Creativity in Puzzles, Inventions, and Designs: The Sudden Mental Insight Phenomenon

  • Ömer AkınEmail author
Living reference work entry


Introduction: Key Concepts and Definition of Terms

There are many definitions of creativity. Here, one based on commonly held beliefs about creativity and observations from studies designed to unravel its secrets will be used (Akin and Akin 1996). Creativity is the act of producing novel and valuable things. A creative product is different from existing ones on account of one or more features and adds exceptional value to human purposes. Creativity is readily associated with artistic products. Carravaggio’s realism, Joyce’s imagination, and Wright’s abduction are just a few exceptional examples that prove the point. In the annals of human civilization, some of the most valued human creations include the artistic as well as scientific ones.

Developing a unifying theory of the creative process is at best an idealistic goal. This essay will identify a common denominator based on human cognition and its pre- and postconditions that appear to be responsible for the creative act in three domains: puzzles, scientific discoveries, and architectural design. This broad survey of what is known about creativity, inventions, and design will at once tie all three concepts together and in the process elevate the phenomenon commonly known as the Eureka Moment from the realm of the passe to the realm of the plausible. In accomplishing this end, several key sources that examine the connection between cognition and artificial intelligence, abductive reasoning, analogical reasoning, model-based reasoning, alternating between creative viewpoints, and imagery as a vehicle for creativity will be re-visited.

Theoretical Background and Open-Ended Issues: Understanding Creativity

Early work on creativity focused on general behavioral tendencies of individuals (MacKinnon 1967). While these point to probable correlations between personality traits and creative people, they offer little about creativity as an act. What cognitive capabilities underlie the behavior that is commonly known as creativity? How can one measure it and predict the consequences of this metric? Leddy, in two seminal articles on creativity (1990), talks about how the mechanisms underlying inspiration, a common explanation found in traditional creativity literature, has been replaced by the ordinary mechanisms of human cognition. While proponents of this approach including Simon (Newell and Simon 1972) consider this a laudable effort that explains the marvelous through the mundane processes of human cognition, others lament its “reductionist” outcome.

One of the effects of the cognitive explanations led to a proliferation of applications in Artificial Intelligence literature (Boden 1994). For example, Lenat’s system called Cyc demonstrates sufficient intelligence to derive higher order concepts and operations from lower order ones owing largely to the codification of massive amounts of everyday knowledge and knowhow.

One of the instruments of computation that has been used to effectively explain and demonstrate “creative behavior” has been the modeling approach (Langley et al. 1987). In this approach, mind constructs are modeled as structural representations of a real-world or imaginary situation and manipulates this structure in order to reach creative discoveries.

Once again, we observe the prominent role of the so-called Eureka Moment in moving scientific discovery and invention research into a new realm: abductive reasoning. Proponents of the abduction approach propose discovery as a prominent “what-if” construct as opposed to mere heuristics. “In this view, discovery is primarily a process of explaining anomalies or surprising, astonishing phenomena.” This approach is not without its distractors, either: abductive inferences are not considered logical, they are too permissive, and they do not explain the act of a hypothesis that is central to the act of starting the exploration that leads to discovery (Schickore 2014).

Analogy, which is understood as a process of bringing ideas that are well understood in one domain to bear on a new domain, is seen as another prominent venue for exploring the underlying mechanisms of creative acts of discovery (Mitchell 1993). For instance, “Kekulé’s seeing benzene’s carbon ring structure as a snake biting its tail,” or Faraday’s seeing the universe as patterned by “lines of force,” which led to the electric motor (Koestler 1964). Analogy plays an important role in creative process in fiction writing as well, which attempts to create a nonreflective mode that typically involves a fictionworld creating analogic references to viewpoints different from the writer’s own.

However limited, research on expertise in a number of domains, including chess, music, painting, and poetry, addresses some of these questions. Hayes’ work on musical composition (Hayes 1989), linking cognition and creativity, highlights the importance of cognition as the driving force for understanding creativity. He confirms that the Time at Task Hypothesis that sets the high-bar for one’s task of mastery at 10 years holds even for musical prodigies like Mozart and Tchaikovsky among 40 other grand-masters of Western Classical music. Studies in the areas of painting poetry and architecture have also shown how indispensable cognitive processes are for task mastery.

The Creative Nature of Writing

Human intelligence and creativity have developed to high levels due to their ability to encode ideas in stories and narratives. Cognition in verbal composition has been studied extensively with the goal of improving writing skills. Writers’ initial task representations are as important for success, as they would be in puzzles or scientific discoveries. Hayes and Nash (1996) discuss the “nature of the planning activity” in writing. They point out that writers interleave planning and writing tasks in an effort to balance their global and local goals. This kind of approach to writing has many practical benefits including the assisting of memory during the execution of complex plans and discovery of new tasks or the consolidation of multiple tasks into one.

