On Models: Good Models

"A good model makes the right strategic simplifications. In fact, a really good model is one that generates a lot of understanding from focusing on a very small number of causal arrows." (Robert M Solow, "How Did Economics Get That Way and What Way Did It Get?", Daedalus, Vol. 126, No. 1, 1997) [Link]

"[…] no good model ever accounted for all the facts, since some data was bound to be misleading if not plain wrong. A theory that did fit all the data would have been ‘carpentered’ to do this and would thus be open to suspicion." (Francis H C Crick, "What Mad Pursuit: A Personal View of Scientific Discovery", 1988)

"A model is a good model if it:1. Is elegant2. Contains few arbitrary or adjustable elements3. Agrees with and explains all existing observations4. Makes detailed predictions about future observations that can disprove or falsify the model if they are not borne out." (Stephen Hawking & Leonard Mlodinow, "The Grand Design", 2010)

"One good experiment is worth a thousand models […]; but one good model can make a thousand experiments unnecessary." (David Lloyd & Evgenii I Volkov, "The Ultradian Clock: Timekeeping for Intracelular Dynamics" [in "Complexity, Chaos, and Biological Evolution", Ed. by Erik Mosekilde & Lis Mosekilde, 2013)

"When evaluating a model, at least two broad standards are relevant. One is whether the model is consistent with the data. The other is whether the model is consistent with the ‘real world’." (Kenneth A Bollen, "Structural Equations with Latent Variables", 1989)

"A mathematical model is never a completely accurate representation of a physical situation - it is an idealization. A good model simplifies reality enough to permit mathematical calculations but is accurate enough to provide valuable conclusions. It is important to realize the limitations of the model. In the end, Mother Nature has the final say." (James Stewart, "Calculus: Early Transcedentals" 8th Ed., 2016)

"The definition of a ‘good model’ is when everything inside it is visible, inspectable and testable. It can be communicated effortlessly to others. A ‘bad model’ is a model that does not meet these standards, where parts are hidden, undefined or concealed and it cannot be inspected or tested; these are often labelled black box models." (Hördur V Haraldsson & Harald U Sverdrup, "Finding Simplicity in Complexity in Biogeochemical Modelling" [in "Environmental Modelling: Finding Simplicity in Complexity", Ed. by John Wainwright and Mark Mulligan, 2004])

"All models are mental projections of our understanding of processes and feedbacks of systems in the real world. The general approach is that models are as good as the system upon which they are based. Models should be designed to answer specific questions and only incorporate the necessary details that are required to provide an answer." (Hördur V Haraldsson & Harald U Sverdrup, "Finding Simplicity in Complexity in Biogeochemical Modelling" [in "Environmental Modelling: Finding Simplicity in Complexity", Ed. by John Wainwright and Mark Mulligan], 2004)

"In physics it is usual to give alternative theoretical treatments of the same phenomenon. We construct different models for different purposes, with different equations to describe them. Which is the right model, which the 'true' set of equations? The question is a mistake. One model brings out some aspects of the phenomenon; a different model brings out others. Some equations give a rougher estimate for a quantity of interest, but are easier to solve. No single model serves all purposes best." (Nancy Cartwright, "How the Laws of Physics Lie", 1983)