Wax On, Wax Off: Transposability and the Problem with “Domains”9 min read


In the film Happy Gilmore, Adam Sandler plays a hockey player who is a terrible skater but has a powerful slap shot. The main story arc of the film is that Sandler will use this ability in the entirely different sport of golf. This is a fairly common trope. Very often this becomes associated with something biological—we don’t know where Sandler’s character learned to hit the puck as he does, he may just be “a natural.” In the Karate Kid, though, we famously see the “wax on, wax off” motions of waxing Mr. Miyagi’s car turned into blocking motions in hand-to-hand combat. This same scenario occurs in, for example, the zombie series Santa Clarita Diet. Joel is instructed to shove a pear into a dead chicken as quickly as possible. Later, when fighting a zombie, he shoves a lemon into the zombie’s mouth as if by muscle memory. We then see that the odd pear-chicken skill is meant to remove the zombie’s ability to bite. In each case, we see an ability seemingly transposed across domains.

In a recent blog post, Omar offered a critical discussion of the use of “transposability” as a concept in the sociology of culture. Namely, the idea that schematic knowledge is, or must be, “transposable” across “domains” is a critical error:

Bourdieu and Sewell (drawing on Bourdieu) made a crucial property conjunction error, bestowing a magical power (transposability) to implicit (personal) culture. This type of personal culture cannot display the transposability property precisely because it is implicit…

If implicit culture is, by definition, domain-specific, how can it be transposed across domains? The argument, as I understand it is, to the extent schemas are transposed “requires that they be ‘representationally redescribed’… into more flexible explicit formats.” The complication with this discussion thus far, though, is that “domain” is doing a lot of theoretically heavy lifting, and I don’t think it can hold the weight.

The Problem with Domains

Let’s start with Durkheim’s “puzzle” in the introduction to Elementary Forms. As he saw it, in the quest to understand where knowledge comes from there were two camps: the Rationalists and the Empiricists. He thought the Empiricists were on the right track in that we gain knowledge from our moment-to-moment experience. However, the Empiricists didn’t have a solution for integrating what we learn across each moment: 

…the things which persons perceive change from day to day, and from moment to moment. Nothing is ever exactly the same twice, and the stream of perception…must be constantly changing… The question from this perspective, is how general concepts can be derived from this… stream of particular experiences, which are literally not the same from one moment to the next, let alone from person to person.” (Rawls 2005, 56)

As we are exposed to chairs in different moments, what is it that allows us to pull out the basic properties of “chairness”? Indeed, even the same chair at different times and in different places will be objectively “different”—diverse shading, slow decaying, a coating of dust. Of course, Durkheim was less concerned with the mundane (like chairness) than with the “pure categories of the understanding” a.k.a. “skeleton of thought” a.k.a. the “elementary forms” or often just “The Categories.” We would likely call all of these schemas today, and something more like image schemas or primary schemas. 

The developmental neuroscientist Jean Mandler (2004) approaches Durkheim’s problem of knowledge with the question: what is the minimum that must be innate to get learning started? She argues that we have an innate attentional bias towards things in motion, but more importantly, we also have an innate ability to schematize and redescribe experience in terms of those schematizations. Schematization is, in my mind, best understood not as retaining but as forgetting, elegant forgetting. As the richness of an immediate moment slowly starts to fade, certain properties are retained because they have structural analogies in the current moment. Properties that do not have such analogies in the current moment continue along a fading path, slowly falling away (unless brought to the fore by the ecology of a new moment). What is left is a fuzzy structure — a schema — with probabilistic associations among properties. Probabilities shaped by exposure to perceptual regularities. Therefore, the most persistent perceptual regularities will also be the most widely shared.

Mandler also argues that once we have a few basic schemas, as fuzzy and open-ended as they may continue to be, we can then redescribe our experience using these schemas. More importantly for the present discussion, both schematization and redescription seem to implicate transposability. But, Mandler works with infants and toddlers, so much of this occurs rapidly in human development—before what we would typically call “conscious control” is up and running.

It is here where the discussion implicates “domains.” Can we reserve “transposability” as the use of schematic knowledge in a “new domain”? And, then simply call the more pervasive “carrying of schemas from moment to moment” something else? In this setup, if encountering or thinking about a chair in chair-domains (domains where chairs typically are), then drawing on my chair-schema will not qualify as transposability. It is only when chairs are encountered or thought about in non-chair-domains (domains where chairs typically aren’t) that transposition is occurring. Without an analytical definition of what a domain is, however, this becomes slippery: If transposition requires that implicit knowledge be “representationally redescribed into more flexible explicit formats,” then by definition we can only know “new domains” whenever we see this occurring.

Spectrum of Transposability

I think we should ditch domains as the linchpin of transposability rather than salvage it. Schematic knowledge is transposable. At least in the most basic notion of “drawing on implicit knowledge” from moment to moment. But, sure, it is not transposable without constraint. Implicit knowledge is called forth by the recognition of familiar affordances in a moment. The problem is that affordances are not cleanly bundled into mutually exclusive “domains.” 

Perhaps transposition across normatively distinct domains typically occurs via deliberate mediation — but the idea that it only occurs via deliberate mediation is perhaps a step too far. New situations will evoke some implicit knowledge acquired in a prior situation without the individual deliberating. Much of what we call “being a natural” is likely just such a process. True, Mr. Myagi was conscious that “wax on, wax off” would transpose to fighting, but Daniel was not. And, more importantly, it was Daniel who was transposing it, and it was the affordances of the fighting situation that evoked the “wax on, wax off” response.

As a starker example of transposition without deliberation — or even against deliberation — we can look to hysteresis: The mismatch between the person and environment (Strand and Lizardo 2017). When I was a freshman in college, I boxed for extra money. I had never boxed before, but I had wrestled for years.  Luckily for me, someone was kind enough to properly wrap my wrists during my first fight! During that fight, I continually did something I knew was not correct: I got an underhook, a wrestling move involving placing your bicep in the armpit of your opponent and wrapping your hand around their shoulder, giving you leverage over their body position. The second or third time I did this, the referee stopped the fight and informed me that this was not allowed in boxing and I would lose points if I continued to do it. Getting an underhook when the move was “open” was “second nature.” It was “muscle memory.” I  deliberately tried to stop this automatic response. I continued to fail. I lost points. Despite this being a domain distinct from wrestling (normatively), my body interpreted the affordances of the moment as being a familiar domain (ecologically). Transposition occurred against my conscious effort.


Durkheim, Emile. 1995. The Elementary Forms of Religious Life. New York: Free Press.

Mandler, Jean Matter. 2004. The Foundations of Mind: Origins of Conceptual Thought. Oxford University Press.

Rawls, Anne Warfield. 2005. Epistemology and Practice: Durkheim’s The Elementary Forms of Religious Life. Cambridge University Press.

Strand, Michael, and Omar Lizardo. 2017. “The Hysteresis Effect: Theorizing Mismatch in Action.” Journal for the Theory of Social Behaviour 47(2):164–94.

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