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In praise of convergent thinking.Creativity Research Journal, 18, 391-404.
In praise of convergent thinking
Arthur Cropley
University of Hamburg
Running head: In praise of convergent thinking
Submission date: 12/08/04 Resubmitted: 05/29/2005
Correspondence and requests for reprints should be sent to
Arthur Cropley,
Unit 3,
120 South Terrace,
Adelaide, SA 5000,
Australia.
E-mail: ajcropley@gmail.com
Abstract
Free production of variability through unfettered divergent thinking holds out the seductive
promise of effortless creativity, but runs the risk of generating only quasicreativity or
pseudocreativity if it is not adapted to reality. Thus, creative thinking seems to involve two
components: generation of novelty (via divergent thinking) and evaluation of the novelty (via
convergent thinking). In the area of convergent thinking, knowledge is of particular importance:
It is a source of ideas, suggests pathways to solutions, and provides criteria of effectiveness and
novelty. The way in which the two kinds of thinking work together can be understood in terms of
thinking styles or of phases in the generation of creative products. In practical situations,
divergent thinking without convergent thinking can cause a variety of problems including
reckless change. None the less, care must be exercised by those who sing the praises of
convergent thinking: Both too little and too much is bad for creativity.
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In praise of convergent thinking
Discussions of creativity in the early post-Sputnik era were largely shaped by Guilford's 1949
presidential address to the American Psychological Association (Guilford, 1950). Although
Guilford also drew attention to the importance in creativity of factors such as personality, the
ideas of convergent and divergent thinking dominated discussions following his paper. Guilford
also acknowledged the importance for creativity of knowledge of facts, and thus of convergent
thinking, but despite this creativity quickly came to be equated with divergent thinking, and the
two kinds of thinking were not infrequently presented as conflicting or competing processes
(e.g., Getzels and Jackson, 1962). Convergent thinking was sometimes even seen as bad, or at
best a necessary evil that is greatly exaggerated in education and business (e.g., Cropley, 1967).
In more recent years, however, there has been increasing recognition of the fact that actual
creative production does not derive from divergent thinking alone, but also requires convergent
thinking (e.g., Rickards, 1993; Brophy, 1998). The contribution of convergent thinking to the
generation of creative products is the subject of this paper.
Convergent vs. divergent thinking
Convergent thinking is oriented towards deriving the single best (or correct) answer to a clearly
defined question. It emphasizes speed, accuracy, logic, and the like, and focuses on recognizing
the familiar, reapplying set techniques, and accumulating information. It is thus most effective in
situations where a ready-made answer exists and needs simply to be recalled from stored
information, or worked out from what is already known by applying conventional and logical
search, recognition and decision-making strategies. One of the most important aspects of
convergent thinking is that it leads to a single best answer, and thus leaves no room for
ambiguity: Answers are either right or wrong. Convergent thinking is also intimately linked to
knowledge: On the one hand, it involves manipulation of existing knowledge by means of
standard procedures, and on the other, its main result is production of increased knowledge.
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Divergent thinking, by contrast, involves producing multiple or alternative answers from
available information. It requires making unexpected combinations, recognizing links among
remote associates, transforming information into unexpected forms, and the like. Answers to the
same question arrived at via divergent thinking may vary substantially from person to person, but
be of equal value. They may never have existed before, and are often thus novel, unusual or
surprising. Sometimes this is true merely in the experience of the person producing the
variability in question, or for the particular setting, but it may also be true in an absolute sense.
Some examples of the characteristics of the two kinds of thinking are given in Table 1.
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Insert Table 1 about here
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Contrary to what is sometimes assumed, both convergent and divergent thinking lead to
production of ideas. None the less, there is a major qualitative difference: Convergent thinking
usually generates orthodoxy, whereas divergent thinking always generates variability (Cropley,
1999); otherwise it would not be divergent. This seems at first glance to confirm that divergent
thinking is synonymous with creativity. Indeed, in discussing creativity Guilford himself (e.g.,
Guilford, 1959) focused on sensitivity to problems, word fluency, ideational fluency, semantic
flexibility, associational fluency, and originality, all aspects of divergent thinking. However,
production of variability by means of fluency, flexibility and originality does not, on its own,
guarantee creativity. Variability may cause surprise in the beholder, it is true, but this is not
necessarily enough, since surprise can be produced through mere unregulated self-expression
(e.g., daubing paint on paper, writing text in any way that pleases the writer, or picking out notes
at random on the piano), or by doing things differently from the usual regardless of accuracy,
meaning, sense, significance, or interestingness.
Thus, it is necessary to distinguish between mere novelty and novelty that earns the label
"creativity." The former involves what Cattell and Butcher (1968, p. 271) called
"pseudocreativity": The novelty derives only from nonconformity, lack of discipline, blind
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rejection of what already exists and simply letting oneself go. Based on the German of Heinelt
(1974), I have added to this "quasicreativity" (e.g., Cropley, 1997, p. 89), which has many of the
elements of genuine creativity-such as a high level of fantasy-but only a tenuous connection with
reality. An example would be the novelty generated in daydreams. What is needed for creativity,
however, is not just something that surprises by deviating from the usual, but something that
invokes what Bruner (1962, p. 3) called "effective surprise." The questions that arise now are
whether divergent thinking alone generates effective novelty, whether convergent thinking plays
any role in generating such novelty and, if it does, what this role is.
