Understanding, explaining and simplicity
One of the best ways to see if you actually understand something is to try to explain it to someone else. It very quickly exposes gaps where you thought you had a clear understanding but in reality, you just had a passing one. (This is also one of the things I like about math, and code - they are really other ways of explaining something and seeing if you really understand it).
We value clean, simple designs in many areas - user interface, code, even organizational structure. But we often don’t get designs that are as simple as we want - why is that? Well, simplification is, again, another form of explaining things. To simplify something, you have to be able to break it down into it’s most fundamental, irreducible pieces and then only present exactly what’s needed. This is almost exactly the process of explaining something to someone - breaking it down into just those ideas you need to understand it.
So - just as trying to explain something will expose how well you understand it, trying to *simplify* something (a design, a team, an email) will show you how well you understand the problem. This is very useful - usually the instinct is to add to a design until it seems to do what you want. But the real trick is to take away, until you understand it will enough for it to be simple.