A model is an informal or a formal **representation of a system**, made by an observer, to **distinguish features** of a system which are significant and to predict the consequences of a disturbance or change on the system. Modeling is a process everyone engages in every day. We have a model of the commuter traffic patterns on the way to work, models of the members of our family and our coworkers; in short a model of almost every significant aspect of our lives. If our models are good ones, we will be able to make sense of the world and predict, with some accuracy, how it will behave. Models come in many kinds and types, depending on the distinctions the observer wishes to make. The observer may choose a physical model, a working model, a mathematical model, a mental model, a game theoretic model or many others.
In "Cybernetics and Management" (Beer, 1959,) there is a helpful description of four key notions about models: "There is a scaling down in both size and complexity - a model of Shakespeare's birthplace, for instance, could stand on a table and would not be expected to incorporate miniature timbers in equivalent numbers to the building in Stratford Upon Avon. There is a transfer across, whereby actual parts of actual things are represented again in their relative positions. And arising from this is workability, by which I mean that the model can, in principle anyway, operate like the original. Thus a model train actually runs around a model railway, and it looks so much like the thing modeled that cine films of models can be substituted for film of actual trains and successfully pretend to be real. That this may be so, although the engine may be driven by clockwork introduces the fourth point. The mode is a good model if it is appropriate."
Models vary according to how rigorous they are, how comprehensive they are and so on. Two particular types of models are of special interest. An isomorphic model replicates each and every feature of the thing modeled on a one-to-one transformation. In a complex situation, the only possible isomorphic model is **the thing itself**: the identity mapping. An homomorphic model represents the situation as a many-to-one transformation, aggregating some features of the original and ignoring others. Sometimes there will be more than one homomorphic model of a system and they may be isomorphic with one another. In the limit, almost everything can be seen as a model of a given system with varying degrees of relevance.
# SOURCE The word model comes from the Latin 'modus' meaning a measure, conveying both its consciously chosen and its purposive features.
# EXAMPLES • a business simulation • a balance sheet • the report of a certified public accountant • a civilization’s mythology • the ecological model of the Chesapeake Bay • a tailor's dummy • a map, chart or drawing • a toy airplane
# NON-EXAMPLES • a random collection • a political explanation that is based on bigotry rather than fact (although it may be a model of the source of the explanation) • a fanciful account of an event
# PROBABLE ERROR • Failure to make the model of a system in use explicit, leading to confusion and misinterpretation, in the limit, the belief that the model is the system
# SEE System observer; Distinction; Filter; Environment; Conant-Ashby Theorem