Balance As A Student
As a student, there’s no shortage of things I could be doing to help my academic career. I could do some side research, I could read more about my field, I could network with other researchers, I could study more for my upcoming exams, I could work through another textbook, I could volunteer for any number of academic events, and the list goes on. There are so many things I could be doing to advance my career and invest in my future that I could be busy every day for the rest of my life. If I wanted to, I could fill my schedule up with these activities and never be done.
Let’s take a simple example: practice problems. If I wanted to do really well in my classes, I could do extra problems every night in order to be prepared for my exam. I wouldn’t get “rewarded” for doing this, except that my exam scores would probably be higher. I’ve done this before an exam, but I could do this throughout the whole semester in order to improve.
I won’t do this though. In fact, I do almost none of the things in the list I gave above. Even if those items would advance my career in academia, I forget about them. Why? Because if you don’t achieve balance in your life first, you won’t be able to do anything else.
Balance is more than just an athletic skill
The problem with that list is that it’s incredibly seductive. If I do just a few more things, I will be giving myself a much better chance at fulfilling my goals in the future. This is the thinking that leads to the slippery slope of spending too much time trying to “advance” your career as either a student or a researcher.
The truth is that your pursuit isn’t going to be fun all the time. There will be times when you’re frustrated, exhausted, and maybe even sick of your work. But if all you do is think about your work, you don’t have an outlet to ponder other things. You then end up telling yourself that you should be better and more disciplined, before soldiering through.
This may sound like the way to go, but it isn’t. Pushing through when things aren’t going your way is a good skill to have, but you can’t do it all the time. At some point, you need time to recharge. This is why balance in your life as a student is so important. You can’t just keep your focus on academics all the time, or else you will risk burnout. And make no mistake, burnout doesn’t mean you take an extra bit of time to recover. Burnout can be catastrophic, killing your desire to do the activity that you once enjoyed. I think it’s safe to say that none of us want that.
As a student, I feel this pull to do more all the time. Even now, when I’m still on summer break, I feel like I should take some time to start reading ahead and working through the material. My reasoning is that this will lead to better results in my courses, so it seems like a good investment. However, I’ve been fighting this urge for the last few weeks, because I know that I will have plenty of work to do as soon as the semester starts. Do I really want to inundate myself now?
The answer is clear: I want to enjoy my studies, not have them feel like a burden.
So what’s the fix? How can we avoid burnout and the urge to keep on working all the time?
There are two things that work for me. The first is to establish clear boundaries, and the second is to find side projects or hobbies that you enjoy doing.
The most important thing to do in order to protect your personal time from your work time as a student is to create boundaries. The clearer, the better. The goal here is to make sure there’s no question about whether it’s “work” time or “personal” time.
You might think this sounds simple, but I’m serious. For example, I know many students who say they are going to do homework in the evening. What this ends up turning into is a marathon session in which they work a little bit on homework while also doing other things throughout the whole night. By midnight, they find themselves still working on their homework, with no end in sight. This happens because homework tends to take longer than one session. But, if you aren’t careful, it can end up taking over your whole life outside of class.
I get it, homework is important. You don’t have to make a sale’s pitch to me about the importance of doing the homework in a class. That being said, I have strict boundaries on my time with respect to homework.
Here’s what that looks like for me. When I get home, I eat dinner. After that, I start doing homework, and I’ll work until 20:00. Once 20:00 rolls around, I stop working. I don’t say, “Oh, I’m almost done this problem. I’ll just do a bit more.” No, when it’s 18:00, I stop. I used to be bad at this, but now I’m at the point where I won’t go further.
What I’ve done here is set a clear boundary. There’s no question as to when it is “homework time” and when it is “relaxing time”. The boundary is at 20:00, and I stick to it. By doing this, I’ve made sure that I never do school work beyond that point. This is even true when preparing for tests and exams.
Why don’t I make an exception? The reason is that I find that people tend to work within their timelines. Give someone a week to do a project, and most will take that full week. Give them the same project but with only half the time, and chances are (assuming it’s reasonable) they will still get the project done on time. This happens because we fill our time within the constraints we are given. If I let myself work past 20:00, you bet I would end up working until later. But, I know two things. First, if I set myself some reasonable, sharp boundaries, I can get my work done. Second, I want to be healthy and prioritize other aspects of my life too. In order to do this, I need to acknowledge that my studies aren’t everything.
