Scrutinizing Creativity

Each person referentially interprets problems, as well as any imposed "structures" constraining their solution, according to his or her own history (the sum of developmental and experiential histories unique to each person). Each such personal reference, call it "epsilon," is itself a structure. (Therefore, no experience--including the creative process--is free of constraints or poised to explore "infinite" solution space.) Epsilons of members of creative groups add noise to the solution criteria, which means that a solution set arrived at by creative groups, while of higher "quality" than that arrived at by an individual, is also much less likely to be unique, because of the contributions of multiple epsilons.

Broadly speaking, groups use an algorithmic type of solution method to produce conventional solutions to well-defined problems, whereas functionally, individuals are better at producing the long-shot solutions to problems that connect disparate elements in unintuitive ways, the type of solutions that occasionally reach a Kuhnian status (1). Such new ideas emerge through the structured environment in a manner similar to new species' emergence through natural selection in biological evolution, an analogy described by A. Hudder in her letter (Science's Compass, 1 Oct., p. 49). In more general terms, ideas emerge through a complex series of clustered dynamical systems and environments (2). Biological species are solutions to the problem of which organism type suits the existing environment (3). The mystery attending all such emergences derives from the abstrusely ephemeral network connections between problem-solving elements and their multidimensional dynamical environments (3). Predicting the suitability of a solution (in trivial cases) is directly related to semantic meaning (2, 3).

Contrary to Goldenberg et al., neither reappraisal of "our fundamental approaches to creativity" nor reevaluation of "its operational definition" seems necessary, because any proposed methodology will only be useful in defined settings. Depending on the problem and the desired type of solution, a group or an individual will be a more appropriate choice to address the problem. Groups (and computers) derive the algorithmic kinds of solutions to those problems having well-defined solution spaces. Individuals, on the other hand, are better at those larger-than-life kinds of problems having no apparent solution method (the problem itself is often only dimly recognized).

Dennis Hollenberg
364 Franklin Lane,
Ventura, CA 93001-1420, USA

1. T. S. Kuhn, The Structure of Scientific Revolutions (Univ. of Chicago Press, Chicago, ed. 2, 1970).
2. D. Hollenberg, in Encyclopedia of Computer Science and Technology, A. Kent and J. G. Williams, Eds. (Marcel-Dekker, New York, 1990), vol. 21, supplement 6, pp. 153-162.
3. D. Hollenberg, Beginnings, in press.

Response
We found that "creativity templates" (implicit regularities in the creative process) are effective in extracting creative ideas from a potentially infinite-dimensional space of solutions. The fundamental problems solved by scientists in the framework of the Kuhnian paradigm (1) do not fall within this class. Such problems have unique, singular solutions because of the overwhelming constraints imposed (independently, in addition to, and above the creativity requirement) by the scientific data. For example, Albert Einstein's theory of relativity has been adopted because it is the best hypothesis to fit the data, not because it is creative. As for the class of solutions drawn from an infinite-dimensional space, without Pablo Picasso, Les Demoiselles d'Avignon would have remained forever immersed in the infinite sea of creative potentiality (2).

To understand the difference between these two dynamical regimes, imagine the space of ideas as a "conceptual space" in which each location represents a particular idea. Similar ideas are represented at neighboring locations. The solutions to a given problem might be concentrated in a few spatial regions ("conceptual basins") separated by thick "walls" of inconsistent (nonsolution) ideas. A usual idea search that requires logical consistency at each step will therefore rarely be able to escape the conceptual basin in which the search has started: It will keep bumping on the "inconsistency walls" that delimit the basin.

The templates are (as Hollenberg alluded to in his letter) similar to cluster algorithms (3, 4) that facilitate global, directed (rather than local, random) jumps between different conceptual basins. This is achieved by forcing the concept dynamics to pass at intermediate stages through the "walls" of inconsistent logic. These methods are not suited for problems in which there are no such basins and walls and where the solution is just a unique, singular point (5).

We maintain that our findings require a reappraisal of the human relation to creativity: According to the Webster dictionary (6), the words "creative" and "mechanical" are antonyms ("creative evolution is evolution that is a creative rather than a mechanical, explicable process"). Yet our human judges systematically gave high creativity grades to the output of a mechanical computer procedure, showing that there is a clash between what humans declaratively define (6) as creative and the operative definitions that humans actually apply in practice.

Contrary to the central issue raised by Hollenberg, the similarity we drew between the creativity of structured groups and that of individuals merely exemplified the deficiency of unstructured methods in enhancing creativity. However, this issue was only remotely related to our main focus on human incapability to outperform a template-based, idea-generating computerized routine.

Jacob Goldenberg

David Mazursky
School of Business Administration,
The Hebrew University of Jerusalem,
Jerusalem 91905, Israel.
E-mail: msgolden@mscc.huji.ac.il and msmazur@mscc.huji.ac.il

Sorin Solomon
Racah Institute of Physics,
The Hebrew University of Jerusalem,
Jerusalem 91905, Israel.
E-mail: sorin@vms.huji.ac.il

1. T. S. Kuhn, The Structure of Scientific Revolutions (Univ. of Chicago Press, Chicago, IL, ed. 2, 1970).
2. L. B. Meyer, Crit. Inq., (September 1974), p. 1.
3. J. Goldenberg, S. Solomon, D. Mazursky, Int. J. Mod. Phys. C 7 (no. 5), 655 (1996).
4. J. Goldenberg, D. Mazursky, S. Solomon, Market. Sci. (November 1999), p. 333.
5. N. Persky and S. Solomon, Phys. Rev. E 54, 4399 (1996); S. Solomon, in Annual Reviews of Computational Physics II, D. Stauffer, Ed. (World Scientific, River Edge, NJ, 1995), pp. 243-294.
6. Webster's Seventh New Collegiate Dictionary (Merriam, Springfield, MA, 1976).