Analogies as the engine of thought

The recent conceptual obsession has been the concept of an analogy. Douglas Hofstadter has a book called Surfaces and Essences where he argues that analogy is a crucial capacity in human thought. He claims, in fact, that analogy is the central engine of thought. Let me try to explain how.

What is an analogy? It’s basically a connection between concepts. You’re a child who lives in Paris, and you learn that Paris is in France. And you meet a child who is from London, and London is in England. And someone makes the comment to you that Paris is to France as London is to England. You’ve now made a connection between those two pairs of concepts: <London/England> is linked to <Paris/France>. The link has a name: “capital city.” Now you have “capital cities” as a category in your mind, and it contains a number of elements like <London/England>, <Paris/France>, and you add more items to it over time, like <Berlin/Germany> and <Rome/Italy>.

What if every concept you ever learned vaguely followed this trajectory? You had a pre-existing category or concept in mind, like “kitchen” and “bathroom.” Someone tells you that they are both examples of “room”. Now those two items have a link in your mind. There is an analogy taking place because there are structural similarities between “kitchen” and “bathroom” – they are both physical spaces inside a house, they are both vaguely cordoned off by walls, and they both act as a supporting context for specific human activities.

So we can think of an analogy as “making a connection between two concepts in your mind,” and that connection has some richness to it given the shared features of those two concepts, and the connection serves to form a category containing those two concepts (and potentially many more concepts), and the category might have a name (e.g. “room”, “book”, “large”).

Woah – did you just say the word “large” is a category, born of an analogy? Yes, I did just say that. You see, we have to ask the question of how you ever learned the concept of “large”, how you were taught what the word “large” means. Well, by the standard picture of language acquisition, you learned the meaning of the word “large” through usage – you observed people using that word, and you did some pattern-matching to figure out what was shared between the various situations in which that word was used. So, you learned saw that it was used in the context of talking about pizzas, t-shirts, intestines, and boxes. And you learned that it means something like, “of a bigger size, in contrast with smaller sizes that it could hypothetically be.”

You learn at some point that the word “large” and the word “big” are strongly overlapping categories. That in more or less any place where one word is used, you could substitute it for the other. Voila, a new connection has been formed, an analogy. This analogy, you soon learn, has many other examples that fit it. “Large” is to “big” as “small” is to “little.” “Large” is to “big” as “small” is to “little” as “smart” is to “bright” as “fast” is to “quick.” This category has a label of its own: synonym.

So we can think of the concepts in our head as points in conceptual space, except that new concepts are formed out of connections between previous concepts, and that indeed, any given concept is just a glue connecting yet other, more primitive concepts. “Mother” is a concept that glues together your actual mother (perhaps labelled in your mental lexicon as “mama”), your cousin’s mother (perhaps labelled as “Aunt Jenny”), your childhood friend’s mother (perhaps labelled “Barbara”). When you were very young, those were discrete, separate concepts, and at some point you learned a connection (an analogy) between all of them, and that analogy was labelled with the word “mother.”

Analogies are the handles by which we can grasp abstract concepts. The only reason we can grasp abstract concepts at all is our capacity to form analogies – to make connections between less abstract concepts. When you look at the development of language in children, it starts with very tangible, concrete words like “ball,” “Mom,” “Dad,” “dog,” and so on, and slowly you get to more abstract words like “red,” “fair,” and “proud.” ¹ What is actually happening when you grasp an abstract concept like “power” is that you’re effectively bringing to mind slightly more primitive concepts like “big,” “authority figure,” physical threat,” and so on, and some of those are made of more primitive concepts, for example “authority figure” might be an amalgamation of “my strict principal from first grade” and “the fifth grader who was really mean to me one time.” So “power,” which is a pretty abstract, high-level concept (good luck teaching that to a toddler who only knows thirty words), is a constellation of these more simple concepts.²

Now, here is where we get a modicum of practical wisdom. If you want to think clearly and have productive conversations, it’s worthwhile to inspect the analogies that implicitly make up the words you use. Each of us has a particular web of meanings, memories, and concepts that are loaded up in the words we use, and understanding this helps you speak more clearly about them. The rationalists have a tradition of going “down the ladder of abstraction”, always bringing any high-level debates into the domain of concrete examples. So: if someone says, “information should be free!” rather than asking “what is information?” you can instead ask “should I not have to pay for my copy of To Kill a Mockingbird?. Or, when asking for what “green” means, rather than saying “the color that is midway between “yellow and blue”, you can say, “go to your nearest intersection, and when the cars move, green is the color that the stoplight is shining.”

I might go further than the rationalists in saying: it’s not just practically helpful to ground our abstract concepts in concrete examples, but that our abstract concepts are built out of these concrete examples. David Chapman makes this point when he says that abstract reasoning emerges out of concrete activity. What Hofstadter does in his book, in which he lists out hundreds of examples of how everyday concepts are undergirded by a vast web of analogies, is make this concept much more tangible.

The other practical takeaway from this view is to take analogies more seriously. They are not just clever tricks that make an essay more interesting – they are the very foundation of our understanding of the world, and the foundation of science. One of my favorite passages from the book is Hofsadter describing how the discovery of Jupiter’s moons by Galileo was itself a subtle example of analogy-making:

Not everyone would have seen what Galileo saw, even if they had been given a telescope, even if they had observed the celestial lights over several weeks, and even if they had focused on Jupiter in particular. The reason is that until that moment, the word “Moon” had been applied to only one object, and the fantasy of “pluralizing” that object was well beyond the imagination of anyone alive at that time (and if someone original had the audacity to think such a thought, that was sufficient to bring about their swift demise). Moreover, Galileo’s daring act of pluralization was the fruit of an analogy that might have seemed laughable to most people — after all, it was an analogy between the entire world, on the one hand (since for most people back then, the terms “Earth” and “world” were synonyms), and on the other hand, an infinitesimal dot of light. This analogy, which might seem far-fetched, nonetheless led to the pluralization of the Earth, since it began by taking Jupiter to be another Earth, and it was rapidly followed by the pluralization of the Moon, which naturally led to the lower-casing of the initial “M”. The concept of moon had been born, and from that moment on it was possible to imagine one or more moons circling around any celestial body, even around moons themselves.

When you realize that analogies are all you have, you can be less preoccupied with getting to the “fundamental essence” of a concept – whether it’s moon, power, or Mom. Instead you can just perpetually enrich your understanding of it, by both looking at the parts it’s made of (the memories and associations that underlie it in your mind) and the ways it connects to all the other things you know.