Now published: My new theory of emergence!

Glimmers of free will

The coolest thing about science is that sometimes, for a brief period, you know something deep about how the world works that no one else does.

The last few months have been like that for me.

I’ve just published a paper sharing it (available on arXiv as a pre-print). It outlines a new theory of emergence, one that allows scientists to unfold the causation of complex systems across their scales.

Congrats Erik, but um, why does science need a theory of emergence?

Glad you asked. Because almost every causal explanation you’ve given in your whole life about the world—like “What caused what?”—has been given in terms of macroscales. Sometimes called “dimension reductions,” they just mean some higher level description of events, objects, or occurrences. Temperature is a classic macroscale. But so are most other things. If your child asks “Why is the water hot?” and you answer “Because I turned the hot water faucet on,” that’s an explanation given entirely in macroscales. “Faucet turned on,” macroscale. “Water,” macroscale. “Hot,” macroscale. “I,” macroscale.

In fact, most of the elements and units of science are macroscales. Science forms this huge spatial and temporal ladder, one with its feet planted firmly in microphysics, and where each rung represents a discipline climbing upward.

Science as a “ladder” of dimension reductions

This entails a tension at the heart of science. Scientists, in practice, are emergentists, who operate as if the things they study matter causally. But scientists, in principle, are reductionists. If pressed, many scientists will say that the macroscales they study are just useful compressions. After all, any macroscale (like temperature), can be reduced to its underlying microscale (the configuration and behavior of the particles). So they’ll happily say things like “this gene causes this disease,” despite the fact that a gene is just some set of molecules, and then in turn atoms, and maybe underneath that strings, etc.

So then how can that macroscale description matter? Why doesn’t causation just “drain away” right to the bottom, and there’s no real way for anything but microphysics to matter? This is in tension with how the scientific category of “genes” seems like it’s adding to our knowledge of the world in a way that goes beyond its underlying atoms.

This problem keeps me up at night. Literally, this is what I lie awake thinking about. Years ago, in my paper “When the map is better than the territory,” I sketched an answer I found promising and elegant: error correction. This is a term from information theory, where you can encode the signals along a noisy channel to reduce that noise. Your phone works because of error correction.

Well, I think macroscales of systems are basically encodings that add error correction to the causal relationships of a system. That is, they reduce uncertainty about “What causes what?” And this added error correction just is what emergence is. So if a macroscale “emerges” from its underlying microscale it’s because it adds, uniquely, a certain amount of error correction, in that there’s a clearer answer to “What causes what?” up at that macroscale.

If you want a popular article explaining this idea, you can read this old one here in Quanta, featuring my earlier work (the work of someone who comes across as a very young man—I look like a baby in the photo!).

But, while the conceptual understanding was there, I always felt there was more to do regarding the math of the original theory. Holes and flaws existed. Some only I could see, but sometimes others did as well (not everyone was convinced of the original theory, due to how the initial math worked; particularly the measure of causation, called effective information, that we initially used, and that this new version of the theory moves beyond). Since then, other scientists have tried to offer alternative theories of emergence, but none have gained widespread acceptance, usually falling into the trap of defining what makes macroscales successful compressions (rather than what they actually add).

So this new version, which radically improves the underlying math of causal emergence by grounding it axiomatically in causation, making it extremely robust, and also generalizes the theory to look at multiscale structure, has been a decade in the making. I think it provides an initial account of emergence with the potential for widespread acceptance and (most importantly) usage.

You can now find the new pre-print on arXiv.

link

There’s a ton in the paper, but it’s freely available to examine in-depth on arXiv, so I’ll merely point out one interesting thing that I purposefully don’t touch on in the paper, which is that…

Causal emergence is necessary for a definition of free will.

Of course, I can’t talk about this issue in the paper without poking a hornet’s nest. The moment you mention “free will” everything descends into debate; it’s an omnivorous intellectual subject that obscures everything else of interest or import. So I usually avoid it completely.

This isn’t me complaining. Things need to be done in a certain way, and a theory of emergence has many implications beyond some notion of free will. A theory of emergence has practical scientific value, and this is what the research path should focus on: making causal emergence common parlance among scientists by providing a useful mathematical toolkit they can apply and get relevant information out of (like about what scales are actually causally relevant in the systems they study).

But it’s also obvious that, if you simply turn the theory around and think of yourself as a system, the theory has much to say about free will. The many implications of which are left as an exercise for the keen-eyed reader, but here’s an early hint:

This new updated version of causal emergence would indicate that you—yes, you—are a system that also spans scales (like the microphysical up to your cells up to your psychological states). Importantly, different scales contribute to your causal workings in an irreducible way. A viable scientific definition of free will would then have a necessary condition: that you have a relatively “top-heavy” distribution of causal contributions, where your psychological macrostates dominate the spatiotemporal hierarchy formed by your body and brain. In which case, you would be primarily “driven,” in causal terms, by those higher-level macroscales, in that they are the largest causal contributors to your behavior. This can be assessed directly by the emergent complexity analysis introduced in the paper. Possibly, one could design experiments to check the scientific evidence for this… but that’s all I’ll say.

What’s next?

Obviously, these are important subjects. It looks like I will be publishing on them over the next few years using my re-established affiliation with Tufts University. As a theoretical toolkit I think causal emergence deserves the kind of application and influence that something like the Free Energy Principle has had (albeit over a different subject). And the simple truth is that you can’t just put out ideas and expect others to see the potential and run with them. You have to get the ball downfield yourself before others join in. I think this research even has important implications for AI safety, as things like understanding “What does what?” in dimension-reduced ways is going to be important for unpacking the black boxes artificial neural networks represent.

In case you’re wondering, during this mission, I don’t plan on changing anything about writing The Intrinsic Perspective—I wrote here for years while I was doing similar science. But this new research is worth adding to my plate, because one thing I’ve learned in the course of my life is that good ideas, really good ideas, are very rare.

In fact, you only get a few in a lifetime.

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