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The Mathematical Theory of Information (Hardcover, 2002 ed.)
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The Mathematical Theory of Information (Hardcover, 2002 ed.)
Series: The Springer International Series in Engineering and Computer Science, 684
Expected to ship within 12 - 17 working days
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Total price: R1,710
Discovery Miles: 17 100
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The general concept of information is here, for the first time,
defined mathematically by adding one single axiom to the
probability theory. This Mathematical Theory of Information is
explored in fourteen chapters: 1. Information can be measured in
different units, in anything from bits to dollars. We will here
argue that any measure is acceptable if it does not violate the Law
of Diminishing Information. This law is supported by two
independent arguments: one derived from the Bar-Hillel ideal
receiver, the other is based on Shannon's noisy channel. The
entropy in the 'classical information theory' is one of the
measures conforming to the Law of Diminishing Information, but it
has, however, properties such as being symmetric, which makes it
unsuitable for some applications. The measure reliability is found
to be a universal information measure. 2. For discrete and finite
signals, the Law of Diminishing Information is defined
mathematically, using probability theory and matrix algebra. 3. The
Law of Diminishing Information is used as an axiom to derive
essential properties of information. Byron's law: there is more
information in a lie than in gibberish. Preservation: no
information is lost in a reversible channel. Etc. The Mathematical
Theory of Information supports colligation, i. e. the property to
bind facts together making 'two plus two greater than four'.
Colligation is a must when the information carries knowledge, or is
a base for decisions. In such cases, reliability is always a useful
information measure. Entropy does not allow colligation.
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