Sloppy models, Differential geometry, and How Science Works

Models of systems biology, climate change, ecosystems, and macroeconomics 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? We have found that predictions can be made despite huge uncertainties in the parameters -- many parameter combinations are mostly unimportant to the collective behavior. 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.