Michael Levin has been a pretty big intellectual influence on me since being more formally introduced to his work by Pro during the after hours of the Systems Distributed 25 conference in Amsterdam, last year. A lot of my research time and overall thinking since then has been about getting a real mental model of both what is Levin really looking for, and what are the questions/goals in the fields he’s in really about (I lack a lot of the formal knowledge on biology etc to truly understand some of his research).
Later in December, with Pro once again, we spent over a month on and off in the same city, meeting nearly every day and discussing Levin’s ideas and research, sharing his papers, having various, unrelated, math workshops and discussing and debating our thoughts. This led us to considering taking a more serious stab at answering our own questions along the ones which we feel are still open all around Levin’s research program. So we started a small and independent research lab, which I’ve been working on since then.
First, here’s a bit of context: he is a developmental and synthetic biologist at Tufts University, where he runs the Allen Discovery Center. He has this experimental program and this empirical way of looking at things along with a philosophically-charged way of interpreting the results. He’s done a lot of research over many years on things like planarian regeneration, ectopic eye induction, cancer as a collective goal-scaling failure, bioelectricity, xenobots, anthrobots, etc. A lot of his research centers around the concept of diverse minds, collective intelligences, non-neuronal cognition, bioelectric networks and various other things.
There are different layers to Levin’s work: he has a truly solid, scientific approach and has made some stupendous discoveries, and he interprets some of these using a truly unique teleological mindset (at least, to my knowledge). Partly, this is what has allowed him to be able to think of the experiments he has done. It’s also a very broad research program, with many different layers and angles and as I mentioned, I found it soaked in profound philosophical implications. Overall, it’s been energizing and refreshing, inspiring and mind-expanding. It’s also helped me concretize a lot of the thoughts I had on intelligence as whole, which I had a lot of floating around since I started thinking about it more rigorously in late 2022 with the rise of LLMs. At the same time, because of my own varied interests, I think I am in a fairly niche position to eventually help out and further that research (or at least, interpret it and link it to other things!), even in some small ways.
I want to try to introduce his work here because I think that his research program is fascinating and his approach feels relevant to many (even in say, the ML field) but also because a lot of what I’m working on lately is downstream of it, in many ways.
This whole article is a barely touched up 31 minutes transcript of me talking about all of this off the dome, so I do not think it’s a solid all encompassing introduction. His youtube channel has many longer, better introductions to slices of his work, although you have to dig in and spend some time with all of it before you get the sensitivity required to paint an accurate picture of Levin’s approach and latent claims and conjectures (off of his undeniable empirical work).
A soft introduction to Levin’s experimental program
Arguably, one of Levin’s core thesis is that cognition is a “graded, substrate-independent continuum” rather than a binary property of brains. A central idea, which is empirically supported by his research, is that intelligence exists at every scale, from ion channels to cells to organs to organisms to swarms or societies, and one of his mental models for this is what he calls the cognitive light cone: the spatiotemporal range over which a system can pursue goals. It does sound a little abstract, but it is backed by a very concrete experimental program, and I think the best way to get a sense for it is to first walk through some of the experiments and findings he’s had.
Xenobots are these living organisms that are assembled from embryonic frog cells and they have behaviors which are not present in the source organism and can’t be explained by things like evolution. They weren’t evolved, they were completely manufactured, and yet they still exhibit behaviors which are not encoded in the physical substrate that is a xenobot, which is a bunch of frog cells. Where did those behaviors come from?The seminal papers: Kriegman et al., “A scalable pipeline for designing reconfigurable organisms,” PNAS (2020); and Kriegman et al., “Kinematic self-replication in reconfigurable organisms,” PNAS (2021), where xenobots were shown to self-replicate through a mechanism with no evolutionary precedent. ↩︎
In planarian regeneration you have these flatworms which can regenerate with different head-tail configurations based on bioelectric signaling. If you cut a planarian worm, it will regrow. Cut the head off, it grows a head. Cut the tail off, it grows a tail. What Levin has done is modify the bioelectric signals that the cells receive to grow two-headed planarian worms. They manipulate the gap junction connectivity and they permanently rewrite what is essentially a bioelectric memory, and then subsequent amputations, even without further intervention, produce two-headed worms, many times over. You do it once and then they regenerate two heads indefinitely. It’s a showcase of bioelectricity as a kind of “pattern memory”.See Levin, Pietak & Bischof, “Planarian regeneration as a model of anatomical homeostasis: Recent progress in biophysical and computational approaches,” Seminars in Cell & Developmental Biology (2019), for a comprehensive treatment of the bioelectric mechanisms underlying this. ↩︎
There’s also the Picasso tadpole experiments (Vandenberg et al., 2012). Tadpoles need to rearrange their face to become frogs, and it was assumed this was a hardwired process where each organ just moves a fixed amount in a fixed direction. They tested this by surgically scrambling the tadpole’s craniofacial layout: eyes on the back of the head, mouth off to the side, everything in the wrong place. The animals still made quite normal frogs, because the organs navigated through novel paths that don’t occur in normal development, sometimes overshooting and correcting. Separately, Levin’s lab has shown that this target anatomy is prefigured in a bioelectric pre-pattern, an “electric face” visible in voltage imaging long before any genes turn on to regionalize the actual face. So the system has a target and can navigate to it from configurations it has never encountered, which is striking evidence for goal-directed navigation in morphospace.