I also want to note that this isn’t my only boundary. I also have one in the morning, which is the period when I run. Therefore, I never do homework in the morning before class. I don’t finish assignments, and I don’t cram in some extra studying. Even if it’s the final exam and I know my classmates are spending their morning studying, I’ll be out on my run, because it’s what I do.
Setting boundaries is important, but it’s also crucial to plan ahead. What I mean by this is that you still need to get your work done. If you have projects or homework with deadlines, you need to work with those. Yes, sometimes those deadlines can be inconvenient. As such, you should have a system in place to accommodate that. For myself, this means doing homework in the evening, and also in-between classes or in the late afternoon. Despite my sharp 20:00 cut-off, I still spend a lot of time doing homework. It’s just that I make sure there’s an end in sight. If I leave it open-ended, I will naturally go past my usual time.
The worst thing you can do is try to get things done whenever you can fit them in. I’m not saying this can’t work, but it encourages you to work more than you should. If something isn’t done, it’s easy to tell yourself that you will spend another hour on it instead of figuring out a way to finish within the timeframe. By establishing clear boundaries and planning how you will accomplish things ahead of time, you’re ensuring that you won’t let your academic life infiltrate the rest of your life.
Take things in chunks
Related to the idea of planning ahead from the above section is to take things in chunks. What I mean by this is simple. If you have a week to do something, please don’t wait until a day before the deadline to start working on it. It sounds like a bad idea no matter how you say it. This is why many of my classmates end up having to work through the night in order to do homework. It’s not that they had to do that. It’s that they didn’t plan ahead to finish it during reasonable hours.
I want to take a moment here to acknowledge that not everyone is in the same situation that I’m in. I have the luxury of coming home to prepared meals and only having to worry about my school work. I don’t need to work a job on the side, and I don’t need to worry about a million other tedious tasks. I can focus on my homework from the moment I’m done dinner to the time before I go to bed. As such, I realize that I’m very lucky.
That’s why I don’t think it’s realistic to expect for everyone to take up my specific schedule and boundaries. Rather, it should be something everyone reflects about. Am I planning ahead of time? Am I establishing clear boundaries? These questions should be asked again and again.
Instead of waiting until a few days out to finish a project or homework, start it right away. Don’t wait until you’re pushed up against a deadline, because that’s when your boundaries start to break down (out of necessity). Instead, if you do a bit every single day, it becomes a lot easier to finish things on time and without worry.
In fact, I’m at the point where I’m done a lot of my homework way before it’s due. This may seem like overkill, but I like doing this because it lets me relax before a deadline comes. By being done super early, I can be comfortable with the upcoming deadline. If it turns out I need to make a change in my work, I can do that without a hassle. Plus, being done early lets me review my work so I can make it even better. For me, it’s the best scenario.
The point here is that you don’t want to take projects or homework as a huge commitment that you leave until the last minute to do. Instead, you want to break it up into chunks, because this lets you deal with small, manageable parts. Plus, it means you don’t have to worry about deadlines as much. The result is that the boundaries you have settled on won’t be tested, because you will be done your work on time.
Finding a hobby
Finally, if you want to achieve balance between your academic life and the rest of your life, it helps to have something to balance your studies with. This is where having a hobby comes in. The goal of a hobby is to let you relax and disconnect from your academic life. You shouldn’t be worrying about your projects and commitments during the time you dedicate to your hobby. Your hobby is the chance for you to enjoy yourself, without any expectations and pressure associated with it.
For example, my main hobby is running. I’ve been running for years now, and it has been a fantastic way to disconnect from my homework, upcoming exams, and any other stress. In particular, I enjoy that running is a physical activity which is completely different from my studies in theoretical physics and mathematics. I think this is a good way to go when choosing a hobby. Find something that is different than your focus in academia, since it will make the boundaries between the two clear. If you have a hobby that’s too close to your academic life, it could lead to thinking about your work all the time.
Of course, you can still make it work. Another hobby I have is writing here on my site. I write about a bunch of topics related to mathematics, physics, and academia, which is about as connected as can be to my education. Still, I make it work because writing is a different kind of activity than going through an intricate calculation. That being said, I think this arrangement works because my main hobby of running is so different from my other interests that it helps balance things out.
