How Do You Make a Good Analogy?

I’ve long argued that good analogies are a key to learning well. Abstract subjects like math, science and philosophy are difficult to learn because they aren’t anchored to anything in our experience. Analogies moor these ideas adrift.

But analogies are also hard to construct. They’re a creative act, so there’s no step-by-step which will produce them reliably. Their formation also depends on the very insight they are trying to generate. Therefore, a good analogy can be impossible to make when it is needed most.

I want to share my thoughts on what makes an analogy good, as a learning tool. Then, I’d like to share some tricks I’ve found to make them.

What Makes an Analogy Good?

A good analogy is a compromise between two conflicting goals: familiarity and representativeness.

Good analogies are familiar. They express an abstract idea in terms of a familiar one. The odometer and speedometer on a car are a good analogy for a function and its derivative, because we all understand how speedometers work, but maybe not calculus.

Concrete experiences are good breeding grounds for analogies because they can be appreciated by anyone. When I say voltage is to the electric force what height is to the gravitational force, that is helpful because height is more concrete than electric potential.

But a good analogy doesn’t need to be concrete, it only needs to be expressed in terms of an idea you already know deeply. One of my favorites was from an MIT ecology class which expressed the idea of biological niche as a section of an n-dimensional feature space. If you didn’t study linear algebra, that may not make any sense, but it was widely appreciated by the audience who had a stronger math background.

That latter fact is important when creating analogies for yourself. Concreteness is good, but as long as you understand the analogous domain well, anything works.

Good analogies are also representative. They match at least some of the features of the idea you’re trying to explain. More matches means the analogy has more intuitive power. Fewer means you need to be careful about applying the analogy to understand new situations.

Making new analogies is like making a key for a lock you haven’t seen before. You’re limited by your past experience as to what kind of keys you can make. New key designs take a lot longer to learn than borrowing old ones. That’s familiarity.

But you also want the key to fit the lock. If the key shape deviates too much, it won’t open the lock. That’s representativeness.

How to Think of Good Analogies

Good analogies are like inventions. You can learn some rules to help dream them up, but ultimately it’s a creative act and can’t be fully controlled.

Like inventions, the best analogies aren’t invented wholesale, but built upon the work of others. When you’re learning something abstract, first try to look for other analogies people have generated.

If you can’t find one, you’ll have to make one. That process can be daunting, but there are a few steps to make it easier:

1. Gather examples

Examples are easier than making imaginative analogies which hop domains. In some areas, they may even be better. I always found economics and philosophy to be more amenable to examples than more cosmopolitan analogies which travel beyond their native subject.

Sometimes the analogy is an example. Speedometers aren’t just an analogy of derivatives, that’s what they actually are! Nothing will be more representative of an idea than an example of the idea itself.

Even if you desire a more creative hook to hang your thoughts, examples become a gateway to more imaginative understandings.

2. Pick fertile ground

My next step, if I want to force an analogy out of a concept, is to look for a setting where I might be able to generate one. There are some grounds which are more fertile for harvesting analogies than others. Here are some of my favorites:

  • Children playing. The rules of games children play can be very flexible to fit many different patterns and the games themselves are easy to imagine. I once used this to remember the Cournot competition model by imagining a game where children had balloons which they could steal from each other to get more, but doing so would also pop some of them.
  • Soap-opera drama. Affairs, romance and class systems are also good fertilizer for analogies. Imagining the periodic table of elements as a town where the inhabitants have different personalities—an affluent class of noble gases, coercive halogens and gullible alkali metals.
  • Simple physical systems. Unusual systems can be described using more familiar physical ones. Electric circuits are a system of pipes with bottlenecks (resistors), pumps (batteries), water flow (current) and different heights (voltage).

The key is to start with a fertile domain and then start matching features. For the Cournot competition model, I started with children playing, then added:

  1. They need to be competing over something. Let’s make it toys.
  2. They need to be able to act selfishly. They can steal the toys too.
  3. They need to reduce the total when they act selfishly. Switch toys to balloons, now some pop when there’s stealing.

3. Compare and contrast.

No analogy is perfectly representative, unless it is actually the idea itself. Even examples fail to generalize perfectly, which is why we have abstractions in the first place. A speedometer may be a derivative, but it doesn’t go negative when you change directions.

One way around this is to examine the metaphor more closely. Where does it match the idea? Where does it not? Just doing this exercise will improve your understanding, even if you don’t modify your analogy as a result.

