Geometry vs Binary: AI/Binary Failures — neural network fails at geometric reasoning spatia — E8 Intelligence Research

## Binary Failure → Geometry Solution **Analysis of Findings:** The search results reveal a classic failure mode: neural networks struggle with **spatial reasoning puzzles** (e.g., Mensa Norway puzzle #12, odd-one-out pattern recognition) and **analytical reasoning tests** that require understanding of **transformations, symmetries, and relational structures** rather than statistical pattern matching. **Where Binary/Statistical Approaches FAIL:** 1. **Mensa Norway Puzzle #12** (spatial rotation/reflection): Neural nets treat pixels as independent features; they cannot *inherently* encode the group-theoretic concept of a rotation or reflection as a *continuous symmetry operation*. They memorize surface patterns, not the underlying geometric invariance. When the puzzle requires applying a rotation to a shape and then comparing it to a rotated version of another shape, the net fails because it has no built-in representation of the rotation group (e.g., SO(2) or the dihedral group). 2 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com