The other great thing about finding a hobby is that it lets you practice setting clear boundaries. If you commit to going on a run every morning like I do, there’s no possibility for doing homework or trying to fit in extra work time. Instead, you learn to plan ahead and make sure that every activity has its own time slot. This prevents your academic life from “spilling” into every part of your life.
Related to this is the fact that having multiple interests lets you “forget” about all of your commitments. When I’m out on a workout during my run, I don’t have the capacity to think about my upcoming deadlines or exams. I can only think of the effort I’m giving right now to move fast. I get to live in the moment, and forget about the rest. This feeling is quite liberating, and it doesn’t have to come from running. It only requires you to find an activity that demands your focus. Through the act of focusing, you learn to give yourself a break from all the rest.
A hobby also gives you something else to look forward to in your day. It gives you a way to look at the day as a “success”, even if other things go wrong. By running each morning, I get to start my day at school feeling that, even if everything else goes wrong, at least I have my run to be happy with. That can’t be taken away from me. In this way, my hobby lets me find other meaning in my life. Of course, this can also be found through family and friendships, but I wanted to point out that a hobby is a great way to find success as well. This doesn’t mean you have to turn a hobby into a “professional” success, but it means you can set yourself small goals and be proud as you achieve them.
Achieving balance between your academic work and the rest of your life isn’t easy. It’s an unstable equilibrium, where any small nudge can send the balance out of whack. In order to combat this, you need to be vigilant all the time about how you’re spending your time. Letting yourself drift through your life is a recipe for ruining the balance (if there was any to begin with).
Instead, you want to erect clear boundaries between different aspects of your life. Don’t let yourself be ruled by your commitments. Establish a plan and stick to it. This is helped by doing tasks in smaller chunks, since you won’t be in “panic mode” to get things done. Finally, it’s easier to balance your life when you have a hobby or some other pursuit to focus on. Ideally, it’s something outside of your academic interests, but if you’re creative you can still stick to your interests.
In the end, the goal I have for you, the reader, is to be happy with the way you spend your time. It might seem reasonable to “supercharge” your career by spending all of your time on it, but I would argue that this is a recipe for burnout. Sure, if we were robots that never needed different stimuli, we could do the same thing every day with zero novelty. However, we are human, and novelty is what we crave. I know as well as anyone else that it’s important to focus one’s attention if you want to succeed (whatever your definition of success is), but we need some novelty. This is why it’s important to find balance, or else you will quickly become disenchanted by your academic career. And, if you’re anything like me, this is something you don’t want. We all got into academia because we loved learning and asking questions. It would be unfortunate to leave because we did too much of it.
If you want to be in academia (long past being a student) for a long time without burning out, my suggestion is to find a way to achieve balance as quickly as possible. At the risk of sounding melodramatic, forgetting about this is risking your future health.
The Grit to Push Through
If you ask someone what the point of a mathematics or science degree is, chances are they will tell you a tale about becoming a great problem-solver and seeing the world through new eyes. This has become a sort of battle cry for many who want to encourage people to learn about science and mathematics. The problem-solving skills you develop during these degrees allows you to be valuable in a wide range of careers later on.
While this is true, I would argue that it’s not one of the main skills you learn as a student. Instead, the skill you develop is persistence.
Let me tell you a story. When I was taking a quantum mechanics class, the professor assigned homework from a textbook. A few of the problems were marked as “very difficult”. When I began working on them, I knew I was in for a long calculation. It’s not that the problem was difficult so much as it was time-consuming. I even knew what I needed to do, but it just took forever (and it wasn’t clear where to start).
Multiple times, I felt like giving up. I wanted to find a shortcut, some way to make this less painful to do. If I was being rational, I could have decided that my time was being wasted on such a problem. I would only lose a few points, so it wouldn’t be the end of the world.
Of course, I have the “lovely” problem that I can’t hand in work that isn’t completed to the best of my ability, so skipping the question because it was too tedious wasn’t an option. Even with the hours ticking by, I gritted my teeth and finished the question.
