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Information Theory

Formal Science

Information Theory 1Information theory is the mathematical study of the quantifying, transmitting, storing, and processing information.  Information is not interpreted in terms of meaning or semantics, but rather in terms of uncertainty, probability, and the structure of messages.  The central objective is to determine the fundamental limits of data representation and communication, independent of the physical systems used.

A concept in information theory is entropy, which measures the average uncertainty or unpredictability associated with a random variable or information source.  Higher entropy corresponds to greater uncertainty and thus a higher information content.  Another fundamental idea is mutual information, which quantifies the amount of information that one random variable contains about another, thereby measuring the reduction in uncertainty due to knowledge of a related variable.

Science
Formal Science
Information Theory
 

Information theory also defines the theoretical limits of communication systems.  The concept of channel capacity specifies the maximum rate at which information can be transmitted over a communication channel with arbitrarily low probability of error, given the presence of noise.  This leads to the development of coding schemes, including data compression (source coding) and error correction (channel coding), which aim to approach these limits efficiently.

Basically, information theory is a mathematically discipline that analyzes how information is quantified and manipulated, establishing universal limits and optimal strategies for communication and data handling.

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