生命的普适层级——Prof. Chris Kempes [SFI]

Tim Scarfe

The eye is so complicated, maybe it only gets discovered once and then everything that has an eye has a common ancestor.

Not true. Eyes evolve many times. There are differences in the details of eyes, in terms of how exactly they see, how they're constructed, and slightly what they're made of and so forth, but in some notion, they're all doing the same sort of physics.

So I'm a professor at the Santa Fe Institute, which is a massively interdisciplinary research institute trying to bring together minds from across the spectrum of academia to really think about some of our hardest problems. My own background is that I was a physicist, and then I became a biophysicist, and then that's taken me into ecology and cities and human organizations, and thinking about the whole history of life and also origins of life and astrobiology.

That's really the SFI thing: to try and take a core expertise and use that as a nucleation to expand into all these different topics and areas.

Tim Scarfe

And it's so interesting that you work at the Santa Fe Institute. I spoke with David Krakauer recently, a very inspiring gentleman. What you folks are really doing is, I guess, what you would call a multidisciplinary lens on science.

You were talking about three cultures in science. So there's the variance culture, where we look at diversity and deviation; the exactitude culture, where we have quite a high-resolution mapping of everything; and this coarse-grained, abstract culture, where we look for principles. Even in machine learning, we have similar terms for this. We have the neats and the scruffies. How can you reconcile these different aspects of science?

Part of the inspiration for us in writing that paper was to say if we look at the history of physics, which has had enormous success. Part of that amazing success is that it was such a set of easy questions in relative terms. Biology, the economy, and intelligence are all much harder questions. But for physics, trying to answer relatively simple questions like gravity and planetary motion, they had what I call the magic loop.

The magic loop is this: observation leading to theory, theory leading back to observation. People took huge sets of observations that we had and tried to find regularities, tried to find simple equations that predicted those observations. Then, once they had those theories, they would explore them mathematically. Often, that gave rise to new sorts of surprising predictions, and then experimentalists would go looking for those predictions.

This loop continued as people uncovered most of the laws for most of the fundamental forces. Obviously, there are still open questions in physics, but that trajectory has been really successful. I think our proposal in this paper was that we need to do a similar sort of thing for the biosciences and for a science of the biosphere.

We need more ways to bring the huge amount of observations we have today together with new types of theory to get this loop, where we're compressing what we know into simple theories, using those theories to make surprising predictions, testing those with data, and so forth. That's really the variance culture and the coarse-grained culture.

In our current moment, we have this new thing that we call exactitude culture, which is just the ability to model everything. Galileo didn't have this. He didn't have the ability to write down an arbitrarily large number of equations that he wanted. He couldn't write down an agent-based model for the planets and simulate that in a computer. He was forced to try and find these compressed mathematical representations.

In today's world, we can simulate huge numbers of things and make exceptionally complicated simulations. That's a third category. We have this with certain Earth system models, very detailed models of the economy, and artificial intelligence is certainly in that space.

We think each of these has trade-offs. Each of these three cultures has trade-offs, and we really need to find a way to walk amongst the corners of that triangle to get the best knowledge. There are certain things coarse-graining is best for, and there are other things simulation is best for. We always need observation to test both types of knowledge, and that's where we find ourselves.

Tim Scarfe

Chomsky said to us that deep learning is a bit like—he used the term “anything goes”—and, in his estimation, as a theory, it didn't demarcate what something isn't versus what it is. In your estimation, what makes a good scientific theory, and what does it mean for us to actually understand something?

For me, it's all about compactness and compression. I think the amazing thing about equations is that we can transmit them to each other quickly, easily, and in small forms. Now, there's a huge amount of knowledge that one requires to then decode those equations. You and I might both have to spend 30 years learning all the mathematics it takes to transmit a certain sort of equation to each other.

But once we've done that, once we have that training, this compact form is really an easy way to transmit understanding and knowledge. One of my favorite ways to test understanding is to predict the unseen or the unexpected.

Many theorists get very excited when they have a theory that predicts something that hasn't been seen yet, because it's what I think Rob Phillips once called a “dangerous prediction.” There's no data for it yet. There's no way you could have tuned your theory to match some old data. You're making a prediction that will either be right or wrong about something that hasn't been seen yet.

