Machines as Deterministic Systems
Computational machines operate deterministically, producing predictable and repeatable results from algorithms, fundamentally distinguishing computer operations from physical randomness.
Middle Square Method: First Pseudorandom Algorithm
Von Neumann developed the middle square method to mechanically simulate randomness through simple arithmetic, creating deterministic sequences that appear random without requiring memory storage.
Pseudorandomness: Simulating Random Properties Deterministically
Pseudorandom algorithms generate sequences that mechanically simulate the scrambling aspect of true randomness while remaining completely deterministic and reproducible.
Random Walks: Visualizing Unpredictability
Random walks provide a visual method for detecting patterns in number sequences by drawing paths that change direction according to each value, revealing whether sequences exhibit true randomness.
Seed-Based Random Number Generation
Pseudorandom generators begin with a truly random seed—an initial value obtained from physical noise or timestamps—that determines the entire subsequent sequence through deterministic calculation.
True Randomness from Physical Noise Measurement
Truly random number sequences emerge from measuring physical noise in the world—random fluctuations observable everywhere in natural phenomena.
Von Neumann's ENIAC Random Number Problem
In 1946, John von Neumann faced the challenge of repeatedly calculating nuclear fission approximations for hydrogen bomb design using ENIAC, requiring quick access to random numbers within severe memory constraints.