Time For Reflection

When you’re going to school, it’s all too easy to dedicate an enormous amount of time to your studies. This is particularly true if you are in a difficult program and want to get the best marks possible. When you have your mind set on getting a certain average, it doesn’t always seem that unreasonable to push other things in your life aside in order to achieve that goal. I know this because I am in a constant struggle to stop myself from doing that, and I can see the effect it has on others that I know.

The problem is that we aren’t machines. After a while, we do get tired. I can’t keep on studying for hours and hours. After a while, I burn out, and I doubt it is only me. We can’t be hyper-focused on one thing all the time. Apart from getting tired and not having enough energy to focus anymore, there’s also the issue of stress. I’ve seen firsthand how stress can affect those who spend a lot of time on schoolwork. The most dangerous example of this is when students start skipping out on sleep in order to finish homework. I am saddened each time I hear of this, because it points to a shortcoming in how they’ve set up their lives. If one is cutting their sleep in order to finish schoolwork, their situation is not good (and I can imagine some scenarios where students don’t have a choice, but those are not what I’m referring to here).

It shocks them when I say I go to bed so early (compared to them), and that in the mornings I run for over an hour on average each day. They don’t get how I can still get my homework done, or how I choose to go to bed before a big test even though I didn’t get a bunch of time to study for it.

To me, the answer is simple: the best way for me to achieve my goals is to treat my body and mind well. That means taking a break from schoolwork at regular times and doing other things I enjoy. That’s why I go running each day and go to bed early. Running gives my body something to do and my mind a chance to just wander. It’s cathartic in a way. I’m not forced to think about school or methods of solving problems (though that is what I sometimes do). More often, I can just focus on the effort, which is a nice change of pace and one that I deem absolutely necessary for my well-being.

Therefore, my best advice to those going to school is this. Study regularly and become knowledgeable at your subject, but never sacrifice your time spent away from studying in order to do more school work. Without giving yourself something else to do to rest and recover, you risk burn out, which will be much worse than taking a regularly scheduled break.


I have to be honest: I’ve often not taken other disciplines seriously because I’ve always seen physics as the “purest” science there is. That means I would disregard biology, chemistry, geology, and social science, as well as the arts and humanities at large. I think the two other fields which I did have a certain affinity too was mathematics and computer science, since they were about rigorous logic. Other than that, I found the other fields mildly interesting at best, but never something to take too seriously.

Obviously, this shows how blind I was to the world in general. I had projected the somewhat arbitrary categories of education to the universe, even though it wasn’t at all a good reflection. It’s not that I thought that the other subjects weren’t useful or important, but I didn’t see any use for me to care about them. They were subjects for other students to worry about, because I wasn’t going to waste my time doing them.

This narrow view of the world was one I’ve thankfully grown out of. As I read more about science, I’ve started to see how all the subjects we have can be important to the world. Furthermore, I’ve seen how interconnected they all are. It’s nice and all to separate the sciences into their own domains, but at one point, everything boils back down to physics, so there’s a definite link between the sciences. Additionally, disciplines such as computer science are useful to physics, mathematics, biology, chemistry, and basically every other branch of science. With the massive amount of data we’re acquiring in experiments now, it’s so important to be able to know the ins and outs of programming and how computers work in order to do your experiments.

What’s also interesting is how many disciplines are blending into one another. Physics isn’t just in a bubble. There’s biophysics, geophysics, physics in the medical setting, and plenty of other examples in industry. Heck, a lot of theoretical physics couldn’t be done without having some knowledge of how computer programming works. Likewise, you can find these “blends” of disciplines within biology, chemistry, and other sciences. We don’t have silos anymore.

The other thing to think about is that some of the most interesting problems in science today will probably be achieved by merging different sciences. Just to give one example, the idea of consciousness being information-processing can be tackled on the side of living organisms, but it can also be looked at through the lens of AI and computer science. Of course, if this is true, it will be interesting to analyze the various particles and properties needed in order to exhibit what we call consciousness. This isn’t a one-discipline problem. It’s something that many of the sciences can tackle.

This is why I’ve been trying to do more to learn about other disciplines as well. It’s fantastic to learn more about physics, but I think it’s equally important to look at subjects like biology and chemistry, as well as computer science sand mathematics. I’m not saying that I want to become an expert in all of these disciplines (besides, an expert would only be on one branch of that discipline), but I want to see how the sciences connect together. I think it’s my duty as a scientist to make sure I keep myself knowledgeable about other fields in addition to my own.