But that's a real notion of understanding, I think: we've never looked for this, we've never seen this, but if X is true and Y is true, then certainly Z must be out there. Let's go find it. I think that's a real demonstration of understanding.

Tim Scarfe

I've just read your paper with David Krakauer, “The Multiple Paths to Life,” and towards the end of the paper, you said you want to have a universal theory of life. Tell me about that.

It's something that's been of interest for almost as long as human thought: what is life? How do we understand living things and so forth? That question has been more and less obvious to people over the history of science. Sometimes people say, of course, we know what life is. It's a frog. You see one there and so forth.

But what we're really after is: what are the principles that go into a theory of the living? How do we have a set of principles that helps us understand how life first came to be? How do you get an origin of life? How does that life start to gain more complexity? How does it eventually start to add more and more intelligence? How do you get new types of what are called major transitions in evolution?

As life gets bigger and more complicated, how eventually do you get new types of life? In that paper, we argue that from certain theoretical perspectives, human culture should be seen as life. It's just life living on a very strange substrate. That substrate is human minds.

Language is the same sort of thing. We argue that in silico life, artificial life, should also count. There should be no question that that counts. Again, it's just life living in a very weird substrate: the substrate of computers that are built by humans and so forth.

Our interest was really what sort of theories, what sort of principles, help us understand all of those different cases. In that paper, we're very careful to say we don't think we know what the theory is yet. We're far from it, but there's a style of thinking that hopefully can push us down that path.

We point to some emerging theories that are sort of exciting. There are new theories of agency. There are new theories of semantic information. David Krakauer and a bunch of colleagues have a paper on “The Information Theory of Individuality,” which helps us understand what an individual is.

All this work that I and many collaborators do on scaling laws looks like something that we can start to build into theories of life. In that paper, we say that these are all ingredients, and at some point in the future, hopefully we'll have some projection of all these ingredients into some new thing that we'll call life.

Maybe that's a set of equations. Maybe that's a set of concepts. Maybe it's more agency, less intelligence. We don't know. But we think we're in an exciting time where people are building quantitative theories to get at some of the ingredients.

Again, looking at the history of science, there are many cases where all the ingredients were there, and then people figured out, “Oh, this is the right combination. This is the right projection to give us the theory that really gives us traction on something.”

Tim Scarfe

Searle, for example, had this paper, “Minds, Brains, and Programs,” and what he was basically saying is that the physical instantiation is very important, and if you remove the instantiation, then it doesn’t work anymore. You had this wonderful quote in the paper where you were saying that the materials on Earth might be the universal life machine. Do we need the material?

So I think we need a material. [laughter] Right, I agree with instantiation. I agree with embodiment. Partly, that’s because embodiment is what connects software or concepts to real constraints. That’s a lot of what I focus on: once you have a cell, once you have an encapsulation for the simplest life, that then has to interact with the physical world in ways where we understand what the dominant physics are, and that allows us to predict quite a lot about life.

It’s important to separate the universal from the particular, or the path-dependent or the contingent. There are many reasons why the particular material may not be essential. Life is such a hard problem that one way we’ve gotten traction is just to focus on the things we have: DNA and RNA and ribosomes and the folded proteins that produce a lot of function in cells, and the lipid membranes that encapsulate them. All of that is the biochemistry we know, and I think we’ve gotten very attached to that because we’re still trying to understand how it came to be, all the things it does, and how it gets more complicated.

But if we really step back for a second, there are lots of ways to achieve the same sorts of functions. One can make a functionalist argument about what life might be, and then the materials become much less central. You could have radically different materials performing the same sort of function. We talk about this in that paper in computational terms. You can say there’s an abstract algorithm, and then there are often many different hardware implementations on which you could implement that algorithm, and the mapping is what one has to think about. That’s where there’s some trickiness.

You could even say there’s a process for which there are many algorithms that will have the same sort of outcome, like sorting, and that then could have multiple software implementations and multiple hardware implementations, and the outcome is the same somehow: a sorted list. You could talk about relative efficiencies and other sorts of constraints. I think it’s about going back and forth between all those layers to say what types of things we want in life and in understanding life, according to those same sorts of principles.

