Jeremy Côté

Clarity and Words

A cornerstone of physics and mathematics is the process of labeling. If you want to learn any subject, you need to get familiar with the jargon of the field. In physics, terms like “work”, “resistance”, “capacitance”, “energy”, “potential”, and many more have precise meanings. Likewise, the terms “function”, “continuous”, and “one-to-one” have precise meanings in mathematics. When you first start learning the subject, it’s easy to be overwhelmed by the sheer number of terms. By the time you remember one term, several more have been introduced. Frankly, it can be frustrating and can ultimately turn you off from the subject.

Alternatively, I’ve also seen people just accept the words and end up using them without really knowing what they mean. We learn when these words apply, but we don’t have a mental picture of what the term means.

I’ve done this before, and I hate it. I feel like I’m a fraud, using terms to blend in with the others, hoping no one asks me any questions that are too specific. To give you a simple example, for the longest time I didn’t have a good conception of what a dielectric was. I simply associated it with something that popped up in my studies of electromagnetism. I never really thought of what it was. By the time I wanted to know the answer, it felt strange to ask. Nonetheless, I asked my professor and he explained that it was simply a non-conducting material.

Upon hearing this, I was immediately able to understand what he was talking about. That’s because I have a mental picture of what a conductor is. It’s a material that has mobile electrons which can move around and produce a current. Therefore, a dielectric was the opposite of that, meaning a sort of insulator. This definition made sense to me, and it allowed me to fill this hole in my knowledge.

I think a lot of terminology we use is stupid. It often only makes sense in hindsight, but a good majority of terms have no relation to their actual meaning (think of ideas named after people). This is needlessly confusing for beginners. I understand that we sometimes have terms that just stick in the canon of a field, but it’s something I fight against whenever I can.

What I find amazing is that we carry these holes in our knowledge all the time. There are terms we don’t know, but we go through our education without figuring out what they mean. I get it, a lot of terms are stupid and a description would be better. However, we can’t easily change what the majority of physicists or mathematicians do, so we need to become comfortable with the terminology.

I would suggest to avoid using terms you don’t know. This is something I try to adhere to all the time, because it’s precisely where your ignorance gets put on display. If you start using terms because you heard them from others (but you don’t know what they mean), you’re setting yourself up for questioning. This will only create an awkward situation in which you can’t explain what the term is, even though you used it. You will look ridiculous, and it isn’t a good learning experience for you. Instead, use the words and terms that you do have a clear mental picture for, because this will make explanations so much easier. I’m not saying you can’t get anything wrong, but be honest with yourself about what terms you do and don’t know.

Mental pictures and pinpointing misunderstandings

Terms might not be fun to learn and memorize, but they provide a springboard for launching new ideas. If everyone has the same idea of what “energy” means, there won’t be any debate when we use the term. This makes conversations easier, so it’s worth building up those mental images of various terms you learn.

When I’m working with a student and they don’t understand something, my greatest wish is to peek into their minds and see what they’re imagining. If I could do this, it would be so much easier to help them out. I know that a lot of misunderstandings stem from talking about the same word, yet having different mental pictures of what’s going on.

This is why I like to draw diagrams and pictures while teaching. My hope is that, by sharing a little about what I see for the problem, the student will be able to figure out where our thinking diverges. They can then stop me and we can have a more fruitful discussion about what’s happening.

Understanding the jargon of a field is a process with a steep initial learning curve that slowly gets easier with time. There are two important points to remember when learning the terms. First, make sure you have a mental picture of what’s going on. There are so many tools available for effective visualization that there is virtually no excuse for not having a good sense of what a term means. In physics and mathematics, diagrams are super helpful for this. I could tell you in words what it means to have a four-vector that is spacelike or timelike in general relativity. Or, I could just show you a diagram that makes this distinction clear. This really is a situation where a good diagram is worth a thousand words.

Second, avoid using terms you don’t know. This sounds simple and obvious, but it’s funny how often I find myself in situations where using words I don’t know can occur. This is a bad habit to have, and it’s one I recommend you avoid as much as you can. If you feel like you’re going to use a word you don’t know, I recommend asking someone else for clarification about what it means. This then lets you use the word without falling into the trap of saying words which have no meaning to you.

Finding your footing in a subject isn’t easy, but having a good grasp of the terminology certainly helps. The best way I’ve found to boost your knowledge is to build a lot of mental pictures of the terms. Then, you can refer to them when you hear them versus having a completely blank mind.

Don’t let yourself be swept up in the sea of confusing terms. Build yourself a raft, and learn to be comfortable with the ideas. (No matter how stupid the names are!)