Effortless creativity: Effective novelty without convergent thinking?
The idea of effortless creativity is seductive: It would involve effective novelty produced without
any of the tiring and time consuming activities typical of convergent thinking (such as acquiring
information, puzzling out, testing and checking, and so on). Of course, it is possible to imagine
lucky hits or flukes, wild speculations, or dreams that turn out to be novel and effective.
However, the key question is whether creativity can, in the normal course of events, result from
divergent thinking alone. Two well-known mechanisms that seem to involve production of
effective novelty without convergent thinking are luck/chance and intuition.
Luck and chance
There are many examples of apparently lucky combinations of events that led to
acknowledged creative solutions (see Rosenman, 1988): For instance Pasteur, Fleming,
Roentgen, Becquerel, Edison, Galvani and Nobel all described chance events that led them to
breakthroughs. Some famous thinkers such as Ernst Mach, Etienne Souriau, or Alexander Bain
have even concluded that luck is the main factor in creativity. Austin (1978) identified four kinds
of happy chance: blind chance (the individual creator plays no role except that of being there at
the relevant moment; serendipity (a person stumbles upon something novel and effective when
not looking for it); the luck of the diligent (a hardworking person finds in an unexpected setting
something that is being sought-Diaz de Chumaceiro, 1999, p. 228, called this
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"pseudoserendipity" since in genuine serendipity the person would not be looking for what was
found); self-induced luck (special qualifications of a person-such as knowledge, close attention
to detail or willingness to work long hours-create the circumstances for a lucky breakthrough).
Case studies suggest that genuinely creative people enjoy a combination of all four kinds of luck,
which raises the question of whether it is a matter of luck at all, since at least the luck of the
diligent and also self-induced luck clearly contain elements of convergent thinking (hard work,
knowledge, etc).
Among the more theoretical discussions of the role of chance in creativity is the
evolutionary view of, among others, Campbell (1960) and Simonton (1988). This approach is
highly reminiscent of Darwin's theory of the origin of species and, indeed, Simonton (1999)
drew attention to this similarity when he referred in the title of his book to "the origins of
genius". According to the evolutionary view of creativity, ideas evolve through what Sternberg
and Davidson (1999, p. 68) called "haphazard recombinations" in a process of "blind variation"
(Campbell, 1960, p. 380). Occasionally, a happy combination of ideas occurs: When this is
recognized as involving a creative "configuration" (Simonton, 1988, p. 2), "selective retention"
(Campbell, 1960, p. 380) takes place. However, even if this is an accurate description of the
process of production of effective novelty, the "mental elements" (Simonton, 1988, p. 6)
involved in the haphazard recombinations are themselves pieces of information (facts, principles,
relations, rules, laws, formulae, etc)—in other words, they are the result of convergent thinking.
The case study of Becquerel below gives an example of what looks at first like a lucky accident,
but in reality is based on convergent thinking.
Intuition
In his now classical stage model Wallas (1926) identified a stage of incubation, during
which ideas seem to churn and work in a person's head without the person being aware of them,
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until-apparently out of the blue-an answer pops up. This is the classical definition of intuition: A
process of fermentation until an idea is suddenly there, even seeming to come from nowhere.
Mozart, for instance (see Hadamard, 1954), described how complete musical compositions just
came into his head-for instance during sleepless periods at night- and only the details had to be
tidied up later. There is, however, considerable doubt about the accuracy of Mozart's description
of how he composed. For instance, corrected trial versions of Mozart compositions have been
found that, according to his account, never existed.
In fact, far from being an example of production of effective novelty without convergent
thinking, intuition may well derive from convergent thinking at least as much as from divergent
thinking. Even people who have not consciously acquired knowledge and experience in an area
sometimes already have in their head a rough outline of the solution they are seeking, despite not
necessarily being aware of this. The task involved in solving a problem is that of defining and
refining this rough idea, not producing something from nowhere. The preliminary outline is
acquired via the convergent process of implicit learning-of which the learner is unaware-for
instance in the course of everyday life (for a fuller account of what is meant by implicit learning
see Seger, 1994). To take a simple example, during the course of riding to school every day in a
bus and sitting just behind the driver a child might learn a great deal about how buses work,
without realizing it and without ever having thought of the ride as a learning experience.
Implicit learning leads to tacit knowledge that people do not know they possess. Such
knowledge can pre-structure thinking about an issue. For instance, the person in the example
above might possess a great deal of tacit knowledge about the design of buses. As a result, upon
being hired in adult life to design a new bus this person would already possess a preliminary
framework that could suggest where the required answer might be found or approximately what
the eventual solution might look like. The apparent bolt from the blue would really involve
logical extension of what the person in question already knew. In other words, the basis of
intuition-which appears at first glance to be the epitome of creativity coming from nowhere-is
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knowledge, and knowledge is acquired via convergent thinking. In fact, both luck and intuition
seem to derive from psychological characteristics which are, to a considerable degree,
convergent in nature. The importance of such characteristics was summed up by the celebrated
father of vaccination, Louis Pasteur, in a frequently cited aphorism he uttered in a lecture in
1854: "Chance always favors the prepared mind." The essentially convergent nature of the
prepared mind is sketched out below.
