Scientific Abstraction
While many of these ideas have an origin in the discovery and development of universality and critical phenomenon, we can consider a form of modeling as producing an even more general abstraction.
Typically when developing a simple model, it is beneficial to represent the particles (players) and forces (dynamics) in an abstract form.
Players are often represented as an abstract elements (sites/bonds, in a regular lattice, points is space, nodes/edges in a graph, etc.) with one or more properties (spin, strength, burning, etc.). In the model this property is typically assigned a numerical values (boolean, int, float, etc.) or a values from an enumerated list.
Forces are typically represented by a prescriptive rule that is applied at each time step (flip a spin, light a fire, add a site, break a bond, etc.).
Typically the rule changes the values associated with one or more elements.
While a physical process guides the initial choice of elements and rules, we end up with a set of elements, each with a set of values, and rules for updating those values.
Ultimately, a model is a set of elements and a set of rules for changing the values associated with the elements.
This abstraction means that an element can represent any number of different actors.
Example: Site if a forest fire model. Initial meaning: patch of forest. Possible meanings: small volume of fluid, person, region of a solid, etc.
Because many models involve scale-free phenomenon (forest-fires, earthquakes, epidemics, etc.) the element can represent any sized unit of actors (forest-fire:square meter forest section, single tree, acre, etc. epidemic:person, family, neighborhood, city, etc.)
Similarly, the rule can represent any number of physical forces
Examples: Changing a forest-fire model site to black. Initial meaning: burning. Possible meanings: phase-transition, infection, dielectric breakdown, etc.
While the modeler might have had a specific physical system involved when developing the model, the model really represents all physical systems that have properties similar to those produced/predicted by the model. It is the interpretation of the model that gives the model a physical meaning
A simple example of this type of abstraction is whole numbers and algebraic operations.
We can sider the number 1 to be a representation of all single discrete/integer things
1 \rightarrow apple, person, etc.
We then consider the rule of addition (+). We know that 1+1=2 \rightarrow apple+apple = apples, person+person=people, etc.
We can write 1+1=2 in pure abstract without requiring 1 or + to have a physical meaning.
Once we do this we can interpret what we mean by 1 and +
Abstraction: 1+1=2 Interpretations: apple placed next to one apple gives two apples, one person marries another person making a couple.
Thus when we write 1+1=2 we might mean a specific example but the same process represents unlimited different situations.
This is one reason why simple models can be so powerful.
The same model can be used for fluid flow, earthquake ruptures, and financial markets.