My last example used balloons and children to explain an economics model. But some features of the model are hard to force into this analogy. The model says that firms make their decisions in advance, that doesn’t correspond well to children playing. In the model, nobody is stealing, rather it’s their decision to produce more which increases supply and reduces prices for everyone. In my analogy, children are presumably stealing from a specific person, not a general pool.

Going meta, keys and locks are an analogy of analogies and ideas. Keys have features which attempt to match the features of the lock (similarity). But a lock either opens completely or not at all, whereas an analogy can give a partial explanation for some parts and not others (difference).

An Appreciation for Good Analogies

I appreciate good analogies like art or inventions. An analogy compromises between familiarity and representativeness, with good analogies choosing just the right amount for the context.

The best analogies not only explain, they inspire. They pour color into a featureless void and breathe life into something static. They make the entire subject they cover more beautiful and interesting. Good analogies aren’t just tools, they’re art.


  • Greg

    I’ve noticed analogies can be extrememly powerful in learning and comedy, which I believe is correlated with intelligence. Personally, I could use a lot of work in improving the way I construct analogies. I guess practice makes perfect. I’ll be paying more attention to these when learning a new subject going forward.

  • Sebastian Aiden Daniels

    I do appreciate a good analogy. They do make learning easier. I like the advice of fertile ground. Using soap opera drama for the periodic table is brilliant. I love it : D. IF you can figure out some good analogies then you can make brain tracks and easily go from one subject to another.

  • Stephen

    I liked the way you used an analogy to describe analogies. very clever.

  • Olga

    Regarding fertile ground, I’ve found that deep knowledge of a particular field or discipline helps spawn analogies to other completely unrelated things. For example, at the height of my pianistic training, I could make an analogy from practice or performance to almost anything I put my mind to. Often analogies would just occur to me in ‘eureka’ moments – a wonderful and poignant experience!

  • Cody Mann

    I have often tried to create a system of memory palaces to remember things in my field of study. Analogies are a huge part in association because, like our brains, we think about things best when there is an association between something we already know and that. In stumbling upon meditation I am much better at making a key association between two things because meditation takes all the distractions away, leaving crystal clear clarity and focus. This was a great article and I appreciate you taking the time out of your day to share this very valuable knowledge with us 😀

  • VCB

    Yo.

    I’m not quite sure why you’re so fond of analogies and metaphors. “They facilitate understanding,” you say, (Okay, okay – I don’t know if you’ve actually said that, but the fictitious Scott figuring in my thoughts just did. And hopefully he’s speaking for you, too.) but the relevant question isn’t whether making up some analogies is better than doing nothing; it’s whether analogy making is more valuable than engaging in some other relevant activity, all things considered. If constructing a satisfactory analogy takes you as long as it does to work through some additional examples, or to articulate interesting questions about the thing you’re studying, or constructing an argument for… whatever, why would you choose analogysmithing? And I’m not just being negative here – I genuinely want to know.

  • James Jesson

    I really appreciate this post. I oftentimes find myself craving analogies when I am turning over a concept in my head. Moreover, I usually end up very frustrated when one does not come to mind right on the spot. I can be oddly perfectionist when it comes to this and obsessed with getting a perfect feel or fit to what I am trying to express.

    For instance: I read this morning about how a political candidate suggested that a solution for income inequality would be to allow low-wage workers or part time employees the option to work longer hours. This seemed ridiculous to me and for some reason I desperately wanted to come up with an analogy for this claim. Basically, I’m trying to think of a scenario where there is a problem where there is a rather clear solution, but someone advises someone to do a certain act that is much more effort that would clearly be fruitless in solving the problem to obtaining the desired goal. I came up with many different ideas but each one of them had something slightly off to it…sort of how you described above…and so I kept being dissatisfied!

  • James Jesson

    I really appreciate this post. I oftentimes find myself craving analogies when I am turning over a concept in my head. Moreover, I usually end up very frustrated when one does not come to mind right on the spot. I can be oddly perfectionist when it comes to this and obsessed with getting a perfect feel or fit to what I am trying to express.

    For instance: I read this morning about how a political candidate suggested that a solution for income inequality would be to allow low-wage workers or part time employees the option to work longer hours. This seemed ridiculous to me and for some reason I desperately wanted to come up with an analogy for this claim. Basically, I’m trying to think of a scenario where there is a problem where there is a rather clear solution, but someone advises someone to do a certain act that is much more effort that would clearly be fruitless in solving the problem to obtaining the desired goal. I came up with many different ideas but each one of them had something slightly off to it…sort of how you described above…and so I kept being dissatisfied!

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