Broken arm semiotics, part II: Plaster cast, rheme, interpretant

…it has never been in my power to study anything, — mathematics, ethics, metaphysics, gravitation, thermodynamics, optics, chemistry, comparative anatomy, astronomy, psychology, phonetics, economic, the history of science, whist, men and women, wine, metrology, except as a study of semeiotic. (C. S. Peirce, in a letter to Lady Welby, 1908)


First, a medical update: I’m not wearing the brace any more, I’ve got most of my range of movement back, and I’m expecting to start physical therapy early- to mid-August. Still can’t ride my bike, though.

In response to my last post, a reader* writes in:

I think you forgot one thing in your thoughts regarding your brace–ambiguity. If it were a classic cast, people would know that you have a broken arm. If it were a splint, it would be assumed that you have a sprain. Both of these are temporary and traditional. But your brace does not reveal the same info. It could be permanent, or not orthopedic or you could be a transitioning bionic person. So, I am guessing that some people you meet, don’t know how to react to your “presentation.”

This is a really good point that I’d like to explore at more length. In this (now) series of posts, I’m playing with the semiotic theory that I’m also using in my dissertation. In this theory, it’s not enough to talk about signifiers and signifieds; rather, a sign not only has an object that it refers to, but it also has an effect on the people that perceive and interpret it, which is called the interpretant of the sign. A cloudy sky, for example, is a sign whose object is impending rain; its interpretant might be a headache, a gloomy feeling, my tossing an umbrella in my bag, or saying “Guess I don’t need to worry about watering the plants today.” So when my correspondent is talking about what “people would know,” that’s the interpretant of the brace, sling, splint, plaster cast, or whatever.

The key point here is that the meaning of my elbow brace was ambiguous, while a hypothetical splint or cast would have been clearer. And in fact, when I told people I had a broken arm, they were often surprised that I wasn’t in a cast. I heard a few stories about other people’s broken bones and how lucky I was not to have a cast.** While my elbow brace is an index of a broken bone every bit as much as a cast would have been, there seems to be a difference in the way they’re perceived—cast means broken bone in a more fundamental, even “iconic” way. What’s going on here?

I put “iconic” in scare quotes above because, as I outlined last time, icon has a specific technical meaning: a sign that stands for its object because it resembles the object in some way. In this sense, a cast isn’t an icon of a broken bone, but it is an icon of the part of the body that it’s immobilizing. It’s also, in a different sense, an icon of every other cast that you’ve ever seen, and this is the sense in which indexes are build up out of icons: you know that those casts were on people with broken bones, and so you would have made the same conclusion about me, if I had a cast. You probably don’t have that association regarding braces like the one I was wearing. A sign like this—one where you can figure out what it means because it’s a token of a type that you’ve seen before—is called a replica.

But this issue of the cast seems to be more than just a replica. That doesn’t account for why people are surprised to learn that my arm is broken, given that I don’t have a cast. It seems like people aren’t just associating broken arm with cast; they’re acting as if having a cast is just what a “broken arm” looks like.

In other words, they’re interpreting the cast = broken bone sign as if it really were an icon.

A sign like this, that is interpreted as an icon even if it doesn’t technically resemble its object, is called a rheme, and it’s something I’ve blogged about before in the math education context. The same way that we understand cast = broken bone, we also understand 3 = set containing a number of objects such that if I counted them, I would count “one, two, three.” This whole process becomes so naturalized to us that the association becomes transparently obvious. This erases all the semiotic work that has to happen—why should a cast seem to “resemble” a broken bone every bit as much as an X-ray does?

* Hi, Mom!
** People often attributed this to advances in medical technology, but my impression is that it’s more about the specifics of my break; an elbow brace isn’t exactly high-tech, and if you can’t put a broken collarbone in a cast, then there’s nothing to be done.

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