xkcd on purity of scientific fields

My daughter is a psych grad student, and she falsifies hypotheses all the time. Usually her own. Which is really annoying when she wanted to write a paper on the results of a study.

How about modeling purity as the elegance of the mathematics behind the field. Math itself starts from fairly simple postulates, and is the most elegant by far. Physics is more complex but you can model some things quite elegantly. In chemistry math breaks down at the fundamental level, and biologists hardly use any math except for statistics. Beyond that you give up actually getting solutions and start using statistics and simulation. And economics would be all the way to the left, where there are massive models all of which give the wrong answers because they are based on overly simplistic assumptions.

I’ve often heard the term “elegant” and I’d like to know what it means in the context of math.

How would economics be improved by making the assumptions less simplistic while still enabling precise quantitative predictions?

I’m not a mathematician, but an equation with the fewest variables and terms possible seems to be most elegant. F=ma is really elegant. Of course it also has to be right.

As for economics, the simplifying assumptions have been around the behavior of economic actors and rational choices. Which we’ve found out to cause problems. Modeling actual behavior certainly doesn’t make anything easier, but it can prevent us coming up with results which don’t match reality. For instance, that you don’t need regulation since you can trust lenders and borrowers to act in their long term best interests.

I put economics to the left because the lack of elegant equations does not come from lack of smarts but from the inherent complexity of the job. I think that overly simplistic assumptions can lead to precise quantitative predictions - just not accurate quantitative predictions.

This might help answer your first question.

As for your second, Voyager exaggerates quite a bit but there is some truth to it.

Often in economics we don’t care exactly about precise quantitative predictions because the units themselves are not measurable. How many utils do you derive from an hour of leisure? The nature of the relationshps among variables is what really matters. We care about the structure of peoples’ choices and the effects of aggregating individual choices together. So we really care about deriving closed form solutions to economic problems in order to see these relationships clearly. In order to get there, we have to make some assumptions. Sometimes these assumptions can be tough to justify intuitively. The purpose of these assumptions is to isolate just a few moving parts in what is perhaps a larger and more complicated system in order to see precisely how some smaller economic mechanism works. So the universe of a particular model is usually stark and stylized. We model only as much as we absolutely need to shed some light on a phenomenon.

When we relax the assumptions to seem more realistic, we often lose the ability to make clean predictions about what X is going to happen given some circumstance Y. So not only are the problems technically more demanding, the intuition we get is diluted.

Chronos said above that the behavior of an electron is too complicated to model analytically. Yet more or less everything has to be modeled analytically in economics. We need to check the results of our models against some basic intuition because the very purpose of the models is to capture something essential about human decision-making. To my knowledge we are not so constrained when we try to model the behavior of electrons. Not only do the results of economic models have to more or less fit the data, they also have to be broadly consistent with how we think we make decisions in the first place. Humans are fairly complicated, so this is not all that easy. We have far fewer tools than physics because most would be inappropriate, and humans are arguably more difficult to model than particles.

The purpose of models in the first place is not to predict individuals but to learn more about how people in general make decisions than would be possible without a model.

Sorry I meant “astronomy which isn’t experimental science”.

Can’t she publish in www.plosmedicine.org or something along those lines? One of the problems with dead tree journals is the difficulty of publishing negative results. Researchers will stretch their results totally out of shape to get a publishable paper.
Obviously if science advances by finding out what isn’t true, then negative results are the real science. Everything negative result is another brick in the wall and you don’t build a wall by throwing away the bricks.

http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020124