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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
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