Random Walks in 10 Dimensions: Defying Intuition in High-Dimensional Spaces

High-dimensional physics is the norm in modern dynamics, from string theory's ten dimensions to complex systems. However, high dimensions present the 'curse of dimensionality': visualization is impossible, overfitting is rampant, and intuition fails. This article uses a 10-dimensional random walk to illustrate high-dimensional space characteristics. In high dimensions, mountain ridges are far more common than peaks, profoundly impacting evolution, complex systems, and machine learning. Random walks efficiently explore high-dimensional spaces, even maximally rough landscapes, potentially traversing the entire space. This helps understand the evolution of complex structures in life and how to avoid local minima in deep learning.