And lastly, the arts and humanities. While I respect the wonderful work they do, it’s not an area that I find myself as interested in, at least professionally. I’m a person of science, and so I tend to stick within scientific fields, though I can see the use of philosophy (however much I may dislike some aspects) as an important part of discussing how we govern and build an ethical and just society in the future.

The point I wanted to share here is that school makes it too difficult to be aware of the various disciplines outside of your own. My classes are solely in physics, mathematics, and the odd computer science course. Therefore, I don’t learn about biology, chemistry, or any of the social sciences. As such, the picture I have in my mind of these fields is woefully wrong (I’d imagine), since I have little to no exposure. I think this is a problem, and so I try to address it by reading books and following smart authors in other fields who can bring me information on things I’ve missed from my own education. Of course, it doesn’t mean the information will be useful to me (in the sense that I’ll use it in my life in what I do), but I think there’s something great about being able to know a little about various disciplines. As long as I stay mindful of how little of a picture I’m getting from these small bits of information, I can develop a more fleshed-out story of what science has taught us, and that can only be a good thing.

Remember, as you go further into school, your work gets narrower and more focused. Don’t forget about everything else that is going around you, because you will really miss out if you ignore it all.

Playing With An Idea

When we learn new concepts in class, I think we tend to focus on what we’re taught, confining ourselves to the scenarios that were introduced in class. To be fair, that’s not a bad strategy, since most professors are only going to test the material that was explicitly seen in class. As such, there’s an implicit sort of agreement that students are not going to see any “surprises” on the test (not the euphemism).

But even though that’s true, I think there’s a huge benefit to looking at more than just the scenarios and cases that are outlined in class. In particular, I think it’s a useful practice to look at the edge cases of a concept, as well as alterations on the regular scenarios you’ve seen in class.

Just to give a brief example, consider the regular kind of differential equations you see in an introductory course. During this course, one learns about the various techniques that can be used to solve differential equations. One usually learns about integrating using the integrating factor and integrating via separable equations before they start learning about the characteristic equation.

If you were boring and didn’t like exploring, you’d cleanly separate each use case out and find ways to identify when one method should be used versus another. Or, you could be like me and try to skip the first techniques that I learned and try to apply the characteristic equation to first order differential equations, for example. It was here that I was able to try and see how the different methods could work and produce the same answer for a given equation. It also helped me gain an intuition about which methods are better for a problem.

Being good at a certain subject in mathematics or science can seem to others as though you have a magical ability to see things they don’t. One way to hone this ability is to explore different ways you can go about answering the same question. This may seem boring and repetitive at first, but the real reward is in the potential application of this experience to future problems. When you encounter a new problem that has given others pause, you might be able to solve it because you’ve already explored different ways to tackle a problem, and one of those ways can you help you out.

If you want to be good in mathematics and science (at least, on the theory side), it’s always a good idea to work on answering questions with multiple methods.


It’s not exactly a secret that I don’t like how mathematics is done in secondary four and five. I feel like the mathematics course for those not pursuing a career in STEM isn’t exactly the best use of a student’s time, because the curriculum doesn’t give students the full picture.

I just want to talk about one particular concept that drives me nuts: the parabola function. In secondary four and five, I studied them in essentially their full glory, looking at how a parabola is constructed (using a directrix), as well as the full equation (given by $f(x) = ax^2 + bx + c$). In the “science” flavour of mathematics for secondary four and five, you look at all of that. It’s more or less all you need to know about the function.

However, when you’re in the regular flavour of mathematics in secondary four, you still look at the parabola function, but it has been castrated. I’m not kidding when I say students literally look at the function as only this: $f(x) = ax^2$. Said differently, while I studied any kind of parabola on the Cartesian plane, those in the other mathematics class look solely at the parabolas with their vertex at the origin.

The only question I can think of is, “What’s the point?” If they aren’t even going to look at parabolas in general and confine them to the origin, is there any real use to showing them? I mean, you literally cannot make a physical example of throwing an object because the parabola at the origin won’t describe that sort of motion! The classic use case of the parabola isn’t even applicable to these students.

I think it’s a shame that these kinds of topics are in the regular secondary mathematics. In my mind, they are just filler for the year, because there’s no further explanation of them when there is so much more they could look at (without too a lot of added difficulty, either). I just don’t get how concepts like these can be shown in the form that they are now.