As another example, he’s also got this paper on “ectopic eye induction”, where eyes are induced at arbitrary locations on a frog’s body and cells migrate and self-organize to form functional visual structures, which indicates that the target morphology acts as an attractor that is accessible from wildly different initial conditions.
One other interesting approach from Levin is his reframing of cancer as a breakdown of the bioelectric network that maintains the higher level collective tissue-level goals. When cells lose their connection to the tissue-level cognitive light cone, they revert to doing their own thing e.g. proliferating and migrating, basically acting like unicellular organisms again. His lab has shown that if you reconnect tumor cells to normal embryonic tissue via gap junctions, the cancer actually reverses.See Chernet & Levin, “Long-range gap junctional signaling controls oncogene-mediated tumorigenesis in Xenopus laevis embryos,” Frontiers in Physiology (2014). ↩︎
Anthrobots are also worth mentioning briefly: they’re made from ordinary human tracheal cells (not frog cells), and they spontaneously develop distinct swimming behaviors, with around 9,000 differentially expressed genes compared to the source tissue. They can even repair neural wounds. The fact that human cells, outside their normal context, self-organize into something with novel competencies makes the same point as xenobots but without the “amphibians are unusually plastic” objection.
It goes on and on. He has so many people working around him, in different domains, from physicists like Chris Fields to people in C.S, many of them contributing to what’s become a broad research program on basal cognition – the idea that non-neural biological systems exhibit genuine cognitive properties.See Lyon et al., “Reframing cognition: Getting down to biological basics,” Phil. Trans. Royal Society B (2021), which Levin co-authored, for a good entry point into the basal cognition program. ↩︎ There’s just a lot to digest.
Maybe the most important thing I am struggling to convey here, is that, this cancer case from above, is a perfect example of the value of having a teleological approach vs a pure mechanistic, reductionist approach. If you think of cancer purely mechanistically, eg it’s just genetic mutations that cause some uncontrolled proliferations, the experiments you’re gonna come up with are mostly going to be these very micro-managed things like figuring out how to kill cancer cells, or mediate the mutations, or mediate the effects. But if you take that teleological approach of cells losing their connection to a higher-level goal, then you could much more easily come up with ideas to experiment with “what happens if we somehow reconnect them to the collective and see if they remember their original goal”. This is truly a key part of his approach, that I hope sinks in here or that one keeps in mind if they decide to read up on Levin’s work.
Interlude - on criticisms to the methodologies and some semantic stretching
Despite the strength of the empirical results Levin’s approach have yielded, there are sometimes issues with his theoretical framing. I don’t believe it to be “meant”, in so far as I don’t think there is really any malice, but it would be good to point them out. This criticism is most visible when he applies his framework to purely computational models, where he often has a tendency to redefine mechanistic concepts to fit his teleological narrative (which again, is very fruitful! But I have to mention this).
