I Figured Out How to Engineer Emergence

“Look to the rock from which you were hewn” — Isaiah 51:1

Earlier this year I returned to science because I had a dream.

I had a dream where I could see inside a system’s workings, and inside were what looked like weathered rock faces with differing topographies. They reminded me of rock formations you might see in the desert: some were “ventifacts,” top-heavy structures carved by the wind and rain, while others were bottom-heavy, like pyramids; there were those that bulged fatly around the middle, or ones that stood straight up like thin poles.

Consider this an oneiric announcement: almost a year later, I’ve now published a paper, “Engineering Emergence,” that renders this dream flesh. Or renders it math, at least.

But back when I had the dream I hadn’t published a science paper in almost two years. I had, however, been dwelling on an idea.

A little backstory: in 2013 my co-authors and I introduced a mathematical theory of emergence focused on causation (eponymously dubbed “causal emergence”). The theory was unusual, because it viewed emergence as a common, everyday phenomenon, occurring despite how a system’s higher levels (called “macroscales”) were still firmly reducible to their microscales.

The theory pointed out that causal relationships up at the macroscale have an innate advantage: they are less affected by noise and uncertainty. Conditional probabilities (the chances governing statements like if X then Y) can be much stronger between macro-variables than micro-variables, even when they’re just two alternative levels of description of the very same thing.

How is that possible? I posited it’s because of what in information theory is called “error correction.” Essentially, macroscale causal relationships take advantage of the one thing that can never be reduced to their underlying microscale: they are what philosophers call “multiply realizable” (e.g., the macro-variable of temperature encapsulates many possible configurations of particles). And the theory of causal emergence points out this means they can correct errors in causal relationships in ways their microscale cannot.

The theory has grown into a bit of a cult classic of research. It’s collected hundreds of citations and been applied to a number of empirical studies; there are scientific reviews of causal-emergence-related literature, and the theory has been