What does it really mean to understand something? I think it comes down to being able to take the topic and mould it, depending on who you’re presenting it to and what angle you’re looking at it from. It’s being able to actually connect the topic to other topics you know, or apply it to different scenarios you haven’t seen before. A physicist who truly understands gravity can explain it to a child using a trampoline analogy, to an engineer in terms of vector fields, or apply it to model the trajectory of a new spacecraft they’ve never worked on before. A barista who truly understands how to make coffee can adjust the grind and brew method depending on the bean’s origin and the customer’s taste. I think there’s a fundamental property of truly understanding things where your overall knowledge is greater than the sum of its parts. If you don’t truly understand something, it’s like you just have a PDF file in your brain, where you can read it, but you can’t “mould” it based on the scenario. But if you understand something, it almost becomes a part of you, rather than something you’re just “holding.”

A subset of this type of “moulding” is being able to break down the topic into simpler terms. Richard Feynman believed that if you truly understand something, you should be able to explain it simply. I think of Michelangelo, who said “I saw the angel in the marble and carved until I set him free.” The sculptor doesn’t begin by chipping aimlessly. They study the stone and carefully remove only what doesn’t belong. Simplifying an idea works the same way. You need to see the whole shape clearly, and only then can you strip away the rest without losing what matters.

Another part of knowledge involved in simplifying a concept involves metacognition, where you compare your own understanding to that of your audience. For example, a calculus professor might find it intuitive to think about limits using rigorous epsilon-delta proofs. But a really good professor puts themselves in the students’ shoes and imagines how the material might look when seen for the first time. They aim to make the explanation intuitive for the students, not just for themselves.

But on the other hand, being able to explain a topic in incredibly complex detail is also part of understanding. If simplification is like sculpting, this is more like building a cathedral, where you’re layering arches, windows, and flying buttresses in just the right places. Each addition adds complexity, but it also serves a purpose, and the result is coherent and deliberate. For example, picture a professor giving a guest lecture in an advanced undergraduate biology course. They begin with a basic diagram of a membrane protein involved in cystic fibrosis. As the lecture unfolds, they expand on how a single mutation affects protein folding, how that misfolding disrupts ion transport, and how it leads to symptoms in patients. They introduce lab techniques such as Western blotting and patch-clamp recordings, and then relate those methods to clinical trials using small-molecule drugs. The complexity builds gradually, and each part contributes to the larger picture, which ultimately helps the students understand the topics with extensive detail, rather than being lost in a pile of confusing jargon.

If you think you understand something, try unsettling it. Strip away the examples you usually rely on. Change the audience. Shift the context. What stays the same? What falls apart? The parts that still hold together when everything else is stripped away might be the parts you truly understand.