Effortful creativity: The prepared mind
In 1896, the French physicist, Antoine Becquerel, left a piece of photographic paper and a
container with uranium salts in it in a drawer of his desk. On opening the drawer some time later
he noticed that the photographic plate had fogged. This unexpected event piqued his curiosity.
He eventually concluded that the uranium had emitted some kind of radiation, which was
responsible for the fogging. He then showed that this differed from X-rays in being deflected by
electromagnetic fields, i.e., it was a previously unknown phenomenon. After initially being
called Becquerel rays, the radiation subsequently became known as radioactivity. Was the
discovery of radioactivity an example of creativity? It would be hard to answer, "No."
(Becquerel shared the 1903 Nobel Prize for physics with Marie and Pierre Curie.) Did the
creativity, then, come from nowhere, either through blind good fortune, intuitive inspiration
based on nothing, or in a burst of pure divergent thinking (which if it did not produce a winner
would be regarded as wild speculation)? Does creativity perhaps involve nothing more than
being open for ideas and being able to recognize that a particular idea is a solution to something
or other, thus seizing the opportunity when it occurs? Ghiselin (1955) seemed to support this
view by arguing that recognizing a solution when one occurs is the key to creativity.
What is easy to overlook is what it was that made it possible for Becquerel to capitalize
on the opportunity chance presented. He could not have done this had he not possessed, among
other things:
• the general knowledge that permitted him to realize that the fogging was unusual
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and important,
• the specific knowledge that told him that some kind of radiation had caused the
phenomenon,
• the research skills that enabled him to clarify the whole situation.
Indeed, had Becquerel not already been engaged in relevant research the uranium and the
photographic plate would not have found themselves in the drawer together in the first place:
Thus, he could be said not only to have been able to profit from chance because of, among other
things, his knowledge and skills, but, in fact, by his own effort to have created the lucky chance
in the first place! This was not an example of effortless creativity, but required the prepared mind
referred to above. Furthermore, the properties of Becquerel's prepared mind were largely
convergent in nature, involving especially knowledge and specialized technical skills.
However, it must be admitted that knowledge does not always facilitate creativity. A
striking example of the unprepared mind is the failure of the German-Latvian pathologist, Eugen
Semmer, to recognize a solution of spectacular proportions in the course of his work in the
Institute of Veterinary Medicine in Riga. In 1870 Semmer published a paper in the widely-read
German-language scientific journal, Virchows Archiv (which still exists), reporting on the
strange return to health of two horses that were suffering from what we would now call
infections. He examined the now recovered horses and discovered that while at the institute they
had accidentally been exposed to spores of the mushroom penicillium notatum, which had
apparently been responsible for them inconveniently getting better. Semmer saw the horses'
return to good health as a problem that made it impossible for him to investigate the cause of
their death, and reported in the journal on how he had succeeded in eliminating the mould from
his laboratory!
Apparently, both Semmer himself, as well as the distinguished readers of the journal,
failed to recognize that he had discovered a novel (and as we now know, extremely effective)
curative agent (i.e., antibiotics), and medicine had to wait another 70 years for Fleming to
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discover penicillin. In a sense, Semmer's mind was unprepared not because he possessed
insufficient knowledge, since he could hardly be expected to have known about bacteria (whose
existence had not yet been discovered), but the wrong kind of knowledge, He was thorough and
skilful enough to discover the presence of mushroom spores and to see that they had saved the
horses, and was thus well on the way to discovering penicillin, but failed to appreciate their
significance because he focused his attention on life-taking rather than life-saving factors: Had
he been a clinician he might immediately have seen the possibilities of his accidental discovery.
This raises the question of what role knowledge plays in creativity and, since knowledge is the
principal product of successful convergent thinking, once again of the role of convergent
thinking.
Knowledge and creativity
Although some writers (e.g., Hausman, 1984) argued that true creativity is always so novel that it
is unprecedented, and thus has no connection to anything that went before, others such as Bailin
(1988) have stated unequivocally that creative products are always conceived by both the
creative person and external observers in terms of existing knowledge. To take an obvious
example, many of the inventions of America's most distinguished inventor, Thomas Alva Edison,
were improvements on existing technology or ideas. Edison also worked with a large staff of
engineers and technicians who constantly improved their own existing ideas: For instance, over
the course of time they took out more than 100 patents for the electric light bulb alone. Indeed, in
an aphorism that was printed in Harper's Monthly in 1932, Edison concluded that "genius is 1%
inspiration, 99% perspiration," thus coming down squarely on the side of convergent thinking.
Lubart (2000-2001) expressed the link between knowledge and creativity in a homely but
convincing way: He suggested that there may well be no difference between the processes of
divergent and convergent thinking, but that differences in outcome may depend instead on " ...
the quality of the material (e.g., knowledge) (p. 301)". Lubart extended this thought with the
concrete metaphor: "The engine is the same, but some people use better grade fuel (p. 301)."
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Those who have only limited or narrow knowledge (the poorer grade of fuel) would not be able
to combine ideas, make unexpected associations between pieces of knowledge, or synthesize
apparently unrelated facts, since they would not possess the ideas, knowledge or facts upon
which to operate.
