Randomness

Lore & Background

In ancient history, the concepts of chance and randomness were intertwined with fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. Most ancient cultures used various methods of divination to attempt to circumvent randomness and fate. Beyond religion and games of chance, randomness has been attested for sortition since at least ancient Athenian democracy in the form of a kleroterion. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the 16th century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of calculus had a positive impact on the formal study of randomness. The early part of the 20th century saw a rapid growth in the formal analysis of randomness, as various approaches to the mathematical foundations of probability were introduced. In the mid-to-late-20th century, ideas of algorithmic information theory introduced new dimensions to the field via the concept of algorithmic randomness. Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the 20th century 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 even outperform the best deterministic methods.

Reader's Guide

Randomness is central to many scientific fields. In the physical sciences, 19th-century scientists used the idea of random motions of molecules in the development of statistical mechanics to explain phenomena in thermodynamics and the properties of gases. According to several standard interpretations of quantum mechanics, microscopic phenomena are objectively random. In biology, the modern evolutionary synthesis ascribes the observed diversity of life to random genetic mutations followed by natural selection. The characteristics of an organism arise to some extent deterministically and to some extent randomly. In mathematics, the mathematical theory of probability arose from attempts to formulate mathematical descriptions of chance events. Algorithmic information theory studies what constitutes a random sequence, with the central idea that a string of bits is random if and only if it is shorter than any computer program that can produce that string (Kolmogorov randomness). According to Ramsey theory, pure randomness is impossible, especially for large structures. Mathematician Theodore Motzkin suggested that 'while disorder is more probable in general, complete disorder is impossible.' Cristian S. Calude stated that 'given the impossibility of true randomness, the effort is directed towards studying degrees of randomness.' It can be proven that there is infinite hierarchy of forms of randomness.

Did You Know?

• Random selection, when associated with a simple random sample, requires equal probabilities for any item to be chosen.
• Monte Carlo methods rely on random input and are important in computational science.
• According to Ramsey theory, pure randomness is impossible, especially for large structures.
• The decimal digits of pi have been used to construct a random walk in two dimensions.