**5. Koestler theory of creativity, Aha! Moment and learning**

For Koestler creativity and indeed learning what is subjectively new for an individual, which he refers to as progress in understanding, takes place through the synthesis of two distinct and previously incompatible frames of reference. He refers to these as matrices, each of which has its own rules of the game or codes that govern appropriate activity.

What is a matrix of thought, or a frame of reference?

*The matrix is the pattern before you, representing the ensemble of permissible moves. The code which governs the matrix can be put into simple mathematical equations … or it can be expressed in words. The code is the fixed invariable factor in a skill or habit, the matrix is the variable part. The two words do not refer to different entities, they refer to different aspects of the same activity*. (Koestler ([2], p. 40)).

Referring to individual moments of insight within the learning process, Koestler notes that "*Minor, subjective bisociative processes do occur on all levels and are the main vehicle for untutored learning*"(p. 658). This raises another important question addressed in [16] and in [20], how does one describe interiorization in Koestler bisociative frame? The more general question of how Piaget's notion of reflective abstraction fits into Koestler's bisociative frame is discussed in [22]. Since

constructivist research methodology can be described as minimally guided, it certainly classifies as untutored and therefore should be bisociative in nature. Can the same be said of internalization?

Our analysis of the genesis or birth of a code during a moment of insight, whether during interiorization, internalization or bisociation, is conducted through the lens of three defining characteristics of such moments. (We will use here Koestler's term "blocked situation" as one in which routine matrices fail to accomplish the desired goal: to solve the problem). The first is the search process in a blocked situation. The second is the connection realized during the moment of insight between the blocked situation and a matrix that provides conceptual reasoning that allows for resolution of the blocked features. The third is the novel concept and process based on the concept that acts on the formerly blocked features to obtain the goal.

#### **5.1 Discovery of a hidden analogy, interiorization and internalization**

Koestler describes a blocked situation as one in which routine matrices fail to accomplish the desired goal. Constructivists use the term non-assimilatory situation. Koestler describes the process of trying to resolve a blocked situation by searching for a connection to an analogous matrix as the discovery of a hidden analogy, as a search for something that is unknown:

*[T]he subject looks for a clue, the nature of which he does not know, except that it should be a 'clue' … a link to a type of problem familiar to him … [H]e must try out one frame after another … until he finds the frame into which it fits, … an analogy with past experience and allows him to come to grips with it*. (pp. 653-654).

This search process in such a blocked situation to find a connection to an appropriate matrix-scheme in our repertoire can itself be considered a matrix-schema Mo. The search process follows in its general outlines the steps of [8, 9]. We may consider the code to contain some or all of the following guiding principles. First, identify relevant features of a problem situation that are blocked. Second, review our toolbox or collection of matrices that are even remotely associated with these features. Finally, select and proceed-verify the one most appropriate. If this fails, Koestler notes that mathematicians recommend to sit tight and wait for inspiration.

We note that contemporary instructional methodology of teachers encourages students to seek external assistance during the process of these transitions. As a result, the search process from constructivist pedagogy turns to internalization. This search process is highly subjective. Individuals vary in their ability to discriminate or identify what objects are relevant and abstract the conceptual relationship between these objects and appropriate activity. There is also a wide variety of motivation. Patience on the part of individuals during this search and finally even the motivation to seek assistance varies. All these factors impact the success or failure of this process.

#### **5.2 Interiorization**

Interiorization occurs during a child's transition from empirical-spontaneous to abstract reasoning, and thus, M1 is an intuitive matrix and hence limited to situations

#### *Bisociation: Creativity of an Aha! Moment DOI: http://dx.doi.org/10.5772/intechopen.110694*

where input present low cognitive demand. When a situation involves objects with more structure or cognitive load, the subject becomes perturbed, their attention has two foci—it is so-called dyadic attention. One is their Mo search to understand the structural objects that cannot be assimilated, and the other is that part of the M1 matrix that acted upon the analogous spontaneous concepts. In a moment of bisociative insight between the search matrix and their intuitive matrix when the shift of attention shifts from dyadic to triadic attention of seeing the whole [19], the subject abstracts the spontaneous concepts.

This allows the formerly intuitive reasoning to become conceptual-based reasoning, and a pseudocode is born, through the bisociation of Mo and M1. This particular description of interiorization in creativity theory is known as selective encoding. In this, the subject's attention is on a relevant matrix-scheme or tool that they previously could use only in a limited context and their insight allows them to use it more fully. Thus, interiorization as described consists of bisociation through selecting an object(s) that cannot be assimilated, search to connect them with the spontaneous concepts of a person's intuitive scheme, and the result is scientific concepts simultaneous with a process or conscious scheme.

#### **5.3 Internalization and interiorization: the search matrix Mo**

The distinction between interiorization and internalization as it relates to moments of insight in the learning process begins with the nature of the search matrix Mo. In Koestler's description of searching for a hidden analogy, the search matrix Mo is focused on the subject's collection of even remotely related schemes in the hope of finding an unknown connection. The second tenet of constructivism is that all prerequisite knowledge should be present in a learning situation.