As a clear example is his 2024 paper Classical Sorting Algorithms as a Model of Morphogenesis (Zhang, Goldstein, & Levin). This was the first paper I went in and reproduced, played with the repository, and the first one we wrote a follow-up on (just a preprint on Arxiv). Levin sells this paper incredibly well, and it is very interesting, but my problem is with his framing: he says this works demonstrates that “plain bublbe sort” possesses unexepected, emergent competencies when implemented on unreliable hardware. However, the actual implementation breaks some of the key fundamental assumptions of classical sortnig, namely: it replaces top-down deterministic execution with a decentralized, cellular automaton-esque approach where individual array elements act as independent “agents” which are subject to simulated hardware failures (such as “frozen” cells).
The “surprising” behaviors that emerge, and that are mentioned in this paper, such as elements navigating around obstacles or algorithsm spontaneously clustering, are much better understood when looked at for what they are: dynamics of decentralized cellular automata. If you inject non-determinism and “agent-based” local rules into your bubble sort, it is a tough sell to say that “this is just plain bubblesort”. This is a very misleading way to interpret the results which are still interesting without this unecessary framing, imo.
The loose application of computer science concept does warrant some caution. It did also make me wonder: if his computational analogies are sometimes strained, or at least over-interpreted, is there similar “semantic stretching” happening to his biological interpretations?
Thankfully, a lot of his empirical work is is undeniable, but often the teleological vocabulary associated to it is like a double-edged sword: it’s what empowers him to look at these things in the first place, but in some places, it projects a lot more than I think is warranted. If anything, this paper should have been much more honest with what the results they noticed.
[[need to add quote here on “this algorithm has been understood for 70yrs”, “deterministic etc”, and allusions to “free lunch”]]
Key approaches and frameworks
The spectrum of cognition
Because Levin has been going at this for a long time and the scope of it is so board, I want to try and talk about some of his more recent work and maybe of the more subtle philosophically interesting parts.
He and Chis-Ciure published Cognition All The Way Down 2.0 in 2025, which was a follow-up to Levin and Dennett’s earlier piece from 2020, and what they tried to do there is to formalize biological intelligence as a sort of search efficiency, the ratio between random search cost and how efficient a biological agent is comparatively in a given problem space. So instead of asking “is this system cognitive?”, you get to somewhat grade “how efficient is this system at traversing this given problem space?” It’s more of a gradient than a binary, and under their conservative assumptions, planarian head regeneration turns out to be a sextillion-fold more efficient than random search, which is pretty neat. There’s a lot more cool stuff in that paper. Even amoeboid chemotaxis is hundreds of times more efficient. These numbers come from the Cognition All The Way Down 2.0 paper, Chis-Ciure & Levin (2025). ↩︎
Related to this is the persuadability spectrum from the Mind Everywhere papers (2026, with Resnik). It’s a conceptual tool where you place systems on a continuum from low persuadability to high persuadability. A system that has to be physically forced into its states is low persuadability, like a clock. It’s mechanical, you have to engineer it in such a way that it is physically forced into its state. A thermostat is more persuadable: you build it in a certain way and then it is convinced through information to adjust its state to reach its goal. And then you have things like us with decades-long plans and global coordination.
One of Levin’s points is that where a system sits on that spectrum determines the optimal interaction protocol, and if you recognize that some biological system is more persuadable than expected, that changes how you work with it. I think this is really what empowers Levin to have these experimental breakthroughs and allows him to not think of cells as these things that need to be micromanaged and forced into specific states. He’s trying to find ways to communicate goals to collective intelligences at various scales and then let them use what they can already do to get there.
“Technological Approach To Mind Everywhere”
Then there’s the TAME framework, the Technological Approach to Mind Everywhere. The core idea here is that the formal tools that describe neural computation can also describe things like pattern recognition in non-neural tissue. The original TAME paper is from 2022 and the Mind Everywhere papers (Parts 1 and 2, 2026, with Resnik) are the fullest philosophical defense.Part One is basically a historical review of teleology and a showcase of the current experimental evidence. Part Two tries to propose a mentalistic approach to teleology informed by cognition, intelligence and intentionality, not as a metaphysical commitment but as a hypothesis about what the optimal interaction protocols are with these systems. ↩︎
Here are, imo, some of the key concepts:
The fecundity criterion. How do you evaluate whether a framework is worthy? In a very Deutschian way, it is not by asking whether it’s true in some absolute sense, but rather whether it generates novel predictions and enables you to gather new empirical data, that generalizes things, that is resistant to novel data. The mentalistic framing of cells as agents with goals is truly what I believe has allowed Levin to find these novel things and do these experiments. The reductionist alternative wouldn’t have put you in the mental frame to even attempt them. Reframing cells as agents with goals and thinking about collective intelligence and the nesting of cognition at different scales has been very productive for him, and I think there are a plethora of things here to be inspired by regardless of your exact field.