Was it worth the extra time to get a few more points? Not really. The tedious part was a bunch of algebra, which also meant that the problem wasn’t any more illuminating when I finished. In the moment, it felt like a thankless task. However, the benefit came later. What I learned from doing a problem like this is that I can get through it with perseverance. If I set my mind to it, I can get a problem done. This is what I believe to be one of the best skills I’ve acquired through my science and mathematics degrees. Being unreasonable and pushing through the tedium and difficult parts of a problem to see it to the end is important. If not, you will tend to give up when you should push through.
Having the grit to push through is a skill that’s much more applicable than to just mathematics and science. Grit is an essential part of doing work that is important to us. Whether it’s writing, drawing, dancing, practicing a sport, making music, working on a business, or doing science and mathematics, grit is what helps us make breakthroughs when everyone else has given up. Plus, while it can be argued that others have more skill or talents from genetics or the environment, you control your decision to continue working when it seems useless.
This idea of developing grit during a science or mathematics degree is also why I don’t like having tests with time limits. Think about it. If you establish a time limit, you’re telling students to give up after this point. But isn’t it more impressive if the student keeps on working until they succeed? Sure, it might mean they have more trouble than others, but I would want to have that person on my team before the person that gives up after a few minutes.
One might object and say that people would all just stay until they get everything right, so the class average would be 100 (barring any mistakes). I don’t think this would be true, since my experience is that most students tend to give up quickly when they don’t know what to do. They don’t want to sit and think when they are stuck.
The point I want to emphasize here is that problem-solving skills are great, but I think developing grit is a skill that isn’t recognized as much as it should be. Of course, I’m not saying that we should persevere to the point of delusion, but being able to push past the initial point of discomfort is something we should all want to do. That’s why I think it’s one of the most important benefits of doing a science or mathematics degree, since you’re frequently put in the position of struggle. You learn that being stuck isn’t a bad thing, and is often temporary. You learn that giving up shouldn’t be your initial instinct, but one that is only considered after all other options are exhausted.
I know that this will be something I carry with me throughout my life, even if I don’t stay within the areas of science and mathematics forever. I’m thankful for learning this skill no matter where life takes me.
Behind the Equations
In secondary school, students in physics learn about the kinematics equations. These equations describe the motion of objects under a constant acceleration (often gravity). There are several equations, which describe the relationships between acceleration, speed, position, and time. In particular, here is one of the equations:
x(t) = x0 + v0t + at2/2.
This equation lets us find the position at any time t, since the other parameters are known. You might even recognize this as the equation of a parabola.
Students learn about this equation and the others during their first course in physics. They are then encouraged to write down all the equations, and decide on which one to choose based on the parameter that is missing. In the above case, the speed of the object at time t isn’t present.
I once was working with a student, and I could see that they did not see the link between the equations. Wanting to probe this a bit further, I asked, “Isn’t it a bit strange that this exact arrangement of terms describes how the position of an object changes with time? For example, why in the world do we need to have a t2 term in the equation?”
The student agreed that it did seem strange. At the very least, it wasn’t obvious as to why this combination of terms produced the right answer. After all, if you just look at the equation, there’s not much telling you if this is the “right” combination1. So what’s going on here?
Of course, the answer is that the equations do come from somewhere. They come from analyzing Newton’s equation F=ma under the presence of a constant acceleration. But if that’s it, why don’t students learn about this first? After all, they encounter Newton’s equation early on.
The issue is that one needs to use calculus in order to give a satisfactory derivation of the kinematics equations. In secondary school, students don’t have this background of calculus yet, so they cannot follow the steps (even though they are quite simple). As a result, students are presented only with the final answer. The derivation is left out. The implicit message is that the derivation isn’t that important.
The main consequence of this is that students end up seeing these equations as “magic”. In other words, they feel that there’s no way they would have been able to come up with these equations on their own. This is untrue, but the lack of derivation forces them to accept the equations on authority.
I hope you can agree with me that this is not a good situation to be in. Accepting equations on authority is in the opposite spirit of both subjects. This encourages students to memorize equations without understanding where they come from and why they are true. After all, if you know where an equation comes from, you don’t have to worry as much about memorizing it. If you forget it, you can always work it out again.
