figure 2 jointly constitute the solution path (Figure 1,
A45). If the problem solver only represents the current state
and the goal state, essentially treating each step in the solution
as a new problem, then each of the individual states in
Figure 2 may indeed describe the problem solver’s internal
state in each step, and we would conclude that the path is in
fact monotonic since no state is ever revisited.
Suppose instead that the problem solver uses a technique
like means-ends analysis (Newell and Simon 1961). In this
case the internal search state would need to represent subgoals
and paths with gaps. For example, the first subgoal
in means-ends analysis would be to move the largest disk to
the rightmost peg. This might be represented as:
(1, 1, 1) ! ??? ! (?, ?, 3) ! ??? ! (3, 3, 3)
The path would then be built recursively by filling in
the steps before (?, ?, 3) and then the steps after (?, ?, 3).
Whether this process is monotonic depends on, for example,
whether the problem solver ever fails to achieve one subgoal
and tries another one. Monotonicity would have to be evaluated
according to the sequence of internal states (the search
trajectory; Figure 1, B45), not the states of the problem itself
(Figure 1, A45).
The importance of looking at internal states is clear when
we realize that any search process that successfully finds a
monotonic path may have explored longer paths that were
ultimately edited before emitting the solution. For instance,
a mathematician may prove several different lemmas as part
of the proof of a larger theorem before realizing that they
are all part of one general lemma and collapsing them accordingly.
The final published proof would reflect this realization,
but that does not imply that the mathematician’s
own thought processes followed the minimal path presented
in the publication.
To summarize, when analyzing path searches, the relevant
states to consider are the internal states, which will
contain but may not be identical with the problem states.
Non-monotonicity should be judged using transformation
distance, as this is the most direct measure of whether the
trajectory includes apparently wasted effort.
Monotonicity in Place Searches
We’re now ready to shift our emphasis to place searches,
where the major aim of the search is to find the most desirable
final state (Figure 1, F23). Here we’ll adopt a landscape
metaphor, wherein states, ~x, are thought of as being topographically
organized according to the available operators.
Each state’s desirability is denoted f(~x), which we’ll call
it’s fitness in keeping with genetics-inspired language used
for genotypic and phenotypic distance.
Our discussion in this section considers search processes
that maintain a single current state that is iteratively improved.
Though these processes may consider several alternate
states in each iteration, only one survives into the
next iteration. (As with path-place searches, we leave place
searches where multiple states are under simultaneous re-
finement for future work.) We’re not going to attempt to
show that any particular process fitting these parameters is
most plausible. Instead, we discuss two processes that are
relatively implausible and yet not straightforward to rule out
with trajectory analysis. The first is a computationally implausible
process that always finds the most efficient path
between the initial and final state, which we call the direct
process.1 The second, which we call the hill climbing process,
takes the psychologically implausible steps of evaluat-
1
Practically speaking, finding evidence for the direct process
suggests that the entire search occurred mentally, making trajectory
analysis the wrong analytical approach for that problem.
International Conference on Computational Creativity 2012 52
DG
Hill Climber
Direct
Time
f(x)
Figure 3: Illustration of (a) the hill-climbing process, which shows non-monotonicity in genotypic distance but monotonicity in
fitness (solid lines), and (b) the direct process, which shows monotonicity in genotypic distance but non-monotonicity in fitness
(dashed lines). Times and distances have been normalized.
ing every available move and always choosing the one that
most improves fitness, stopping when no improvement is
possible (regardless of how low the current state’s fitness).
Whereas monotonicity in path search always referred to
the states in the search trajectory, place search lets us look
at the monotonicity of both the intermediate states and their
fitnesses (Figure 1, F3). We’ll call the monotonicity of the
intermediate statesstate monotonicity (Figure 1, DE45). The
same distinctions between genotypic, phenotypic, and transformation
distance apply, and as before transformation distance
is the most relevant form of monotonicity (though usually
not the most convenient to calculate). We’ll call the
monotonicity of the fitness function over time fitness monotonicity
(Figure 1, G45). As we’ll see, different conclusions
can result from considering fitness monotonicity as assessed
during search (Figure 1, FG78) or after search (Figure 1,
H78).
In the following we’ll present visual examples of searches
over two-dimensional grids, with the states in the x-z plane
and fitness on the y-axis. In this way, the ideal endpoint for
a place search is the highest point on the landscape. We’ll
allow single-unit moves in the up-down, left-right, and diagonal
directions. Note that in this case DG, defined as the
Euclidean distance, is a good proxy for DT .
