---
title: "History of randomness"
chunk: 4/4
source: "https://en.wikipedia.org/wiki/History_of_randomness"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:40:15.668742+00:00"
instance: "kb-cron"
---

By the early 1940s, the frequency theory approach to probability was well accepted within the Vienna circle, but in the 1950s Karl Popper proposed the propensity theory. Given that the frequency approach cannot deal with "a single toss" of a coin, and can only address large ensembles or collectives, the single-case probabilities were treated as propensities or chances. The concept of propensity was also driven by the desire to handle single-case probability settings in quantum mechanics, e.g. the probability of decay of a specific atom at a specific moment. In more general terms, the frequency approach can not deal with the probability of the death of a specific person given that the death can not be repeated multiple times for that person. Karl Popper echoed the same sentiment as Aristotle in viewing randomness as subordinate to order when he wrote that "the concept of chance is not opposed to the concept of law" in nature, provided one considers the laws of chance.
Claude Shannon's development of Information theory in 1948 gave rise to the entropy view of randomness. In this view, randomness is the opposite of determinism in a stochastic process. Hence if a stochastic system has entropy zero it has no randomness and any increase in entropy increases randomness. Shannon's formulation defaults to Boltzmann's 19th century formulation of entropy in case all probabilities are equal. Entropy is now widely used in diverse fields of science from thermodynamics to quantum chemistry.
Martingales for the study of chance and betting strategies were introduced by Paul Lévy in the 1930s and were formalized by Joseph L. Doob in the 1950s. The application of random walk hypothesis in financial theory was first proposed by Maurice Kendall in 1953. It was later promoted by Eugene Fama and Burton Malkiel.
Random strings were first studied in the 1960s by A. N. Kolmogorov (who had provided the first axiomatic definition of probability theory in 1933), Chaitin and Martin-Löf. The algorithmic randomness of a string was defined as the minimum size of a program (e.g. in bits) executed on a universal computer that yields the string. Chaitin's Omega number later related randomness and the halting probability for programs.
In 1964, Benoît Mandelbrot suggested that most statistical models approached only a first stage of dealing with indeterminism, and that they ignored many aspects of real world turbulence. In his 1997 he defined seven states of randomness ranging from "mild to wild", with traditional randomness being at the mild end of the scale.
Despite mathematical advances, reliance on other methods of dealing with chance, such as fortune telling and astrology continued in the 20th century. The government of Myanmar reportedly shaped 20th century economic policy based on fortune telling and planned the move of the capital of the country based on the advice of astrologers. White House Chief of Staff Donald Regan criticized the involvement of astrologer Joan Quigley in decisions made during Ronald Reagan's presidency in the 1980s. Quigley claims to have been the White House astrologer for seven years.
During the 20th century, limits in dealing with randomness were better understood. The best-known example of both theoretical and operational limits on predictability is weather forecasting, simply because models have been used in the field since the 1950s. Predictions of weather and climate are necessarily uncertain. Observations of weather and climate are uncertain and incomplete, and the models into which the data are fed are uncertain. In 1961, Edward Lorenz noticed that a very small change to the initial data submitted to a computer program for weather simulation could result in a completely different weather scenario. This later became known as the butterfly effect, often paraphrased as the question: "Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?". A key example of serious practical limits on predictability is in geology, where the ability to predict earthquakes either on an individual or on a statistical basis remains a remote prospect.
In the late 1970s and early 1980s, computer scientists began to realize that the deliberate introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases, such randomized algorithms outperform the best deterministic methods.

== Notes ==

== References ==

== See also ==
Chaparro, Luis F. (April 2020). "A brief history of randomness".
Sheynin, O.B. (1991). "The notion of randomness from Aristotle to Poincaré" (PDF). Mathématiques et sciences humaines. 114: 41–55.