Containment Inversion

[travisrm89]

There’s a mental phenomenon that I sometimes experience which is profound but which doesn’t have a name as far as I know. It’s a form of sudden mental clarification in which I see an inversion of the (more fundamental)/​(less fundamental) relation between two things, like seeing the faces of a Necker cube switch. Just like with a Necker cube, the inversion doesn’t always imply that the new way of seeing things is more correct (although sometimes it is), but seeing the inversion always does result in understanding more clearly the relation between the two things. I’m going to tentatively call this phenomenon Containment Inversion, in the sense that you switch from “Thing 1 contains Thing 2” to “Thing 2 contains Thing 1”; in other words, rather than Thing 1 being a special case of Thing 2, Thing 2 becomes a special case of Thing 1.

Here is an example from physics: when you first learn about the speed of light, you are told that the speed of light in vacuum is constant, and its speed in other materials is slower. This tends to produce a mental model in your mind in which the speed of light in a vacuum is a special case of the speed of light in generic materials; the vacuum is just one special type of material. Eventually, this causes some confusion once you fully grok that materials aren’t continuous fundamental objects of the universe. At some point you suddenly see that the speed of light in a material is just a special case of the speed of light in vacuum: the scattering off of atoms in the material merely conspire to cause the light traveling through the vacuum to interfere in such a way that the wavefront is slowed. Another inversion happens again once you learn about QFT and realize that there is a very real sense in which light in the material actually does gain an effective mass and slows down.

Here is an example from morality: utilitarian-minded folks often see some deontological-like arguments as simply special cases of utilitarianism: doing acts just because the acts themselves are right, for some definition of right, often increases overall utility either because the person doing the act personally gets utility out of doing the act or because people doing things for such reasons tends to increase utility overall. But this viewpoint can be inverted, albeit with some effort: doing acts because they increase overall utility is just a special case of doing acts because they are right, for some definition of right; and even though this broad category isn’t quite what deontology is, it is much more closely related to deontology than to utilitarianism. This is a good example where the inversion, in my opinion, isn’t quite as correct as the original viewpoint, but it still sheds light on the situation.

Does anyone else have this experience of inversion? Is there already a name for it?

[Said Achmiz]

Here is an example from physics: when you first learn about the speed of light, you are told that the speed of light in vacuum is constant, and its speed in other materials is slower. This tends to produce a mental model in your mind in which the speed of light in a vacuum is a special case of the speed of light in generic materials; the vacuum is just one special type of material.

Data point: it never, ever occurred to me to think about the speed of light in this way, until I read your post. It still seems weird. The other view—“the speed of light in a material is just a special case of the speed of light in vacuum”—is what I always took for granted.

This [utilitarianism vs. deontology] is a good example where the inversion, in my opinion, isn’t quite as correct as the original viewpoint, but it still sheds light on the situation.

Similarly, the former of the two viewpoints you list here didn’t occur to me at first (until I started seeing people here on Less Wrong talk about utilitarianism; before then, I knew of these ideas from academic philosophy); and, contrary to what you say, it still seems obviously wrong.

[travisrm89]

Both of the “former” views are positions I held in the past (the one about light when I was very young, and the one about morality much more recently). I agree that the latter ones are right; I’m not sure what I was thinking when I wrote for the morality example that the latter is less correct than the former.

[rossry]

Does anyone else have this experience of inversion? Is there already a name for it?

It sounds to me like something akin to the “figure-ground inversion” that Scott Alexander moots in a review of House of God:

House of God does a weird form of figure-ground inversion.

An example of what I mean, taken from politics: some people think of government as another name for the things we do together, like providing food to the hungry, or ensuring that old people have the health care they need. These people know that some politicians are corrupt, and sometimes the money actually goes to whoever’s best at demanding pork, and the regulations sometimes favor whichever giant corporation has the best lobbyists. But this is viewed as a weird disease of the body politic, something that can be abstracted away as noise in the system.

And then there are other people who think of government as a giant pork-distribution system, where obviously representatives and bureaucrats, incentivized in every way to support the forces that provide them with campaign funding and personal prestige, will take those incentives. Obviously they’ll use the government to crush their enemies. Sometimes this system also involves the hungry getting food and the elderly getting medical care, as an epiphenomenon of its pork-distribution role, but this isn’t particularly important and can be abstracted away as noise.

I think I can go back and forth between these two models when I need to, but it’s a weird switch of perspective, where the parts you view as noise in one model resolve into the essence of the other and vice versa.