Scott (1999) listed a number of creativity researchers who all give a prominent place to
knowledge in creativity (e.g., Campbell, Wallas, Mednick, Chi, Weisberg, Amabile, Simonton,
Albert and Gruber). Ericsson and Lehmann (1999, p. 706) summarized the link between
knowledge and creativity by concluding that:
... the empirical evidence on creative achievement shows that individuals have
not been able to make generally recognized creative contributions to a domain
unless they had mastered the relevant knowledge and skills in the course of a long
preparatory period.
They repeated (1999, p. 700) the idea that there is a "10 year rule": An apprenticeship of at least
10 years is necessary for acquiring the fund of knowledge and skills necessary for creativity.
It is not my intention to discuss in detail here the substantial literature on knowledge and
creativity (for such a discussion, see Scott, 1999), nor to review the highly formalized
discussions found in cognitive psychology. My interest in this paper lies in the fact that a role for
knowledge in creativity would strengthen the link between creativity and convergent thinking.
What, then, broadly speaking, is the role of knowledge in creativity? In what way is knowledge
(and thus the processes of convergent thinking through which it is acquired, stored and retrieved
when needed) linked to generation of effective novelty?
Knowledge provides a well from which ideas are drawn
Already, before the beginning of the modern era, the idea that creativity draws from the
wellspring of conventional knowledge was well established: Rossman's (1931) study of inventors
for instance, concluded that they "manipulate the symbols of ... past experience (p. 82)" [my
italics]. He also showed that they combined "known movements (p. 77)" [my italics]. Feldhusen
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(1995, p. 255) and other writers have made an important point, by emphasizing the "knowledge
base" of creativity. An example of the value of a knowledge base is to be seen in Charles
Babbage's transfer in about 1840 of the punched card system for controlling the work of the
Jacquard loom from the French fabric-making industry to a mechanical calculating machine, thus
laying the foundation for what we now call a "computer"-a momentous piece of creativity that
derived, nonetheless, from knowledge of existing systems for controlling machines. As Bailin
(1988) put it, novelty "always arises out of what already exists (p. 5)." Weisberg (2003) showed
that even an extraordinarily radical product such as Picasso's Les demoiselles d'Avignon derived
from what Picasso had experienced up until the time he painted it.
The position of knowledge as the basis of creativity has been put in more formal terms by
Boden (1994a), using the language of artifical intelligence. What I call "knowledge", she (1994a,
p. 8) calls "cognitive maps" of a "conceptual space". The more structural features of a conceptual
space such as, let us say, music are represented in a person's mind (the more the person knows
about music), the more creative the person can be. Boden gave the example of Mozart and
concluded that his creativity arose from his vast musical knowledge.
Knowledge defines what is creative
As Sternberg and Lubart (1999, p. 3) put it, a creative product must be adapted to "task
constraints". Boden (1994b) made this point very strongly by arguing that it is dealing with the
task constraints that makes a product or idea creative instead of merely original (occurring for
the first time). Without task constraints ideas could not cause surprise, since there would be no
expectations from which they would deviate. Thus, paradoxically, novelty is determined by
existing knowledge, and not just by the product itself. Csikszentmihalyi (1999) extended the idea
of existing knowledge as defining creativity when he described creativity as a novel variation in
a domain of practice that experts in the domain recognize as novel and effective, and regard as
worth incorporating into it. The experts judge according to their knowledge of their domain,
which they have acquired through convergent thinking.
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Although it goes beyond the limits of this paper, it is interesting to note that, since
knowledge in a domain changes with the passage of time (usually by increasing), whether or not
novelty is judged to be effective-and thus creative-may change with time. Indeed, once
incorporated into existing knowledge, novelty of necessity ceases to be novel, thus creating a
further paradox: Novelty (a) derives from what is already known, (b) is judged effective (or not)
in terms of the already known, (c) passes into the body of knowledge if it is judged to be
effective, (d) thereupon ceases to be novel (i.e., it becomes the already known), and (e) having
lost its own status as effective novelty now influences the assessment of later novelty.
It is also interesting to note that additions to knowledge can have the opposite effect from
the one just described, in which novelty more or less inevitability destroys itself. With the
passage of time, novelty initially regarded as not effective (or possibly not even novel) can come
to be adjudged novel and effective, and thus creative. Although this phenomenon can result from
factors such as changes in conventions, social values, or taste (such as in aesthetic creativity),
what is important here is that it can also result from convergent thinking. In 1832, the French
mathematician Evariste Galois, now regarded as one of history's most original mathematicians,
was killed at the age of 20 in a duel so hopelessly uneven that he knew that he was doomed (see
Rothman, 1982). He left a body of mathematical writings that were so important to him that he
worked on his notes even on the night before his death. After the fatal duel his writings were
examined, but their contents were judged to have no foundation in mathematical knowledge (i.e.,
to be lacking in effectiveness). It was only after the passage of several years—during which time
mathematical knowledge advanced enough for other mathematicians to catch up with what
Galois already knew—that the creativity of Galois’s work was recognized. He is now famous as
the founder of group theory, known today as "Galois Theory." In other words, his divergent
thinking could not gain recognition until convergent thinking had advanced sufficiently to make
the effective novelty of his ideas apparent.