I’ll say this is a hugely emerging topic at the moment: focusing on the functional bit of life and using that to say the materials might be less important. David and I wrote about it in that paper. Michael Lachmann has been working on this. Michael, Sara Walker, Lee Cronin, and I have been working on this in other work. I think it’s really an exciting time for trying to step away from the particulars of materials and trying to understand some principles about life.

Tim Scarfe

Yes. As an aside, I’ve spoken to several functionalists this week, for example, Joscha Bach, and he has an information ontology. I suppose you’re pointing to a type of functionalism that is compatible with materialism, where you could have higher-order processes, and these processes could instantiate themselves in other types of material, and we’re not really rejecting materialism.

But I wanted to talk about your hierarchy. This is absolutely fascinating. There are 3 levels. There are materials, so things like chemical bonds and kinetics. There are constraints, so things like the maximum entropy principle and optimization, things like variational and action methods. We’re going to show a graphic on the screen now.

This amazing visual hierarchy that you’ve got in the paper shows that these levels work together. There’s the space of living at the top, where we have these higher-level principles, and that’s not completely homogeneous, but more homogeneous. In the middle, we have quite a diverse, heterogeneous set of constraints, and then we have the set of possible materials at the bottom. Absolutely amazing. Can you explain that?

Our proposal there is that you could get lots of different origins of life on different planets in radically different materials, and all of them would undergo one of these phylogenetic trees, where organisms compete and diversify and mutate and evolve and so forth. That could be happening on really different substrates.

Our proof of concept there is language, which, as I said already, is evolving on the substrate of human minds. People have written down really nice theories for that, showing that it’s an evolutionary dynamic. You can write down the evolutionary process for language. There, you’re getting an evolutionary dynamic on top of a new substrate: human minds.

Now you could say, well, that substrate is still made of carbon and all the rest, but that’s not really the essential piece. It’s the substrate that behaves in a certain way. It has new properties, and on top of that you get something like language and then culture. So we think we’re completely uncommitted to the materials. The materials could be totally different. They’re like different hardware implementations, and we expect that to be quite diverse across the universe for that reason.

We don’t think you should expect to go to, say, a different solar system and find intelligent life built on exactly the same biochemistry. We think that would be exceptionally unexpected. Then you could say, okay, are we just stuck with that? Are we stuck with this huge diversity of life across the universe? Is there nothing more to say about it? Not quite, because all of that still lives in a physical universe. It still lives within the constraints of physics.

If you lift up a layer, then you have the laws of gravity, the laws of diffusion, and all sorts of different physical forces that matter to organisms—matter to any organism made of anything at a particular scale. There you can then start to say, well, if I write down theories based on—imagine I just have a cell in a fluid that has to interact with a diffusive process—great, that’s a really general model. I haven’t actually had to tell you much about the materials. I didn’t invoke DNA in telling you that story. I didn’t invoke proteins.

Now we could say there’s something we can say about any sphere of living material that’s really small, say, bacterial scale, anywhere in the universe. Our strong proposal is that once we lift to the layer of constraints like physics, we’re collapsing a huge amount of material diversity into a more compressed space of constraints. But there still could be ways materials put you in different constraint spaces.

Different planets still could have radically different constraints because of things like temperature and pressure and the particular chemistry and how acidic the environment is, all those sorts of things. So we still allow for some diversity there. The question is, okay, but what would any living process be doing? That’s what lifts us up to these optimization principles.

Many people, including David, have written about how evolution is a learning dynamic. There are certain ways you can write down the equations, and it looks exactly like certain learning dynamics. They’re used repeatedly. That feels much more like an abstracted principle that should be true of any living system, just that it’s following a certain sort of evolutionary dynamic.

There’s actually this wonderful thing called the error threshold, which is how fast you can mutate given how much information you’re trying to propagate to the next generation.

Tim Scarfe

The Miller principle.

Yes, that is equivalent. It also gets called the error threshold. If I mutate too quickly, I can’t adapt anymore, given how much information I have. Again, there I haven’t said anything about materials. I haven’t even said anything about physics. I’ve just said you’re an evolving process with some error rate, and you’re trying to adapt to a new world.

