Reasoning with Models
So far, we have focused mostly on interesting products of scientific research: theories and explanations. This lesson is about one critical part of the process of scientific research: modeling.
This shift—from product to process—is also a shift in perspective about what’s important in science. Science may be less about collecting true statements about the world and more about predicting new events, controlling outcomes, and giving plausible explanations for what happened. Often, perhaps always, doing these things well requires a model.
What Is a Model?
Models represent. An armillary sphere is a model. It represents the earth, the sun, and other planets in a mechanical device that the user can move to both illustrate and predict the orbits of the planets. The US Army Corps of Engineers uses a model to help them manage the unruly course of the Mississippi River: It has channels and dikes and geographical features that correspond to the real channels and dikes and geographical features present in the Mississippi Delta. Watson and Crick built a model of DNA to help them study the molecule’s structure. Little bits of aluminum that mimicked the known chemical structure of the four DNA bases were fastened together and could be altered to explore alternate structures.
These examples are all physical models: The little earth in the armillary sphere represents the real earth. The tiny channels in the model of the Mississippi delta represent real water channels. But scientists often work with mathematical, computational, and conceptual models as well. Consider a simple mathematical model that illustrates predator-prey relationships: One variable represents the number of rabbits, another the number of foxes, and another the growth rate of rabbits. Computational models simulate a situation. We could have 50 rabbits and 10 foxes, each with their own set of behaviors in their own patch of land, and tick time forward in a simplified, simulated world. Conceptual models include analogies, thought experiments, and mental simulations. You can think of the electricity in a closed circuit like water flowing in a pipe.
All models represent some aspect of the thing they’re attempting to model. The little aluminum plates that Watson and Crick worked with to discover the structure of DNA mimicked the structure of DNA bases: They could attach to other bases in certain ways and were generally shaped like the bases are shaped. But there are also parts of the model that do not represent the target: DNA bases are not made from aluminum, and the dikes in the Mississippi Delta model are not really that size. This makes models useful but also a bit dangerous.
Models as Reasoning Tools
Models can be used in several different ways. We can use models to generate new ideas, to test ideas, and to make predictions.
One famous model sought to explore patterns of racial segregation in cities—an extremely common social pattern. The model demonstrated an astonishing fact: Very mild preferences for people who look like you can create massive segregation. The model was quite simple: Each agent had a preference for living near people “similar” to himself. Of course, we would expect that strong preferences would create segregation, but even slight preferences were shown to also create segregated outcomes. The model certainly doesn’t prove that our segregated cities are segregated because of mild preferences and not for some other reason. Rather, it proposes a mechanism to explain the broadly segregated cities that we see.
One of the benefits of thinking about science as fundamentally about reasoning with models is that it accommodates a bit of what we mean by “theories being true,” without needing to claim that our current theories are literally true, which seems, at least philosophically and historically, an untenable position. Models also accommodate the idea of prediction and control.
We often talk about theories being right or wrong: Either the sun moves around the earth or it doesn’t. But consider the limits of the theory of relativity and quantum mechanics. Relativity is a good theory if you’re talking about big things: planets, stars, black holes, vacuum tubes, etc. But it breaks down when we try to apply it to very small things: atoms, quarks, gluons, etc. Quantum mechanics (at least traditionally) has done just the opposite: It’s a good theory for small things but not a good theory for big things. If you’re in the “theory” camp, this is a problem. There must be some way to reconcile them, some overarching theory that can derive both quantum mechanics and relativity.
People in the “model” camp, however, think this is far less of a problem. We can be pluralists when it comes to models. A mathematical model of predator-prey relationships doesn’t have to be perfectly accurate to be useful. Models are, after all, useful simplifications of reality. Think of models like maps. Want to navigate to that food joint your friends have been raving about? Try Google Maps. Want to know the kinds of rock in the surrounding area? You’re going to need a geological map. You can try to cram more and more information into a map, but it gets complicated quickly. No map can display all the information of the real landscape.
Next time: the power of the instrument.
Question to ponder
What models do you use in your work, and how do you use them?
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