Knowledge guides and shapes the search for novelty
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Despite the position of writers such as Simonton (see above), I take the view that
production of effective novelty does not occur by what Simon (1989, p. 377) called "brute
force": making blind associations among already known elements and occasionally recognizing,
perhaps by good fortune, that a new combination offers the required solution. To generate
effective novelty, divergent thinking must be guided by knowledge about how to acquire,
organize, or apply knowledge: heuristics, strategies, hunches or "rules of thumb" (Rickards,
1999, p. 219), or what is sometimes called "metacognition" (e.g., Flavell, 1976, p. 232). Such
knowledge indicates which kinds of attack on a problem are likely to be fruitful (or are already
known to be fruitless), defines the pathways, methods and tools through which progress can be
made, and specifies the nature of acceptable solutions. To take an absurdly simple example, a
person lacking knowledge of electricity would not spend much time developing radio or the
telephone as communication devices. Looked at the other way around, engineers working in the
product development department of a large automobile manufacturer would be unlikely to stake
their careers on an electronic matter transmitter as a means of mass transport.
Even aesthetic creativity in fields such as poetry or music rests on a foundation of skills,
expectations, conventions, and the like: Poets or musicians have to know and stick to the rules in
order for the novelty they produce to be judged effective. To take a simple example, sonnets
always have 14 lines (otherwise they are not sonnets), while there are rules about the rhyme
schemes that are permissible or even about the contents: For instance, sonnets are often divided
into an eight-line section in which a general theme is introduced, followed by a more specific
six-line section offering some conclusions, consolations, or the like. In "On his Blindness" John
Milton lamented in the first eight lines that his blindness was hindering him in serving God, but
then in the closing six lines consoled himself with the thought that God can get along perfectly
well without the humble work of a mere mortal. Sawyer (1999) showed that even jazz
improvisation, which may look to the uninitiated like pure divergence, is governed by rules, and
involves organized re-use of the already known. He gave the example of Charlie Parker, who
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developed for himself a repertoire of about 100 "motifs" or "licks" (p. 36), each between 4 and
10 notes in length, which he then combined and re-combined to generate effectively novel
performances out of the already existing elements.
Converting existing knowledge into new ideas
Sternberg (1999) turned to the question of the processes through which existing knowledge is
used to produce creativity. He introduced the useful idea of creativity as "propelling a field (p.
83)," and suggested a number of ways in which this can occur:
1. conceptual replication (the known is transferred to a new setting);
2. redefinition (the known is seen in a new way);
3. forward incrementation (the known is extended in an existing direction);
4. advance forward incrementation (the known is extended in an existing direction
but goes beyond what is currently tolerable);
5. redirection (the known is extended in a new direction);
6. reconstruction and redirection (new life is breathed into an approach previously
abandoned);
7. reinitiation (thinking begins at a radically different point from the current one and
takes off in a new direction).
Of these, only the last involves something quite new. All the others are based on modifying what
already exists.
Savransky (2000) also discussed the processes through which existing knowledge is used
to develop effective novelty: He argued that inventive solutions to problems always involve a
change in what already exists. He discerned six ways in which this can occur. Slightly modified
for present purposes, generating effective novelty involves, according to Savransky, one or more
of:
1. improvement (improvement or perfection of both quality and quantity of what
already exists);
15
2. diagnostics (search for and elimination of shortcomings in what already exists);
3. trimming (reduction of costs associated with existing solutions);
4. analogy (new use of known processes and systems);
5. synthesis (generation of new mixtures of existing elements);
6. genesis (generation of fundamentally new solutions).
As was the case with Sternberg's list, only the last of these involves something fundamentally
new.
The Russian researcher, Altshuller (1988), also emphasized the role of the already known
in his procedure for finding creative solutions to problems- known as TRIZ (a transliteration of
the Russian acronym for "Theory of inventive problem solving"). This procedure is based on an
analysis of thousands of successful patent applications, i.e., on effective novelty that is already
known. It argues that all engineering systems display the same systematic patterns of change.
Creativity is the result of development of what exists according to these trends. TRIZ identifies
these systematic processes of novelty generation so that people working with a new problem can
apply them to derive their own novel solutions.
The joint role of divergent and convergent thinking
What, then, is the role of convergent and divergent thinking in generating effective novelty?
How do the two combine to produce it?
Generating and exploring variability
Finke, Ward, and Smith (1992) distinguished between two broad processes in the
production of effective novelty: on the one hand generating novelty and, on the other, exploring
this novelty, once it has been generated. The first kind of process produces novelty, to be sure,
but on its own it can easily lead not to creativity but to quasi- or pseudocreativity (unless there is
a blind hit). Suppose that a civil engineer noticed that both steel reinforcing rods and spaghetti
are long, tubular, and under certain circumstances flexible, and thus saw that spaghetti has some
similarities to steel rods. This would involve a changed perception of spaghetti (generation of
16
novelty). There really are similarities between reinforcing rods and spaghetti, and settings may
well exist where this variation from the usual perception of steel and spaghetti really could lead
to effective novelty (even if it is difficult to imagine what these settings might be). However,
most civil engineers would probably reject out of hand the actual use of spaghetti instead of
reinforcing rods, and would predict a catastrophe if spaghetti were used to replace steel (i.e., they
would explore the novelty and would decide against it). This rejection of the novelty would be
based on the engineers' knowledge of basic principles of civil engineering, such as strength of
materials. Thus, converting mere novelty into effective novelty (i.e., creativity) requires both
generation (via divergent thinking) and also exploration (via convergent thinking).
