“I’m a physicist, I have a working knowledge of the entire universe and everything it contains” –Sheldon, “The Big Bang Theory”
While ridiculous, it’s instructive to consider the precise point where this logic fails – indeed, why is it that while physics has understood most of the building blocks of the universe up to very high energies (small scales [e.g., quarks]), it still cannot answer most every-day questions we encounter in practice? [e.g., what makes me happy?] It seems to me that the problem is that physics has mostly been guided by a reductionist philosophy, by which I mean “to understand the whole, we must understand its parts.” Nonetheless, with the advent of thermodynamics and an understanding of phase-transitions in the 20th century, we learned about emergence: where macroscopic properties of materials or systems are independent of most details of their constituent parts [e.g., evaporation of water depends little on structure of H2O molecules]. This way, in addition to pushing our understanding of the universe into the very small and the very large, another, entirely independent and non-reductionist direction, is that of complexity.
Complex and emergent systems inherit their structure not from the properties of their fundamental building blocks, but from the structure of the mathematics that describes how those blocks fit together into the whole. As the math is universal, so are many of the features of the emergent systems [as with, e.g., evaporation of liquids]. I find this universality extremely elegant, as well as practically exciting, as it gives hope for understanding systems whose parts are themselves impenetrably complex: could we understand a living cell without needing all the details of biochemistry, or an organism without all the details of cellular machinery, or an economy without the details of individuals’ behavior?
There are many tools in theoretical physics that are suited to exploring such questions – some very old, and some brand new. I have worked with some aspects of nonlinear dynamics and chaos theory, and found hints of a potentially universal mechanism that guides the evolution of complex dynamical systems to self-organize when subjected to predictable environmental forces. I am looking into the deeper roots of this mechanism by recasting it in the language of renormalization group (RG). RG is itself a fascinating tool to study, as it explicitly allows working out many examples of emergence, but only for systems that have self-similar structure across scales. To generalize beyond these, we tried to build bridges from RG to information geometry and sloppy models – a set of very general tools for finding emergent models (https://arxiv.org/abs/2011.12420). Information theory turns out to be fundamental to these questions, as it gives a formal way to judge when a macroscopic emergent description is appropriate (https://arxiv.org/abs/2010.09390). Statistical Mechanics, and its recent nonequilibrium generalizations, provide another set of potentially useful and universal methods.
In all, there seems to be a vast number of highly practical and immediately testable applications for any theoretical progress on understanding emergent behaviors and structures – in biology, sociology, economics, data science, or machine learning. On the other hand, there are also many elegant tools that have been developed in various areas of theoretical physics over the last few decades that may be up to the challenge. Moving forward, I hope to connect these tools with real-world problems to develop more principled ways to make business and policy decisions.
One particular application that I have thought of quite a lot in my PhD is abiogenesis: how does “life” emerge from a “dead” molecular soup? What are the necessary properties of the building blocks and their dynamics, and what is the simplest system that realizes these? Do we really need the entire complexity of Carbon-based organic chemistry, or can some completely different dynamical system reproduce the “important” features? And what are these “important” features of life anyway? These questions motivate the discussion in my PhD Thesis (https://dspace.mit.edu/handle/1721.1/123349).