Note: this is cross-posted from the post here, where I had a few videos that I could not add in here - see the original post for the full experience

I spent the 6 years in my Ph.D. thinking of the broad topic of origins of life, or “abiogenesis”: how does non-living matter turn into living matter? This was a lot of fun, big ideas, wild speculations, and crazy discussions with friends and colleagues – along with heart-wrenching frustration of trying to actually produce some concrete novel scientific results in a topic this big and old. When the smoke cleared, the few concrete results I managed to publish were annoyingly narrow and specific, or abstract and hard to follow. All in all, the relationship between the big exciting question and my published work is probably clear only to me, since journals don’t like publishing a 10 page philosophical discussion in the intro. So I decided to take the matter in my own hands and publish said discussion in this post. I’ll try to keep it shorter than 10 pages, will avoid getting too technical, and will illustrate the ideas on a concrete example system that I studied in my research, but that was too simple to warrant its own publication. A word of caution right from the start: this article will open a lot more questions than it will give answers, so rather than explaining how life originated on Earth, my intention here is to set some groundwork for future research on this.

So where does one start to think about how life came up here? Most people start by looking into the chemistry of the primordial molecular soup, and then ask questions like: “how could some simple self-replicating molecule first come up and transmit genetic information?” (termed “RNA-first” approach), or perhaps “could a group of molecules learn to stick together in a little puddle that could eat, self-heal and adapt?” (termed “metabolism-first” approach). Being a physicist, and worse yet a theorist, I started from a totally different point: what is the simplest possible dynamical system I could find that could show some signs we might typically associate with being ‘alive’? The hope was that if found, I could then study such system in detail, and understand what caused it to cross the line from apparently “non-living” to “living.”

This formulation already hints at one unique aspect of origins-of-life research: that we don’t exactly know what it is we are even looking for! If we look on the fundamental molecular scale, it might not be very obvious where we should draw the line between living and non-living. If so, this distinction becomes largely a matter of our human intuition and our colloquial use of the word “living.” Even within biology, there isn’t a consensus on a clear definition: rather than defining life, they try to describe some key aspects of life (like growth, reproduction, metabolism, etc.), but make no claim to these conditions being necessary nor sufficient. In looking for extraterrestrial life, NASA tried to be less committal about all these conditions, defining life to be merely "a self-sustained chemical system capable of undergoing Darwinian evolution."

But I did not want to restrict myself to looking for emergence of only chemistry-based life. In our familiar example of life, the variety of possible chemical interactions is what mediates most of the structure-formation, information-processing, and movement of the organism. But we already know that this isn't the only possible way. Our computers are capable of wonderfully rich, complex and intelligent behaviors that is underpinned not by chemistry, but by electronics. In particular, some behaviors of living organisms can already be replicated by computers in a way that is indistinguishable to an outside observer (passing some generalized Turing tests). I.e., the same life-like high level behavior can sometimes be implemented using two different microscopic "hardware" - chemistry or electronics (cf. universality).

As such, giving chemistry a monopoly over "life" seems quite restrictive to me. Sure, we don't yet think of our computers as "alive" - but if we discover an extraterrestrial civilization of sentient robots, it seems restrictive to dismiss them as "non-living" merely because they are not using chemical interactions to manifest their actions.

And so, if we want to study the origins of life in the most general sense, and try to isolate the simplest possible example of it, chemistry may be too complicated a system to start with. Which brings us back to the question: what is it that we are looking for, and how do we know when we find it?
 

"Life" as an effective description

In practice, we tend to think of "life" as a "you-know-it-when-you-see-it" sort of phenomenon. And this is already a good place to start, as it directly raises the question of "how do we know things?", or more precisely, "how do we ascribe categories and labels to things around us?" It might at first seems like a cognitive science question - and, in fact, this was where I first started studying it. But thankfully, it is by now fairly established that much of our cognition may be described in terms of information processing - and information theory gives us some precise tools to work with questions such as this. Which finally brings me to a topic where I was able to make concrete technical contributions to warrant a couple publications.

