Friday, October 24, 2008

Theory and thinking: my favorites

My favorite thing about being a theorist is that you can ignore things you don't like. Let's say you have some particles but can't or don't want to model silly real world things like their shape, size variation, and attraction/repulsion between them. You can just say they are hard spheres! Sure, not everything can be modeled as hard spheres, but it is something to know what hard spheres would do in a certain situation, regardless of applicability to a particular problem. Even if you want to know about a real system that isn't following the trend you calculated for hard spheres, the way in which it deviates likely tells you a lot about how the stuff that the real system is composed of is different than hard spheres. This is just an example, of course . . . the point is that you can learn something, perhaps even something relevant to a particular "real world" system, by greatly simplifying the problem. As a theorist, you are in control of your simplifications! After you have a basic understanding, you can add in the details and continue to explore! What I really love about this is having an exact answer, something that I know is right, even if it only applies in a limit that is not particularly "real world"-y. That's not to say that experimentalists can't also ask fundamental questions, get relatively exact answers to certain things, or that they can't make simplifications . . . just that they are seemingly more often constrained by actually having/measuring a particular thing that exists, which has certain properties which can't be turned on and off or changed at will.

This is why undergrad was so satisfying to me--the homework problems had answers. Much more often than for research (understandably), you could spend a certain block of time working something out, and come to a conclusion that was either right or wrong. There's something very soothing about having an answer at the end of a bunch of calculations, especially if it is something simple like a quantity or graph (as opposed to working on a research project over the course of many months eventually contributing to a better general understanding of the area). Of course, open-ended questions or long-winded (by necessity) answers aren't without their merits.

My second favorite thing about being a theorist is getting to think about the limits. If you are measuring the temperature dependence of something, you must have a certain range of temperatures at which you can reasonably take data. If you instead have an equation to describe your system, you can ask (and answer) what happens as temperature goes to any value. What happens as temperature goes to zero, or is extremely large? Are there certain temperatures at which the behavior changes in a qualitative way? Of course, your equation may be completely invalid, as it relates to the real world, at near-0 or very large temperatures (or even may be mathematically invalid at some point). However, the limits or critical points tell you important things about the theory itself, and if it describes the "real world" over a certain interval, then you have a better understanding of what effects are operative during that interval. In trying to be general, I hope I have not descended into something that will be read as near-gibberish. If confused, you may rest assured that I know exactly what I mean.

My work here has taught me to immediately ask what the limits would be, even for non-work-related problems. On occasion, I have amazed TE with surprising insight into his research, homework problems, or design work for tinkering projects. On other occasions, I have also gone a bit too far with this sort of thinking without fully understanding the problem, and have made assertions and mistakes that may be considered patently ridiculous to the typical person residing in the "real world".

I guess both of my favorite things boil down to this: as a theorist, you are not constrained by the "real world". You may note I did not attempt to define "real world". I do not intend to do so, but I think the point here should be relatively clear without a formal definition.


GM? said...

It was good to know in undergrad, that your problems had solutions. In grad school, you always have a tiny bit of fear that your problem may not be solvable, or not be solvable with the tools you are using. But this is an area where an advisor can come in very handy, and the uncertainty itself can be exciting. I think part of being a better scientist is knowing when your tools, or any set of tools don't apply. I'll take you cue about limits and try to see things in that light more often.

AbdultheScientist said...

With theory, we can go more fundamental than any experiments could ever attain. In fact, our knowledge of the world is not very useful without theories to explain them. Even though the calculations afforded by a theory might be approximate, it tells us a lot about the behavior of things. A theory is not very useful unless we know its limits. That's why we conduct experiments to test the results and predictions of theories.