Sloppy models, differential geometry, and why science works

Models of systems biology, climate change, ecology, complex instruments, 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 and approximation theory to explain sloppiness as a ‘hyperribbon’ structure of the manifold of possible model predictions. We show that physics theories are also sloppy – that sloppiness may be the underlying reason why the world is comprehensible. We will describe how to use these hyperribbon to systematically coarse-grain complex systems into human-comprehensible form. We will present new methods for visualizing this model manifold for probabilistic systems – such as the space of possible universes as measured by the cosmic microwave background radiation.