# Physical Complexity of a Cognitive Artifact

arXiv: https://arxiv.org/abs/2509.12495 · HTML: https://mlsanity.com/paper/2509.12495/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 70 references that are in the map.
- First posted on arXiv 15 Sep 2025.

## Builds on (most cited first, 3 of 3)

- [Simulation Intelligence: Towards a New Generation of Scientific Methods](https://mlsanity.com/paper/2112.03235/) (2021)
- [Exbodiment: The Mind Made Matter](https://mlsanity.com/paper/2412.10957/) (2024)
- [An Origami-Inspired Variable Friction Surface for Increasing the Dexterity of Robotic Grippers](https://mlsanity.com/paper/2404.09644/) (2024)

## Built on by (most cited first, 1 of 1)

- [Universality in Collective Intelligence on the Rubik's Cube](https://mlsanity.com/paper/2511.18609/) (2025)

## Abstract (arXiv)

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.