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Julia's Thoughts on Models

Page history last edited by Julia Gouvea 8 years, 10 months ago

I thought I would more formally and publicly clarify my view of models and modeling in science, so that when I say "models," you all know what I mean. In what follows I give a summary of these views and then try to link the to aspects of the course.


What is a model?

I use model is the broadest sense possible - a model is, in the simplest sense, a set of ideas about how some aspect of the world works. In this sense, models underlie everything that scientists (and scholars in all fields of inquiry) do. They bound and organize the historical and contemporary structure of scientific knowledge, they suggest areas that are in need of further study, they serve as epistemic forms that can be reasoned with, they suggest particular empirical studies, they can be applied to a particular phenomenon in order to explain and they can be used to make more formal predictions - mathematically and computationally.  


Importantly, what a model does for a scientist depends on the context: What is the phenomenon under investigation? How much is known about it? What is the aim of the investigation? Is any empirical data available? etc. Because of the range of practical aims, historical trajectories and philosophies of different fields, models often tend to serve different sorts of purposes in different fields, and of course the role of models can change over time. This is particularly evident in biology: evolution by natural selection is a conceptual model, but has, overtime led to a series of quantitative models that can be used to predict changes in allele frequencies i.e. population genetics. The descriptive quantitative models of ecology and now bolstered by agent-based models that include more ideas about mechanisms of interaction between organisms. The main point I want to make though, is that the use of models is highly variable between, but mostly within fields, even within labs! This diversity again, reflects the diversity of epistemological and cultural commitments that guide scientific practice.


While I acknowledge all this diversity, I want to return again to the idea that at a higher level of abstraction there is actually quite a bit of similarity among disciplines in that ALL use models to "make sense" of the world. Models in some form are always there, (to use the forms/games terminology) guiding the games that scientists play. Or to put it in the reverse - all the games that scientists play result is models of some form.


What is the form of a model?

It is worth making the distinction upfront between models (ideas) and the representational forms they take. Models can be represented physically, mathematically, verbally, diagrammatically, etc. But it is the IDEAS that matter, and the ideas are brought to the model by the person who is making sense of that model (in this sense I would say that a model is part of a distributed cognition system). So a diagram, equation, even a string of sentences is NOT a model by itself without a mind to interpret those symbols. This may seem like an obscure philosophical point, but I think it has real consequences in classrooms. Just because students are drawing, manipulating equations does not mean that they are engaged in the practice of modeling or model-based reasoning.


So what does it mean to reason with a model?

While models organize scientific knowledge, what is important for science students is not simply that they know the models, but that they can use them - reason with them. This means that students can use existing models - to explain phenomena, make and evaluate predictions, design experiments, that they can evaluate models using relevant epistemic criteria - is the model too simple, not simple enough, what assumptions does it make, are they reasonable, does it help us think about something complicated in an intuitive way? And that eventually, students begin to learn how to construct and revise their understanding by formally constructing and evaluating models - making decisions about what to include, what to leave out, how to formally represent their ideas. Again, the forms those models take will depend on the scientific context. The principles of natural selection have great explanatory power, but can't make accurate predictions. Epidemiological models can make predictions, but are missing much of the details of reality, descriptive models of cellular processes might be detailed but lack accuracy. The point is that part of learning to reason with models means learning to use them appropriately given the context you are in.


How do models relate to the structure of the disciplines?

One of the most useful features of models is that they help us divide the world into chunks. Each model can explain some part of what we observe in the world, but no single model can account for it all and all levels of detail. The most intuitive way to categorize models is in terms of the things that they explain (phenomena). While there are many ways to divide up the phenomena that we observe, one rather obvious way has to do roughly with the idea of scale - that is moving from macro-level phenomena to micro-level phenomena. In the Passmore/Potter world this idea is captured using the metaphor of "turtles" to mean that models are hierarchically nested within one another in ways that reflect the hierarchical structure of the world. This idea is stolen from the following anecdote from Stephen Hawking's 1988 book, A Brief History of Time: 


"A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever," said the old lady. "But it's turtles all the way down!"


We use this metaphor to convey the notion that the world can be chunked by "turtles" (models) that help us make sense of different chunks of the world, but that underneath each turtle is yet another turtle that helps you make sense of yet some deeper aspect of the world. Of course it's not linear, but the basic idea is that whenever you are looking at the world you have to bound that observation in some way (we do this by making assumptions and simplifications and by choosing a particular scale at which to work). 


This has philosophical consequences for what a discipline means. In this view, a discipline is a group of folks that are interested in a particular chunk of the world. Most of what they are up to is trying to explain this chunk by building/refining models of some kind. Different disciplines tend to use different techniques and tools to do this. Some focus on doing a really good job of collecting data about the world to fit with these models (the experimentalists), some focus more of their time on building and refinined the ideas themselves (the theorists) but BOTH are using models - either directly interacting with them or using them to decide what aspect of the world needs to be filled in and described.


