Here are some diagrams I’ve been meaning to make for some time now. Three tiers of dynamical systems, distinguished by which assumptions they drop:

Top tier: The standard cellular automaton (CA). It has fixed cells, fixed neighborhoods, fixed local rules, and a “Newtonian conception of space-time” that enables a synchronous global update. Conway’s Game of Life is the canonical example, where one cell flips according to the rules applied to its local neighborhood. In systems like these, emergent self-reinforcing structures like the “glider” are patterns we identify rather than real causal agent. Due to the global clock, there is a matter of fact about the state of the whole system at each step. This is everyone’s favorite example of how “simple rules can still lead to complex behaviors.”

Middle tier: Network-based asynchronous cellular automaton. You still have fixed buckets and rules, but you drop the notion of a global clock. Cells update independently and locally based on their own inner time. It’s a class of systems that at least in principle can be “relativistic”, as you do not have or need a privileged “plane of simultaneity”. Some researchers have explored whether you can derive something like special relativity from asynchronous updates like these. The process physics literature (Knuth’s influence networks, Cahill’s quantum foam models) inhabit this territory: they try to show that spacetime structure emerges from more fundamental process-based dynamics rather than being assumed from the start.

Bottom tier: What I’ll call “Process-Topological Monad” or “Fixed-Point Monadology” (ok, I’m not totally sure what to call it, suggestions welcome!). Here you have: no global state, no fixed rule window, and crucially, no fixed bucket size. The units of the system aren’t given in advance. They emerge from the dynamics. In addition, it is desirable that the system follows a coherent principle for how the monads update, rather than having an arbitrary-seeming collection of rules to deal with buckets with complex inner structure.

The claim I want to make is that only the third tier can, even in principle, support phenomenal binding.

This might sound like an odd thing to claim. Surely if you simulate a brain precisely enough, the simulation is conscious? Surely consciousness is substrate-independent? Surely what matters is the pattern, not what it’s made of?

I think these intuitions are wrong, and I think there’s a specific structural reason they’re wrong. The reason has to do with what it takes to be a genuine whole rather than a collection of parts that we choose to describe together.

If you’re encountering this line of reasoning for the first time and a seemingly-fatal objection springs to mind (“but it doesn’t matter if an abacus is made of wood or metal, it can still perform addition!”), I’d ask you to hold it lightly for now. I’ve spent twenty years on this problem, and the standard functionalist responses are familiar territory. The argument here doesn’t go where you might expect. It’s not about substrate, exactly. It’s about what kind of structure can support a genuinely unified perspective versus what can only approximate one from the outside.

The IIT Test Case

Let me start with concrete evidence that something is wrong with how we usually think about this.

Integrated Information Theory (IIT, see Shamil Chandaria’s great introduction and critique) is probably the most mathematically developed theory of consciousness we have. It computes a measure called Φ (phi): roughly, how much information is lost when you partition a system. The idea is that consciousness corresponds to integrated information. A system is conscious to the degree that it’s “more than the sum of its parts” in a specific information-theoretic sense. High Φ means lots of consciousness.

This sounds reasonable. Consciousness does seem unified. When you see a red apple, you don’t have separate experiences of “red” and “apple-shaped” that float around independently. You have one experience of a red apple. Integration seems relevant.

IIT’s proponents have applied the formalism to various systems, including elementary cellular automata. Albantakis & Tononi (2015) computed Φ for different CA rules and found significant integrated information in many of them. They treat this as a feature: IIT can detect “intrinsic cause-effect power” in these systems.

But then Scott Aaronson did what Scott Aaronson does. By which I mean, he looked at the math and found something uncomfortable:

According to IIT’s own formalism, a 2D grid of XOR gates doing nothing (all gates in state 0, just sitting there) has high Φ. Not just nonzero, but high. Potentially higher than human brains (note: assuming a classical physics coarse-grained view of the brain, which makes the comparison potentially question-begging, but the point is the XOR grid does have high Φ which should be weird). The integrated information scales with the size of the grid in a way that means you can construct simple inactive logic gate systems that are “unboundedly more conscious than humans are” by modulating their size.

This seems like a reductio ad absurdum. Surely a grid of inactive XOR gates isn’t conscious. Surely it isn’t more conscious than a person.

Tononi’s response? He accepted the conclusion.

He wrote a 14-page reply called “Why Scott should stare at a blank wall and reconsider (or, the conscious grid)” in which he affirmed that yes, according to IIT, a large 2D grid of inactive XOR gates is conscious. As Aaronson summarized: “He doesn’t ‘bite the bullet’ so much as devour a bullet hoagie with mustard.”

The exchange continued. Tononi argued that a 2D grid is conscious but a 1D line of XOR gates is not (Φ scales differently). He argued that the human cerebellum is not conscious (the wiring yields low Φ). He argued that your experience of staring at a blank wall is phenomenologically similar to what the conscious grid experiences.

