[1]Principia Cybernetica Web

                            The Law of Requisite Knowledge

   In order to adequately compensate perturbations, a [2]control system must "know"
   which action to select from the [3]variety of available actions
     ____________________________________________________________________________

   Control is not only dependent on a [4]requisite [5]variety of actions in the
   regulator: the regulator must also know which action to select in response to a
   given perturbation. In the simplest case, such knowledge can be represented as a
   one-to-one mapping from the set D of perceived disturbances to the set R of
   regulatory actions: f: D -> R, which maps each disturbance to the appropriate
   action that will suppress it.

   For example, a thermostat will map the perception "temperature too low" to the
   action "heat", and the perception "temperature high enough" to the action "do not
   heat". Such knowledge can also be expressed as a set of production rules of the
   form "if condition (perceived disturbance), then action".

   This "knowledge" is embodied in different systems in different ways, for example
   through the specific ways designers have connected the components in artificial
   systems, or in organisms through evolved structures such as genes or learned
   connections between neurons as in the brain.

   In the absence of such knowledge, the system would have to try out actions
   [6]blindly, until one would by chance eliminate the perturbation. The larger the
   variety of disturbances (and therefore of requisite actions), the smaller the
   likelihood that a randomly selected action would achieve the [7]goal, and thus
   ensure the survival of the system. Therefore, increasing the variety of actions
   must be accompanied by increasing the [8]constraint or selectivity in choosing
   the appropriate action, that is, increasing knowledge. This requirement may be
   called the law of requisite knowledge. Since all living organisms are also
   [9]control systems, life therefore implies knowledge, as in Maturana's often
   quoted statement that "to live is to cognize".

   In practice, for complex control systems control actions will be neither blind
   nor completely determined, but more like "educated guesses" that have a
   reasonable probability of being correct, but without a guarantee of success.
   [10]Feedback may help the system to correct the errors it thus makes before it is
   destroyed. Thus, goal-seeking activity becomes equivalent to heuristic
   [11]problem-solving .

Mathematical representation

   Such incomplete or "heuristic" knowledge can be quantified as the conditional
   uncertainty of an action from R, given a disturbance in D: H(R|D). (The
   uncertainty or [12]entropy H is calculated in the normal way , but using
   conditional probabilities P(r|d)).

   H(R|D) = 0 represents the case of no uncertainty or complete knowledge, where the
   action is completely determined by the disturbance. H(R|D) = H(R) represents
   complete ignorance. Aulin has shown that the [13]law of requisite variety can be
   extended to include knowledge or ignorance by simply adding this conditional
   uncertainty term (which remained implicit in Ashby's non-probabilistic
   formulation of the law):

   H(E) >= H(D) + H(R|D) - H(R) - K

   This says that the variety in the essential variables E can be reduced by:

   1) increasing [14]buffering K;
   2) increasing variety of action H(R); or
   3) decreasing the uncertainty H(R|D) about which action to choose for a given
   disturbance, that is, increasing knowledge.

Conclusion

   This principle reminds us that a variety of actions is not sufficient for
   effective control, the system must be able to (vicariously) select an appropriate
   one. Without knowledge, the system would have to try out an action [15]blindly ,
   and the larger the variety of perturbations, the smaller the probability that
   this action would turn out to be adequate. Notice the tension between this law
   and the [16]law of selective variety : the more variety, the more difficult the
   selection to be made, and the more complex the requisite knowledge.

   An equivalent principle was formulated by Conant and [17]Ashby (1970) as "Every
   good regulator of a system must be a model of that system". Therefore the present
   principle can also be called [18]the law of regulatory models .

   Reference: Heylighen F. (1992): " [externallink.GIF] [19]Principles of Systems
   and Cybernetics: an evolutionary perspective ", in: Cybernetics and Systems '92,
   R. Trappl (ed.), (World Science, Singapore), p. 3-10.
     ____________________________________________________________________________

   [20]Copyright© 2001 Principia Cybernetica - [21]Referencing this page

   Author
   F. [22]Heylighen, & C. [23]Joslyn, ,

   Date
   Sep 3, 2001 (modified)
   Aug 1993 (created)

                                       [24]Home
                                       [up.gif]
                           [25]Metasystem Transition Theory
                                       [up.gif]
                      [26]Principles of Systems and Cybernetics /

                                          Up
                           [27]Prev. [4arrows.gif] [28]Next
                                         Down
     ____________________________________________________________________________
   ____________________________________________________________________________

                                    [29]Discussion
     ____________________________________________________________________________

                                  [30]Add comment...

                                      [space.gif]

References

   1. LYNXIMGMAP:http://pespmc1.vub.ac.be/REQKNOW.html#PCP-header
   2. http://pespmc1.vub.ac.be/CONTROL.html
   3. http://pespmc1.vub.ac.be/VARIETY.html
   4. http://pespmc1.vub.ac.be/REQVAR.html
   5. http://pespmc1.vub.ac.be/VARIETY.html
   6. http://pespmc1.vub.ac.be/BLINDVAR.html
   7. http://pespmc1.vub.ac.be/GOAL.html
   8. http://pespmc1.vub.ac.be/REQCONS.html
   9. http://pespmc1.vub.ac.be/CONTROL.html
  10. http://pespmc1.vub.ac.be/FEEDBACK.html
  11. http://pespmc1.vub.ac.be/PROBSOLV.html
  12. http://pespmc1.vub.ac.be/ENTRINFO.html
  13. http://pespmc1.vub.ac.be/REQVAR.html
  14. http://pespmc1.vub.ac.be/MECHCONT.html
  15. http://pespmc1.vub.ac.be/BLINDVAR.html
  16. http://pespmc1.vub.ac.be/REQVAR.HTML
  17. http://pespmc1.vub.ac.be/CSTHINK.html#Ashby
  18. http://pespmc1.vub.ac.be/ASC/Law_model.html
  19. ftp://ftp.vub.ac.be/pub/projects/Principia_Cybernetica/Papers_Heylighen/Systems_Principles.txt
  20. http://pespmc1.vub.ac.be/COPYR.html
  21. http://pespmc1.vub.ac.be/REFERPCP.html
  22. http://pespmc1.vub.ac.be/HEYL.html
  23. http://pespmc1.vub.ac.be/JOSLYN.html
  24. http://pespmc1.vub.ac.be/DEFAULT.html
  25. http://pespmc1.vub.ac.be/MSTT.html
  26. http://pespmc1.vub.ac.be/CYBSPRIN.html
  27. http://pespmc1.vub.ac.be/REQCONS.html
  28. http://pespmc1.vub.ac.be/REQHIER.html
  29. http://pespmc1.vub.ac.be/MAKANNOT.html
  30. http://pespmc1.vub.ac.be/hypercard.acgi$annotform?

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