Polycomputing. The same physical substrate can simultaneously implement multiple computations at different scales, and the more nested that is, the more complex the goal-orientedness can be. A cell is simultaneously computing its own metabolic goals, active in tissue-level pattern formation, and contributing to organism-level morphogenesis. The ion channels and the voltage states carry information for several levels of concurrent processes.
Operationalized teleology. The cognitive and teleological claims are really hypotheses about what’s the best toolkit to interact with and predict the system. When you call a cell “goal-directed” you’re not making some deep cognitive science claim, you’re making a claim that the conceptual apparatus and toolkits from behavioral science will be more productive than a purely mechanistic reductionist description.
There are a lot of very thought-provoking and potent ideas there, and so much of it is by clean scientific experiments and empirical observations. Again, a big part of the appeal of his program.
Bioelectricity is central to all of this. Levin considers bioelectric signaling to be a sort of cognitive glue, or computational medium. In the case of molecular biology, it’s concrete: you have gap junctions that form a network substrate, voltage patterns across cell membranes that encode information about target morphologies, etc. I think the planarian two-headed regeneration experiment illustrates the full stack pretty well: bioelectric pattern memory, gap junction networks, and collective goal navigation, all in one system.
What’s with all this Platonic space talk?
Where do xenobot behaviors come from? They weren’t evolved. They definitely weren’t engineered to swim or replicate. The genome is frog, the selection history is frog, but the behaviors are completely novel. If competencies can “emerge” in systems with no relevant selection/evolutionary history, then you need some account of where those competencies were before they were instantiated, or at least that is Levin’s angle of approach. That’s what I think kind of forces, in a good way, toward the idea of a structured space of patterns. Levin has this idea, this framing, that physical systems (computers, xenobots, machines, embryos) are pointers to a space of patterns. There are “interfaces through which these patterns ingress into the physical world” (that’s a verbatim quote). Something Levin says often is that you get more than what you put in, and that the mapping between an interface and the pattern it channels is not linear, it needs to be investigated and explored. To call up the patterns you want, you have to look beyond the pointer towards the structure of the space. I think it’s important to mention a few things, off the bat:
- Platonic space is overloaded and heavily connoted depending on the context. He uses it fairly loosely, has been moving away from that exact terminology and people shouldn’t get caught up on the Platonic part too much
- As with the fecundity criterion discussed above, Levin’s approach here is in my opinion, thoroughly Deutschian: the value of the framing is in what it generates, and it has generated a lot.
There’s a quote from his 2025 article Platonic Space: Where Cognitive and Morphological Patterns Come From that captures pretty well what his notion of Platonic Space in one of its latest rendition:
Triangular objects are haunted by the spirit of relevant rules of geometry, while brains are also able to pull down and force the incarnation, literally bringing into meat, of patterns of a very different kind in sophistication. I propose that the objects on which we often fixate in physics, biology and AI, be they embryos, machines, language models running on PCs, or robots, are just pointers […] to the deeper space of patterns.
So yeah, his argument is something like: physicalism is already known to be incomplete because both engineers and evolution can exploit what he calls “free lunches,” facts about prime numbers, bounds on physical constants, certain computational properties, etc that are genuinely useful and guide physical events but are not set or modifiable by physics. So there’s something else out there, something closer to having to do with the nature of Mathematics, and his move is to kind of extend classical mathematical platonism and conjecture that this space doesn’t contain only what he calls “low agency” forms like geometric truths and number theory but also these higher patterns, these “kinds of minds”.As mentioned, Levin is careful about the naming: “I chose it because mathematicians immediately know what I mean… but I make no attempts to stick close to Plato’s views.” From A Short Argument on Platonic Space (2026). ↩︎ Physical bodies in his view don’t create minds, they are pointers that enable the ingression of patterns from this space. Whenever anything is built at all, whether it’s an embryo or a machine or an AI, it acts as an interface to patterns that guide its form and behavior beyond what is encoded in the algorithmic or material architecture alone.
