Meaning Does Not Emerge from Structure Alone: Evidence from Two-Axis Evaluation of Visualization

Visualizations produced by dimensionality reduction are routinely interpreted as if spatial proximity reflects semantic similarity. This practice implicitly assumes that two properties—semantic alignment (whether nearby points share meaning) and structural preservation (whether the original relational geometry is maintained)—covary. Whether these quantities are in fact independent has not been systematically tested. Here we show that semantic alignment and structural preservation are statistically independent: they respond to different manipulations, occupy orthogonal axes under controlled perturbation, and dissociate in real data. Applied to human similarity judgments (THINGS dataset), the method with the highest semantic alignment (MDS) exhibited the lowest neighborhood preservation—a dissociation invisible to any single-metric evaluation. These findings indicate that meaning does not emerge from structure alone; rather, meaning becomes observable only when an external evaluative criterion specifies which structural relations are relevant. We introduce the SSC-SP framework—Semantic-Spatial Correlation and Structural Preservation—which separates these axes into reproducible, independently reportable quantities, providing a foundation for more precise interpretation of visualization across disciplines.