I’ve been thinking about this for a while. I’ve read through Hestenes’ articles (see below) and ended up in the same place that I started. Sometimes he uses ‘model’ as a verb and sometimes as a noun. I’m confused. Can anyone help? The articles are below, with some parts quoted.
1st Article: Modeling is the name of the game
Here’s a quote:
“To summarize, a conceptual model in science is defined by specifying the following:
(1) Constituents: Names for the thing of interest and the things in its environment.
(2) Descriptors: Object variables, State variables, Interactions.
(3) Laws: Laws of change, Interaction laws.
(4) Interpretation: Relates descriptors of the model to properties of the object.
A great variety of models can be constructed for any given thing, depending on the purposes of the modeler. Scientific theories supply advice on what variables and laws to use. No single model characterizes a concrete thing completely. Nor would such a model be desirable, because its complexity would make it too cumbersome to be useful. One of the most important objectives of modeling is to focus on the most significant or relevant properties of a thing by constructing simple models that eliminate or suppress minor details. ”
Here’s a quote:
The defining axioms of Newtonian theory are called laws, because they
have been empirically tested and validated in a broad empirical
domain. That domain is so broad, in fact, that they were believed to
be universally valid (or true!) throughout the eighteenth and
nineteenth centuries. Only in the twentieth century have definite
limitations of the validity of Newtonian theory been set by
relativity theory and quantum mechanics. The axioms of the theory
cannot be empirically tested either directly or independently. They
can only be tested indirectly through their implications for model
building. Only models can be tested experimentally, models of
physical phenomena which can be studied experimentally. Thus,
theories are empirically validated only by validating models derived
from them. The confusion is rampant in science, I find. My intent is to help
Here’s my attempt at a summary from these articles:
“Theories inform the creation of models, and laws are part of models.” …?
Here’s what I think:
Scientific conceptual models are ideas or sets of ideas (encoded somehow in neurons in the brain that we can create, access, and use to interpret sensory information) that are used to represent or explain parts of physical reality. Physical representations (drawings, diagrams, symbols, physical objects) can be used to represent and communicate the conceptual model. To me, theories and laws also fit this definition of a conceptual model. The articles seem to imply that laws are somehow only part of a model and that a theory is somehow outside of a model. What do you think?