What's the Story?
Imagine you’re trying to learn quantum field theory, and you just got to a tricky part: deriving the LSZ reduction formula (don’t worry, you don’t have to know what this is!). The calculation and algebra are a little messy, particularly if you’re working with the fermionic case. When going through the derivation, it’s easy to lose the forest for the trees.
In these cases, I find it helpful to ask, “What’s the story here?”
This reframes the learning experience. Instead of focusing on the formulas and algebra, try and figure out why you’re going through these manipulations. What’s the story being told? Why is this specific calculation important, and what does it represent?
There’s a time and place for being particular about the details, but I think it would have benefitted me much more during my education to ask why we were doing things.
The reason is simple. Once you understand why you’re doing something, it becomes easier to remember the specific steps. It doesn’t feel like you’re walking randomly through a crowded area, but instead forging a specific path. Conversely, when you don’t know what the story is, it can highlight areas that you need to brush up on.
I ask myself this question when I learn any new topic now. It has become my go-to strategy for understanding the conceptual side of an idea.
Why is this important? Because I’ve found myself capable of going through a computation and yet having no idea what was happening in terms of the theory. I was a looking at things on the most granular level, without raising my head and understanding the reasons behind these calculations.
The unfortunate part is that you’re rewarded for doing this. When you’re an undergrad, it’s your job to master the details. After all, you’re going to be tested on this material, so you need to know each step. Rarely is attention given to the conceptual part of the topic, so it’s unlikely than an undergraduate will spend time puzzling this out.
Things change when you go to graduate school, but I this change is more abrupt than it needs to be. Instead, we should be challenging students earlier to think about what a topic means. I’m not even referring to cutting-edge stuff like the various interpretations of quantum mechanics. Rather, I’m talking about understanding the assumptions that are built into a model, where things can be improved, and what kind of cost this extra richness incurs on our model. These are questions which aren’t addressed very much during the undergraduate years (at least, they weren’t for me), but I think it would be worthwhile.
I think there’s a balance to strike between computations and conceptual ideas. At the moment, I feel like we overemphasize computation during the undergraduate years. If we raised the issues of assumptions and model-building earlier, I suspect students would have an easier time transitioning from undergraduate studies to graduate studies.
As a graduate student, I’ve found this transition to be a rough one. This is to be expected, since I didn’t spend a ton of time interpreting what I was doing. Instead, I just calculated, leaving me unprepared for the expectations of graduate studies.
I learned that there’s more to physics (and other subjects) than simply absorbing models and doing calculations. At one point, I’ll be the one building the model, which means I need experience thinking about these conceptual questions. I would have loved for my undergraduate education to prepare me more for this.
If you’re reading this as an undergraduate, my suggestion is simple. Ask, “What’s the story?” more often. By doing this, you’re training yourself to think past the information being presented to you and towards connecting with reality (which a model can only be partially successful at). It’s a skill worth developing as soon as possible.