Why theories and models?

Yet another brand new year has arrived. Some people view it as a time for reflection, introspection and resolution-making. Personally, I am not keen on resolution-making but I see nothing wrong with reflection.

One issue that has long concerned me, whenever I have tried to reflect upon what I am doing in my research work, is that of defining the balance between theory and empirical experiment. My work is centered on AI and machine learning algorithms as applied to problems in robotics and biology. Some practitioners of the application domains believe that it is pointless to theorize and that every day should be spent getting one’s hands dirty in a ‘real’ lab – nothing more, nothing less. On the other hand, I view applications somewhat differently. To me, the robot plays a role that is somewhat analogous to the lab rat. The point isn’t just to study what happens to the rat. Instead, it is to glean some deeper scientific principle that elucidates some aspect of nature. So, I study robotics because it is a nice playground to understand more fundamental issues in AI, learning and algorithmics. I firmly believe in using experiments to guide the generation of questions and verification of answers, but there is something in between as well – the abstraction that leads to scientific principles!

Recently, I came across an interesting article in a different area that does a nice job of explaining why this is a reasonable viewpoint. The article is based on A. Rubinstein’s presidential address to the Econometric Society, from which I quote:

As economic theorists, we organize our thoughts using what we call models. The word “model” sounds more scientific than “fable” or “fairy tale” although I do not see much difference between them. The author of a fable draws a parallel to a situation in real life. He has some moral he wishes to impart to the reader. The fable is an imaginary situation that is somewhere between fantasy and reality. Any fable can be dismissed as being unrealistic or simplistic, but this is also the fable’s advantage. Being something between fantasy and reality, a fable is free of extraneous details and annoying diversions. In this unencumbered state, we can clearly discern what cannot always be seen in the real world. On our return to reality, we are in possession of some sound advice or a relevant argument that can be used in the real world.

Although Rubinstein is talking about an area that is somewhat removed from the more exact sciences that directly concern me, I do believe that his words are relevant – particularly for the class of synthetic, i.e., design, problems. When faced with a real world design problem, the utility of a model or theoretical principle is that it enables us to construct a “plan of attack” leading to the eventual solution. Occasionally, one may arrive at solutions by just hacking away at the problem – without recourse to these principles. Also, clearly, there are going to be cases where some details are not addressed by the theoretical model or principle. Nonetheless, there is still value in searching for these organizing principles as they are precisely the things that allow us to make sense of really massive problems that characterize any reasonable reality.

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