In calibrating the quality of the writing tasks performed by both experienced and inexperienced writers, Hayes and Nash found that the amount of abstract planning positively correlated with quality.

The Creative Nature of Musical Mastery

Some of the most memorable accounts of creativity include statements directly from universally accepted creative individuals, like Tchaikovsky:

Generally speaking the germ of a future composition comes suddenly and unexpectedly. If the soil is ready – that is to say, if the disposition for work is there – it takes root with extraordinary force and rapidity, and shoots up through the earth, puts forth branches, leaves and, finally, blossoms.

Tchaikovsky reveals something about that which arrives in the mind and how it reaches fruition. He implies that what arises so suddenly does so due to substantial cognitive preparation that anticipates and evokes the idea in the first place. There is no doubt that the soil upon which Tchaikovsky’s sudden realization of a creative idea has blossomed has been properly and painstakingly cultivated.

This phenomenon observed in many cognitive task domains is commonly known as the Aha!-response, Eureka Moment, or Sudden Mental Insight (SMI). Puzzles are one of the most elementary forms of complex cognitive activity exhibiting the SMI response.

The Creative Nature of Puzzles

The Mutilated Checkerboard Puzzle

The Mutilated Checkerboard Puzzle (MCP) employs a standard 8 × 8 checkerboard (Fig. 1), two of whose diagonally opposite corners have been removed (Kaplan and Simon 1990).

Imagine placing dominos on the board so that one domino covers two horizontally or vertically (but not diagonally) adjacent squares. The problem is either to show how 31 dominos would cover the 62 remaining squares, or to prove logically that a complete covering is impossible.

Fig. 1

The Mutilated Checkerboard Puzzle. (Source: Akin 1989)

The MCP is difficult to solve and the solution usually involves the sudden onset of the idea about the proof upon realizing the Parity Principle. This principle states that each domino piece needs to cover a pair of black and white squares regardless of where it is placed while the mutilated board has an unequal number of black (32) and white (30) squares.

Kaplan and Simon (1990) systematically delineate and classify the clues, found in the problem context or in the subjects’ long term memory, as well as the hints provided by the experimenters, which help induce the recognition of the Parity Principle. They go on to describe the cognitive components needed to develop the solution: (1) the sudden onset of the Parity Principle; (2) the three sources of information: puzzle features, relevant knowledge, and hints about the colors of missing squares; (3) the development of a new problem space; and (4) a new problem space based on the invariant features of the puzzle.

The Nine-Dot Puzzle

The Nine-Dot (N-DP) is another puzzle that utilizes the SMI event (Akin and Akin 1996; Newell and Simon 1972). It involves graphic manipulations on a sheet of paper based on nine regularly spaced dots on a 3 × 3 grid (Fig. 2a). The goal is to draw four straight lines that are connected end to end so that each dot has a line going through it (Fig. 2b). In order to successfully solve the problem, subjects must realize that they should extend a line beyond the square shaped field formed by the nine-dots (Fig. 2b, shaded area). This is often the moment when a subject exclaims “Aha!” the tell-tale sign of the Eureka Moment.
Fig. 2

The Nine-Dot Puzzle. (Source: Akin 1989)

However, most subjects attempting to solve this puzzle restrict themselves to the square field, which is called the Frame of Reference (FoR) in SMI literature. This makes the solution impossible to attain since two intersection points in the solution have to lie outside of the square. Typically, subjects solving this puzzle fall into three categories: (1) those who solve it without help (Table 1, Type A); (2) those solve it after assistance is given to help them lift the FoR – usually in the form of an instruction: “you may go outside of the field of dots” (Table 1, Type B); and (3) those who cannot solve the puzzle even with this instruction (Table 1, Type C). Hence, solving the N-DP requires more than just removing the FoR: operations that enable drawing lines outside of the FoR (Fig. 2c) and aligning the vertices (Fig. 2d). Those who solve the puzzle on their own do so by satisfying all three conditions (Table 1, Type A or Type B). Those who are given the hint to go outside of the FoR solve the puzzle by achieving the remaining two conditions (Table 1, Type B). Those who are not able to solve the puzzle despite the hint proved (Table 1, Type C).
Table 1

Cognitive thresholds to solve the Nine-Dot Puzzle. (Source: Akin 1989)

Subject category


Removing the FoR (self)

Removing the FoR (by hint)

Drawing lines outside the FoR

Aligning vertices of the lines

Puzzle solved

Type A


Type B


Type C





For both puzzles (MCP and N-DP), it is possible to solve them only after removing their FoRs, and more importantly defining the requisite problem structure for the solution state without the restricting FoR. The development of the new problem structure is an example of the cognitive dimensions of creative behavior. The obstacle in applying these findings to the larger domains of human creativity is to be able to scale them up to other domains like scientific discovery and design (Akin and Akin 1996; Newell and Simon 1972).

