## Friday, 3 August 2012

### Randomness

Randomness has somewhat differing meanings as used in various fields. It also has common meanings which are connected to the notion of predictability (or lack thereof) of events.

The Oxford English Dictionary defines 'random' as "Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard." This concept of randomness suggests a non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination.

Applied usage in science, mathematics and statistics recognizes a lack of predictability when referring to randomness, but admits regularities in the occurrences of events whose outcomes are not certain. For example, when throwing 2 dice and counting the total, we can say 7 will randomly occur twice as often as 4. This view, where randomness simply refers to situations in which the certainty of the outcome is at issue, is the one taken when referring to concepts of chance, probability, and information entropy. In these situations randomness implies a measure of uncertainty and notions of haphazardness are irrelevant.

The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. A random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in the probability calculus.

Randomness is often used in statistics to signify well-defined statistical properties, such as a lack of bias or correlation. Monte Carlo methods, which rely on random input, are important techniques in science, as, for instance, in computational science.

Random selection is a method of selecting items (oftentimes called units) from a population where the probability of choosing a specific item is the proportion of those items in the population. For example, if we have a bowl of 100 marbles with 10 red (and any red marble is indistinguishable from any other red marble) and 90 blue (and any blue marble is indistinguishable from any other blue marble), a random selection mechanism would choose a red marble with probability 1/10. Note that a random selection mechanism that selected 10 marbles from this bowl would not necessarily result in 1 red and 9 blue. In situations where the population consists of items that are all distinguishable, a random selection mechanism would require equal probabilities for any item to be chosen. That is, if the section process is such that each member of a population, of say research subjects, has the same probability of being chosen then we can say the selection process is random. Random selection can be an official method to resolve tied elections in some jurisdictions and is even an ancient method of divination, as in tarot, the I Ching, and bibliomancy. Its use in politics is very old, as office holders in Ancient Athens were chosen by lot, there being no voting.