Note: this post is a sort of mental marker, as I am partway thinking through a particular issue and do not want to lose my place.
One of my colleagues, Micki Chi, has divided causal modeling into two sorts, the type with narrative structures and the type without, which she calls emergent and has some evidence is more difficult for students to learn.
I think that one can take this a little further. Of narrative causal models, there is the incremental or contributory causal argumens, of the sort medical researchers or social-scientists commonly make in terms of a unit of X will cause beta units of Y–microeconomists’ notions of elasticity or the results of regression or experimental claims on behalf of various treatments in one domain or another.
There is also a narrative causal model that is more contingent or categorical, such as, One end of the American Civil War was the end of legally-defended slavery in the country. Historians at this point are cautious of making monocausal arguments, and I do not think one needs to be monocausal to have contingent models of how the world works–of the Y depends on X sort.
So, too, emergent models can be divided. There are the universal, scale-free emergent models most common in physics, such as Neuther’s theorem and its various analogues, which connect symmetries to conservation principles. There are also emergent models that are scale-specific, such as molecular diffusion and natural selection. Chi argues that these types of emergent models are more difficult to grasp than narrative models because they do not fall easily in our experience of sequential storytelling.1 A good part of her recent work lies in exploring how to help students learn emergent models.
Then there are also types of emergent models that move across scales — neither specific to scale nor invariant across scales. Some of this complex behavior is emergent from small-scale dynamics, such as the famous Conway’s Game of Life and similar “cellular” automata. Some is related to the existence of boundary limits that are not visible at the small-scale level: economists still have no consensual method of scaling up microeconomic behavior in ways that include the macroeconomic effects of economy-wide demand. And some is related to the multiple roles of a single phenomenon–and here, education is a prime example with its symbolic cultural role, the instrumental role for both individuals and societies, and the unpredictable (even emergent) effects of expanding formal schooling.
I am currently stuck at this point, which is primarily classification. There are more subtle, interesting ideas at the margins of this, but nothing specific enough to write about. I do not want to lose track of this classification and thus this non-specific, non-topical blog entry for a holiday.
- I am omitting the scientific analogues of narrative models, such as the cyclical “story-like” dynamics of lunar tides, blood circulation, etc. Chi argues that learning these models are easy because they have narrative versions one can use in teaching. [↩]