Insufficiency of Either Monotonicity Alone
Now we can evaluate whether fitness or state trajectories
are individually sufficient to rule out either the direct or hill
climbing processes. For the landscape shown in Figure 3,
a hill-climber that follows the fitness function, f, will trace
a path like the solid line shown in the figure. This trajectory
is non-monotonic in genotypic distance but monotonic
in fitness. The direct process would form a trajectory that is
monotonic in genotypic distance but non-monotonic in fitness.
Therefore, finding one but not both of state or fitness
non-monotonicity is not sufficient to rule out both null hypotheses
processes.
Partially Observable States
The trajectory traced in Figure 3 is a spiral. While this is
literally a roundabout path to take, it is at least free of cycles
where the trajectory revisits previously-encountered states.
A trajectory with cycles seems to clearly contradict both null
hypotheses. Indeed, the presence of a cycle can rule out
the direct process, as editing out the cycle will not prevent
the path from reaching the same final state. A cycle is likewise
impossible with hill climbing, unless the internal state
is only partially observable (cf. Gabora 2011).2
Consider the landscape in Figure 4, where the complete
state ~x = (x, xˆ) has an observable part (x) and an unobservable
part (xˆ). Projecting the full trajectory into x shows a
cycle, but the cycle disappears with (x, xˆ).
Criteria Change
In a case almost identical to the previous example, suppose
that people’s criteria change during search. This is akin to
having an unobserved portion of the state that affects the
evaluation function. Here again, cycles could emerge in the
observable state that are in fact monotonic if the evaluation
function’s hidden parameter were observable. (The cases
are not quite identical since changes to this hidden parameter
are dependent on some higher-level process, and hence
aren’t fully explainable by reference to f.) If one considers
changes to evaluation criteria as separate from the main
search process then it’s still possible for this apparent nonmonotonicity
to occur with a hill climber.
A special problem can occur when criteria change occurs
since the same state will be evaluated differently before and
after the change. This could lead to retrospective evaluations
of fitness over time showing non-monotonicity while
in fact fitness was experienced as increasing monotonically
during the search (see Figure 1, FH78). Suppose that the
2
Cycles could also occur in the special case where all of the
states in the cycle are indistinguishable in terms of fitness.
International Conference on Computational Creativity 2012 53
x
^
x
DG
Observable State
Complete State
f(x)
Time
Figure 4: Illustration of an apparent cycle using a hill climbing process where the state is only partially observable. Projecting
the trajectory into observable space (horizontal axis) shows a cycle, while the complete trajectory is non-cyclic.
DG
Contemporaneous
Retrospective
f(x)
Time
Figure 5: Illustration of a search over x while a criteria weight w is simultaneously changing. The path (solid line) starts in
the foreground and proceeds to the background. As shown in the right graph, contemporaneous fitness is monotonic. However,
retrospective evaluation of the traversed points would be non-monotonic, as shown by the dashed lines in both graphs.
x1
x2
Distance
DG
DT
f(x)
Time
Figure 6: Illustration of a path that is non-monotonic with DG but monotonic with DT . The gray region in the left plot shows
infeasible configurations that can be represented with the genotype but that cannot be realized.
International Conference on Computational Creativity 2012 54
state is a scalar x and that f(x) depends on a weight parameter
w such that f(x) = w · f1(x) + (1 ! w) · f2(x).
Figure 5 demonstrates how retrospective fitness evaluation
could show non-monotonicity even though contemporaneous
fitness was monotonic.
Infeasible Regions
So far we have considered problems where DG is a good
proxy for DT . However, there are problems where the state
representation does a poor job reflecting the actual diffi-
culty of transforming one state into another. Consider the
landscape in Figure 6, where the gray regions are infeasible
states. Though a hill climber would fail on this particular
landscape, the direct process would find the path shown. As
can be seen, the state trajectory appears non-monotonic with
DG but isn’t when judged with DT . The fitness trajectory is
also non-monotonic, though that could occur with any direct
process.
