![]() Some other important measures in information theory are mutual information, channel capacity, error exponents, and relative entropy. For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a die (with six equally likely outcomes). Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. The field is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering.Ī key measure in information theory is entropy. The field was fundamentally established by the works of Harry Nyquist and Ralph Hartley in the 1920s, and Claude Shannon in the 1940s. Information theory is the scientific study of the quantification, storage, and communication of information. A 2011 Science article estimated that 97% of technologically stored information was already in digital bits in 2007, and that the year 2002 was the beginning of the digital age for information storage (with digital storage capacity bypassing analog for the first time). ![]() For example, the information encoded in one "fair" coin flip is log 2(2/1) = 1 bit, and in two fair coin flips is log 2(4/1) = 2 bits. It is 'that which reduces uncertainty by half'. The bit is a typical unit of information. Information theory takes advantage of this by concluding that more uncertain events require more information to resolve their uncertainty. Uncertainty is inversely proportional to the probability of occurrence. The uncertainty of an event is measured by its probability of occurrence. It can also be encrypted for safe storage and communication. Information can be encoded into various forms for transmission and interpretation (for example, information may be encoded into a sequence of signs, or transmitted via a signal). That which is perceived can be construed as a message in its own right, and in that sense, all information is always conveyed as the content of a message. Information is expressed either as the content of a message or through direct or indirect observation. Information can be transmitted in time, via data storage, and space, via communication and telecommunication. The information available from many orders may be analyzed, and then becomes knowledge that is put to use when the business subsequently is able to identify the most popular or least popular dish. For example, data may be collected from a single customer's order at a restaurant. The information available through a collection of data may be derived by analysis. Redundant data can be compressed up to an optimal size, which is the theoretical limit of compression. The derivation of information from a signal or message may be thought of as the resolution of ambiguity or uncertainty that arises during the interpretation of patterns within the signal or message. The concept of information is relevant in various contexts, including those of constraint, communication, control, data, form, education, knowledge, meaning, understanding, mental stimuli, pattern, perception, proposition, representation, and entropy. The key characteristic of information is that it is subject to interpretation and processing. ![]() In a digital signal bits may be interpreted into the symbols, letters, numbers, or structures that convey the information available at the next level up. For example, in written text each symbol or letter conveys information relevant to the word it is part of, each word conveys information relevant to the phrase it is part of, each phrase conveys information relevant to the sentence it is part of, and so on until at the final step information is interpreted and becomes knowledge in a given domain. Information is often processed iteratively: Data available at one step are processed into information to be interpreted and processed at the next step. Information is not knowledge itself, but the meaning that may be derived from a representation through interpretation. Whereas digital signals and other data use discrete signs to convey information, other phenomena and artifacts such as analog signals, poems, pictures, music or other sounds, and currents convey information in a more continuous form. ![]() ![]() Any natural process that is not completely random, and any observable pattern in any medium can be said to convey some amount of information. At the most fundamental level information pertains to the interpretation of that which may be sensed. Information is an abstract concept that refers to that which has the power to inform. ![]()
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