The first thing to establish here is relativity of "truth": "all models are wrong, but some are useful" -George Box (also see this blog post). More precisely, while it is unclear what it means to ask for a "true" description of the world, a much clearer question is to ask for an effective description. In interacting with the world, our brain looks for such effective explanations of the complex sensory inputs we get streaming in. This way, we learn to segment the kaleidoscope of colors seen by our eyes into patches we call "objects," each imbued with its own sets of properties and characteristics (see this post for more on this). Moreover, each such description will be specific to its relevant use-context: so while the atomic theory of matter may be the best description to a physicist designing new experiments, it will not be the most effective to that same physicist to safely drive home after work. Fun fact: even in math - the bastion of black-and-white truths - some of the long-standing questions about nature of probabilities are now finding progress by shifting the focus away from what is "correct," and towards what is "useful" for winning a particular game (e.g., see Deutsch's paper).

This way, rather than arguing about whether something is "really" alive or not, it is more fruitful to ask whether calling it alive is useful to whatever task it is we are doing. The beauty of this approach is that information theory gives us a concrete way to put a number on "effectiveness" of a description - and thus to objectively say which description is the "best" (most effective) in a given context (check out our paper on this).
 

Inverse causality?

One fun hypothesis I have here is that we can identify "living" things as systems whose most effective description has reverse causality (future causing the past). While this might sound surprising at first, it is actually how we habitually understand living things: we explain their present actions in terms of their future goals (cf. Dennett's intentional stance). For example, why is the chicken crossing the road? Getting to the other side is a potential event in its future that could explain its current actions. If we later see that the chicken found a seed in the middle of the road and came right back, we might update our explanation retrospectively to say that actually it just wanted to get that seed. In either case, we probably would not revert to the direct forward-causal explanation of its actions, as that would require us to describe the state of its neurons and sensory input in minute detail. While such causal explanation would be microscopically "correct," it would usually be much less practical or effective than the one in terms of intentions (reverse causality).

This is in contrast to descriptions of physical non-living systems, which do seem to prefer forward-causal explanations. Historically, in fact, we spent a long time trying to describe physical systems in terms of their intentions or future states (e.g., "a ball wants to roll downhill"). Aristotelian physics, which dominated our understanding of the world for almost 2000 years, explained the motions of all things in terms of their desire to re-establish "the natural order" (with earth at the bottom, then water, air and fire moving up). Nonetheless, when Newtonian physics came about, it showed that describing motion in terms of forward causality was a much more effective approach that allowed many new practical applications.

Still, when it comes to living things, intention-based or goal-oriented explanations seem to be more effective for now. As such, to look for some minimalist "origins of life," we could try to look for some self-organization phenomenon in a simple physical systems whereby an apparently reverse-causal description becomes more effective than the microscopic forward-causal one. Since we can use information theory to quantify the relative effectiveness of the two descriptions, we can thus directly look for a crossover point where "non-intentional" matter turns into effectively "intentional" matter. Since I only arrived at this idea towards the end of my Ph.D., I did not actually get a chance to work it out (though I do think it's promising and perhaps will get to it someday - feel free to reach out if you want to collaborate on this!). Instead, during my work I used a less precise, more intuition-based heuristic to identify "living."
 

A "minimal interesting definition"

Rather than looking for a "correct" definition (which we could never sell everyone on anyway), I looked for a "minimal interesting definition" of life: just something that we might clearly find surprising and exciting if we saw a non-living thing do it "on its own" (without any intelligent designer). Imagine you're an alien that came to Earth and has no clue what organisms or life is (you've a very different alien) - could you tell that something strange / surprising / interesting is happening here, compared to some "dead" planet? What would you look for? Just as biology uses a list of descriptors to try to identify “living,” let’s try to identify a few abstracted criteria we might look for. If we don’t restrict ourselves to chemical systems, and ultimately want to study this in simplest possible dynamical systems, then the above list from biology cannot be directly applicable – as concepts like “growth” or “Darwinian evolution” are themselves quite non-trivial if we are looking at, e.g., the dynamics of atoms and don’t have a well-defined notion of which atom cluster is to be considered an “individual.” We need to start much more basic than that: for one, whatever it is we’re looking for must be somehow unusual, and for the case of origins of life, must arise spontaneously:

1. Driven self-organization: the system finds some highly atypical, fine-tuned configurations that are selected and stabilized by dissipating energy from external driving forces [cf. metabolism]

E.g., of all arrangements of atoms, just a few select ones (which we call organisms) can thrive in a given environment. Here we use “external driving forces” (or simply “the drive”) as a generalization of “environment” from biology – the external influences experienced by our system. Such environment must play a key role in our definition, since we still need some way to distinguish “the special arrangement of atoms making up this one particular rock” from “the special arrangement of atoms forming the miracle of life.” This gives us two more criteria:

2. Adaptation: the selected configurations carry information about the structure of the driving forces, and can adjust and re-learn if the drive changes slightly / gradually [cf. responds to the environment]

3. Prediction: the selected configurations can use this information to anticipate / predict the drive

These criteria now require us to look for configurations that are not only special, but also a little bit ‘smart’ – they know how to survive (remain viable) in their specific environment and can also adapt to slight environmental changes. One key advantage thus becomes possible for such configurations over others:

4. Self-healing: the fine-tuned configuration is restored after most small disturbances, using the energy from the external driving [cf. homeostasis]

This allows such “alive” configurations to be more stable in the long run than their non-living counterparts: while granite may be more rigid, it irreversibly erodes with time, while a living population can adjust and heal, thus persisting over generations. I think one other interesting aspect of this is that while most disturbances typical in the organism’s environment will heal, some specially chosen adversarial perturbations will not (e.g., a small bullet to the head). Another aspect I find curious about living systems, although perhaps not as important as the others is

5. Persistence: if the external driving is stopped, the fine-tuned configuration persists for some time, retaining a memory of the drive’s properties [cf. heredity]

If I find a shell on the beach, it is not alive and does not exhibit any of the properties I described – and yet we somehow recognize it as special, fine-tuned, and capturing some of the properties of the oceanic environment in which it developed. After a sufficiently long time, it will disintegrate completely into sand. Still for some transient time after the organism’s death, I can use the corpse to infer much about the environment it lived in and the challenges it faced.

Note that these criteria, while far abstracted, fall in the camp of “metabolism-first” approach to origins of life – since in our context we lack a clear concept of an individual to talk about “replication-first” approach.

Toy examples

We can now consider what systems might fit these criteria. And immediately we run into an apparent disappointment: the equilibrium distribution of some particles diffusing in a potential energy landscape pretty much fits all of these! Of course, this would not be “driven,” as it is an example of equilibrium self-organization – but it would be fine-tuned (particles sitting only in the bottoms of potential wells), the particle distribution would carry information about the shape of the potential landscape, it would adapt to small gradual changes of the landscape, would self-heal if perturbed, and persist for some time if we suddenly remove the landscape.

Still, I think we are on the right track with this – why not think of different coexisting organism species in a given environment as the local optima of some effective energy landscape? The question then becomes how such an effective energy landscape can emerge in a complex far-from-equilibrium context. The criterion that the configurations should somehow be “predicting” the driving forces is also missing in the example of energy landscapes – so let’s see if we can get that one too.
 

Kicked Rotor

To do this, let me introduce a simple toy-system – only slightly more complicated than particles in an energy landscape, but with very interesting emergent dynamics – the Kicked Rotor. Consider a simple pendulum, allowed to rotate all the way around its pivot. Now imagine that the gravity, rather than being always constant, gets switched on for a brief moment once every second:

[see video at in the original post]

The configuration of this system is thus fully specified by the rotor’s angle and angular velocity (θ, ω) at the time of kicks, and follows the equations of motion:

where n is any integer – to make the periodic kicks with period τ, and K - the kick strength. This system is non-equilibrium because of the external periodic kicking – which thus constitutes the “drive” we referred to in our criteria. For strong values of kick strength K, this system is fully chaotic for all configurations (see K=7, τ=1 in the figure below), for weak K, it approximates a regular pendulum, which is everywhere non-chaotic, or “orderly” (see K=0.5, τ=1). The interesting behavior is between these extremes, where we get “mixed chaos”: depending on the initial configuration of the system, it will either move around chaotically, or orderly. Such a structure immediately implies that the “sea of chaos” and “islands of order” cannot mix – if you start in one, you’ll stay in it always.

This way, we have a dynamical system that can either be in disordered chaotic behavior, with no structure or predictability, or in a structured orderly behavior, whose properties are matched to and encode the information in the drive (the only information in a drive as simple as this is the kicking strength and period – both of which are reflected in the location and shape of the islands of order). While certainly oversimplified, this seems to reflect some key features we were considering for a “minimal interesting definition” of life: we can heuristically think of the chaotic states as “inorganic dust,” while the ordered motion acts like “primitive organisms” - sustained by anticipating and coupling predictably to the environmental forces. For values of K around 5, the sea of chaos accounts for the vast majority of system configurations, and so any orderly motion can be reasonably said to be atypical and fine-tuned.

