Modeling is expedient simplification. It is the process of constructing a network of related concepts or patterned structures which aspire to simplify the chaotic complexity of an observed phenomena in such a way as to suit certain objectives. It is an attempt to impose conceptual forms on the incomprehensibly variable and perturbational nature of the cosmos and to try and somehow image the behaviour and form of a reality system so as to maximize convenience. A water-color of clouds is an optimized artistic color-patterned précis of a subject. An orrery is a mechanically simplified model of the solar system which emphasizes the reduced complexity of circles and ellipses over cycloids. Convenient economic models of commercial behaviour are designed to justify and facilitate various business endeavours. In an educational setting, models of appropriate complexity should be chosen to match the capacities of students. Models for chess, DNA, biochemical pathways or nuclear particles can be as complex as the situation demands. In general however, every attempted interaction with nature by an individual awareness relies upon a conceptual model having been created. The very survival of an individual in its environment depends upon the fabrication of pragmatic operational models.

In very general terms a model needs to be assessed according to its "goodness-of fit". That is to say, how well does the model support the apparel of reality? Is it unnecessarily complex? Is it pragmatic? Are there too many unexplained and unpredictable outcomes? Just as garments are hung on a skeletal form but only fit where they are able to be conveniently pegged, so might the elements of a reality system conform more or less appropriately to the devised concepts of a reality model... but only where opportune points of attachment are available. The promoters of a model drape reality over their suppositions in an attempt to make it appear as if they were meant for one another.

A simplification model which is quantifiable can be symbolized mathematically. A mathematical model is a set of symbolic relationships and boundary conditions which are hypothesized as representing a simplified version of the behaviour of a quantifiable reality system. An equation is a symbolic mathematical concept model of the supposed relationship between numerical parameters. No matter how sublimely sophisticated the devised mathematical structures are, be it fourier analysis, probability distribution functions, relativity theory, polynomial interpolation, vector analysis or whatever, it is the contrived mathematical structures of simplification which are imposed upon the chaotic complexities of physical phenomena. The mathematics explains nothing whatsoever. The mathematics is not intrinsic to the phenomena. The mathematics is an intellectual imposition of a quantifiable simplification on observed natural patterns.

Unquantifiable models vary in merit from the pragmatic facilitation of a mundane activity thru to the global impositions of blanket constraints and penalties. If the mental model of singing out thru the top of one's skull facilitates the production of a strong and clear head tone for an aspiring vocalist, who cares how much sense it makes? On the other hand, all extreme social simplifications are designed to achieve nothing less than power. Political laws and religious commandments are attempts to impose a simplified structure on an infinitely complicated human society. They propose models which incorporate rewards and punishments, dwellings for gods, afterlife accommodation, prisons, and rehabilitation and then attempt to impose it on the remainder of the population by whatever resources they can contrive to acquire. Political or religious models however, are no more capable of allowing for the infinite deviations and disturbances of human nature than scientific models are capable of allowing for the infinite inter-reactions of a chaotic universe.