用积木谜题解析认知策略如何降低任务复杂度
Physical Complexity of a Cognitive Artifact
- 通过搜索树分支因子量化任务难度，分析认知策略对复杂度的影响
- 分层优化试错过程，使有效时间复杂度显著下降
- 适合研究认知科学与人机协同智能的读者
认知科学与理论计算机科学均致力于分类和解释任务难度。智能机制的作用在于降低任务难度。本文将物理谜题Soma Cube的计算复杂性概念映射到认知问题解决策略中，提出“物质性原则”。通过测量搜索树出度，定量评估任务难度，并系统分析不同策略如何改变复杂度。逐步优化试错搜索：引入预处理（认知分块）、价值排序（认知自由排序）、变量排序（认知支架）和剪枝（认知推理）。讨论熟练使用工具如何利用物理约束降低有效时间复杂度，提出智能是心智与物质共同调用算法库的模型。
原文摘要 · Abstract (English)
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.
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