  This paper explores the paradoxical nature of computational creativity,
focusing on the inherent limitations of closed digital systems in emulating the
open-ended, dynamic process of human creativity. Through a comprehensive
analysis, we delve into the concept of the State Space Paradox (SSP) in
computational research on creativity, which arises from the attempt to model or
replicate creative behaviors within the bounded state spaces of digital
systems. Utilizing a combination of procedural and representational paradigms,
we examine various computational models and their capabilities to assist or
emulate the creative process. Our investigation encompasses rule-based systems,
genetic algorithms, case-based reasoning, shape grammars, and data mining,
among others, to understand how these methods contribute to or fall short of
achieving genuine creativity. The discussion extends to the implications of SSP
on the future of creativity-related computer systems, emphasizing the cultural
and contextual fluidity of creativity itself and the challenges of producing
truly creative outcomes within the constraints of pre-defined algorithmic
structures. We argue that while digital systems can provoke sudden mental
insights (SMIs) in human observers and potentially support the creative
process, their capacity to autonomously break out of their pre-programmed state
spaces and achieve originality akin to human creativity remains fundamentally
constrained. The paper concludes with reflections on the future directions for
research in computational creativity, suggesting that recognizing and embracing
the limitations and potentials of digital systems could lead to more nuanced
and effective tools for creative assistance.