Lonergan, Scott and Mumford (2004) summarized recent thinking in this area, and
concluded that the idea of a two-step process is now widely accepted. In my terms, this would
involve novelty generation followed by (or accompanied by) exploration of the novelty from the
point of view of workability, acceptability, or similar criteria, in order to determine if it is
effective. Only then would we speak of creativity. It is tempting to think of exploration as
essentially a process of evaluation, and Runco (2003) supported this view. He argued that
creativity requires a combination of divergent and convergent thinking, and argued further that
the convergent thinking involves "critical processes (p. 432)", critical meaning not merely that
the processes are necessary for creativity, but also that they involve criticism of the results of the
divergent thinking, i.e., what I have just called "evaluation".
Continuing with the (admittedly whimsical) example of making a link between spaghetti
and reinforcing rods via divergent thinking, Table 2 gives examples of processes of divergent
and convergent thinking in both generating and evaluating phases of idea production, and
suggests what the results might be if divergent thinking were not tempered by convergent
thinking.
--------------------------------------------------
Insert Table 2 about here
--------------------------------------------------
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I do not intend to deny the importance of divergent thinking in production of effective
novelty. However, although necessary it is not sufficient on its own, except perhaps for
occasional flukes when blind luck leads to effective novelty. Convergent thinking is necessary
too, because it makes it possible to explore, evaluate or criticize variability and identify its
effective aspects. In the enthusiasm for divergent thinking it is thus important not to forget the
contribution of convergent thinking, although it is also important not to overemphasize it, as I
believe is usually done in schools and universities. Table 3 gives examples of vital convergent
thinking processes in both the generating and exploring phases of generation of variability.
-------------------------------------------------------
Insert Table 3 about here
-------------------------------------------------------
Risks in introduction of novelty
What are the risks if novelty is introduced without appropriate exploration (i.e., if
divergent thinking is not accompanied by convergent thinking)? Figure 1 considers a number of
possibilities.
-------------------------------------------------------
Insert Figure 1 about here
-------------------------------------------------------
If no variability is generated (no divergent thinking), nothing changes and orthodoxy rules,
bringing, however, the risk of stagnation and similar problems. This is the situation depicted in
the first row of the figure. It is, of course, the safest pathway in settings where errors are
punished but doing nothing is tolerated without sanctions, but absence of creativity is of no
interest to us here.
A new set of possibilities opens up when variability actually is generated. It is possible
for this to be accepted without exploration (i.e., divergent thinking without convergent thinking).
If such novelty proves to be ineffective we can speak of "recklessness", which raises the danger
of disastrous change. If, despite the lack of exploration, the novelty proves to be effective, this is
more a matter of luck than judgment and we can speak of "blind creativity", with the danger of
18
overconfidence in the future. Thus, not only does lack of knowledge reduce the possibility of
generation of variability in the first place, but even where variability is generated, lack of
exploration (convergent thinking) raises the possibility of reckless variability, and exposes the
system in question to the risk of disastrous change or over-confidence.
Figure 1 also depicts the various possibilities if exploration does take place (i.e.,
divergent thinking accompanied by convergent thinking). Where convergent thinking following
on divergent thinking leads to a correct decision-in the case of convergent thinking we can speak
of "correct" and "incorrect"-to implement change (i.e., to the introduction of effective novelty),
creativity occurs. This is the ideal result. Where convergent thinking correctly leads to rejection
of the variability generated through divergent thinking, the possibility of disastrous change is
avoided, but at the risk of resignation or complacency. Of course, the convergent thinking is not
always correct: In the Computer Users' Committee at the University of Hamburg in the early
1980s I fought against the introduction of remote computer terminals, on the grounds that desk-
top computing would never catch on! Errors of exploration (mistakes in convergent thinking) can
lead to "stifled" creativity (false negatives) or "mistaken" variability (false positives), and raise
the danger of a lost chance or, again, disastrous change.
How do divergent and convergent thinking work together?
I have argued that both divergent and convergent thinking are necessary for the production of
effective novelty, and that achievement of such novelty without appropriate convergent thinking
brings risks such as over-confidence. How do the two work together?
Pre-Requisite models
The simplest explanation of the joint roles of divergent and convergent thinking in
production of effective novelty is based on the idea that convergent thinking is a pre-requisite for
effective divergent thinking. An example is to be seen in Vincent Van Gogh. His early work was
driven by humane impulses (personal disappointment in love and a desire to bring other people
beauty and consolation), which he initially tried to express by becoming a missionary, before
19
turning to painting. However, his paintings lacked formal, technical skill (convergent
knowledge) and he had to return at the age of 32 to the Academy of Art in Antwerp, where
training in painting techniques allowed his flair for colour and light to come to fruition. No-one
had to teach van Gogh how to produce novelty, but it was only after he had mastered techniques
through hours of repetitious, convergent work that his paintings satisfied the prevailing norms for
effective novelty.
