Why this matters
You cannot test a new bridge by driving trucks over the real thing first, and you cannot replay tomorrow's weather to check a forecast. Instead you build a model, a stripped-down stand-in for the real thing, and study that. Knowing which kind of model fits a problem is the first step toward predicting how anything behaves.
The idea
A model is a simplified representation of a phenomenon, and modeling is the act of building one. Models come in two big classifications.
By how they behave over time:
- A static model does not change with time, like a seating chart, or the link between a sphere's radius and its volume.
- A dynamic model changes over time. It splits again:
- A deterministic model has no randomness, so it always gives one result, like a bank balance, or the distance a car covers at constant speed.
- A probabilistic model has irregular, random behaviour, so the result varies: a dice roll, a lottery draw, a weather forecast.
By how they are expressed:
- A physical model is a physical object: enlarged (molecular model), full-scale (a life-size dummy), or reduced (a globe).
- A diagrammatic model is drawn, like a flowchart or route map.
- A mathematical model is written as a formula, such as speed times time equals distance, or Ohm's law.
To build one you (1) decide the purpose, (2) pick the elements and their relationships, then (3) choose the way to represent it.
Picture it
flowchart TD M[Model] --> S[Static: no change over time] M --> D[Dynamic: changes over time] D --> DET[Deterministic: one result, no randomness] D --> PRO[Probabilistic: random, many outcomes]
Worked example
Sort four things. The radius-to-area link of a circle never changes, so it is static. A dice roll and a weather forecast both involve chance, so they are probabilistic. The distance a bicycle covers at constant speed is fixed once you know the time, so it is deterministic. Now by form: a molecular model is a physical model, a program flowchart is a diagrammatic model, and Newton's equation of motion is a mathematical model.
Your turn
Try the practice questions: sort examples into static, deterministic, and probabilistic, and match each model type to what it is made of.
Recap
- A model simplifies a phenomenon; modeling is building one.
- By behaviour: static, or dynamic (which is deterministic, one result, or probabilistic, random).
- By form: physical, diagrammatic, or mathematical.