It also provides a way of seeing where disciplines intersect. They intersect in these boundary turtles where phenomena from one discipline require us to reach up or down to get a model from another discipline in order to make sense of what we are seeing. This can happen at multiple places and at multiple scales. For biology and physics it often happens when we go down in scale. But I can think of places at higher scales were we borrow turtles from other disciplines. Consider "mass action" models of disease spread for example. I have been writing a narrative of the models of biology and how they all fit together. If you feel like reading it, here it is (Biology as Models). I could imagine a concept map that would link all these models together and show how particular phenomena invoke models at different scales.


What does all of this mean for a physics for biology course?


1. Science as sensemaking. From my (our) perspective, the most important thing a biology student can get out of a physics course like this one is the general appreciation for science as a sense-making endeavor. This means emphasizing again and again, that while the details of what physicists and biologists do sometimes (not always) differ, at their CORE they share a similar commitment to understanding the world. I think this idea is present in the The nature of scientific knowledge text, but I still think the The disciplines: Physics, Biology, Chemistry, and Math text gives the impression that biology and physics are different (I know we already talked about this and that a change is probably in the works).


2. Science as model-based. More specifically, both biology and physics use models to organize knowledge and to structure practice. Both biology and physics use mathematical models to formalize relationships and to make testable predictions, both use conceptual models, with varying degrees of detail, to make sense of mechanisms and to generate explanations for phenomena and both generate descriptive, phenomenological models to simply capture patterns that are in need of explanation. Some of these ideas are present in the Phenomenology and mechanism section, although the use of a variety of models in both disciplines could be made more explicit. I am not sure to what extent it is necessary to use the word "model" with students in the way I have defined it. I would like to discuss this with the group. When we say "model" and "modeling" in this course, what do we mean? I would hate for biology students to think (as I did) that modeling is something that a small subset of biologists (who are really good at math) do. I think this message is coming through with the emphasis on Modeling with Mathematics.


3. The connection between physics and biology. Physics underlies and constrains living organisms - how they are structured, how they behave, how they evolve. BUT, physical models are not always necessary for biological explanations (see Tackas and Ruse, 2011 for an excellent up-to-date discussion of the philosophy of biology). I think this has serious implications for what "authentic biology problems" means in a physics class. At some scales, and for some classes of problems, the physical models are needed as part of biological explanations (e.g. parts of molecular, cell bio, biomechanics, fluid dynamics etc). In other cases, while physical principles constrain models, they are not part of the explanatory structure (e.g. evolution, ecology, behavior). My sense, although I could be wrong here, is that trying to layer some physics into these more "macro-level" phenomena is going to feel artificial. Does that mean that a physics for biology course is only relevant to those biology students interested in molecular/cell bio or biomechanics/morphology? Absolutely not (see points 1 and 2). To reiterate, for those biologists (I was one) who never really gave much thought to specific physical models in biology, what I wish I had gotten from physics was practice reasoning with models. I wish I had been told that thinking about science as a model-generating, revising process is a useful epistemological stance. I wish I had learned that trying to represent my understanding in different ways - with pictures, words, equations would help me enrich and revise my understanding. I wish I had known that math is just another way (a powerful way) to represent ideas. And that once externally represented mathematically or computationally, I could play with those ideas, rearrange those ideas, consider the implications of those ideas for different parameter sets. So all of this is to say, that as a (former) biologist, I am much more concerned with authentic reasoning than I am with bringing in biology content - although I think that is useful too, to the extent that it is possible. One problem I anticipate is that a lot of the biological examples that draw heavily on physics might be really complicated, and it might be hard to use the physics in an authentic way without diluting it so much that it no longer has much power. Whether or not this is a problem will become more clear as we work through specific examples.


4. The empirical side. So far, I have neglected talking about experiments, observations, data - all the ways we interact with the "real" world. I completely agree that students should be comfortable with the empirical side of science, but I am much more worried about their ability to connect empirical practices with the underlying theoretical ideas than I am worried about the precision of their measurements or even their experimental design skills out of context. My sense is that students get plenty of practice measuring and designing controlled experiments. When push comes to shove I think most students know how to do this stuff. The problem is that they see it as largely irrelevant and boring. So like I said the other day, dealing with error, uncertainty, precision, accuracy, sig/figs only matters when it matters. The same goes for scientists. I need to have a good reason to need to make accurate measurements - or else why am I going to waste my time staring at a stopwatch or squinting at a ruler (ro transcribing every word someone says)? My sense is leading with measurement without a context in which measurement in needed is not going to get us very far. Instead, I think we should lead with the ideas and then create the need to measure. That is, start with a model, make some predictions, design an experiment to test those predictions. And it is in the designing of the experimental protocol with the ideas that you want to understand in mind that the details of what and how you measure and how accurate you need to be become important.



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