So now the only thing remaining for our toy example of “origins of life” is to explain when, how and why the dynamics starting at some point in the sea of chaos could end up in one of the islands of order – so starting in an inorganic, chaotic state, why would our system learn to encode and predict the environment?

The beautiful answer here is that all we need to do to achieve this transition is merely make this idealized system a bit more realistic. A real pendulum would be embedded in a thermal bath: air molecules that bounce against it and create atmospheric drag. This would modify our equations of motion to be:

where b is determined by the bath density, and T – its temperature, with ξ being standard white noise. This small modifications has profound consequences on the system dynamics: at a sufficiently low T, the entire sea of chaos becomes unstable, and all trajectories eventually go to one of the islands of order:

Heuristically we can understand this in terms of energetics: in order to stably maintain “spinning” configurations (with ω > 0), we must resist the dissipative drag force, which requires a steady input of energy from the drive. In the chaotic state, the system couples to the drive in unpredictable, essentially random, ways – and so on average gets little energy from it. In the ordered states however, the energy input is steady and persistent. Moreover, in such ordered states the energy drawn form the drive can be tuned to match the needed dissipation - by moving the islands of order slightly left or right. Such tuning happens spontaneously in response to changes in system parameters - e.g., if we increase b (or vary K or τ) – thus fulfilling the “adaptation” criterion we were looking for: as we vary the drive parameters, the system state gets sort of “stuck” to the islands of order as those adjust their location – as long as we vary the parameters slowly.

This way, it seems that this system gives us everything we were looking for: spontaneous fine-tuning to encode and anticipate the behavior of the external drive (kicks), which adapts to variations in the drive properties, and is stable to small external perturbations. It also exhibits persistence in the sense that if the kicks are stopped, the pendulum continues to spin around at its current speed for some (short) while before it gets damped out – and so by looking at its motion directly after the kicks were discontinued, I can infer the properties the kicks had. The following video illustrates this point: starting with a bunch of uniformly distributed initial conditions, we see all the system configurations eventually find one of the islands of order and settle there. When we then turn off the kicks towards the end of this video, the phase θ of the islands (on the horizontal axis) is forgotten immediately, but the speed ω (on the vertical axis) persists for some time and can be used to infer the period τ the kicks had:

[see video at in the original post]

So overall, we can think of this behavior as giving us an effective energy landscape in the system’s configuration space, with the islands of order being its local minima. The different islands are sort of like “different possible species” of animals that can stability exist in this environment. To make the analogy to energy landscapes more formal and precise, in our papers we defined a quantity that we called “Rattling” – which captures how noisy / messy the dynamics are at a given configuration. This allowed us to define Rattling landscapes and make testable predictions about system behavior in such landscapes. Namely, we argued that spontaneous discovery of low-Rattling configurations is a generic property of damped-driven dynamical system – and verified this in a bunch of toy examples from the Kicked Rotor here, to a robotic swarm which we built and tested in the lab (check out the paper here, and also cool pictures / videos of the self-organized dynamics across a variety of systems on the NotArt page).
 

Satisfying?

So how satisfying do these results feel in the context of understanding the origins of life? Of course, our examples are oversimplified and the minimal interesting criteria we listed for “living” are still quite far from our conventional understanding of the word. The Kicked Rotor example seems, on the one hand, quite exciting and miraculous, and on the other, far too boring to be meaningfully compared to living systems. To me, one particularly promising and general insight we get here may be states as “dynamical systems with mixed-chaos dynamics will spontaneously discover ordered behaviors when coupled to a dissipative bath at low temperature.” While this conjecture remains to be verified, it does feel relevant to origins of life:

1. whatever dynamical system underpins life, it will likely be capable of both chaotic and ordered dynamics (i.e., mixed chaos);
2. once the system is subjected to dissipation, it must find a way to couple predictably and orderly to the available energy sources (drive), or else damp out and become inert;
3. starting from many different initial conditions, while many trajectories might damp out, some will find the islands of order where the dissipation is reliably matched by energy input from the drive. These states may be exactly the ones we then call "living."
4. The "low temperature" condition here evokes a possible view of such self-organization as a phase transition, which has been suggested as a perspective on origins of life by a number of authors.
    

