A model is an abstraction, a physical abstraction of an object or a conceptual abstraction of a situation. An architect might use a cardboard physical model to illustrate a proposed building. Conceptual models can represent complex systems like population dynamics, economics, or schooling fish. By “complex systems” I mean the things described in Blog 2 and Blog 3, situations with many independent agents governed by nonlinear rules of interaction among the agents and their surroundings. A conceptual model often takes the form of a set of equations with which the system can be simulated by computer, thereby becoming a “computer model.” Note I said simulated by computer, not solved by computer.
Let’s consider things that evolve in time, like the economy, the weather, or traffic. The term, “solved” implies a closed-form solution, which is an equation (or set of equations) into which you can put a value of time and calculate the future situation in a single step. For example, if you travel at 50 miles per hour, your distance is 50 multiplied by time.
X = 50*T
Put in any value for time; you get the value for distance. In 10 hours X is 500 miles. But a complex system has a whole set of equations, such as one equation for the movement of each ant around an anthill, where each ant moves randomly until it either finds food or it finds smells left on the ground by other ants that carry food. For such a system, there is no closed-form solution. You need a computer to adjust the direction and speed of each ant at a particular instant of time, then move each ant slightly and update the map of smells before performing the whole calculation all over again for another small step in time. This is a simulation, resulting in a movie that depicts the location of every ant, the food moved, and the smelly tracks of the food-carriers. You can see a short clip of the anthill simulation, or click for the entire 7-minute presentation offered by the Santa Fe Institute.
A model can reveal emergent properties of the system—for example, how the ants form tracks to food. Repeated runs of the model with different parameters can reveal the effects of a rapidly dissipating smell-track, or even the effects of garlic in the limburger if the equations include the dietary preferences of ants.
Modeling can disclose unexpected effects, but in each case you must run the model from time zero and watch as the situation evolves. You can’t jump to the situation at an arbitrary future time as you could with a closed-form solution. In many complex systems, a slight change in the starting condition can dramatically alter the situation much later. That’s called the “butterfly effect.” If your social system is susceptible to a butterfly effect, you want to know it.
So why does this matter?
As our society and the world become increasingly complex, decisions regarding regulation, subsidies, social security, taxes, and immigration need examination of both the intended consequences and the unintended consequences. Instead, most political decisions are based on simplistic statements made in ignorance of (or in denial of) the causes and effects. Because the world is a set of nested complex systems, modeling provides the best means for exploring and predicting the emergent consequences of our collective decisions.
I’ll invite other opinions by stating that our most crucial social decisions today deal with climate change. Climate-related political debates are often based on partisan interpretations of today’s temperature, or today’s cash flow, or today’s ideology, although all of our knowledge about future climate development comes from increasingly sophisticated modeling tested against historical data.
I suggest that the future of the earth depends on how well we do our modeling, and whether we pay attention to the results or proceed in ignorance. A good model wouldn’t have predicted the sinking of the Titanic with certainty, but it would have predicted the odds of collision with an iceberg. A good model would not have predicted current values for the Dow Jones, but it might have predicted the probablility of economic recession from the known indebtedness combined with the ideological deregulation of the banking industry. We should apply good models during decisions regarding our complex society, and pay attention to the predictions during our debates.