There are constraints on how fast you can mutate and still be able to adapt, given the size of the information and how big your population is and some other things that matter for evolutionary theory. But that’s really fundamental, right? That should apply to language and culture and cells and genomes and all the rest.

Tim Scarfe

Yeah. Even that as a principle of life is fascinating. That conversation I had with David was just earth-shattering for me. He was talking about these adaptive processes that kind of surpass traditional evolution. For example, ontogenetic hacking, which is where we can store information in our nervous systems and brains and culture and so on.

There was a quote from David’s paper. I’m not sure if you were on that paper as well, but the definition of life was “the union of 2 crucial energetic and informational processes, producing an autonomous system, metabolically encoding and extracting information of survival value and propagating through time.” Isn’t that fascinating?

I love that. Yeah. I think, again, that definition has all of the ingredients that we think will eventually be in a definition or a theory of life. The community at present has different weightings on those different pieces. Some people are very focused on metabolism and energy. I work a lot on energy, although I don’t think it’s the only thing.

Some people are very focused on autopoiesis, self-generation, and replication to the next generation. Other people are very focused on information. Other people are very focused on computation. I think all the ingredients are there, and there’s something exciting happening in the field because many people’s theories have these overlapping ingredients. I think it’s just about weighting them and quantifying the details of how we bring each into a sophisticated set of metrics, right? Yeah.

Tim Scarfe

What I love about this functionalist perspective is the substrate independence. There’s this beautiful idea of a kind of memeplex, where you have certain patterns of functional processing and they can jump into different phylogenies. Can you give me an example of that? I mean, does that potentially explain how the sophisticated life that we have in our phylogeny could have transferred from another one?

Yeah. So, I think there are different ways to think about that. One is that there is a whole lot of lateral transfer that can happen across the tree of life in lots of different ways, right? So, even in bacteria, you have these lateral gene transfers where you can move bits of genome from one genome to another. You can discover something in one lineage and then bring it over to another lineage.

That's great. There's this whole other process of just good old-fashioned convergence [laughter], which is an old idea. It just says that, in certain cases, there are targets for a function that, if you achieve that function, it's likely to look a certain way, and so you see similar solutions across the tree of life.

Right? So, we get many origins of the eye. You can imagine that the eye is so complicated that maybe it only gets discovered once, and then everything that has an eye has a common ancestor. Not true. Eyes evolve many times. There are differences in the details of eyes in terms of exactly how they see, how they're constructed, and slightly what they're made of and so forth. But in some sense, they're all doing the same sort of physics.

So, that's the convergent bit. The convergent bit is because the physics is a target, right? We understand that there are certain ways to focus light and obtain a picture at a distance, and so forth. That's really the target for convergence.

I think there are two things happening. Sometimes something gets discovered in one lineage and transferred, and the other is that something is so predicted by physics that, if the function happens, it will look a certain way, even if some of the details are different.

I think what's really interesting about human society is that we're really, really good at the transfer bit, right? For example, you can have things discovered in entirely different cultures with different languages. Sometimes things like agriculture get discovered multiple times. That's maybe more of a convergent thing. But then there are other cases where you have some really neat thing discovered in one part of human society, and then it can immediately propagate to the rest, right?

Our genomes for intaking and taking on information or rejecting it are really flexible. I mean, "genome" is very abstracted—our cultural genomes, right? Because that process is, if you tell me an idea, I can filter it, think about it, decide if I want to integrate it, and so forth.

You might try to mutate my mind in some way by giving me a little bit of information, but I get to think about that and process it and decide if I want to integrate it, and decide what actions I might want to take on it. That's all really key. I think that's the extra sauce of society and culture: we have a higher rate of transfer, but we also have really good procedures for deciding if we want to allow the transfer or not, right? If I tell you a bad idea, you might remember it for 0 seconds, right? And that's important.

Tim Scarfe

Does convergence happen at multiple levels? With this hierarchy that you've proposed in mind, I can understand how the principle of least action, or something similar, will give rise to the convergence of certain patterns in different parts of the phylogeny. Then, perhaps at the optimization level, we might have a higher level, more abstract form of convergence in different parts of the phylogeny.