Darwinism

What’s still missing then? What other key ingredients do we need to have something even remotely life-like? To me it seems that, in line with NASA's definition of life, finding some form of Darwinian evolution is key – and this comes with a whole bunch of complications. In the familiar context, we need some sort of self-replication with a balance of heredity and mutation, as well as an environmental selection mechanism. That is a lot to ask of simple dynamical systems. But in the above example, we already have a bit of this flavor: while not quite “survival of the fittest,” we could describe the spontaneous discovery of the islands of order as “survival of the stablest” configuration. As such, there is already a selection mechanism there given by the structure of the drive! We could stretch the analogy and say that there is also heredity in that the system’s configuration at a given moment gives rise to a very similar configuration in the next moment (i.e., heredity), and mutation due to the additional thermal noise ξ in the above equation. The main advantage that self-replication gives over this scenario is that it allows for more exploration around already successful configurations – thus increasing the chances of finding the islands of order faster.

It’s interesting to consider what self-replication might look like in simple dynamical systems. For the Kicked Rotor example above, we considered a “self” to be a particular dynamic configuration of the system – not the physical Kicked Rotor system itself, but a particular way in which it moved. This is somehow similar to the case of origins of life in the primordial soup: a cell is not so much a particular set of atoms themselves (which were always there anyway), but rather a particular dynamical arrangement of these atoms. And so self-replication is not about creating a new set of atoms, but rather about inducing some atoms in the surrounding environment to arrange themselves into a dynamical structure similar to the parent (cf. auto-catalysis).

In the language of dynamical system, this sounds a lot like entrainment - where one system induces another to copy its dynamical state through a weak coupling between them (e.g., synchronizing pendulum clocks). In the case of the Kicked Rotor, we can imagine two weakly coupled such Rotors, with one spinning in an island of order, and inducing the other to transition into that same island from a chaotic initial state. I did some preliminary numerical experiments on this – by putting together a 2D lattice of weakly-interacting Kicked Rotors (with interactions like in the XY-model) and seeing if neighbors would tend to find the same islands of order, thus forming “magnetic domains” of sort. Here is a video showing the dynamics from random initial conditions: each node is a Kicked Rotor, with links showing interacting neighbors, node color shows the rotor angular speed ω and the node gets a black circle around it when it is in one of the islands of order:

[see video at in the original post]

This worked somehow, as we see neighbors tend to end up in the same island of order – though much development remains to allow for Darwinian-like evolution of these dynamical states to be possible. One limitation is that the simple Kicked Rotor already learns as much as is possible from its simple environment – not much there to predict in a periodic signal! To allow the possibility of more interesting behaviors, it needs to face a more interesting challenge – and it is not obvious how to increment the challenge here in a smooth way.

Conclusions

In this post I tried to give a high-level overview of my understanding of origins of life based on the available current literature, many discussions with other fun smart people, and the concrete research I did over the years of my PhD. It seems to me that lots of great results and example systems are available these days showing a variety of relevant emergent behaviors, both experimental and theoretical – but we are still needing some paradigm shift in how we think of these questions before we’ll be able to unify all such examples in one framework and claim an understanding of the origins of life. One of the key problems, I think, is that we still lack a clear definition of what it is we are looking for – what is life? what is agency? In the above, I discussed these questions and proposed some of my own thoughts on the issue. I then presented a toy example that I find quite illustrative: the Kicked Rotor. I think this system does a good job fitting a lot of the criteria we might have for an example of the origins of life, while at the same time seems far too simple and boring to be too relevant to the question. This highlights how much lacking clear goals and definition holds back our progress.

Another problem I mentioned is that we don’t have a clear understanding of the role the environment and its complexity plays in this process. To encourage emergence of complex structures, we need to pose complex problems. But does this have to be externally imposed through a pre-defined environment, or should we look for open-ended evolution cascades - where an “ecology” emerges spontaneously and automatically forms an ever-more-complex environment? Combining these two problems, we might even wonder whether environmental complexity might need to serve as a part of the definition of life itself - as I tried to suggest by including the ability to predict and anticipate its environment among the criteria for "life."

All in all, the question of origins of life remains wide open, and is becoming intertwined with many other key questions about complex dynamical systems, information theory, agency, AI and even social dynamics. But even if we haven’t found many satisfying answers yet, it does seem to me that we are finally starting to ask the right questions.

[Cross-posted from my personal blog here]