The simplest pre-requisite approach is the summation model: Divergent thinking and
convergent thinking seem to add something to each other, or even to compensate for defects in
each other. More dynamic is the threshold model: Below some threshold level of convergent
thinking effective divergent thinking is thought to be impossible, but as the level of convergent
thinking approaches the threshold from below, the possibility of divergent thinking rises (i.e.,
divergent and convergent thinking are positively correlated to this point). Once the threshold has
been passed, convergent thinking has no further effect on divergent thinking-van Gogh, for
instance, did not continuously become more and more creative as his technical skills increased.
Once these had become adequate as a vehicle for expressing his divergent thinking, creativity
was inhibited or facilitated by factors other than convergent thinking.
A further elaboration of this approach is the channel model, according to which
convergent thinking provides the channel or pathway through which information reaches the
systems responsible for divergent thinking, and thus determines how much and what kind of
information is processed. A variant of this is the capacity model, which argues that convergent
thinking determines the amount of information that reaches cognitive systems, divergent thinking
then being applied to whatever information becomes available. As in the sense of Lubart (see
above) convergent thinking would thus influence the level of performance by providing high or
low octane fuel (channel model) or sufficient or insufficient fuel (capacity model), but divergent
thinking (or absence thereof) would influence the kind of performance.
20
Style models
A second way of conceptualizing the interaction between production of variability and
production of singularity is the style approach. According to this, convergent and divergent
thinking do not directly influence each other. Both involve application of a superordinate ability
to acquire, process and store information, form abstract, general networks, develop knowledge
matrices, form systems, and the like. Whether convergent or divergent products result depends
upon the way in which this thinking power is applied: to produce more of the same, or to
generate novelty. This conceptualization of the interaction regards difference between
convergent and divergent thinking as qualitative rather than quantitative: Regardless of level,
mental ability can tend to be convergent or divergent. An example of this approach is seen in the
work of Hudson (1968).
The alternation approach
I prefer a conceptualization based on the "classical" phase model, first introduced into
creativity research about 80 years ago (Wallas, 1926). In the phase of Preparation, a person
becomes thoroughly familiar with a content area. In the Incubation phase the person "churns
through" or "stews over" the information obtained in the previous phase. The phase of
Illumination is marked by the emergence of a solution, not infrequently seeming to the person
involved to come like a bolt from the blue. Finally comes the phase of Verification in which the
person tests the solution thrown up in the phases of Incubation and Illumination. The solution
may emerge into consciousness all at once, thus seeming to have appeared from nowhere and
creating the subjective feeling of effortless creativity. This would explain why some creative
people overlook information and incubation in describing their own creativity.
Empirical studies of the process of creation in people actually engaged in producing
something new, as well as retrospective studies in which acknowledged creators described how
they obtained new ideas, have cast doubt on the validity of the phase model (see Glover,
Ronning and Reynolds, 1989) as an exact literal description of the production of an effectively
21
novel product in real life settings. Nonetheless it offers a helpful way of looking at the
production of effective novelty as a process, and of describing the contributions of divergent and
convergent thinking to this process.
Various considerations that I have spelled out elsewhere (e.g., Cropley, 1997) suggest
that Wallas's four stages need to be extended by adding after Verification two further stages:
Communication and Validation. Furthermore, an initial stage of Information needs to be taken
into account: In this stage the necessary problem awareness and intention develop. These
considerations yield an extended model involving seven phases (see Table 4).
-------------------------------------------------------
Insert Table 4 about here
-------------------------------------------------------
Information and Preparation may be vital in the whole process. Without problem awareness
there will be no pressure for divergent thinking. Furthermore, the way the problem is defined, the
pathways to a solution that are considered appropriate, and the kinds of solution regarded as
feasible may all be determined in these phases via convergent thinking. Thus, Information may
be both decisive and yet potentially problematic, as I will discuss below, for instance because it
involves placing limits on divergent thinking, quite possibly without any intention of doing so.
Normally, those who know the most are the best prepared, so that problems of Information may
apply particularly to experts (see below).
Striking about the phase model, for present purposes, is that in some phases divergent
thinking is needed, in others however, convergent thinking, while in yet others both are
necessary. The crucial idea here is that although both are needed for production of effective
novelty, this is not necessarily at the same moment in the process; the creative person may
alternate from one kind of thinking to the other, according to the demands of the particular phase
of the process of production of effective novelty. Facaoaru (1985) showed that creative engineers
were good at both divergent and convergent thinking, while Hassenstein (1988) went so far as to
22
argue that a new term is needed to refer to the rounded intellectual ability that combines both
divergent and convergent thinking, and suggested Klugheit (cleverness).
A precautionary note
I do not want to imply that convergent thinking is always beneficial for creativity. In
addition to possibly leading to errors, as shown in Figure 1, for instance as a result of lack of
knowledge, incorrect information, misunderstanding, and the like, convergent thinking can
channel information processing into a narrow range of approaches-possibly without the person
concerned being aware of this-and thus narrow the range of variability produced (via divergent
thinking), or even block it altogether. Thus, from the point of view of creativity, convergent
thinking can be a good or a bad thing. For instance, working successfully in an area over a long
period of time (i.e., enjoying an extremely thorough Preparation and even becoming an expert,
thus possessing large amounts of Information) can provide a substantial knowledge base that can
be manipulated to yield effective novelty, i.e., it can benefit divergent thinking. However, the
pre-existing knowledge of an expert can also act as a corset that blocks novel ideas, so that
thinking leads only to production of tried and trusted, "correct" answers. As Gardner (1993, p.
