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).

Inferential Distance

Suppose you're trying to teach someone calculus. Before they can learn calculus, they have to learn algebra. Before they can learn algebra, they have to learn arithmetic. This is the basic idea of inferential distance - background knowledge needed the understand the matter at hand.

Put this way, it looks simple, maybe not even worth talking about. But it's more subtle than that. To start with, arithmetic, algebra and calculus aren't single subjects. They're a whole bunch of related but still different subjects, which need to be learned independently. The learn integration, you have to learn differentiation, before that you have to learn limits, before that functions, variables, division, mulitplication, subtraction, addition... And don't forget the really fundamental things like what a number is.

And that's the really tricky part of inferential distance. There are a lot of things you know that you don't know you know. That is to say, you know them so well, it doesn't even occur to you to that someone else might not know it. Things that are so fundamental to your point of view that they're invisible to it. And so when you try to explain something to someone, you accidentally skip over a bunch of inferential steps, resulting in misunderstanding and each party will walk away thinking the other is stupid or crazy.

Consider a biologist talking to a creationist. They might try to explain the evidence for evolution, but before the creationist can understand that, they have to understand what evidence means, how science works, maybe even something as simple as why truth is important...