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Computational Legal Scholar; Assistant Professor of Statistics, Columbia University
Phase Transitions And Scale Transitions: Conceptualizing Unexpected Changes Due To Scale

Physicists created the term "phase transition" to describe a change of state in a physical system, such as liquid to gas. The concept has since been applied in a variety of academic circles to describe other types of systems, from social transformations (think hunter-gatherer to farmer) to statistics (think abrupt changes in algorithm performance as parameters change), but has not yet emerged as part of the common lexicon.

One interesting aspect of the concept of the phrase transition is that it describes a shift to a state seemingly unrelated to the previous one, and hence provides a model for phenomena that challenge our intuition. With only knowledge of water as a liquid, who would have imagined a conversion to gas with the application of heat? The mathematical definition of a phase transition in the physical context is well-defined, but even without this precision I argue this idea can be usefully extrapolated to describe a much broader class of phenomena today, particularly those that change abruptly and unexpectedly with an increase in scale.

Imagine points in 2 dimensions — a spray of dots on a sheet of paper. Now imagine a point cloud in three dimensions, say, dots hovering in the interior of a cube. Even if we could imagine points in four dimensions would we have guessed that all these points lie on the convex hull of this point cloud? In dimensions greater than three they always do. There hasn't been a phase transition in the mathematical sense, but as dimension is scaled up the system shifts in a way we don't intuitively expect.

I call these types of changes "scale transitions:" unexpected outcomes resulting from increases in scale. For example, increases in the number of people interacting in a system can produce unforeseen outcomes: the operation of markets at large scales is often counterintuitive, think of the restrictive effect rent control laws can have on the supply of affordable rental housing or how minimum wage laws can reduce the availability of low wage jobs (James Flynn gives  "markets" as an example of a "shorthand abstraction," here I am interested in the often counterintuitive operation of a market system at large scale); the serendipitous effects of enhanced communication, for example collaboration and interpersonal connection generating unexpected new ideas and innovation; or the counterintuitive effect of massive computation in science reducing experimental reproducibility as data and code have proved harder to share than their descriptions. The concept of the scale transition is purposefully loose, designed as a framework for understanding when our natural intuition leads us astray in large scale situations.

This contrasts from Merton's concept of "unanticipated consequences" in that a scale transition refers both to a system, rather than individual purposeful behavior, and is directly tied to the notion of changes due to scale increases. Our intuition regularly seems to break down with scale and we need a way of conceptualizing the resulting counterintuitive shifts in the world around us. Perhaps the most salient feature of the digital age is its facilitation of massive increases in scale, in data storage, processing power, connectivity, thus permitting us to address an unparalleled number of problems on an unparalleled scale. As technology becomes increasingly pervasive I believe scale transitions will become commonplace.