Julie Moronuki has a very special mind. I’ve always loved her essay The unreasonable effectiveness of metaphor. I am going to rephrase wholesale from it as part of my usual “active reading” style; if you want to know what she’s talking about you’ll be much better served by reading her essay instead.

Sometimes we’ll look out at the world and try to “cleave it at the joints” somehow. Sometimes there are “natural” ways to do such cleaving; for instance, we can take in noisy irregular real-world input and somehow intuit a property called “triangularity”, despite there not being a single thing in the real world that’s actually triangular. This is well-motivated by asking of a group of things: “which one doesn’t belong?” If you choose your examples well, it becomes possible to argue that any member doesn’t belong, which turns the exercise from the boring get-the-right-answer to the interesting let’s-do-mathematical-argumentation.

In some contexts, the properties that matter for “excluding outsiders” is obvious: color, size, shape. But sometimes it isn’t so obvious. Depending on context, sometimes we are called to see each member in terms of how it’s different from the rest, and sometimes we are compelled to see how they’re all the same. Julie gives the example of the mappend operator in Haskell; it’s instructive to come up with your own.

This is the point of abstraction: finding the ways things are the same and ignoring the ways in which they differ. It lets us make these things “law-abiding”, hence letting us “concretize new layers” that we can build upon (“generalize”) further.

This process, crucially, relies on analogy and metaphor – which are not quite the same thing. Analogy is the similarity between two things, usually thought of as finding the essence they share, and is the core of cognition; metaphor is the linguistic expression of this similarity, but more fundamentally it’s when we structure our understanding of one thing in terms of another.

When the former is something we can’t directly experience, this structuring is called conceptual metaphor. Some structuring is universal: all cultures talk about time in spatial terms, e.g. “bad times are behind us”. Some isn’t, like the “orientation of time”: the future “lies ahead” for us, but “lies behind” for some cultures.

Lakoff operationalizes the defintion of conceptual metaphor as “grounded inference-preserving cross-domain mapping”. “Grounded” means there is a “ground truth” or “source frame” we understand better and are mapping from. “Inference-preserving” means inferences that hold true “on the ground” are also true “at the target”.

(to be continued)