Good explanations are written for people who don't know. They start from zero, assuming you've never seen the trick before, making sure not to skip any steps. Skipping steps of an explanation is just another way of saying you should already know this. A good explanation takes you by the hand, shows you the pieces, and only then puts them together, making sure you understand how each part fits.
The test for whether something is a good explanation is simple: could a smart beginner follow it? If yes, then it's good. If the only people who nod along are the ones who didn't need the explanation in the first place, then it's bad. Good explanations open doors, bad ones just show you that the door exists, and expect you to already have the key.
Take the Fourier transform as an example. A bad explanation might say, it's just projecting a function onto a basis of complex exponentials and move on. If you already know what that means, you nod along. But if you don't, you're left in the dark. The explanation is really just a password for insiders. A good explanation, on the other hand, starts from the ground up: it introduces the basic concepts, explains what a "basis" is, what "projection" means in this context, and why complex exponentials are relevant. It might walk through a simple example, step by step, showing how the process works and why it matters. A good explanation relies on clear definitions, analogies, and careful unpacking of each step, making sure the reader can follow the logic. The key is to build up the necessary background and connect each new idea to something the learner already understands, so that even the most abstract concepts become accessible.
People rarely invest enough time or effort to explain things clearly to each other at work. Too often, knowledge is passed around in shorthand, with the assumption that everyone already knows, or that people will just figure it out. But this leaves newcomers and even experienced colleagues confused, slows down progress, and leads to repeated mistakes. This connects directly to why I think clarity is speed. When explanations are bad - when they only make sense to people who already know - teams waste time. People stop asking questions, make wrong assumptions, or worse, pretend they understand and make mistakes later. Good explanations, like clear communication in general, eliminate this friction. They let everyone move forward with confidence, knowing exactly what's expected and how things work. The investment in a good explanation pays dividends every time someone new encounters that knowledge, just like clear conventions and processes pay dividends every time the team makes a decision.
Interestingly, the most talented engineers sometimes struggle the most to explain things to beginners. This seems counterintuitive at first: shouldn't the people who understand a topic most deeply be the best at teaching it? But deep expertise can actually make it harder to remember what it's like not to know. When you've internalized a subject so thoroughly, the basic steps and concepts become second nature, and you may not even realize which parts are confusing or unfamiliar to someone new. As a result, experts sometimes skip over foundational ideas, use jargon without thinking, or assume background knowledge that a beginner simply doesn't have. This "curse of knowledge" means that the people best equipped to solve hard problems are sometimes the least equipped to explain their solutions in a way that others can follow. That's why the best explanations often come from people who still remember what it was like to be confused, or who make a conscious effort to see things from the learner's perspective.