We are doing a disservice to students by forgetting about working out the details. We are teaching them that it’s more important to know how to use an equation than where it comes from. We are sending the message that equations and formulas are something to be recalled, but the proofs themselves don’t matter.
Yes, it will take more time to present the material. That means there won’t be as much time to do practice problems, and the pace might be slower. But students want to learn about the explanations behind the equations! I’ve found that students are interested in finding the connection between the formulas they have and the concepts they learn. It’s much more satisfying to be able to connect these in one’s mind, and students agree with me.
Therefore, we need to move beyond only presenting formulas. This will require a lot of work to create proofs of equations that students learn. It will also require creativity in the presentation, which is where the expertise of the teacher will come in.
I’m not suggesting that everything needs to be proved. Even in university, some proofs are skipped due to time constraints. But don’t let results stand on their own. If you don’t have time to prove them, give the students the appropriate resources so that they can look at the connections on their own. Do all you can to make sure that students aren’t forced to accept statements and equations out of the blue. If the students don’t have the requisite background, explain that to them. Don’t just say that “it works”. Give some intuition so that their explanation of a concept doesn’t only involve stating the equation.
Our purpose in teaching these concepts should not be about the results. It’s about the links between concepts and the way of thinking that is important. Proofs exemplify these principles, while the formula at the end is just a nice endpoint. The real learning comes through understanding where this equation originates, not the fact that it works.
Anyone can learn to substitute numbers into an equation and get an answer. But why does this equation do the thing you want it to do? Is this form particular, or are there different ones that can be used? Does the equation seem surprising? If so, can a student work from first principles to get back to that equation? These are the questions that should be asked more often in the classroom.
Behind every equation lurks an explanation. Don’t be fooled into thinking the equation itself is the point. Always shine a spotlight behind an equation to illuminate its origin and the reason it works.
The one thing that you could argue is that the dimensions of both sides of the equation are the same. If you look at each term, they all have the dimensions of length, so that matches up. It doesn’t explain why there is a 1/2 in front of a term, though. ↩
Quantities in Context
One of the differences between physics and mathematics is that mathematicians don’t tend to care about the units they are working with. In fact, they will usually consider all quantities as unitless1. This makes it easy to compare quantities, because one only has to look at the number itself. If you have two numbers, 5 and 9, you know that 9 is the larger quantity.
In physics, however, the situation isn’t quite the same. That’s because our quantities have dimensions attached to them. As such, it doesn’t make sense to say that 5 L is larger than 3 m, since they don’t describe the same property of a system. Therefore, in physics we require more than just a comparison between the value of numbers themselves. We want the dimensions of the quantities to match up as well.
Things can get tricky though, because different people use different units to describe the same dimension. For our notion of length, we have plenty of units, from the metre to the yard to the light year. They all represent length, but there’s a huge difference between one metre and one light year. From this, we conclude that in addition to requiring quantities to be in the same dimension in order to compare them, they also need to have the same units.
A related notion is that of a quantity being “large”. If anyone tells you that a quantity is large, your first question should be, “Compared to what?”
There is no such thing as an “absolute” size. In other words, a quantity can only be large compared to something else. You might think that 300,000,000 m is an enormous length, but light travels that distance in about one second, which means that a light year is about 31.5 million times this length. As such, it doesn’t make sense to only say that 300,000,000 m is large. It needs to be compared to something else. Only then can the notion of “large” have meaning. (Think of it like an inequality. You can’t have an inequality with only one quantity. You need two.)
If this seems like it can get messy with all of the different units people use, you are correct. This is why many physicists like to use dimensionless quantities such as ratios. If the ratio involves two quantities with the same dimension, the ratio will “cancel out” the dimensions, leaving a dimensionless quantity. This is useful because it means one doesn’t have to worry about the units involved in the problem. No matter what units you use to measure my weight and your weight, the ratio of our weights will be the same no matter what instrument we use.
The next time you hear someone saying that a quantity is large, make sure to remind yourself what they are comparing their quantity too. Without doing this, there’s a chance for misunderstanding or manipulation. Therefore, don’t jump to conclusions when numbers are thrown around with the implication that they are large or small. Demand another number to compare it to!
Actually, theoretical physicists like to do this too, since everyone agrees that dealing with units can be annoying. This is why you might see physicists saying that the speed of light is c=1. ↩