Why Normal Distributions Emerge—From Binary Search to Steamrunners
A normal distribution, often visualized as a symmetric, bell-shaped curve, describes how values cluster around a central mean with decreasing probability toward extremes. This shape arises naturally in systems shaped by many small, independent influences—making it a cornerstone of probability theory. The mean defines the center, while the standard deviation quantifies the spread, determining how rapidly values deviate from the average.
The ubiquity of normal distributions spans biology, engineering, and social systems—from height measurements and measurement errors to random walks and algorithmic behavior. Their power lies in their predictability amid complexity.
The journey toward emergent normality begins with Alan Turing’s 1936 abstract machine,