Phenotypic Distance
In real-world situations, both transformation distance and
genotypic distance can be impractical to compute. In contrast,
phenotypic distance, which is based on comparing the
state’s salient features, can be assessed fairly directly, such
as by having several human raters make intuitive similarity
judgments for pairs of intermediate products. However,
there are two issues with this approach. From a psychological
standpoint, it has long been known that human similarity
judgments are not well-behaved metrics, meaning that
they can be context-dependent, asymmetric, and intransitive
(Tversky 1977). These properties could introduce nonmonotonicity
that was is not in the original stimulus (Gabora
2011).
Another problem with similarity judgments lies in the fact
that genotype and phenotype may be non-monotonically related.
Let the state be a scalar x 2 [0, 1] and suppose that this
maps to a single salient property, p(x) = sin(2⇡x) (see top
half of Figure 7). If a search proceeds linearly from x = 0 to
x = 1, DG (the absolute difference in state representations)
will be monotonically decreasing but DP (the absolute difference
in the level of the property) will be non-monotonic
(see bottom half of Figure 7). This is true regardless of what
sort of landscape or search process is used.
Discussion
This paper has introduced a set of important distinctions
that must be made when analyzing creative search trajectories,
as summarized in Figure 1. We have argued that
path searches and place searches must be understood differently.
With path searches, we have claimed that the important
measure of the efficiency of the search process is the
transformation monotonicity of the problem solver’s internal
states, which may or may not be the same as the states of the
problem itself. With place searches, we have argued that researchers
claiming that people use complex search processes
must first reject two null hypothesis processes, the direct and
hill-climbing processes. We have shown how rejecting these
processes entails demonstrating not just that there is nonmonotonicity
in both states and fitness, but also that:
x
x
p(x) Distance
Time
DG DP
Figure 7: The top graph shows the relationship between the
state x and its salient property, p(x). The left graph shows
monotonicity in DG (and presumably DT ) as x goes from
zero to one, but non-monotonicity in DP .
• State non-monotonicity occurs with transformation distance,
not just with the more convenient indices of genotypic
and phenotypic distance
• The observed state non-monotonicity does not reflect
movement on unobservable dimensions or the effects of
criteria changes
• Fitness non-monotonicity assessed retrospectively would
also have been non-monotonic when assessed contemporaneously
We have also illustrated how non-monotonicity may result
from processes that are at either end of the spectrum from
intelligent and informed (the direct process) and mechanical
and uninformed (the hill climbing process). Regarding
existing empirical work, we have shown that authors have
differed on whether they’ve analyzed state (Simonton 2007;
Damian and Simonton 2011) or fitness (Kozbelt 2006;
Kozbelt and Serafin 2009) monotonicity. Though we don’t
claim that the counterexamples provided here disprove the
claims made by these authors, we have raised important issues
that future work must address.
We also acknowledge that our work has several significant
limitations. First, for simplicity we have falsely dichotomized
path and place search, even though we are quite
sure that real creativity involves elements of each. Indeed,
the joint operation of these searches may map nicely onto
the problem finding/problem solving distinction that Getzels
and Csikszentmihalyi (1976) introduced. Second, though
we have alluded to criteria change as an important consideration
when analyzing place searches, we have avoided discussing
how and when this would occur and what could
drive it. This decision was ultimately practical, since any
International Conference on Computational Creativity 2012 55
discussion of changes to criteria leads to the question of
what guides criteria selection, and whether this itself can
change—leading to an infinite regresss that may not be resolvable
at the level of an individual creator (cf. Jennings
2010a). We have also treated criteria change as compatible
with the hill climbing process, which we recognize may not
be without controversy. Third, we recognize that we have
not carefully considered the role of operators, and in particular
how the discovery of new operators mid-search may
affect conclusions about state monotonicity. Finally, we are
fully aware that all of our counterexamples involve highly
abstracted problems, and so ultimately they serve more to
illustrate our points rather than provide an existence proof.
We look forward to addressing these and other limitations in
future work.
Our purpose here is not to cast aspersions on the trajectory
analysis approach. Indeed, we are actively pursuing empirical
techniques that rely upon trajectory analysis (Jennings
2010b; Jennings, Simonton, and Palmer 2011), although
these techniques promise to reveal more about the underlying
problem than can be obtained from a search trajectory
alone. Beyond this, we continue to believe that trajectory
monotonicity is an eminently practical way to study the creative
process, particularly in cases where the available data
are slim. The objections that we’ve raised in this paper do
not seal the fate of this approach, but rather offer constructive
critiques that should be addressed in future research.
<references_biblio/>
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