“With four parameters I can fit an elephant; with five I can make it wag its tail.” Systems biology models of the cell have an enormous number of reactions between proteins, RNA, and DNA whose rates (parameters) are hard to measure. Models of climate change, ecosystems, and macroeconomics also have parameters that are hard or impossible to measure directly. If we fit these unknown parameters, fiddling with them until they agree with past experiments, how much can we trust their predictions?
In studying a variety of multiparameter models from different fields, we have unearthed several surprising facts. First, they are often sloppy; the parameters can vary over enormous ranges and still agree with past experiments. (There are a few ‘stiff’ combinations of parameters that are important, but the individual parameters can all range over factors of fifty to thousands without changing the predictions.) Second, they can often make useful predictions about future experiments, even allowing for these huge parameter uncertainties. Third, these sloppy models all appear strikingly similar to one another – for example, the stiffnesses in every case we’ve studied are spread roughly uniformly over a range of over a million. We will use ideas and methods from differential geometry to explain what sloppiness is and why it happens so often. Finally, we shall show that field-theory models in physics are also sloppy – that sloppiness makes science possible.