Pictures, Stories, Models

for Andrew Gelman

Simplifying somewhat, pictures represent facts, stories represent acts, and models represent concepts. Did you see what I did there? What does “simplifying” mean in that sentence? Is it a simplification to say that pictures, stories and models do these three distinct things? Or do they do these things while simplifying something? The sentence doesn’t commit itself to either reading; it is ambiguous about what is being simplified. And it turns out that I mean it in both senses. Pictures are simplified representations of facts and to use this to draw a hard and fast line between pictures and stories and models is itself a simplified picture, story or model of pictures, stories and models. Sometimes a picture tells a story. Sometimes a model represents a fact. The world is a complicated place and the mind is a complicated instrument for making sense of it. Still, simple distinctions can be useful, so I ask you to indulge my simplemindedness for a few paragraphs more.

When I say that a picture represents a fact I mean that it makes an arrangement of things present in your imagination. It’s true that we sometimes also try to imagine what is “going on” in, say, a painting, but we know that this is an extrapolation from the facts it represents. There’s also usually a whole atmosphere or “mood” in a picture, which is hard to reduce to a mere state of affairs. In David Hockney’s “A Bigger Splash,” for example, the fact is a splash of water in a pool with a diving board. We don’t know exactly what made the splash but we assume it is a person. There’s a feeling about the scene that I will leave it to you to experience for yourself, but we can imagine a photograph representing roughly the same facts. It could be made true or false by whether the state of things we imagine when we look at them actually existed at the time the picture was taken. Not just whether the things and people (the pool, the diver) existed, mind you, but whether they were in the state that the picture causes us to imagine. Pictures can misrepresent the facts. Even photographs can be doctored.

When I say that a story represents an act I mean that it gets us to imagine people doing things, or things happening to people. That’s a gross simplification, to be sure. It’s possible to tell a story about a pool freezing over or ducks landing in it. Things happening to things or animals happening to them. But I think we do actually always anthropomorphize these events a little bit when we tell stories, sometimes barely perceptibly. If we didn’t, I want to argue, we wouldn’t be able to tell a story. David Hockney painted “A Bigger Splash” in 1967, with no people visible in it, and then painted “Pool with Two Figures” in 1972. Jack Hazan saw a story unfolding in the intervening years and made a film about it. Like most stories, indeed, it is about what some people were doing at the time, what happened to them, how things affected them. They are true or false according to whether the acts they cause us to imagine actually took place. Was London really like that in 1970s? Did Hockney actually lose a lover? Did it actually inspire a painting? Perhaps he did, but the film is no doubt a simplification of the relationship, just as the paintings are a simplification of the scenes at the pool.

Models are simplifications in perhaps more obvious ways. They will always represent only selected aspects of the reality they are modelling. When I say that a model represents concepts, I mean that they get us to imagine what it is possible to think about a certain population of things or people. Where pictures have to be accurate, and stories have to be plausible, models must be probable. Indeed, they are models of probabilities, which we can actually understand as “pictures” of probability spaces (rather than physical spaces like swimming pools). What is probable or improbable in a model is whether one thing, for example, causes another thing. Was the splash caused by a person jumping off the diving board? That’s certainly the most likely explanation. But there are other possibilities and they are (logically) no less compatible with the concept of a “splash”. How many splashes in swimming pools are caused by something other than a person jumping into them? What percentage? What are the chances? The model lets us know, but this does not tell us what exactly caused this splash. If it was a stone, the model that said it was likely to be a person is not wrong. We would need much more data to decide. Not to mention whether the breakup was caused by the man swimming towards the artist in the pink jacket.

Just as you can look at a picture of a splash in a swimming pool and read a whole story into it, you can hear a story about two artists and extrapolate a model of human behavior, a model of human suffering. It takes imagination to do these things, of course; you don’t just see the picture, or hear the story, or think of the model. You give them a place in your imagination, where the facts (the objective arrangement of things), the acts (the subjective intervention of people), the concepts (the possible arrangements of things) and even the emotions (the possible intervention of people) can meet. You then bring this imagery back to the seeing, to the hearing and the thinking, which allows new facts and acts, as well as new concepts, to enter the picture, to shape the story, to reconstruct the model. Next week, let’s talk about how to write these images down. After all, you don’t have to paint pictures or make films or draw graphs. You can put them into words on the page — a thousand words should do.

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