[1]Principia Cybernetica Web

                                      Constraint

   Constraint is a measure of the reduction of [2]variety or reduction of freedom
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   A system's [3]variety V measures the number of possible states it can exhibit,
   and corresponds to the number of independent binary variables. But in general,
   the variables used to describe a system are neither binary nor independent. For
   example, if a particular type of berry can, depending on its degree of ripeness,
   be either small and green or large and red (recognizing only two states of size
   and color), then the variables "color" and "size" are completely dependent on
   each other, and the total variety is one bit rather than the two you would get if
   you would count the variables separately.

   More generally, if the actual variety of states that the system can exhibit is
   smaller than the variety of states we can potentially conceive, then the system
   is said to be constrained. This means that the system cannot fully use the
   "freedom" that would seem to be available to it, because some internal or
   external law, relation or control prohibits certain combinations of values for
   the variables. Another example of a constrained system is a planet orbiting the
   sun, which cannot leave its ellipsoid trajectory because of the gravitational
   force that binds it to the sun, or an atom in a molecule, that can at most
   vibrate or rotate around its equilibrium position, but cannot get away from the
   other atoms in the molecule.

   Constraint C can be defined as the difference between maximal and actual variety:

   C = V[max] - V

   Constraint is what reduces our uncertainty about the system's state, and thus
   allows us to make non-trivial predictions. For example, in the above example if
   we detect that a berry is small, we can predict that it will also be green.
   Constraint also allows us to formally model relations, dependencies or couplings
   between different systems, or aspects of systems. If you model different systems
   or different aspects or dimensions of one system together, then the joint state
   space is the Cartesian product of the individual state spaces: S = S[1] x S[2] x
   ...S[n]. Constraint on this product space can thus represent the mutual
   dependency between the states of the subspaces, like in the berry example, where
   the state in the color space determines the state in the size space, and vice
   versa.

   Variety and its complement, constraint, can be generalized to a probabilistic
   framework, where they are replaced respectively by [4]entropy and information.
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   [5]Copyright© 2001 Principia Cybernetica - [6]Referencing this page

   Author
   F. [7]Heylighen, & C. [8]Joslyn,

   Date
   Sep 14, 2001

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References

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

[USEMAP]
http://pespmc1.vub.ac.be/CONSTRAI.html#PCP-header
   1. http://pespmc1.vub.ac.be/DEFAULT.html
   2. http://pespmc1.vub.ac.be/HOWWEB.html
   3. http://pcp.lanl.gov/CONSTRAI.html
   4. http://pespmc1.vub.ac.be/CONSTRAI.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#CONSTRAI
   9. http://pespmc1.vub.ac.be/SEARCH.html