[1]Principia Cybernetica Web

                                        Variety

   Variety is a measure of the number of distinct states a system can be in
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   The set of all possible states that a system can be in defines its state space.
   An essential component of cybernetic modelling is a quantitative measure for the
   size of that state space, or the number of distinct states. This measure is
   called variety. Variety represents the freedom the system has in choosing a
   particular state, and thus the uncertainty we have about which state the system
   occupies. Variety V is defined as the number of elements in the state space S,
   or, more commonly, as the logarithm to the basis two of that number:

   V = log[2] (|S|)

   The unit of variety in the logarithmic form is the bit. A variety of one bit,
   V=1, means that the system has two possible states, that is, one difference or
   distinction. In the simplest case of n binary variables, V = log[2](2^n) = n is
   therefore equal to the minimal number of independent dimensions.

Background

   Variety has always been a fundamental idea in [2]Cybernetics and Systems Science,
   and is so in [3]Metasystem Transition Theory. Variety is defined as a
   multiplicity of distinctions. The existence of variety is necessary for all
   change, choice, and information. A reduction in the quantity of variety is the
   process of [4]selection. If variety has thus been reduced, i.e. if actual variety
   is less than potential variety, then we say that there is [5]constraint.

   Frequently the quantity of variety and the change in the quantity of variety
   (positive increase or negative decrease) is critical to understand system
   evolution. Where variety is manifest in a process, then we sometimes want to say
   that there is uncertainty about the outcome of the process; when that uncertainty
   is relieved but the occurrence of one of the possibilities, then we gain
   [6]information. The are many possible ways to measure the quantity of variety,
   uncertainty, or information. As defined above, the simplest is the count of the
   number of distinct states. More useful can be the logarithm of that number as a
   quantity of information, which is called the Hartley entropy. When sets and
   subsets of distinctions are considered, possibilistic nonspecificities result .
   The most celebrated are the [7]stochastic entropies of classical information
   theory, which result from applying probabilistic distributions to the various
   distinctions.
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   [8]Copyright© 2001 Principia Cybernetica - [9]Referencing this page

   Author
   C. [10]Joslyn, & F. [11]Heylighen,

   Date
   Sep 3, 2001 (modified)
   Jan 1992 (created)

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References

   1. LYNXIMGMAP:http://pespmc1.vub.ac.be/VARIETY.html#PCP-header
   2. http://pespmc1.vub.ac.be/CYBERN.html
   3. http://pespmc1.vub.ac.be/MSTT.html
   4. http://pespmc1.vub.ac.be/SELECT.html
   5. http://pespmc1.vub.ac.be/CONSTRAI.html
   6. http://pespmc1.vub.ac.be/ENTRINFO.html
   7. http://pespmc1.vub.ac.be/ENTRINFO.html
   8. http://pespmc1.vub.ac.be/COPYR.html
   9. http://pespmc1.vub.ac.be/REFERPCP.html
  10. http://pespmc1.vub.ac.be/JOSLYN.html
  11. http://pespmc1.vub.ac.be/HEYL.html
  12. http://pespmc1.vub.ac.be/DEFAULT.html
  13. http://pespmc1.vub.ac.be/MSTT.html
  14. http://pespmc1.vub.ac.be/SYSCONC.html
  15. http://pespmc1.vub.ac.be/TRIALERR.html
  16. http://pespmc1.vub.ac.be/CONSTRAI.html
  17. http://pespmc1.vub.ac.be/MAKANNOT.html
  18. http://pespmc1.vub.ac.be/hypercard.acgi$annotform?

[USEMAP]
http://pespmc1.vub.ac.be/VARIETY.html#PCP-header
   1. http://pespmc1.vub.ac.be/DEFAULT.html
   2. http://pespmc1.vub.ac.be/HOWWEB.html
   3. http://pcp.lanl.gov/VARIETY.html
   4. http://pespmc1.vub.ac.be/VARIETY.html
   5. http://pespmc1.vub.ac.be/SERVER.html
   6. http://pespmc1.vub.ac.be/hypercard.acgi$randomlink?searchstring=.html
   7. http://pespmc1.vub.ac.be/RECENT.html
   8. http://pespmc1.vub.ac.be/TOC.html#VARIETY
   9. http://pespmc1.vub.ac.be/SEARCH.html