Scott H. Young wrote an excellent article comparing and contrasting books vs. blogs for learning complex material. One point I found interesting was the idea that certain ideas need to be taught in book format since they’re too complex to be broken down into articles. I thought: I’ve been able to understand complex ideas both in article form and in book form. What allows complex ideas be able to be squeezed down to something as short as an article?
I think of complex ideas as ones that are situated deeply in a knowledge tree. That is, imagining a complex idea as a point on a tree, complex ideas require more branches, or prerequisites, to reach it, than simple ideas. To get to that point, you need to go through all the branches, understand them, and then you can understand the idea in question.
But some ideas follow patterns—patterns that people may have seen before in a different situation. Using an analogy is like compressing that knowledge tree into a more accessible format. By using an analogy, one removes the requirement of needing to understand all of those branches on the knowledge tree before being able to understand that complex idea. Instead, that complex idea can be communicated in a more compact way, using an analogy to fill in the points that would otherwise be time-consuming to understand. Analogies co-opt behaviors of patterns that we already understand to illustrate similar behaviors in the new idea.
An example: quantum computing
I think quantum computing is a pretty good subject to look analogies for. Here’s one, from bigb1 on Reddit’s Explain Like I’m Five (edited for clarity):
While a usual computer is like a mouse trying to find a way out of a labyrinth. A quantum computer would be like flushing the labyrinth with water and look where it comes out.
We’re already used to the pattern of how water moves through a space, and this explanation uses it to illustrate the idea that the power of a quantum computer is in its ability to find a solution instantaneously. Here’s a more detailed one by Rispetto on the same thread (edited for clarity):
Imagine you're in a maze, starting in the centre. There are a lot of paths going left, right, ahead, and backwards. Your typical computer will go "hmm.. lets take every single route until we find which one leads to the exit." So it begins the process of going through every route, until it hits a dead end, then starts at the beginning and tries again, avoiding the previous path. It is a slow process. Even though computers can do this very quickly (millions of attempts per second) if the maze is big enough it will still take increasing amounts of time.
A quantum computer works on an entirely different level. Instead of taking each path separately, it takes them all at once. Logically speaking, one of those paths is the correct one, so therefore it finds it much quicker than a normal computer.
This one expands on the idea of a maze to explain a bit more about the mechanism by which a quantum computer might solve a problem. We’re using the analogy of how we would move through a maze against how a quantum computer would. But these analogies haven’t really brought out how a quantum computer does that, only that it is able to basically do a lot of computations at once, more so than regular computers. (For a rough explanation on how they work, I think this video, which connects quantum computing to regular/classical computing, explains it well.)
We see here that analogies do a pretty amazing job of compressing a complex idea into a more digestible format. But while we’ve gotten the gist of what a quantum computer does, our understanding is imperfect.
Problems with using analogies
Analogies are lossy compression for knowledge trees. When you unpack an analogy, it’s not so much that you’re rebuilding the tree that leads to the thing that the analogy is pointing to. Unpacking an analogy is more like unpacking a ladder that gives you the capability to reach and understand that complex idea, but often skips details that are important to fully understanding that idea—like our example with quantum computing above. That’s obvious—but the gist is that one should cultivate a habit of skepticism and questioning when using analogies. When using an analogy to make sense of something, it’s best to try to be aware of where the analogy may be skipping details and what it is ignoring—like how this analogy of analogies being a ‘ladder,’ not the tree itself, is incomplete and doesn’t impart the full
Analogies can be surreptitiously invalid. Analogies are attractive because they give you the feeling that you understand something. But when we use an analogy, we have to not only ask the question of ‘does this make sense?’ but also ‘is this analogy valid in this situation?’ It’s easy to accept analogies that seem to allow us to make sense of things, but people often don’t question whether it’s valid to use a particular analogy in that case. For example, one could say that there should be fewer choices for healthcare plans in the health insurance market, tying it to the analogy that people have trouble choosing between many choices in other situations. That helps us make sense of the situation at hand (the number of choices of health insurance plans), but we also have to question whether the analogy to choice in general is valid in this situation. How might health insurance choices be different than other choices? Do people have an increased need, and thus potentially an increased propensity to spend time finding the right decision, when it comes to health insurance choices?
Yet, these aren’t reasons we should avoid using analogies to try to understand complex ideas. It’s much better to use an imperfect analogy to understand a complex idea (and potentially develop a desire to find out more) than to see it as totally intractable and hopeless to understand. We should keep in mind that analogies are lossy compression for complex ideas, and we need to question whether a given analogy is really applicable for a certain situation. But both of these pitfalls are actually great things—analogies give us a lens through which to view something complex and understand it well enough to ask questions about it.
Oh, and this entire article is an analogy between lossy compression and analogies, right? Damn, that's meta.