This relates to his concept of cognitive light cones. His idea is that mind precedes and is a superset of life, and that what we call living things are things that are really good at scaling up the competencies of their lower-level parts into collective intelligences with bigger cognitive light cones. An ion channel has a cognitive light cone of a couple nanometers and microseconds and it just responds to local voltages whereas an organism like us has years temporally and global reach spatially. Same with societies and generations and planetary-level cultural stuff. It’s a hierarchy.
The patterns, in his view, are attractors in a presumably structured space, not random, organized in a way that can be mapped. And one of the things he says a lot is that we need to understand the contents and structure of that space of patterns and the ways in which the objects we build can pull down the desired patterns from it. There’s a lot to say about Whitehead here, about potentiality and actuality, but I’ll save that for another time.
Morphogenetics, anatomical morphospace, and space in general
Morphospace, attractor landscapes, what Levin calls Platonic space or “space of patterns” are somewhat related but distinct claims, sometimes distinct objects entirely. A morphospace is a configuration space determined by a system’s degrees of freedom, I think is one way to put it. An attractor landscape is a dynamical object within a morphospace. Platonic space is a much stronger thing: it is a kind of “ambient” space, that there exists a structured space of substrate-independent patterns that physical systems interface with. Evidence about one obviously doesn’t automatically transfer to another, and it matters to keep track of which level a given result actually speaks to. Levin does this well, and I think he decorates all of his statements with the appropriate level of “empirical evidence” vs “conjecture” etc..
Here, morphospace is the space of possible forms that a biological or even synthetic system can take. When talking about say, an anatomical morphospace to friends around me, I quickly realized how confusing that idea is, how suspicious people can be about it. D’Arcy Thompson introduced the basic idea in 1917 in On Growth and Form, by showing that the shapes of related species can be connected by smooth coordinate transformations, and Morozova & Shubin (2012) later attempted to formalize the morphogenetic field as a section of a fiber bundle. But the geometry of morphospaces themselves (or morphospace itself?) has not been formally characterized, and as a side note, I think this is one of the most interesting open problems in this space.
When the planarian regenerates its head, it’s moving through morphospace from a damaged configuration to an attractor, which is the target morphology. When the Picasso tadpole corrects its scrambled face, Levin would say that it’s navigating morphospace around obstacles, navigating a problem space and finding a solution. The attractors are discrete stable configurations: in planaria, that’s normal polarity, two-headed, two-tailed; in gene regulatory networks, fixed points of dynamical systems with basins of attraction; in Lenia, self-organizing patterns that maintain identity under perturbation.
There is a lot of open work here. What is the distance between two forms? What are the geodesics, meaning the lowest-cost developmental trajectories? What determines which attractors can exist, and where are the barriers between attractor basins? No computable morphospace currently exists where the topology, metric, and barrier structure are all known. Cano-Fernandez et al. (2025) did some interesting work exploring morphospace using EmbryoMaker and found a basic set of morphologies for early animal development, and Fields & Levin (2022) proposed navigation as the invariant for cognition across substrates. But we’re still far from a formal characterization, and I find that very interesting.
Practical consequences and future possibilities
I have had trouble touching concretely on some of the more “out there” but truly real practical consequences that can come out of this program. Levin often uses the word “prompt” in the context of “communicating to a biological system” the desired goal and letting system achieve it (eg by messing with its bioelectrical network). It can’t be understated how different of a model for biological intervention it truly is. Nearly all of the modern methods consist of mechanically flipping various knobs and intervening directly to produce the desired effect, rarely understanding “why” it works. One of his big goals I believe is to basically find the “right level of description” and to communicate the goal to the system directly. An anatomical compiler, so to speak, where instead of micromanaging individual genes (which is so far impossible), you set some target morphology and you let the cells “do the work” and figure out what to do, using their own competencies. So you’re prompting the system, so to speak. Sci-fi for now, but the idea of going from “high level description of the results we want” to bioelectric inputs to align the system to work towards it is something they are really working on over there. He’s made that analogy somewhere but it’s a similar jump from hand-flipping individual transistors to being able to write in a higher level language.
