Statistical Methods for Dynamical Systems

I just returned from a conference in Montreal on statistical methods for dynamical systems. It was absolutely amazing! I'm starting to get the feeling that people are just beginning to recognize the vast potential waiting around the corner for modeling complex high dimensional temporally and spatially dynamic systems while dealing with the tricky issues of appropriate model selection and statistical inference for parameters. There are of course a myriad of tricky issues and problems that need to be solved, but fortunately there are some powerful brute force methods that may usurp elegant computational and mathematical tricks as raw computing power becomes increasingly cheap and ubiquitous.

I envision a point where we have complicated hierarchies of spatiotemporal models that use dynamic models as building blocks. A sort of object oriented approach to modeling function spaces, where one can swap out various model types and parameterizations to best capture the essence of the observed process. Of course, a lot of this is data driven, in that these models will require vast quantities of data to validate or falsify, but as technology continues to improve this will not be a limiting factor. I think the largest limiting factor is going to be our ability to intuitively manipulate and understand these complicated models, though this may not be a huge problem as they become increasingly autonomous in their design and implementation.

We're definitely going to need these models if we're going to answer the question, "What is life?" I think this is one of the biggest and most important questions all of humanity is faced with. If we could elucidate the true nature of the autocatalytic process that is biology we would have a deep insight into not only ourselves, but also the complex web of relationships between all organisms and their environments/contexts. I imagine that truly internalizing the full magnitude of the complexity and subtlety that it is to be a living organism would be somewhat akin to a spiritual experience.

Of course, there may be reasons not to suffer such an understanding. We may swoon in despair, or annihilate ourselves and our environment out of fear and rage. It also may be impossible for us in our current state to ever truly model such complex processes...yet I find this argument incredibly weak and close minded. The most concerning and most likely possibility is that a relative few rich and powerful gain control of this knowledge, and use it for their own self interests. That is why I suggest in general all research towards understanding this question should be available in the public domain. Also, active outreach programs promoting the involvement of many people and organizations in policy making decisions concerning the ethical and moral implications of such knowledge would be absolutely essential for careful and responsible investigation. Ideally, we could use this knowledge and understanding to bootstrap ourselves out of many ills, while minimizing further risk.

I know that I'm going to continue to not only think about exciting new ways to build more powerful models, but the long term moral implications of understanding the systems I'm modeling.