If You Can't Explain It...

There is a common saying with a variety of forms that generally goes like this:

If you can't explain it simply, you don't understand it well enough.

You do not really understand something unless you can explain it to your grandmother.

If you understand something, you can explain it in its simplest form.

If you can't explain it to a six year old, you don't understand it.

I disagree with this saying. The ability to explain something well is a skill separate from the thing you're trying to explain.

Consider a watchmaker who can make intricate watches that work correctly, but who can't tell you why certain pieces go where they do. Not only can he build watches, but he can also innovate designs to make them better. Does he understand watchmaking? Clearly, he does, otherwise he wouldn't be able to make them work at all. His inability to explain is a problem with his communication skills, not a problem with his understanding.

Further, how difficult something is to explain depends not only on how well you understand it and how good you are at explaining, but also who you're explaining it to. This is the concept of inferential distance. It's a lot easier to explain calculus to someone who understands algebra than it is to explain it to someone who doesn't even understand arithmetic.

And if you're really good at certain forms of communication, you can explain something that you don't understand at all (though not correctly).