What I'm driving toward here is: do you think that there could be some kind of information phylogeny which can eventually transcend the material substrate? Does it resemble a basin of attraction, where patterns can't really migrate to very different materials, or do you think there's something higher-level going on which really allows patterns to move around? Wouldn't that be cool?

Yeah, I think many people have a notion that there might be something like that if we can find the right projection—a general enough theory. I don't think it's something we currently have a ton of traction on, but maybe it is. People are thinking very hard about software evolution, how that looks like, biological evolution, and all these different things.

Maybe someday we will find a notion where we realize, "Oh, right, life just has this process," and then, when we started to build software systems, it did exactly the same thing in terms of a bunch of people working on some open-source piece of code that then had a very particular evolutionary dynamic. I don't think we know what those projections look like, other than at these very coarse-grained levels: what's the macro-scale evolutionary dynamic?

So, there's still some fuzziness there, but I think the hope is that someday one can find that projection. I mean, I think in general—this is a very meta point—in general, theories are often, you know, good theories should either tell you a bunch of things that look different, or actually just a projection onto one space. When you see it at exactly the right angle, all the things line up and you realize, "Oh, that was just one thing."

Or a theory should tell you, no, at the most fundamental level, these things are provably different. There's no way to project them into the same space; they're fundamentally different in some interesting way. Or these are the similarities they share, and these are the similarities that we know provably can't be shared by the two things. To me, that's the whole goal of theories: to tell us what's the same but hiding in plain sight, where the sameness is hiding in plain sight, and what's fundamentally different.

Tim Scarfe

Similar to how we started the conversation, in this paper you said there are extant theories of life. So, comparing existing life-history theories, looking at the trajectories and principles—abstract principles for all possible life—we are a little bit Earth-centric in how we think about life. The million-dollar question for me is: could we simulate life in a computer?

Oh, it's a very interesting question. I think if you can get enough constraints and enough complexity in the environment, then there's no reason you couldn't simulate life in a computer. Computer viruses, we say, are lifelike, right? They get passed around, they have functions, they're hard to get rid of, and all these other sorts of things. Some of them might even evolve and so forth, right?

There are perpetual debates about whether anything counts as life in any context, whether that's creating synthetic life in the lab or creating artificial life in the computer. There's endless debate about where the threshold would be. I think part of that is that we don't have a strong theory.

If you and I wrote down a 2-dimensional simulation for a gas in a computer and asked, "Okay, is this obeying the second law of thermodynamics?" you and I would immediately be able to say yes or no. There's just a calculation we could do. Obviously, your computer's obeying the second law of thermodynamics: it's heating up the room, and the air conditioner is fighting against that, and all the rest.

But even in the environment of the computer, someone could look at my code and run my simulation and say, "That's a really interesting simulation you created, but I don't think it obeys—I don't think you've built in it obeying the second law of thermodynamics." Now, if we wanted to try and do the same thing for a living system, that becomes a much harder conversation.

If we wanted to say, "Okay, I really have a simulation on my computer that is life," then we're into this whole axiom space where the thresholds are, and we just don't have a good, compact theory to tell us when we've crossed that threshold. But I think in principle, there's just no reason why, with enough compute, enough constraints, and enough complexity inside some artificial world, you couldn't create life.

Now, there's a whole other question here about embodiment. There are people who have strong commitments to a certain sort of materialism that would rule out certain computer simulations. That's part of a really interesting philosophical debate, right? For me, I'm mostly interested in principles, and so I don't have strong commitments to those debates yet because I don't think we understand all the principles.

Tim Scarfe

Yeah, I mean, we intuitively know that the causal graph will be different. The energy usage will be different. There are differences, but David said something interesting: he thinks about life in terms of representation, inference, and adaptivity.

That brings up all of these interesting questions, like: is a virus intelligent? Is culture intelligent? With the virus one in particular, we kind of feel that it doesn't make sense to talk about it as being a life form when it's so obviously parasitic on its instantiation.

We're increasingly going to this abstract level now, where we're talking about things that supervene on the physical many levels down as possibly being agents or intelligent organisms in their own right. The language that we use is the same thing as in language models: we use mentalistic terms like beliefs, deception, and thinking. It's hard for us to think about this because the language that we use is so grounded in the way we do it.

