Randomness
Randomness is a measure of uncertainty, not haphazardness.
Randomness is the apparent or actual lack of definite patterns or predictability in information. It applies to concepts of chance, probability, and information entropy, and is a measure of uncertainty of an outcome. The fields of mathematics, probability, and statistics use formal definitions of randomness, typically assuming some 'objective' probability distribution. In common usage, a random sequence of events or symbols shows no order or intelligible pattern, and individual events are unpredictable. However, when a probability distribution is known, the frequency of different outcomes over many trials becomes predictable; for instance, rolling two dice yields a sum of seven twice as often as a sum of four, even though any single roll is uncertain. In statistics, a random variable assigns a numerical value to each possible outcome, aiding in probability calculations, while a random process is a sequence of such variables that evolves without a deterministic pattern. Random selection, as in a simple random sample, ensures each item in a population has a probability of being chosen equal to its proportion in that group. Notably, according to Ramsey theory, pure randomness—a complete absence of pattern—is impossible for large structures. Mathematician Theodore Motzkin observed that while disorder is more probable, complete disorder is impossible, a misunderstanding that can fuel conspiracy theories. Cristian S. Calude noted that because true randomness is unattainable, research focuses on degrees of randomness, forming an infinite hierarchy of quality or strength. Historically, randomness was intertwined with fate; ancient cultures used dice and divination, and sortition appeared in Athenian democracy via the kleroterion. The formalization of odds began with Chinese thinkers three millennia ago and later with Italian mathematicians in the 16th century. In the 19th century, random molecular motions underpinned statistical mechanics, and in the 20th century, quantum mechanics revealed objective randomness at microscopic scales. Computer scientists also recognized that deliberate randomness in algorithms can outperform deterministic methods, leading to randomized algorithms.
- field
- Mathematics, probability, statistics, computer science
- known_for
- Formalization of randomness, random sequences, Monte Carlo methods, algorithmic 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.
More in Probability & Statistics 1-24
Spotted an error? Know more?
This is a living reference — every entry is fact-audited, and reader corrections feed straight into our audit queue. Suggest an edit · See this site's audit record