Thus, the search process is typically on solution activity determined by an existing scheme (M1) that is deemed appropriate and yet remains insufficient to resolve the non-assimilatory situation. As such, interiorization involves selective comparisons between the non-assimilatory objects in Mo and an intuitive M1 leading to an abstraction of the underlying conceptual-invariant relationship. Reflective abstraction is the name given by Piaget to the mechanism of accommodation that includes interiorization. It has two steps. In the first step, an appropriate M1 is projected into the search matrix Mo for a non-assimilatory situation. The second constructive generalization step involves perturbation between and reflection upon these two matrices. The creativity of Aha! Moment arises during the search within unconscious or semiconscious Incubation Gestalt stage through the shift of attention from the separate matrices to the whole revealing the new structure.

Social constructivists use the term reflective thinking, instead of reflective abstraction, to include any form of conscious reflection on collective discourse, for example, shared activities, including observation of, or communication with, an exterior source of knowledge. Thus, the search process Mo in internalization includes co-creation of knowledge in all its forms, making it ideal for analysis of classroom discourse. Social constructivists use the term socially mediated activity to describe solution activity that involves assistance through any form of cultural artifacts, or guided communication, for example, written text, pre-recorded videos, other internet search sources, peer-mentor, or teacher etc. As students attempt to internalize material presented in the classroom, their primary motive is to understand or assimilate externally directed activity. Thus, they may have a motive but not realize the problem goal.

#### **5.4 Moments of insight: connection**

The moment of insight has a transcendent nature as a student is led to this connection by intuition not reason. As a result, in Koestler's view, pedagogy should be (re)structured to support such moments of insight into the guided discovery as math and science cannot be appreciated outside such experiences.

In the constructivist frame, during interiorization the moment of insight occurs as the individual struggles to employ an intuitive situation-dependent scheme M1 in a non-assimilatory situation, that is due to the presence of Mo objects beyond the capacity of spontaneous thought. The perturbation between Mo and M1 is resolved in a moment of insight or, shift of attention which abstracts the formally intuitive reasoning. This experience transcends the reasoning from the situation as it becomes an abstracted activity–effect relationships. This moment of insight or abstraction allows the individual to have conscious control over the process and thus to act independently. Thus, for constructivists, Mo contains an existing M1 scheme, Situation/Activity/Effect (S-A-E) triad, which in a moment of insight is transformed into an abstracted Activity/Effect (A-E) dyad. That is one not dependent upon the situation. The pedagogy is guided discovery to promote reflection and abstraction upon such an M1. In Koestler's search for a hidden analogy, the focus is on the formation of a S-A-E triad. During internalization, as in Koestler's frame, there is typically no existing S-A-E link within the search matrix Mo.

However, the pedagogy of internalization is not centered on guided discovery but instead on the mentoring of students as they accommodate new situations at the upper limit of their zone of proximal development. That is the upper limit of what they can realize with assistance. So, where is their own individual creativity? It must be beyond the assistance: beyond the upper limit of their individual ZPD. Where is the bisociative frame?

#### **5.5 Creativity as deviation during the process of appropriation**

Here, we can use an important suggestion provided by [23] who informs that internalization encounters difficulties in the proper description of the concept formation, also from the sociocultural points view. To address these problems, we need to introduce the concept of appropriation. The term appropriation is often used to analyze learning within social discourse; it has its origins in the work of the Russian psychologist M.M. Bahktin to understand how children learn language.

*The word in language is half someone else's. It becomes "one's own" only when the speaker populates it with his own intention, his own accent, when he appropriates the work, adapting it to his own semantic and expressive intention.* [24]

When analyzed in sociocultural terms as the interaction between learners in the learning community, appropriation facilitates the development of concepts of individual learners. Let me continue here with the words of [23]:

*"Where is creativity related to the appropriation process? This is its own deviation. Table 2 lists some of the possibilities of a wide variety of deviations. This includes the gap between the concepts of the learners interacting with each other and between the concepts of the learning community as seen by each learner. The cause of these deviations lies in the learners' historical and cultural constraints. By interacting according to* *these deviations, each learner may misunderstand what he/she is talking about. Simultaneously, the learner may create a new concept not included in the speaker's concept. In other words, the deviation of appropriation can be the source of creativity that leads to new ideas that the speaker did not intend."*

In other words, creativity in sociocultural theory originates in the differences between the learner's and the community's matrices of thought owing to different historical and cultural constraints. Hence, we have recovered the bisociative frame between the two matrices of thought at exactly the unique site of creativity within sociocultural theory. If one of two matrices is that of the community and another of the learner, it might be natural to call creativity a deviation from the community's point of view. It is interesting to trace out how that particular process of appropriation of the concept interacts with the relevant inner spontaneous concepts of the learner. We leave that subject as an open research question: how do appropriation and interiorization interact?
