Jeremy Côté

Something Deeply

When I was an undergraduate, I learned all there was about physics and mathematics.1 I learned how to wield the tools of calculus, how to wrestle with differential equations, how to employ the machinery of quantum theory, and how to zip through classical physics problems using Lagrangian mechanics.

In essence, I learned the tools of the game.

This was a key part of my education. It gave me the bedrock for graduate studies. I became proficient at performing calculations that every physicist should know, and I absorbed a lot of facts. I worked through proofs, and sweated the details.

What I didn’t do though was really think about the things I was calculating.

I suspect that’s normal for undergraduates. When we are trying to make sure that our calculations have no missing factors of two, we don’t take the time to stop and ponder what we’re doing2.

I would say that a large part of my undergraduate education dealt with understanding the tools and algorithms needed to solve problems. I wasn’t as concerned with the assumptions that went into the theories or proofs, and we didn’t spend a whole lot of time discussing them.

Graduate school is where you start questioning things. I like to think of this as taking a trip from A to B. When you’re an undergraduate, the goal of your professors is to show you the path that connects the two points as efficiently as possible. This tends to be the highway rather than the winding countryside road.

In other words: You get to the destination quickly, but you might not remember the journey.

In graduate school, the emphasis is flipped. Now, your job isn’t to necessarily calculate things perfectly and work through proofs that others have done before. Instead, your job is much more open-ended. It’s about paying closer attention.

You start investigating the assumptions that you once blew by. You take that countryside road, and you meander. Before you proceed from any area, you ask yourself if you really understand the ideas. Not just in terms of being able to perform a calculation, but why the assumptions you took on without thinking during your undergraduate studies were necessary.

You begin seeing how you were in a large but fenced-in area. While you had the room to explore, everything was orchestrated in order for you to get the answers your professors wanted. Being an undergraduate meant staying within those boundaries.

As a graduate student, you notice that the fenced in area—which we might call “scientific knowledge”—is tiny compared to the vast unknown regions that lie outside.

It’s not as simple as when you were an undergraduate. But you’re also more knowledgeable now, capable of handling the extra complexity. Above all, understanding why you need to take on certain assumptions is what hooks you. Can they be relaxed? Are there other ways to get a result? What new area is worth exploring? These are the questions that fill up your time.

Is graduate studies for everyone? Absolutely not.

Graduate school is not just a more detailed version of undergraduate studies. The focus shifts from acquiring all the tools and performing calculations correctly to understanding the “why” behind everything. If undergraduate studies were about getting from A to B as efficiently as possible, graduate studies is about taking the time to examine each step.

That’s not how you start though. In the beginning, you try to absorb everything. Then, you find you can’t, at least, not to the level you desire. So you try homing in on a few areas. You dig deeper, and sooner or later you find yourself sucked in. It’s not automatic, and it takes work to find a niche, but it comes.

Then, your job is clear: become an expert at this one thing. It’s a good idea to still keep abreast of other areas, but your focus is not to learn everything, but something deeply.

It’s a different environment, and it’s not for everyone. But it might be for you, and if so, it can be quite the adventure.

It’s still physics, though not in the way you’ve learned it before.

It’s studying one aspect of the world deeply.

  1. Understatement of the century, but you get the idea. 

  2. Okay, maybe some students think about it. I just wasn’t one of them.