A New Physics of Emergence

Assembly theory gives a precise answer to the question: what is life?

For one week as a college freshman, I was obsessed with asking people what their “central question” was. That is, if they boiled down all of their interests and everything that drives them into a single question, what would it be? I actually still have a few answers safely stored away in my notes app (though it took a bit of digging to find them):

• What is the best way to be human?

• How is individual related to environment?

• How can I live a meaningful life?

• Is love a form of dependency?

• What does it mean to exist?

My own question was very clear to me. What is fundamental? As a fresh 18 year old I found it exhilarating to think that all the apparent complexity of the world could be built off of some simple rules. The fashion in popular science writing of the time only fueled this fire: my favorite science book back then, James Gleick’s Chaos, was filled with examples of the same patterns emerging in disparate fields (physics, economics, biology), and with proofs that infinitely complex-seeming patterns like the Mandelbrot set were really built out of simple equations.

Simple Complexity: This is a fractal I made in Blender using a technique called ray-marching. The rule behind this fractal is pretty simple, and involves squeezing spheres in the space in between spheres, repeatedly.

And so I pursued the most fundamental science I could: particle physics. The approach was reductionist to the extreme. One Master’s degree later and I had enough; I was getting bored, and the world was starting to look a bit more interesting if I tried taking off my reductionist goggles. (Biology, life, art, and consciousness in particular started to draw my eye, but more on those things later.)

The entire project of physics is reductionist. Physics asks: what are building blocks of the universe? Between the lines of that question lies a sentiment: only the building blocks and the rules they follow matter. When you are deep enough down the hole of theoretical physics, you start to believe that these are the only things that really exist - electrons, quarks, quantum fields, force-carrying bosons, maybe vibrating strings if you’re radical. Everything else, from the mind, to solar systems, to governments, to celebrity gossip, are all just complicated collections of the fundamental building blocks. With this view, studying these objects in their own right is a glorified process of naming and characterization. Stamp collecting, as you might hear it called.

Behind this sentiment is a glaring oversight: these things clearly exist. In the real way. Gossip affects the behavior of people, which affects the physical world, and so on, in a way that you could never predict from looking at its constituent parts.

We’ve never had a scientific way to understand how things like governments or celebrity gossip or, importantly, life, could emerge out of things like particles and fields. Recently, I’ve stumbled across an attempt to lay a groundwork to do this.

I was sent a pre-publication copy of Sara Imani Walker’s book, Life as No One Knows It, by her agent looking for an interview on my podcast (which made me feel pretty cool, though scheduling has prevented the interview from happening so far). It describes a new science called assembly theory.

The goal of assembly theory is to describe why some things exist and not other things. As it turns out, once you make it from physics to chemistry, the world of possible combinations of atoms far exceeds the number of combinations we really observe. So why some complex molecules and not others? The name assembly is apt because these emergent objects must be assembled, not by an elusive God (that would be unscientific), but by some force within the universe. So how does the universe select for what it chooses to realize?

Assembly theory takes seriously the reality of complex objects. A protein molecule is an object, a sweater is an object, a computer program is an object. And the characteristic feature of these objects is how long it takes to assemble them. How many steps it takes to go from the fundamental objects of physics to your assembled object is called its assembly number, and there are physical ways to measure it. Higher assembly number means higher complexity.

It takes time to assemble complex objects, so the assembly number is also a way to talk about an object’s extent in time. The universe does not and cannot, according to assembly theory, spontaneously create complex objects. (That means no Boltzmann brains!). Instead, the universe slowly learns how to make the object, and stores the recipe so that it can duplicate the process.

As far as I know, this is the first time we’ve had a mathematical language for talking about emergence. Assembly theory allows us to bridge different scales through information - you can think of the “recipe” for making an emergent object out of constituent parts as made up of information, not unlike a computer program.

But it gets better, because this language also gives us a new, precise way to answer the question: what is life? Here is the answer, and I quote:

“what we call life is the mechanism for making specific things possible when the possibility space is too large for the universe to ever explore all of it.”

The combinatorial space of all objects that could possibly exist is enormous. Life carves a trajectory through this space, selecting certain objects of higher and higher levels of complexity to make real.

Through evolution, life has created bacteria, seaweed, crabs, mushrooms, dolphins, monkeys, tardigrade, blood vessels, the prefrontal cortex, ears, nerves. As humans, we’ve created horror movies, freight trains, basketball hoops, leather shoes, memoirs, ambient music, pancakes. This is a lot, and yet the space of all un-realized possibilities contains much more.

There is an assembly number for which objects more complex than that cannot be created (multiple times) through random dynamics. That number is 15. If you find multiple copies of an object with an assembly number above 15, it can only be explained by one thing: life!

I love just how abstract this definition of life is. You don’t need brains or neurons or consciousness, you just need a certain level of complexity, characterized by assembly number. The possibilities for what life looks like are, literally, endless.

It also helps us cope with the strange nature of modern physics that says our universe is either pre-programmed and entirely determined from its initial conditions, or nearly pre-programmed except for some quantum-induced randomness. With assembly theory, the newborn universe didn’t yet know what sorts of creatures it would one day create. And yet there is no need for an external “intelligent designer”, because it’s from within the universe that life reigns.

Walker lets us into one insight inspired by this theory that has really stuck with me since reading it. The idea is that objects with assembly numbers lower than ours as humans appear material to us, and objects with higher assembly numbers feel abstract or even informational. This idea builds off of philosopher Timothy Morton’s idea of hyperobjects - objects so massive and complex that you can’t pin them down to a location or time, and yet are physical and dynamic. His classic example is climate change, which feels so beyond the human grasp that we continue to struggle to understand and control it.

So maybe information really is physical. Complex objects are complex because it takes time to create the instructions used to build them. And by being alive, we can carve a careful path through the space of future possibilities.