# 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              |
||         || w2 = L(w1)     ||          ||
|          | w1  ______- w2  |           |
||         _|_|_ _ _ _ _ _|_ |           ||
|             |           |              |
m1|= E(w1)    ||          || m2 = E(w2)  |
||         _|_|_ _ _ _ _ _|_ |           ||
|             |?          |?             |
|          | m1  ______-m2   |           |
||         || m2 = R(m1)     ||          ||
||         _|_ _ _ _ _ _ _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 = {wi} 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 = {mj} 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 m2 = R(m1) = R(E(w1)) = E(L(w1)) = E(w2). 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 meta-model. 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 - Referencing this page
 Author C. Joslyn, V. Turchin, Date Aug 1993
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