The Mathematical Theory of Information

This text offers a mathematical theory of information, built on a single powerful postulate: the “Law of Diminishing Information”. The concept of information is here defined mathematically by adding this postulate to the axioms of the probability theory. The law of diminishing information is founded on a fusion of two fundamental ideas: Carnap and Bar-Hillel’s “Ideal Receiver” and Shannon’s “Noisy Channel”. This “law” has been applied to information technology, game theory, legislation, logic of research, algorithmic information, chaos theory, control engineering, medical tests, and biological evolution. In physics, both the second law of thermodynamics and Schrodinger’s wave function are derived from the law of diminishing information. Conventional information theory, that of telecommunications, is analyzed as a special case, and eight conditions for its applicability are listed.