Was the moon once part of the Earth? Will we experience a snowstorm next weekend? Did the Big Bang really happen? In past columns I have focused on the concept of what is called the “search” method as a way of arriving at sound answers to important questions. Now I would like to touch upon, for your consideration, another important conceptual tool, modeling. As you will shortly see, our attempts to answers the questions mentioned above as well as many others are aided greatly by the use of this exciting problem solving tool.
Models can take the form of actual physical representations, mathematical equations, or if then propositions. Whichever form they take, their use has been essential in our search for answers to all sorts of questions.
The critical structure of modeling is tripartite: First we have input. In the example of predicting the weather, the input would consist of the atmospheric conditions that are heading our way. Second, we have the mechanism, which is the pattern or patterns we have observed over time. Sticking to my weather example, the patterns would comprise the principles we have developed over decades of observation. We know, for example, what happens when a dry cold front meets a warm front as well as the influence of wind and the dynamics of the atmosphere. All of these observed tendencies become part of our mechanism. When we apply our mechanism to the information we have concerning our present conditions, we arrive at stage three, an output (or prediction), which theoretically will be the weather we will soon experience. The nature of this information makes it very compatible with computer programs. Penn State presently houses one of the most advanced computer systems in the country, which has a remarkably accurate predictive average. During a storm we sometimes feel somewhat cynical if the predictions fall short of the reality. The reason that happens is not because the mechanism was off but rather because the input changed.
The process I have described above is a typical way in which we can attempt to predict the future. The more information we can plug into our input and the more tested our mechanism is will determine the level of comfort we have in making our prediction. But can we use our modeling formulae in other ways? One of its most important features is that it is versatile. Let me show you:
There are three main theories about how the earth was formed. One theory is that the centrifugal force of the spinning earth ejected it as a chunk in the early days of the formation of the solar system. Another theory is that the moon is a separate body captured and held in place by the earth’s gravitational field. A final theory is that the moon was formed when some other large body collided with the earth blasting out material that became the moon.
Employing our three-step approach we can, in essence, work backwards. We begin by building into our mechanism the physical laws: centrifugal force relative to rotation, the physics of velocity and impact, and, of course, gravity. Our output is the way we presently experience the moon rotating around the earth in the manner it does and with the composition we know it has.
If any of the proposed theories (inputs) produce our given output when we apply our known mechanisms, then we have a point in favor of that particular theory. Unlike prediction, where we enter an input and apply a mechanism to arrive at a reasonable answer, here we we’re trying to answer the question: which input produces this output with that mechanism? This is called retrodiction.
In 2008, NASA scientist Jennifer Heldman, put the issue to rest by asserting that their modeling process concluded quite definitely that the moon was formed 4.5 billion years ago from the debris thrown into orbit by a massive collision between a smaller proto-earth and another planetoid, about the size of Mars.
What if we want to know how we arrived at the output given the input we had at the time? In that case, we ask ourselves what mechanism would take us from a specific input to a specific output? Here we are searching for an explanation. How did a certain thing happen?
Why use three-stage models? In general, it’s an easy way to make a hard problem simpler. As I mentioned earlier, it’s a basic logical if x then y proposition. It often helps to think of things in terms of simpler input, mechanism, and output, whether our structure is instantiated physically, computationally, or conceptually.
In 2020, we use models (physical and theoretical) in so many ways it is virtually mindboggling. The efficacy of dams, hurricane formation and direction, housing discrimination, voting patterns, population migration, space exploration, and the solar system itself are just a few of the ways in which humans have applied modeling.
The reason for its popularity is that it has been universally found to be an aid in a number of important ways: to help us in data selection, to evaluate the pros and cons of a process, to provide a cross section of analogies, to illuminate our own uncertainties, to point out overlooked details, to offer options for change or intervention, to show us what is simple about complex processes and what is complex about simple ones and, perhaps most importantly, to suggest new questions.
For those who are skeptical about its advantages, I call your attention to the words of famous computational modeler and scientist Josh Epstein, “You already model. You’re working with models in your head. The real question is just what assumptions you are making and how good that model is.” So, the next time you hear someone predict the future or make some claim about the past, imagine for yourself what model that person utilized.