Why to explain things you already know

I gave the following explanation on my community discord earlier, in response to a question about what the #honk-things channel was for:

This was a joke response, in that it’s not actually that helpful to the person who asked the question, but it’s actually useful for an entirely different audience: People who are already part of the discord community, participate in its culture, and understand it well enough to participate in it. It helps them understand explicitly things that they would previously have understood implicitly and fits together two aspects of the culture they might not have previously seen fit together.

There’s a passage I’ve always liked from Thomas F. Green’s “Voices: The Educational Formation of Conscience”:

[…] philosophy is essentially en- gaged in what I have described elsewhere as unwrapping the ordinary, namely, revealing for understanding what we already know to be so […] It seeks simply to expose those truths and restore to them the power of truth. The aim is that at the end of each step the reader will say, "I knew that." The hope is that to such a test the reader might be disposed to add, "But now I understand and see better how to educate."

In many circumstances, there are useful explanations that are explaining something to someone that they already understand, but doing so in a way that they might not have previously understood it.

As well as philosophy, you’ll often do this in mathematics where you provide alternative proofs of an existing result. Sometimes this is to help you understand the result better, sometimes it’s to help you understand a proof method better, sometimes it’s just for fun, but either way it helps you join the dots between things you already understand.

This sort of explanation is, technically, compatible with what I’ve previously written about how explanation works:

There are exactly three things you need to do in order to explain things well:

1. Decide what you want to explain.

2. Find out what the listener already knows.

3. Express the first in terms of the second.

Nothing here is incompatible with the above example, but I was definitely implicitly assuming that the thing in (1) that you decided you wanted to explain wasn’t something they already understood.

My internal metaphor for this is/was that you’re performing a sort of stacking of knowledge, where you’re adding something on top of a foundation made available by the user’s existing body of knowledge.

Given this metaphor, one might reasonably think of this sort of explanation of new things in terms of old things as vertical explanations - explanations where the links go up and down between old and new knowledge. In contrast, explaining things you already know in terms of other things you already know is a lateral explanation - something that ties together things that are already part of your knowledge, without necessarily increasing it.

Whether an explanation is lateral or vertical depends a lot on who the audience is. e.g. I often read books about things I already understand as part of trying to understand how they are conveyed to others (and also because I usually only 80% understand them and want to flesh out some of the 20%, but many of the useful bits are lateral), although generally you’ll want to tailor the explanation to more explicitly match the audience.

Something this distinction is useful for is a problem I’ve wondered about off and on, which is finding a good general transmissible solution to one key problem with explanations, which is what you do when you need to stack explanations - I want to explain A to you, but in order to do that I need to explain B to you, and in order to that I need to explain C to you, etc.

What I’ve generally found is that this doesn’t work. A single vertical explanation is good enough to give people a rough sense of the thing being explained, but it doesn’t really result in a very solid understanding, meaning that whatever you try to build on top of it doesn’t end up well enough supported to build a very functional understanding.

Previously I’ve just written this off as the difference between explaining and teaching, with teaching requiring a lot more engagement with the student than simple explanation. I still think this is true to a large degree.

But given that one of the benefits of lateral explanation is that it fits things together, it gives you a (to extend the metaphor) broader and more solid foundation to build upon. This should make it easier to build vertical explanations on top of that.

You don’t necessarily need to do this up front, but at some point (if you’ve created a good safe environment for asking questions) in the course of a stacked vertical explanation they’re going to seem confused and you might have to go back to explain some earlier part. When you do that, taking advance of lateral explanations to pull in other things and see how it all fits together seems likely to help.

Also, I think lateral explanations are just good in general, and should be a more normal part of our social environment. A lot of what I write implicitly fits into this pattern¹, and explaining things this way can be the basis of a lot of good conversations.

People are I think resistant to this. It’s possibly a school legacy, possibly a status thing - having something you already know explained to you feels condescending - but hopefully by noticing some of the good things these explanations do for you they can start to feel better to be on the receiving end of.

1. Although it introduces some new terms, I think most of this article is basically a lateral explanation - I doubt you’ve learned anything particularly new from it, but hopefully it’s still useful.