Creative Nature of Architectural Design

Other fields that have adopted design as a central vehicle for creativity include graphics, industrial products, architecture, landscape architecture, engineering, urban and regional planning. Attempts at understanding and describing the design process and the underlying structure of the architect’s creativity by way of expertise go back to the early 1970s (Eastman 1969). Subsequently direct evidence about the relationship of expertise and creativity in architectural design has been provided by Akin (1986). More recently, important steps have been taken towards modeling creativity in engineering design and assessing the role of metaphors and analogies in inducing the SMI response (Casakin 2007).

A study specifically directed at the SMI phenomenon in architectural design and advances the field of research in this area compares cognitive processes of expert architects and novices (Akin and Akin 1996). In an architectural design problem devised by the authors, subjects were asked to design a façade for a given floor plan of an office suite containing five rooms: reception, secretary, conference, staff engineers, and chief engineer (Fig. 3). The restricting FoRs in this task are shown in the lower part of the figure and involve five categories: size, proportion-location of windows, number of stories, and wall construction and floor height(s). The Expert Designer arrives at SMIs following a variety of conditions: exhausting all alternative solutions within the given FoR; trying heuristic rules to leap out of the existing solution cycle (such as inverting the orientation and value of design elements), redefining the FoR based on specific domain knowledge by balancing the elements of a composition, or coming up with design insights resulting from these conditions.
Fig. 3

Plan (above) and FoR-facade (below). (Source: Akin)

Through this process, the Expert Designer breaks out of six FoRs (Fig. 4). The first FoR from which the subject breaks out is the regularity of the windows. She refers to the existing window geometry as “repetitive” and “deadening” (Table 2, FR1-1). She also speaks of specific design operations to fix this problem: infusing variety, hierarchy, and other grouping strategies. In achieving this break-out, she also relies on a well-known principle of composition, namely, bookend that achieves the accentuation of the windows at the two extreme positions of the linear façade layout. This principle has the effect of freeing her to experiment with patterns that are not necessarily in conformance with the floor plan (Fig. 4). This approach is also evident in some of the other design features, such as roof form, materials, and solar shading devices.
Fig. 4

Façade designs by an Expert Designer. (Source: Akin 1989)

Table 2

Break out from Frames of Reference (FoRs) by Expert Designer. (Source: Akin 1989)

FoR category

FoRs in subject’s own words

Source of the FoRs

Break-out from FoR moves

Source of break-out moves

Window Geometry

FR1-1: “(these are) repeated windows”

External: plan view

Vary end-conditions of façade layout

Recall: composition principles

Ceiling Height

FR1-2: “(assume) 12′ ceiling heights”

Recall: building standards

Show functional allocation by ceiling height variation

Recall: spatial design principles

Ground Floor Location

FR1-3.1: “(locate) on ground floor”

Recall: general assumption

Assume ground floor location

Single Story Building

FR1-3.2: “(locate) on ground floor”

Recall: general assumption

Assume single story building

Relief in Building Façade

FR1-4: “…some relief (is needed)”

External: plan view

Create projecting shading devices

Recall: Subject-1’s earlier designs

Façade Construct’n

FR1-5: “(give) texture, contrast to materials”

Recall: knowledge of construction

Use a variety of building materials

Recall: composition and construction in tandem

By balancing the asymmetrical roof forms on the opposing ends of the façade, the Expert Designer re-emphasizes the ending positions of the façade. The eyebrow-like features placed above the middle windows as shading devices (Fig. 4) also help place the differences between middle and end windows at an even keel. Juxtaposition of the shading devices’ metal construction against the heavy, earthy textures of the brick wall presents an attractive material selection.

In the case of the Novice Designer (Table 3), a small number of FoRs are observed and an even smaller number are broken out of. Her solution (Fig. 5) is the same as the normative solution (Fig. 3, façade). The window patterns are the very first FoRs from which the Novice Designer tries to break-out. She remarks “I mean if you’re looking in, I don’t know that I would necessarily see anything. If I stand outside, all I pretty much see is windows… right?” However, the features used to achieve this break-out are standard features found in normalized house images. In this case, the roof is a simple gable, the walls are brick, and the windows are regularly proportioned and spaced. The only two pieces missing from the standard image are the entrance (Table 3, FR2.2) and the chimney. The two materials, brick and shingles, are selected in conformance with the standard house image to which she refers in the protocol as part of a childhood model building activity.
Table 3

Break out from Frames of Reference (FoRs) by Novice Designer. (Source: Akin 1989)

FoR category

FoRs in subject’s own words

Source of the FoRs

Break-out move

Source of break-out move

Window Geometry

FR2-1: “want to make (these) window(s) bigger”

External: plan view & assumption of normal sill height

Lower the assumed window sills height

Recall: general heuristic

Main Access

FR2-2: “…don’t see any doors”

