(Inauguration lecture for the Tage Erlander Guest Professorship)

Even the casual scientific observer would not deny that the Earth’s climate system is a complex nonlinear dynamical system, riddled with feedbacks. Despite understanding many underlying of physical principles we lack predictive acuity because of the confluence of the nature of the system itself, our ability to mathematically and computationally describe it, and to construct tests and data sets to vet predictions over the myriad of relevant time and length scales. Although applied mathematicians and physicists have relatively recently branched actively into rich, complex fields such as biology, we have yet to fully embrace the challenging treasure trove of physical climatology. The origin of biology is distinct from physics, but such is not true of climate, launched by the likes of Fourier, Tyndall and Arrhenius. Over time, the desire (and need) to test principles in the natural record has led to an approach rooted in observations. Whilst our community is certainly intimate with the interplay between observation and theory in astronomy and astrophysics (witness the 2011 Nobel Prize in Physics) a similar interplay in climate is ripe for our efforts. Of particular promise is the impingement of methods and tools from statistical physics upon everything from the long-term observational record to interpretation of noise, to the relevance of fluctuation theorems. It is well known that the modern development of chaos in nonlinear dynamical systems emerged from the desire of Ed Lorenz to understand the feasibility of making very long-range predications of the weather. What is less well appreciated is that his work nearly immediately infused the appreciation of uncertainty into such goals. Uncertainty not only is a defining feature of science, but it is embraced in different modalities in different subfields with different foundations. What is even more poorly appreciated is the connection between modern ergodic theory and number theory, which binds our vision of the fate of say the atmosphere to the mathematics of the real numbers on a line.

I will provide a tour of some of these tendrils and try and point out where physicists and mathematicians may contribute. As with any tour, the waypoints will necessarily be brief and provide the view of the tour guide. The goal is a confluence of education, at the least technical level, invitation, to people seeking a new research challenge, and speculation, about what nontraditional approaches may be of interest to pursue in the future.