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.