01 Sept 22 - Notes: What is a Model?#

These is the summary of the PHY 415 class period on 01 Sept 22. If I missed anything, send me an message on Slack and I will add it here. -DC

Modeling Discussion#

We discussed models and modeling extensively today to start to form a functional definition of both. We talked about what the general idea of models and modeling can encompass. Some of the classes major ideas were:

  • A model takes BIG things and makes them smaller things (approximations and assumptions)

  • A model is only as good as it fits nature/reality/experiment

  • A model is not useful unless it does something we intended it

  • The best models destroy themselves (i.e., are pushed to their limits and need to be replaced/redeveloped)

Mathematical Models in Physics#

We narrows our discussion to mathematical models, the focus of this class, and talked about the variety of models the class has used. We had a couple general ideas. A mathematical model (in physics) is:

  • an equation that has a physics idea behind it

  • the order that you use different mathematical methods to investigate a physics problem

In this discussion, the class brought up several models they had experienced in the past; many of them were from mechanics contexts. And a couple were outside of physics models.

Physics

  • Hooke’s Law

  • Differential equations that describe physical systems

    • example: the Schrodinger equation

  • Taylor expansions

  • Newton’s Laws

    • Kepler’s Laws

    • Newton’s Law of Gravitation

Outside of Physics

Features of a good mathematical model#

We then discussed the features that make up a good model in physics. Ideas included aspects of the model and the modeling process as well as social aspects of engaging in science. The list below is from the class’s discussion, where the highlighted words are starting to form the details of our class’s project rubric.

A good model:

  • depends on its intent and how well it does what it we intend it to do

    • e.g., a model of a galaxy is not useful for modeling the solar system

  • predicts or explains something about a physical system - predictability

  • gives everyone the same results with the same input - reproducibility

  • balances simplicity and applicability - parsimonius

  • cannot be biased towards the data (experiment, etc.)

    • avoid manipulation of the model to fit data

    • overfitting data

  • recognizes limitations and presents its assumptions

  • uses input from outside sources (other theories, data, experiments, etc) to confirm/evaluate - validation

  • can be adjusted for different conditions - investigatory

  • is testable in some way

  • needs to have its results and processes communicated clearly