What excites me about all this
Maybe the ultimate central question, for me, is: if Levin’s intuitions and interpretations are there and there is a structured space of patterns, mathematical, morphological, cognitive or otherwise, and that physical systems interface with it, can that structure be formalized to some extent? Levin provides the biological questions and the conceptual framework (navigation in morphospace, goal-directedness, substrate independence), and what I think is missing is some of the formal mathematical characterization of the spaces he describes systems navigating. I think nobody has really tackled the “softer” spots of his program on that front.
So this is in part what I’ve been working on this in a more formal research context. We’ve moved pretty quick and in only 4 months, one of our first papers has been accepted at a mathematics and neuroscience conference, which is really cool. We’re still early and it has taken a tremendous effort for me to actually clarify my thoughts, digest the firehose of things coming my way, and develop any confidence that I am starting to build my own model and taste for which parts of the incredibly complex and broad research program they’ve got going on, and all the potential interpretations and conjectures that fall out of it. I hope they will be more to share on my own work by the end of the summer, but in the meantime, here’s a very high level sense of what we’re doing, listing some of the angles we’re taking.
One angle we’ve taken is synthetic biology and cellular automata, Lenia as an experimental test bed is an example. Another is applied category theory for the formal structural way to model things. And then, things like homotopy type theory as a source of inspiration and key concepts for now, and if it truly is a fit, maybe something more. I’m not sure there’s a direct formalization target in cubical type theory or anything, but so far, just using the HoTT concepts of transport and path spaces and coherence etc have been really useful to think with.
With Applied category theory, you already get a lot of the machinery that is immediately useful, and there’s even some precedent with ACT x biology. Actually, Spivak himself had a conversation with Levin.
Polynomial functors help you model interfaces/agents to some extent states, and we’ve seen above that this idea of “physical systems as interfaces” is something that comes up often in Levin’s analogies.
Sheaves help encapsulate this idea of context and local-to-global coherence. Fibrations formalize the relationship between a base space and the structures sitting over it.The connections are actually really direct: polynomial functors model the state/interface decomposition that TAME presupposes and lenses are the formal backbone of categorical cybernetics (unifying game theory, control, and learning under one beautiful bidirectional structure), and sheaves capture how local bioelectric signals cohere into global morphological targets. ↩︎
You can then apply all of this to synthetic biology and cellular automata as experimental test beds, and then use minimal computational models (sorting algorithms, search algorithms, theorem proving) for controlled quantification and I guess, so far, hope you model something interesting that allows you to punch further in terms of predictive models than current attempts. It has already yielded both some interesting (very) early results and has otherwise been a “fecund” mental approach to all this.
Some of the research questions I think we have, if I was to resume them:
The structure of the space. Does the space of patterns have some interesting geometry? What determines which regions are accessible, which forms are stable? In algorithmic behavior space, why do sorting agents cluster by type (the paper this comes from is mentioned earlier here).Zang & Levin showed that cells running different sorting algorithms, when implemented in a decentralized way, “spontaneously” segregate spatially. I found that motility-induced phase separation and transport defect models explain the clustering, and other “boring” mechanistic interpretatinos, somewhat ruining the teleological framing of that paper (if only for my labmate and I). ↩︎
In Lenia creature space, what determines which persistent forms exist? We’re looking for the recurrence of similar structural features, limited forms, clustering, history dependence across different substrates etc… to provide evidence that the space has structure independent of any particular instantiation. There’s also some interesting stuff around whether proof agents, under interventions (aka messing with them) converge to the same structure despite using different tactics, and if so, how, in the context of Lean theorem proving.