52) put it, there may be "tension between creativity and expertise."
The well-prepared expert can even develop a vested interest in maintaining the status
quo. Radical new solutions to old and intractable problems may threaten the self-image and the
social status of experts who have laboured long on a particular problem, by rendering their
lifetime's work irrelevant. The result may be that they resist introduction of novelty. Other
processes that can lead to a negative correlation between creativity and expertise are cognitive in
nature (e.g., sets, functional fixity, and confirmation bias). Mumford and Gustafson (1988) and
Martinson (1995), among others, suggested that the relationship between level of pre-existing
knowledge and creativity is U-shaped: Both very high (great expertise) and very low (ignorance)
levels of pre-existing knowledge inhibit production of effective novelty. What is needed is
enough convergent thinking, but not too much!
23
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Table 1. Example of convergent and divergent thinking
Kind of Thinking
Convergent Divergent
Typical Processes
- being logical
- recognizing the familiar
- combining what “belongs”
together
- homing in on the single
best answer
- reapplying set techniques
- preserving the already
known
- achieving accuracy and
correctness
- playing it safe
- sticking to a narrow range
of obviously relevant
information
- making associations from
adjacent fields only
- being unconventional
- seeing the known in a new
light
- combining the disparate
- producing multiple answers
- shifting perspective
- transforming the known
- seeing new possibilities
- taking risks
- retrieving a broad range of
existing knowledge
- associating ideas from
remote fields
Typical Results
for the Individual
- greater familiarity with
what already exists
- better grasp of the facts
- a quick, “correct” answer
- development of a high level
of skill
- closure on an issue
- a feeling of security and
safety
- alternative or multiple
solutions
- deviation from the usual
- a surprising answer
- new lines of attack or ways of
doing things
- exciting or risky possibilities
- a feeling of uncertainty or
excitement
Table 2. Processes of divergent and convergent thinking in generating novelty
28
Generation of variability Generation of orthodoxy
Examples of
processes of
divergent thinking
Result Examples of
processes of
convergent thinking
Result
Generating
Phase
- linking
- transforming
- reinterpreting
- branching out
Engineer sees
similarity
between steel
rods and
spaghetti
- recognizing the
familiar
- reapplying the
known
- sticking to the rules
Engineer does
not see a
similarity
between steel
and spaghetti
Exploring
Phase
- shifting contexts
- exceeding limits
- crossing boundaries
- creating surprise
Engineer con-
cludes that
steel rods can
be replaced
with spaghetti:
Novelty to be
sure—but in
this case, a
disaster!
- avoiding risk
- being certain
- staying within limits
- seeking simplicity
- assessing technical
and financial
feasibility
Engineer sticks
to steel rods to
reinforce
concrete: No
innovation, but
building does
not fall down!
29
Table 3. Examples of the contribution of convergent thinking to creativity
Phase of production of effective
novelty
Convergent thinking
(Necessary but not sufficient prerequisites for
generation of effective variability)
Generating variability
Accumulating factual knowledge
Observing closely
Remembering accurately
Drawing “correct” conclusions
Thinking logically
Processing information rapidly
Exploring variability
Recognizing promising lines of attack
Zeroing in on potential solutions
Seeing limits
Being aware of weaknesses
Weighing up feasibility
Recognizing a solution
Table 4. Creative processes, traits and motives in the phases of production of novelty
Phase Action Result Necessary Process
Information** −identifying
problem
−setting goals
−initial activity
−general knowledge
−special knowledge
convergent thinking
Preparation −perceiving
−learning
−remembering
−focused special
knowledge
−rich supply of
cognitive elements
convergent thinking
Incubation −making
associations
−bisociating
−building networks
−combinations of
cognitive elements
divergent thinking
Illumination −making a
promising new
configuration
−novel configuration
divergent thinking
Verification −checking relevance
and effectiveness
of the novel
configuration
−appropriate solution
displaying relevance
and effectiveness
convergent thinking
plus
divergent thinking
Communication −acting on feedback
−achieving closure
– effective
presentation to others
convergent thinking
plus
divergent thinking
Validation
judging relevance
and effectiveness −product acclaimed
by relevant judge(s) convergent thinking
PHASE RESULT RISK
Generating Novelty Exploring Novelty
(divergent thinking) (convergent thinking)
Figure 1. Consequences of differing combinations of divergent and convergent thinking
No variability
generated
No exploration Orthodoxy (Aban-
doned creativity)
No exploration
(blind insertion)
Reckless variability
(if not effective)
Exploration and
rejection
Blindly lucky
creativity (if novelty
is effective)
Exploration and
acceptance
Orthodoxy (correct
decision if novelty
ineffective)
Over-
confidence
Variability
generated
Disastrous
change
Stagnation
Stifled creativity
(if novelty effective) Lost chance
Resignation or
complacency
G
Mistaken variability
(if novelty
ineffective)
Disastrous
change
CREATIVITY!!
(If novelty effective) Overconfidence
