Physical Complexity of a Cognitive Artifact
This provides a theoretical framework for understanding how cognitive artifacts reduce problem-solving difficulty, though it appears incremental in applying existing complexity methods to a specific puzzle domain.
The paper tackles the problem of quantifying task difficulty in cognitive science by mapping computational complexity concepts from the Soma Cube puzzle onto cognitive strategies, showing how strategies like chunking and pruning reduce effective time complexity through measured branching factor analysis.
Cognitive science and theoretical computer science both seek to classify and explain the difficulty of tasks. Mechanisms of intelligence are those that reduce task difficulty. Here we map concepts from the computational complexity of a physical puzzle, the Soma Cube, onto cognitive problem-solving strategies through a ``Principle of Materiality''. By analyzing the puzzle's branching factor, measured through search tree outdegree, we quantitatively assess task difficulty and systematically examine how different strategies modify complexity. We incrementally refine a trial-and-error search by layering preprocessing (cognitive chunking), value ordering (cognitive free-sorting), variable ordering (cognitive scaffolding), and pruning (cognitive inference). We discuss how the competent use of artifacts reduces effective time complexity by exploiting physical constraints and propose a model of intelligence as a library of algorithms that recruit the capabilities of both mind and matter.