Information as a measure of variation

Abstract

In many applications of information theory, information measures the reduction of uncertainty that results from the knowledge that an event has occurred. Even so, an item of information learned need not be the occurrence of an event but, rather, the change in probability distribution associated with an ensemble of events. This paper examines the basic account of information, which focuses on events, and reviews how it may be naturally generalized to probability distributions/measures. The resulting information measure is special case of the Rényi information divergence (also known as the Rényi entropy). This information measure, herein dubbed the variational information, meaningfully assigns a numerical bit-value to arbitrary state transitions of physical systems. The information topology of these state transitions is characterized canonically by a right and left continuity spectrum defined in terms of the Kantorovich- Wasserstein metric. These continuity spectra provide a theoretical framework for characterizing the informational continuity of evolving systems and for rigorously assessing the degree to which such systems exhibit, or fail to exhibit, continuous change.

Download options

PhilArchive



    Upload a copy of this work     Papers currently archived: 72,722

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

Analytics

Added to PP
2009-01-28

Downloads
18 (#614,101)

6 months
1 (#387,390)

Historical graph of downloads
How can I increase my downloads?

References found in this work

No references found.

Add more references

Similar books and articles

The Information Medium.Orlin Vakarelov - 2012 - Philosophy and Technology 25 (1):47-65.
On Quantifying Semantic Information.Simon D'Alfonso - 2011 - Information 2 (1):61-101.
Some Varieties of Information.Jaakko Hintikka - 1984 - Information Processing and Management 20 (1-2):175-181.
Pre-Cognitive Semantic Information.Orlin Vakarelov - 2010 - Knowledge, Technology & Policy 23 (1-2):193-226.
On a Supposed Conceptual Inadequacy of the Shannon Information in Quantum Mechanics.G. C. - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):441-468.
The Use of Information Theory in Epistemology.William F. Harms - 1998 - Philosophy of Science 65 (3):472-501.