Explore the power and versatility of sampling methods in this comprehensive lecture by Peter W. Glynn from Stanford University. Delve into the historical context, philosophical underpinnings, and modern applications of sampling across various fields. Learn about statistical sampling in surveys, Monte Carlo methods in computational mathematics, and the role of sampling in distributed control systems and machine learning algorithms. Understand key concepts such as dimensional insensitivity, the "curse of dimensionality," and the differences between statistical and Monte Carlo sampling. Gain insights into how subtle modifications in sampling techniques can significantly impact results and why sampling-based approaches are crucial in overcoming computational challenges in high-dimensional problems. Through examples and visualizations, discover the practical applications of sampling in real-world scenarios, from presidential elections to server farm job assignments.