The “interface” problem. How exactly do physical systems act as interfaces into the pattern space? What determines which patterns a given physical arrangement can summon? As a slight tangent, we’ve taken Grodstein & Levin (2023) closed-loop diffusion mathematical model of morphogenesis and re-modeled it using ACT machinery, with cells as polynomial functors, replacing the Markov blanket partition from active inference with the position-direction decomposition that polynomial functors require, as kind of a soft playground to hone my ACT skills. It’s allowed some novel predictions and seems to be an interesting direction. That compositional structure lets you decompose the network of cells forming the “tissue” and rank which cuts are most severe, and the ranking disagrees with what you’d predict from, say, naive connectivity heuristics. The most connected nodes aren’t necessarily the most important ones, because what matters is the compositional role a node plays, not just its degree. This is something the original model can do for 1D tissue, but ours generalize somehwat out if the box. I think that’s kind of neat, potentially not very important but still, we have to write up. This kind of fell out “for free” our categorical modeling choice which also seems neat. ↩︎
Computation versus convergence. If you take a dynamical system that converges to an attractor, say a planarian worm and its bioelectric network regenerating a head, or some gene regulatory network settling into stable expression patterns, when is it appropriate to say that the system was computing versus merely falling out of physics? A ball rolling down a hill converges. It’s not really computing anything. Is regeneration any different? There’s a long philosophical tail there, but I’ve been interested in the heory of computation for a while. Still, I’ve followed it back to nearly 40 years ago with Putnam (1988), Chalmers (1996), and countless others. Probably something to write about in the future, on its own. More recently, a paper I really enjoyed by Wolpert & Korbel (2025) on physical systems -> formal decoding maps <- abstract computational models. I recommend it! I have some ideas and I think there’s a lot of interesting work to be done.
I’m excited about what’s going to come out this year. I’m being cautious though, because we are new to most of these rooms and even if we’re in many of them at the same time, it’s only a couple toes at times. That means getting our formal machinery reviewed on things like the Category Theory Zulip, and the same with the biological side, etc. I am not worried about the engineering side too much, the insilico stuff, because the one area where I am truly comfortable. But yeah, you don’t want to make yourself a fool and cost people time at the same time, hence the “slow is smooth, smooth is fast” approach. And it’s not like we’re scoopable, considering the kind of things we’re looking into! Some of the concrete things in the pipeline: modeling cells as polynomial functors in the context of various experiments, mapping out a synthetic morphospaces for Lenia and comparing the topological structures with results from cell-based simulations like EmbryoMaker, etc. ↩︎
Footnotes
- The seminal papers: Kriegman et al., PNAS (2020); and Kriegman et al., PNAS (2021), where xenobots were shown to self-replicate through a mechanism with no evolutionary precedent. ↩︎
- See Levin, Pietak & Bischof, Seminars in Cell & Developmental Biology (2019), for a comprehensive treatment of the bioelectric mechanisms underlying this. ↩︎
- See Chernet & Levin, Frontiers in Physiology (2014). ↩︎
- See Lyon et al., Phil. Trans. Royal Society B (2021), which Levin co-authored, for a good entry point into the basal cognition program. ↩︎
- Even amoeboid chemotaxis is hundreds of times more efficient. These numbers come from the Cognition All The Way Down 2.0 paper, Chis-Ciure & Levin (2025). ↩︎
- Part One is basically a historical review of teleology and a showcase of the current experimental evidence. Part Two tries to propose a mentalistic approach to teleology informed by cognition, intelligence and intentionality, not as a metaphysical commitment but as a hypothesis about what the optimal interaction protocols are with these systems. ↩︎
- As mentioned, Levin is careful about the naming: From A Short Argument on Platonic Space (2026). ↩︎
- The connections are actually really direct: polynomial functors model the state/interface decomposition that TAME presupposes and lenses are the formal backbone of categorical cybernetics (unifying game theory, control, and learning under one beautiful bidirectional structure), and sheaves capture how local bioelectric signals cohere into global morphological targets. ↩︎
- Zang & Levin showed that cells running different sorting algorithms, when implemented in a decentralized way, segregate spatially. I found that motility-induced phase separation and transport defect models explain the clustering, and other mechanistic interpretatinos, somewhat ruining the teleological framing of that paper (if only for my labmate and I). ↩︎
- That compositional structure lets you decompose the network of cells forming the and rank which cuts are most severe, and the ranking disagrees with what you’d predict from, say, naive connectivity heuristics. The most connected nodes aren’t necessarily the most important ones, because what matters is the compositional role a node plays, not just its degree. This is something the original model can do for 1D tissue, but ours generalize somehwat out if the box. I think that’s kind of neat, potentially not very important but still, we have to write up. This kind of fell out our categorical modeling choice which also seems neat. ↩︎
- Some of the concrete things in the pipeline: modeling cells as polynomial functors in the context of various experiments, mapping out a synthetic morphospaces for Lenia and comparing the topological structures with results from cell-based simulations like EmbryoMaker, etc. ↩︎