Model Perspective

Nov 5, 2026 · Artificial Intelligence

Flatland to High Dimensions: Why Spheres Become Skin and Distance Loses Meaning

Using Edwin Abbott's Flatland as a starting point, this article explains how cross-sections and combinatorial counting reveal properties of higher dimensions, showing that high-dimensional spheres concentrate volume near their surface, peak in size at five dimensions, and cause distances between points to become indistinguishable — the curse of dimensionality affecting machine learning.