Yeah.

I think that's a very interesting point. We would say that a lot of the thinking about what is life has been trying to argue about lists of axioms: life needs to have this and that and that. What you put in the list rules in and rules out what is life, and some lists account for viruses while other lists don't. We really tried to argue in that paper that the dynamics of viruses are clearly living.

Then we tried to point out that there's a really weird thing about parasitism: how we view it. If you think about a virus like language or culture, it's an organism that has a very strange environment. That environment is a host, like us or like bacteria. Viruses infect bacteria as well, so it's a very strange life form with a really complicated environment.

But we're a strange life form with a really complicated environment, right? We don't make our own energy directly. You and I didn't sit outside in the sun for an hour and a half before this interview, photosynthesizing and building up enough sugars to have the mental energy to talk about this. We ate a bunch of vegetables and other things that did all that work, right? We're already, in some sense, all heterotrophs. All predators, in some sense, are a certain sort of parasite: we require other things that are doing the primary work of energy capture and transformation.

We also have this internal microbiome, right? We're a walking ecology. So we're both parasites and an ecology. Our argument in that paper is that if you take a cyanobacterium, which is just a small organism that makes energy directly from the sun, it's simple and self-contained, and it gets all of its energy right from the sun. Maybe that thing is the most living thing.

But as you move away from that toward viruses and us, there are certain perspectives where we'd say we're not necessarily more living than a virus. There are other perspectives where we're clearly more living, right? You and I are having this conversation. We've put things on the moon. There's a certain sort of agency, prediction about the future, and technology construction that is clearly unique about many of the things that we do.

But in the wrong projection—again, thinking about this projection space—us and viruses look like the same sort of parasites living on different types of really complicated environments. So I think we can start to think about how that applies to AI and learning in general.

On this other point you made about intelligence, I think a lot of us want to put all of the things that matter to life on a spectrum, right? That's what physics does a good job of as well. I want to say that something has zero intelligence—or 10 to the minus 20 intelligence, in some units. I don't want to have this binary: is it intelligent or not? I want to be able to arrange all systems that might be intelligent on a spectrum.

Maybe that spectrum goes from 10 to some huge negative number up to some really big number, 10 to some huge positive number, and we're on one end of that spectrum. I think that's what we need for all of these things—for agency, for intelligence, for self-replication. All of those need to be put on a spectrum so that we can fairly compare them.

Tim Scarfe

Yeah. I think it's possible to have categories and spectrums at the same time, so you can have spectrums inside the categories. I'm very interested when we look at the phylogeny: we see these phase changes, and maybe emergence is a term we might use.

For example, going from abiotic to biotic. I also speak to a lot of AGI people, and they adopt a form of cognitive chauvinism where they say humans have cognitive properties that other things don't. We can have a belief in a strong sense. Our form of intelligence and agency is something to do with the types of computation we can do.

At some point we become Turing machines. We have this Promethean moment with language, or something like that. So I suppose the question is: what triggers these Promethean moments where we see huge changes?

Yeah, I think that is important. Even if you have a metric like I was just describing, that metric can have sudden jumps, and it's important then to talk about what those jumps are. There's a reason we call water water and ice ice, right? You can write down an order parameter and you get a jump, and that's cool. That's really nice.

We've been doing a lot of work to try to understand why you have those jumps over the history of life. What we typically see is that you have some set of physical constraints that matter for a class of organisms, which predicts how things will change as the organism gets bigger or smaller. We have nice theory predicting that.

Those theories also tell you that at the boundary of those scaling relationships, you often get these strong asymptotic behaviors where things go off to infinity or zero. There's some hard limit to a category of organization of organisms. That creates a wall—an evolutionary wall—and that is where a phase transition is going to happen, right? You need to do something to jump over the wall.

I'm not sure you always jump over the wall. It's not clear to me that you always get these evolutionary transitions, and I'll explain why in a second. But if you're going to get bigger than a certain scale, it says you need to invent a certain sort of architecture that gets you away from that. That architecture is characteristically different.

