The catch is that complex models are also usually very wrong. Most possible models of reality are wrong, because there are an infinite legion of models and only one reality. And if you try too hard to create a perfectly nuanced and detailed model, because you fear your bias in favor of simple mathematical models, there’s a risk. You can fall prey to the opposing bias: the temptation to add an epicycle to your model instead of rethinking your premises. As one of the wiser teachers of one of my wiser teachers said, you can always come up with a function that fits 100 data points perfectly… if you use a 99th-order polynomial.
Naturally, this does not mean that the data are accurately described by a 99th-order polynomial, or that the polynomial has any predictive power worth giving a second glance. Tacking on more complexity and free parameters doesn’t guarantee a good theory any more than abstracting them out does.
The catch is that complex models are also usually very wrong. Most possible models of reality are wrong, because there are an infinite legion of models and only one reality. And if you try too hard to create a perfectly nuanced and detailed model, because you fear your bias in favor of simple mathematical models, there’s a risk. You can fall prey to the opposing bias: the temptation to add an epicycle to your model instead of rethinking your premises. As one of the wiser teachers of one of my wiser teachers said, you can always come up with a function that fits 100 data points perfectly… if you use a 99th-order polynomial.
Naturally, this does not mean that the data are accurately described by a 99th-order polynomial, or that the polynomial has any predictive power worth giving a second glance. Tacking on more complexity and free parameters doesn’t guarantee a good theory any more than abstracting them out does.