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During the process of "creating" or "discovering" a solution to a problem, or during the exercise of creativity in the forming of a structure to embody or instantiate an example, model, etc., a transitionary process ensues. That process can be indicated in many ways. A few include:
- Clarifying the problem and demonstrating a solution.
- Building a model.
- Creating a structure and demonstrating its validity.
- etc.
At earlier stages in the development of this process there is little structure to be viewed. In communicating with the person working on the problem only vague outlines of structure are possible. In even earlier stages (perhaps before the individual has "fully" chosen to work on the problem) there is little or no distinguishing the condition to be solved or worked on from the agent to do the solving. Intra-personal and interpersonal communication facilitates the development of successively more and more well elucidated forms relating both the problem to be solved and the progress toward solution.
As work on the solution proceeds, the "solver" uses an evaluational mode to determine the degree of closure in resolving the problem and solution. At stages in this process structures begin to form that bear direct relations within the problem and solution distinctions. At the very least the syntactic structure of the problem is met by "related" syntactic structures of the solution - demonstrating that the solution meets the relational structures characterizing the problem.
At some stage in the intimate involvement between the solver and the development of the problem and solution the solver begins to experience some independence from the solution. Characterizing the solution as growing autonomous with some independent structure is also appropriate.
At the stages of development immediately preceding the "beginning of autonomy" the solver experiences some "prelogical" sensations of "appropriateness" to the direction toward solution. This sensation is usually a combined sense of pleasure and "rightness". In many simple problems these processes all occur nearly instantaneously in the form of the "Ah-ha! experience". In more complex situations this process is more drawn out and extended and may be much more intense.
The "pleasure" experienced during the process of "hitting on a solution", "discovering a good lead", etc., can vary in intensity and in its method of instantiation from individual to individual, from time to time, from problem to problem, etc.
There are underlying mechanisms for the instantiation of this sense of pleasure, called the "hedonic response". Gordon states:
Hedonic response as evoked in creative process takes two forms:
1. It is a pleasurable feeling, developed toward the successful conclusion of a period of problem solving concentration, that signals the conceptual presence of a major new viewpoint which promises to lead to a useful solution.
2. It is a pleasurable feeling which occurs in a minor way acting as a moment-to-moment evaluation of the course of the creative process itself.1
Gordon goes on to state:
Emotional response is distrusted in science and technological invention. This is because the way one feels about the solution to a problem is confused with emotional response to a problem during the process of searching for a solution. Artists and writers are EXPECTED to like or dislike their materials and subject matter. The products of art and literature are judged on a "like" or "dislike" basis whereas the criterion of technological products is "are they useful?", "do they work?" ...Synectics... emphasizes that the PROCESS of producing either aesthetic or technical objects is accompanied by certain useful emotional responses, and that these responses must not be rejected as irrelevant, but must be schooled and liberated. Hedonic Response is one of the important responses."1
Abraham Maslow and others write of "Peak experiences" which may be induced, among other methods, by concentration. For example, the concentration from intense involvement in solving or working on problems, in particular, mathematics problems.
Non-Aristotelian methods of evaluating point out that no organism exists without a context, in particular, the evolutionary context of human beings, our biological structure, and the eons of physical evolution and millennia of cultural evolution. The normal functioning of human "knowing" and "understanding" abstracting (generalizing), particularizing, (instantiation by selecting or constructing an example) evolved in a (energy) competitive environment. Our current functioning has a long history of evolving in a highly emotionally structured environment; anger, fear, sexual aggression, (pair-bond or "love"), etc., have all been major factors present during our past problem solving.
It is only the last few millennia that a veneer of "logic" and "rationality" has been touted as our "real" functioning. With the success of the "cold logic" of science, we see even more "disdain" for "emotion" in problem solving. We are guilty of excessive reductionism, elementalism, etc., if we insist that our problem solving process is without "feeling states". From the perspective of non-Aristotelian logic we must account for and include "feelings" as well as "thinking" in any theory of problem solving.
The Hedonic Response, characterized as feelings of pleasure, represents a high level of abstracting. Similarly, other pleasurable experiences, of mild and intense forms, may be abstracted to high levels. Often we have more difficulty think-feeling at higher levels without reference to more objective (lower level) events or experiences to serve as exemplars for the high level abstraction. More intense experiences of pleasure require exemplars from the set of more intensely pleasurable experiences. We particularize the abstract feelings of pleasure, specifically the Hedonic Response during creative problem solving, by instantiating "echoes" of other pleasures within the normal functioning of think-feeling with our body-mind.
A mechanism, generalizing and particularizing, exists which allows evoking think-feel states from other pleasurable experiences during problem solving. The mechanism is available for the hedonic response during problem solving itself, as well as for the "less-involved" state of following the problem solving activities of others.
Sexual arousal, a particular instantiation of intense pleasure, is one form that may be taken by the Hedonic Response during problem solving, particularly during extended periods of intense concentration on more complex problems.
Regarding mathematics, Teresa Conant states:
"Reading a proof is making love with the soul of the intellect."