Beautiful Pictures Stuck in our Heads
Ask a mathematician or physicist to explain their work to you, and chances are you will hear them use the word “beautiful” at some point. This could reference an equation, a proof technique, an entire theory, or even just a nice piece of logic. They can talk to you for hours about this topic, explaining it in full detail with more enthusiasm than a lifelong sports fan.
And yet, even though I’ve spent a large chunk of my life studying mathematics and physics, rarely do I see this translate to the actual presentation of the idea.
It’s a shame. Here we have people who love their work and the ideas needed to explain them, but the actual byproduct which is created while teaching is far from beautiful. In fact, I would say that it’s often downright ugly.
How can this be?
I think it starts with the inability of many researchers to draw. They can only manage scribbles, and this takes away from any presentation of the ideas. This wouldn’t be a problem in and of itself, but then it’s coupled with a lack of caring for presentations. Most researchers don’t take the time to make their presentations optimal for the audience. Is it okay? Sure, but it’s far from great.
This translates to losing key aspects of beauty that these people claim is within the subject. There is beauty in a lot of these ideas, but when they get poorly executed in presentations, I shake my head in despair.
I’m convinced that the pictures these researchers have in their heads are great, but they are hidden from view. I can’t see them. The only way to get a glimpse is for the researcher to do the difficult work of bringing them to life. And like I said, this work isn’t easy.
How often have you seen a diagram on the board, only to be unable to read all of the labels? Perhaps you were lost due to the complexity, the terrible notation, or maybe it was way too small and cramped. The ways for communication to go wrong are numerous, and I have seen them all happen.
On the other hand, there are shining examples of presentations done right. I’m thinking of the work of Grant Sanderson or Burkard Polster, to name a few. When you watch their videos, you can see that care was taken to make sure the beautiful ideas are displayed in their best light. It’s not just something they say, but they show it. This distinction is important, and it’s what we should all be striving for when it comes to presenting ideas. It’s also not limited to animated videos. Jim Propp writes monthly essays on mathematics that capture the beauty of mathematics with mainly the written word.
Mathematics and physics have a lot of beauty built-in. But to appreciate it, we need to craft our presentations with care. Drawing a bad sketch on the board isn’t enough anymore. It takes away from the idea, and students deserve better. We now have the tools and the means to create presentations and explanations that do more than just give the information, but displays it on a pedestal.
Let’s get those beautiful pictures outside of our heads and onto the page.