Going from bacteria to unicellular eukaryotes, you have to put one prokaryote inside another prokaryote. It looks like it was a bacterium inside an archaeon. That's a new sort of architecture, right? Now suddenly you have 2 genomes, you have more internal membranes, and there's something really different happening there.

When you go to multicellularity—true multicellularity, where you're differentiating cell types and creating organs and tissues and all the rest, not just living in a colony—that's another sort of organization. It requires a different kind of regulation, communication, and developmental programs to get you there. That's another phase transition.

Interestingly, when we look at when those jumps happen, they typically happen around huge shifts in Earth history, when the environment of the planet radically changes. We have a paper showing that Snowball Earth—which is this period in Earth's history that happened a few times, when the planet almost completely covers itself in ice—we think induces multicellularity. A bunch of physical conditions become just right then to get bigger and become complex multicellular organisms.

Then when the world thaws out again, that is around and spreads and becomes bigger, and you've found that solution. That's a case where, yes, there are these transitions. We understand what the wall on one side is, and then maybe sometimes you need an environmental inducement to jump the wall.

Tim Scarfe

You invoked David Deutsch in your paper. He had this book, The Beginning of Infinity, and he spoke about the importance of separating matter and logic. What did he mean by that?

I could look at a computer and just say it's a bunch of electrons moving around. It's some complicated network with a current running over it. A river is a complicated network with a current running over it. What's unique about a computer is that we've built it in a certain way to perform certain logical operations in a repeatable way, so that we can give it inputs and give it outputs.

In the case of general-purpose computers, we can reprogram them and have an arbitrary notion of what inputs and outputs we want. We can write software for them. I think that's really the key: in the crudest sense, the physical description leaves out a whole bunch of information.

To understand certain architectures, or why the architecture is there, you would need to bring in a logical or software notion. I think that's what that separation is about.

Tim Scarfe

Can we talk about assembly theory? You've got a paper out about this, and it's a way of quantifying complexity, I suppose, by looking at how something can be built step by step. Can you explain what that is?

Yeah. This is a theory initially aimed at trying to search for life in the universe. A chemist, Lee Cronin, and a theoretical physicist, Sara Imari Walker, along with a bunch of other people who have gotten involved, have been interested in this idea: how do you fairly, and without being committed to the past knowledge I was talking about before—the biochemistry we have—look for life in the universe?

Assembly theory simply says that one way to do that is to look at the recursive use of parts and what the shortest path to build an object is. Here's the thing you're trying to get away from: I hand you a molecule and I say, “Is this molecule complex?” I'm not allowed to tell you anything about the synthesis that we used to make it. I'm not allowed to tell you if a living system made it. I'm not allowed to tell you if that living system shares our biochemistry or has different biochemistry.

How do you decide if that molecule is complex? What we want is something that bounds that complexity. We want an ultimate bound on that complexity. One way to do that is just to say that when you have a synthesis pathway—say you have an evolving set of objects that are following some evolutionary lineage—you invent a set of parts, and the easiest thing to do is take those parts and reuse them in some way. If you invent a new part, that's a more complicated thing to do.

With that notion in mind, you could say, “I give you an object, and you’re just trying to find the shortest path to build it,” where you build up a set of parts and then can recursively use those to make a next set of parts. You ask how often you have to build a new part or use an old part. Each of those counts as a step, and you’re just trying to find the shortest path to get something.

That’s definitely a bound, right? Certain processes could be much more complicated in building that up, but it sort of lower-bounds the complexity. By comparing all these lower bounds of complexity, you can fairly compare how complex an object is in the best-case, shortest-path process.

This gets away from things like, if I hand you carbon-60, which has a large molecular weight, you could say, “Well, that’s a very big object,” but it’s actually not so complex in those terms, in this assembly-theoretic perspective. Experimentally, it looks like there’s a threshold where you can go from abiotic to biotic. Each step in assembly space is in a very rapidly growing space of combinatorial possibilities, so each step is a really big step. You would expect a sharp cutoff somewhere, and it looks like that happens in the experimental data, which is exciting.

Tim Scarfe

Chris, this has been absolutely amazing. Thank you so much for joining us.

It’s been a blast. Thank you so much. Yeah.