It’s tempting to imagine that if you see something, everyone else does too. After all, in our interconnected world, we tend to be reminded every day just how good other people are. This makes it easy to imagine that any supposed “insight” you may have has already been thought of before. Without the right mindset, this can create a situation in which you do almost no creative work, since you’re worried about wasting time on something that has already been done.
I have a few responses to this. First, the obvious one: by doing nothing, you’re wasting time. I feel this when trying to decide what to do next in my writing. If I think too much about what my future projects should be, the result is that nothing gets done and I spin in circles trying to find the new or original thing that no one has thought of before. The reality is that this just makes it difficult to do more work. If you’re always looking over your shoulder, nothing gets done.
Instead, I try and ask a different question. How can I make this explanation or exposition better? This shifts the focus from tackling a novel subject to just thinking about a familiar topic in a new way. What works in an explanation, and what can be improved? By asking myself these questions, I find it easier to move forward without worrying about being original.
Second, there’s value in going over the same topics again. I know, you’re thinking of how boring it is to hear about the same topic over and over again. This is true, but the issue is that you’re overestimating what people consume. On average, people probably sample a bit of everything. Furthermore, they don’t follow everyone, so if multiple people cover the same idea, they just won’t see it or won’t look at it. That doesn’t mean you shouldn’t do it. When I think about possible topics to discuss on the blog, I try to keep this in mind. There are two options. One, the person has already seen this topic, or two, the person is learning about this for the first time. I’ve found that even when I’m in the first case, I still enjoy going over an explanation I’ve heard before. I want to see how this specific person thinks about the concept, and I like trying to approach ideas in different ways.
Then, there’s the person in the second category. Those are who you should be aiming to serve. It’s not the end of the world if some people don’t read or watch because they are familiar with the topic. In fact, it’s going to happen, so there’s no need to stress about it. Instead, focus on delivering the best teaching experience you can.
Second, like the title of this essay says, people don’t think the same. You might think a particular way of looking at a problem is “obvious”, but I guarantee you that there will be people who haven’t ever thought of the problem that way. Just because you see this as the obvious way forward does not mean it’s obvious to everyone. This is particularly true with an audience of non-experts, but even among those that have some background, your way of thinking might not be the same. As such, I would say it’s almost a responsibility to communicate your way of seeing the world to others. I’m referring in particular to science and mathematics here, because there tend to be many ways to solve a problem. It’s valuable to come across different solutions. When I learn about a new way to solve a problem, I rarely think, “Oh, I’m good with my solution here. I’ll just skip this one.” Instead, I’m eager to explore a different way.
This brings me to my final point: we need more explanations. When people are learning a topic, they tend to learn better one way than another. This might come in the form of visual learning versus going headstrong through the algebra, but regardless of the method, some work better than others. I would argue that this implies we need to create more explanations, because that’s how we get everyone on the same page. When I’m thinking about how to get people to appreciate the utility of complex numbers, I don’t care if you come from the intuition of the two-dimensional Cartesian plane or if you learned about the complex numbers as a ring that “quotients out” certain polynomials. The end result is the same. My goal is to get you to that final destination, and there’s value in taking different paths.
This is why I write about science and mathematics. I may not help the majority. In fact, if that was my goal, I would write a textbook for students. Instead, I want to provide an alternative path for people looking for different treatments of concepts. Yes, that means it won’t be for everyone. Heck, it might only be for a few people. But I’m confident that it’s worth it, because treading a different path gives one a sense of how science and mathematics can be seen from different perspectives.
Create explanations, especially when they seem obvious to you. Chances are, you will provide a way of thinking about a concept that someone has never even considered. It’s easy to forget this when a concept is so clear to us, but it’s important if we want to communicate mathematical and scientific ideas.