Course Idea: The Art of Scientific Modeling

Science
#1

Hello Everyone,

I noticed that someone made a post about science class ideas and I had one that I wanted to explore at some point in the future. These courses are primarily for beginners who have no experience with either social or physical science; however, people who have experience would be encouraged to come and make the class even more interesting. I want to both identify whether anyone has any interest in something like this and also receive constructive criticism on the design, methodology, or anything else.

A lot of ink has been spilled about what science is, but its safe to say that Science is, at the very minimum, the art of both making and fitting models to explain and predict phenomena. Modeling is not something that is only good for science though. Models are used everywhere in industrial applications because they encode and abstract physical and social phenomena in such a way that we can make precise statements about things we want to learn about or use. In short, models are for literally everyone. These are examples of the sort of courses I had in mind.

To be clear, I understand that this place isn’t a college. It is not my intention to turn it into one. Anyone who has obtained a STEM degree or taking STEM courses may look at these topics and shake their head. They know, after all, that it took them several semesters to learn some of these topics. However, I will remind them that they also know that roughly 95% of the tricks they learned in calculus and differential equations courses have been automated. Sure, closed form solutions from analyzing functions by hand are nice, but they are not really necessary. Numerical Approximation by computers is king. My goal is to mainly convey enough information so that individuals can learn more about modeling without struggling like I struggled. I hate the idea of science enthusiasts wasting their time away learning how to solve integrals analytically until they lose motivation.

Below is an example of what two courses would look like. I first learned how to model through
statistics and economics, but classical physics was a better way to first learn modeling in hindsight. The systems tend to be simple, non-random, and highly concrete (you can’t see an economy, but you can see a rock roll down a hill). After investigating several different ways of exposing people to this material, I came across Leonard Susskind’s “The Theoretical Minimum”. I was surprised how approachable he was able to make classical physics without compromising too much of the rigor. The structure of his course partially informed the structure of these first courses but I have made significant changes for a couple reasons.

The first reason is that Leonard’s goal is to teach classical physics. My goal with the courses is to use various sciences, classical physics being merely one of those, as a way to teach people about modeling so that when they come across something they wish to investigate, they can at least have a starting point for that investigation. The second reason is that this is a makerspace and makers need to be able to apply what they learn. I chose Julia as the programming language because it has both an easy, clean syntax like python and is as fast as C and Fortran in most use cases.

FIRST TWO COURSES:

The Courses Are Going to Be Part Theory and Part Application.

A) The Art of Scientific Modeling I: Classical Physics and Why Does Science Have So Much Math In It? (All Theoretical Except The Very End)

Topics:

  • What is Science?
  • What would be a desirable way to talk about science? Can we just talk about it like anything else?
  • The Problem with Trying to Do Science in Natural Languages (i.e. English)
  • Pre-WWII Economics: A Brief Case Study in Why Trying to Do Science Without Advanced Mathematics is a Bad Idea.
  • Why Math Works for Science: The Unique Reading Lemma and Truth-Values
  • Math and Models
  • Classical Physics
  • Classical Laws of Physics
  • The Concept of A Dynamical Law
  • Closed Systems, Basic Conservation Laws, and Desirable Properties of Models
  • Positions and Reference Frames
  • Pythagorean Theorem
  • Trigonometry: Except The Way You Should’ve Been Taught It
  • Vector Arithmetic
  • Questions
  • Download Julia
  • Some Suggestions on Outside Stuff to Watch
  • End

B) The Art of Scientific Modeling II: Scientific Computing (About Half Theory; Half Application)

Topics:

  • How should we think about stuff like time when modeling?
  • What is Motion?
  • Scientific Computing: Math Like It’s Actually Done In Practice
  • Discussion of Julia and Basic Programming Concepts
  • Basic Calculus With One Variable
  • Core Ideas behind Uni-variate Optimization
  • Uni-variate Optimization with Julia
  • Work through a couple physics problems together with Julia
  • Give Some Problems for People To Do On Their Own If They Wish
  • Some suggestions on outside stuff to watch
  • End

Let me know what you guys think.

Thanks,
Kevin Thompson

4 Likes
#2

@DanielPhoton and I just chatted with Kevin about this. I think the first part of part B would be really great info and would love to hear more of Kevin’s ideas on that. Thanks for volunteering for this!

2 Likes
#3

I assume you are talking about time. There is so much to say about time when it comes to any type of modelling. Sometimes we care about time; sometimes we don’t. Sometimes we want models that assume continuous time; sometimes we don’t really care. There is an entire branch of statistics called Time Series Analysis that deals with problems concerning time.

Basically, most of the problems can be summed up like this: estimators used in most scientific experiments and observational studies presume that the experiment will be repeated at some point in the future because estimates (even in extremely controlled experiments) are only “right” on average over many experiments(assuming the assumptions are met and the experiment is modeled correctly). This is why you should generally (not always) refrain from using only a single experiment to back up a scientific opinion you have. In order to be right on average, your experiments or observations cannot be allowed to “remember” what happened in the previous experiments or observations. You can do this through adding covariates in a model or changing the experimental design/subjects.

When we are doing prediction, however, we absolutely want the observations to remember what happened during the last experiment/process. This is one instance of the trade-off between explaining and predicting phenomena. You can never build models that are the best at predicting and the best at explaining.

Here’s a simple example. Hot days tend to follow hot days and cold days tend to follow cold days. In a statistical sense, temperatures on one day “depend” or “remember” the temperature of the previous day. This helps you predict tomorrows temperature, but that’s a big problem if you want to know how some phenomena impacts global temperatures.

#4

I would be very interested in anything along the lines of this class since it seems that it’s turned off that one of my hobbies is debunking bad science on Facebook. It seems like that this might could help me hard to explain to people a little more about the scientific method and why we look too. Viewed evidence instead of blogs and opinion pieces. My background is in physics and geology even though I’m basically hardest. I like being able to do to debunking because it allows me to use the science I’ve learned to some useful still.