Model
Metasystem Transition Theory understands knowledge as the existence in a cybernetic
system of a model of some part of reality. The most immediate
kind of a model is a metasystem which implements a homomorphic relation
between states of two subsystems, a modeled system and a modeling
system.
_________________________________________
S
 __ _ _ _ _ _ _ _  
 W 
  w_{2} = L(w_{1})  
  w_{1} ______ w_{2}  
 ___ _ _ _ _ __  
   
m_{1}= E(w_{1})   m_{2} = E(w_{2}) 
 ___ _ _ _ _ __  
 ? ? 
  m_{1} ______m_{2}  
  m_{2} = R(m_{1})  
 __ _ _ _ _ _ _M_  
________________________________________
Figure: The Modeling Relation
Formally, a model is a system S = <W, M, E> with:
 A modeled system or world W = <W, L> with states W = {w_{i}}
and actions or laws L: W > W . For example, W could be
the set of key presses of a computer operator or the physical world,
while L is the behavior of the operator or natural law;
 A modeling system M = <M, R> with internal model states, or representations
M = {m_{j}} and a set of rules, or a modeling function
R: M > M. For example, M could be a set of symbol strings or
neural signals, while the rules R are the activity of a computer
or a brain;
 And finally a representation function E: W > R. For example,
E could be a measurement, a perception, or an observation.
When the functions L, R, and E commute, then we have m_{2} = R(m_{1}) = R(E(w_{1})) =
E(L(w_{1})) = E(w_{2}). Under these conditions S is a good model,
and the modeling system M can predict the behavior of the world
W. We can call S a generator of predictions about W.
However, it is possible that M is itself a model, in which case S is
a metamodel. The representation function then does not generate
a prediction directly, but rather generates another model, which
in turn can generate predictions. We come, therefore, to the understanding
of knowledge as a hierarchical structure to recursively generate
predictions about the world and the self, and which in turn allow the cybernetic
system to make decisions about its actions.
Copyright© 1993 Principia Cybernetica 
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