External: absence of information


Not applicable

Ceiling Form

FR2-3: “nice big curvy ceiling like roof”

External: absence of information

Place hipped roof gable

Recall: typical “house” image

Construct’n Materials

FR2-4: “maybe (the wall) could be brick”

Recall: general assumption

Place brick on the façade

Recall: typical “house” image

Fig. 5

Façade designs by a Novice Designer. (Source: Akin 1989)

These differences between the two subjects point to the same phenomenon observed in puzzles. Recognizing the need to break-out of FoRs is not sufficient to reach creative solutions. One also needs the procedural knowledge with which to implement each break-out. The Novice Designer, due to a lack of training in architectural design, does not have the technical background and experience that enables the Expert Designer with the requisite skills to assemble façade compositions, spatial compositions, sun shading devices, and construction details.

The Creative Nature of Scientific Discovery

History of science is full of accounts of brilliant discoveries that have changed the course of society, such as Fleming’s discovery of Penicillin, Salk’s discovery of the Polio vaccine, Mendeleev’s formulation of the Periodic Table of Elements, Newton’s formulation of the General Law of Gravitation, or Einstein’s Law of Relativity. While these novel formulations of knowledge have proven to be of enormous value to mankind, there should be little doubt that these are also creative acts exhibiting superior cognitive processing.

Kedrov’s meticulous study (1966–1967) of the circumstances around Mendeleev’s formulation of the Periodic Table of the Elements helps unravel the conditions that give rise to the SMI in the sciences. In 1868, Mendeleev was busy with constructing the table of contents of the second volume of his new text books on chemistry. He had already covered the halogens and the alkaline metals in the first two chapters. It was not clear as to which group of elements should be covered next.

Medeleev’s exploration began with a search for a pattern that could be applied to all known elements. First, he compared the atomic weights of the elements. While this was a good start, there were two big obstacles: the number of comparisons with all pairs of atomic weights was far too numerous to undertake exhaustively; and the chemical elements not yet discovered at the time created gaps and made it difficult to see the global pattern in the data. Next, Mendeleev compared groups of elements based on their atomic properties and ordered them according to their atomic weights. His second breakthrough came when he made a modification in his representation. He decided to use playing cards to represent elements ordered in a two dimensional matrix space, with one dimension representing the ordering of atomic weights and the other general chemical properties of the elements. Kedrov speculates that this analogy, marking an SMI moment for Mendeleev, presented itself because he was an avid fan of the card game Patience.

Conclusions and Implications for Theory and Practice

One of the first things that can be stated regarding the creative process is its kinship to most other cognitive processes. The evidence considered in this essay suggests that cognition of creativity shares a great deal with ordinary cognitive acts such as heuristic search, recognition, and problem solving. In addition, an indispensable factor in the creative process appears to be a shift in the structure of the task at hand, called the SMI. Observations in puzzles, scientific discoveries, and design show that new constructs consisting of both a specific problem representation and operations applicable in the domain of this representation must be created.

The fact that the creative process requires the discovery of a new problem space necessitates that the creative individual must have skills not just for problem solving but also for defining new problems. This latter skill has been described in various contexts. Problem seeking, puzzle making problem restructuring, and problem formulation are some of the related concepts that have recently appeared in expertise and creativity literature.

One of the most important aspects of the process of searching for new problem spaces has to do with domain knowledge. As observed in puzzles, inventions, and designs, the knowledge of the creative agent plays a key role in their creative achievements. In the case of the architectural design problem, it is evident that the Novice Designer does not possess this skill while the Expert Designer does. Finally, it is important to underscore that the important role of the SMI or Aha!-response is a related but inessential manifestation of creative acts. It seems that cognitive psychology of creativity is more important for the socio-psychological aspects of discoveries and creative inventions. Hence, several important areas of research are indicated by this review of research in puzzles, inventions, and design:
  1. 1.

    Do creative acts always involve the SMI or the “Aha!” response?

  2. 2.

    Is the SMI relevant only in the initial act of creative revelation?

  3. 3.

    If the moment of discovery filled with surprise lacks all requisite aspects of the SMI, should it still be considered the start of a creative act?

  4. 4.

    Since the differences between novices and experts seem to correlate with the SMI condition, can people learn to seek the SMI?

  5. 5.

    Is expertise a necessary and a sufficient condition for creativity?

  6. 6.

    Since it is culturally regarded as a mysterious process, is there a tautological impediment to uncovering the secrets of creativity? (see “Paradox of Creativity Research”)




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Authors and Affiliations

  1. 1.School of ArchitectureCarnegie Mellon UniversityPittsburghUSA

Section editors and affiliations

  • Marta Peris-Ortiz
    • 1
  1. 1.Departamento de Organización de EmpresasUniversitat Politècnica de ValènciaValenciaSpain