Harry Tam: An Effective Field Theory Approach to Learning
Updated: Sep 28, 2019
How Physics Skills are Transferable into Life
By no means am I writing an introduction to the effective field theory in physics.
(Note: here “field” has an abstract physical meaning: A field stretches over the spacetime, from which particles can be created/annihilated). Most people don’t care about it, even though it is a powerful theoretical idea that physicists use to distill from the complicated reality some simple but universal principles. The reason I bring this up to you is that, if you allow me to over-generalise this beautiful idea, it has taught me how to learn new things effectively.
I am particularly troubled by my slow learning progress. As a graduate student, learning is a constant job that I perform every day. Fundamentally, I am very happy about that (absorbing new ideas is exciting!), but from time to time I feel discouraged when I realise how long I have taken to finish reading one paper, or one chapter of a thick (sick) textbook. I am only given five years, within which I not only need to learn but also generate new knowledge. How can I manage to do that?
Physicists find salvation from the effective field theory, and so do I.
Learning was once easy. I was able to, and always have the passion to, understand every detail in a proof of a theorem or a derivation of an equation. To consolidate my understanding, I would go through the problem set at the back of the textbook and try to come up with different ways of solving a single problem. I would read carefully every single word in the text and make sure that I have digested one sentence before moving on to the next. I would start reading from the first page of the first chapter of the first introductory text in the area that I want to explore so that I can build up my knowledge with a solid foundation. These are the handy habits that I have developed since I was young when the circle of my knowledge was small and its intersection with the unknown minuscule. I thought that was the right way to absorb new knowledge, after all, those admirable scientists are meticulous, aren’t they?
Things changed when I started my graduate studies. Proofs and derivations became much longer (we now call a one-page proof short) and more convoluted. More often then not, I couldn’t faithfully reproduce a derivation that I read just the day before, even though I spent a long time dissecting the details and subtleties, and tried hard to remember them. The time required to solve an exercise has grown exponentially, making it impractical for me to tackle all the problems suggested by the author. I am no longer confident that my research is supported by a firm foundation. Embarking on a graduate study, I also have to read journal articles written by my fellow researchers, and there are tons of them being published every day. I am incapable of developing a complete understanding of my peer’s work, simply because there are so many of them and each of them involves so many details. All these have made me very uncomfortable, as I feel like the recipe I used to hold onto has failed me.
I don’t feel alone though, after reviewing the history of physics. While I lose the delicate control of learning as I approach more advanced studies, physicists have lost their control of theoretical analysis as they approach more complicated systems. When quantum physics was being developed in the early twentieth century, physicists could write down the equation governing the motion of microscopic particles, known as the Schrödinger equation. They first solved it for systems as simple as the hydrogen atom and obtained incredible conformity with experiments and called it a glory. But soon they were unsatisfied and proceeded to write down the Schrödinger equation for a metal, in which billions of billions of electrons interact closely with billions of billions of ions, and then they realised it is impossible to be solved! Their desperation in face of a huge amount of interacting particles is similar to my desperation in face of the fathomless amount of new knowledge. Physicists cannot track the motion of every single electron, nor can I pin down every single piece of detail whenever I learn a new theory/technique. We have the same plight: the problem is getting more complicated, how do we deal with it?
Physicists find salvation from the effective field theory, and so do I. Unlike quantum mechanics or Einstein’s Theory of Relativity, which has very specific rules to tell and can be considered as the law of nature, effective field theory is more like an approach to describe the nature. Physicists acknowledge that nature is indefinitely complicated, while our ability is definitely restricted. Thus instead of worrying about the microscopic details happening at a scale that we can’t perceive anyway, let’s “average out” all those tiny fluctuations and focus on the low-energy macroscopic effect that remains. Though in a metal, a single electron interacts strongly with neighbouring electrons or ions in a complex manner, if we step back a little bit to view this mess, the electron is just being “dressed up” by its environment and become a nearly free particle moving through space. By neglecting what is happening at the finest scale, and proceed by guessing and approximating the average effect of that mess, physicists are able to make very solid (and actually quantitative) statements about these complex systems. Many interesting phenomena like superconductivity and quantum Hall effect, which form the subject of my research, are explained in this spirit.
What a beautiful idea! That even carries some philosophical meaning which teaches me how to learn (anything) effectively. I can now get rid of the uncomfortable feeling when I skim the proof of a theorem while reading a mathematics article, or skim the derivation while reading a theory paper, or skim the methodology while reading an experimental report. Following the spirit of effective field theory, instead of getting hung up on the technical details that I am going to forget anyway, let’s “average out” those details, obtain just a rough and intuitive idea about them and spend the hardest effort to making sense of the big picture that they conspire to present.
It is an approach, not a specific set of instructions, that teaches me how to learn effectively.
Do I disdain the technical details that slow me down? I don’t. Proofs, derivations, and methodologies are indispensable parts of research, they constitute the respectable sciences. It is just that, quite often, they are obscuring the simplicity and beauty that we are looking for. We don’t ignore the details and rigours, we acknowledge their presence and importance. Eventually, we will come back to them, either when we doubt the validity of the statement being made, or when we want to build our new theory upon these results that we want to make sure are well grounded.
Above are some reflections on my graduate studies, and I have focused only on the “learning” part (I haven’t come up with a recipe for generating new knowledge yet, that sounds much harder!). I hope my reflection can trigger you, the reader, to share your own recipe for learning. You may find what I have written to be trivial, and shouldn’t be called a recipe as it does not contain any concrete instructions. Yet, it is a very general problem that plagues me while learning, and its resolution requires just a change of attitude. It is an approach, not a specific set of instructions, that teaches me how to learn effectively.