Many scientific fields are concerned with randomness: •
Algorithmic probability •
Chaos theory •
Cryptography •
Game theory •
Information theory •
Pattern recognition •
Percolation theory •
Probability theory •
Quantum mechanics •
Random walk •
Statistical mechanics •
Statistics In the physical sciences In the 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. That is, in an experiment that controls all causally relevant parameters, some aspects of the outcome still vary randomly. For example, if a single unstable
atom is placed in a controlled environment, it cannot be predicted how long it will take for the atom to decay—only the probability of decay in a given time. Thus, quantum mechanics does not specify the outcome of individual experiments, but only the probabilities.
Hidden variable theories reject the view that nature contains irreducible randomness: such theories posit that in the processes that appear random, properties with a certain statistical distribution are at work behind the scenes, determining the outcome in each case.
In biology The
modern evolutionary synthesis ascribes the observed diversity of life to random genetic
mutations followed by
natural selection. The latter retains some random mutations in the
gene pool due to the systematically improved chance for survival and reproduction that those mutated genes confer on individuals who possess them. The location of the mutation is not entirely random however as e.g. biologically important regions may be more protected from mutations. Several authors also claim that evolution (and sometimes development) requires a specific form of randomness, namely the introduction of qualitatively new behaviors. Instead of the choice of one possibility among several pre-given ones, this randomness corresponds to the formation of new possibilities. The characteristics of an organism arise to some extent deterministically (e.g., under the influence of genes and the environment), and to some extent randomly. For example, the
density of
freckles that appear on a person's skin is controlled by genes and exposure to light; whereas the exact location of
individual freckles seems random. As far as behavior is concerned, randomness is important if an animal is to behave in a way that is unpredictable to others. For instance, insects in flight tend to move about with random changes in direction, making it difficult for pursuing predators to predict their trajectories.
In mathematics The mathematical theory of
probability arose from attempts to formulate mathematical descriptions of chance events, originally in the context of
gambling, but later in connection with physics.
Statistics is used to infer an underlying
probability distribution of a collection of empirical observations. For the purposes of
simulation, it is necessary to have a large supply of
random numbers—or means to generate them on demand.
Algorithmic information theory studies, among other topics, what constitutes a
random sequence. The central idea is 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), which means that random strings are those that cannot be
compressed. Pioneers of this field include
Andrey Kolmogorov and his student
Per Martin-Löf,
Ray Solomonoff, and
Gregory Chaitin. For the notion of infinite sequence, mathematicians generally accept
Per Martin-Löf's semi-eponymous definition: An infinite sequence is random if and only if it withstands all recursively enumerable null sets. The other notions of random sequences include, among others, recursive randomness and Schnorr randomness, which are based on recursively computable martingales. It was shown by
Yongge Wang that these randomness notions are generally different. Randomness occurs in numbers such as
log(2) and
pi. The decimal digits of pi constitute an infinite sequence and "never repeat in a cyclical fashion." Numbers like pi are also considered likely to be
normal:
In statistics In statistics, randomness is commonly used to create
simple random samples. This allows surveys of completely random groups of people to provide realistic data that is reflective of the population. Common methods of doing this include drawing names out of a hat or using a random digit chart (a large table of random digits).
In information science In information science, irrelevant or meaningless data is considered noise. Noise consists of numerous transient disturbances, with a statistically randomized time distribution. In
communication theory, randomness in a signal is called "noise", and is opposed to that component of its variation that is causally attributable to the source, the signal. In terms of the development of random networks, for communication randomness rests on the two simple assumptions of
Paul Erdős and
Alfréd Rényi, who said that there were a fixed number of nodes and this number remained fixed for the life of the network, and that all nodes were equal and linked randomly to each other.
In finance The
random walk hypothesis considers that asset prices in an organized
market evolve at random, in the sense that the expected value of their change is zero but the actual value may turn out to be positive or negative. More generally, asset prices are influenced by a variety of unpredictable events in the general economic environment.
In politics Random selection can be an official method to resolve
tied elections in some jurisdictions. Its use in politics originates long ago. Many offices in
ancient Athens were chosen by lot instead of modern voting. == Randomness and religion ==