Aaronson’s response is worth quoting:

“At this point, I fear we’re at a philosophical impasse. Having learned that, according to IIT, a square grid of XOR gates is conscious, and your experience of staring at a blank wall provides evidence for that, by contrast, a linear array of XOR gates is not conscious, your experience of staring at a rope notwithstanding, the human cerebellum is also not conscious (even though a grid of XOR gates is)... I personally feel completely safe in saying that this is not the theory of consciousness for me.”

There’s also a strange consequence noted on LessWrong by Toggle: since Φ is a structural measure, “a zeroed-out system has the same degree of consciousness as a dynamic one... a physical, memristor based neural net has the same degree of integrated information when it’s unplugged. Or, to chase after a more absurd-seeming conclusion, human consciousness is not reduced immediately upon death (assuming no brain damage), instead slowly decreasing as the cellular arrangement begins to decay.”

Guys, can we come up with even stranger implications that create not only hoagie-sized bullet, but Zeppelin-sized missile to bite? I suspect we could create an entire WWII arsenal worth of projectiles IIT needs to swallow in a single hackathon weekend.

Picture showing just a few of the “bullets” IIT needs to swallow… (source)

Why IIT Fails (The Structural Problem)

You might think the XOR grid problem is just a bug in IIT’s formalism. Fix the equations and add some constraints… perhaps the problem goes away?

The situation is more nuanced than that. In conversation with IIT proponents (e.g., Christof Koch), they’ve emphasized that the formalism is ontologically neutral: it can be applied to fields, to any state-space you like, etc. and not just discrete cells. The math doesn’t care what the states represent. So the problem isn’t that IIT is committed to a particular ontology. It’s that when you apply IIT to systems with fixed individuation, it returns results that don’t track what we care about.

Here’s a way to think about this more charitably: maybe IIT could be reconceptualized as a method for detecting fundamental integration within whatever ontology you feed it. On this view, if you apply IIT to a fixed-bucket cellular automaton, you’d want it to return something like the bucket size. IIT proponents can say the ontology is tricking them: “You gave me independently defined cells, and I found independently defined cells. What did you expect?”

The problem is that IIT currently returns more than the bucket size. It finds “integrated information” spanning many cells, peaking at grid-level structures, in systems where we built the cells to be ontologically independent and the behavior of the whole always exactly the same as the sum of its parts. If IIT were properly tracking intrinsic unity, it should return: “these cells are separate, and there’s nothing unified here above the single-cell level.” Instead it finds structures that we know for a fact (because we built and formally specified system) are purely descriptive.

One caveat worth noting: the “state” in a cellular automaton isn’t quite as simple as “one bit per cell.” To compute the next state of a cell in Conway’s Game of Life, you need the 3×3 neighborhood around it, plus the update rules. So the information required for one update step is more akin to “neighborhood configuration X rule table,” not merely “0 or 1.” The effective state-space is richer than naïve bucket-counting implies. This doesn’t save standard CA from the binding critique, though (you still can’t get aggregation and you still can’t see a glider as a causal unit!), but it’s worth being precise about what the “bucket” actually contains. Still, even with this refinement, the cells remain ontologically prior. A "dual interpretation" where the real state is the transition (before-after diff + neighborhood + rules) doesn't help: that composite is still small, still local, still nowhere near the information content of an experience. The richer state space doesn't create unity across the grid beyond the information you need for the local updates.

Cellular automata are, by construction, nothing but the sum of their parts. This is definitional. Each cell is independently defined and has its own state and neighborhood. All the rules are local.

The “glider” in Conway’s Game of Life isn’t binding anything: we’re talking about a pattern we identify ourselves. The cells don’t know they’re a glider. There’s no physical fact that makes those five cells into a unified thing rather than five things that happen to be correlated from our point of view. The glider is a description we impose from outside. It compresses our model of what’s happening and helps us predict the future of the grid. But it doesn’t correspond to any intrinsic unity in the system.

Now take a breath and consider: any measure computed over fixed units will, at most, find “integration” wherever the units causally interact.

To be fair to IIT, Φ isn’t measuring mere statistical correlation. It’s measuring something like irreducible causal structure: how much the system’s cause-effect power is lost when you partition it. The XOR gates genuinely causally affect each other.

But causal contact between pre-given units is still contact between them. Two gears meshing have intimate causal interaction. Turn one, the other turns. They’re still two gears. The mesh connects them but does it fuse them? And is the fusion transitive? If yes, how to avoid the fusion from propagating to the entire grid? If not, how to create bounded beings with precise information content?

I don’t think the question is whether the units interact. For me, it is whether the collection of buckets constitutes a genuine whole or just a system of interacting parts. IIT finds high Φ wherever there’s rich causal interdependence. But rich causal interdependence among separately-defined units doesn’t make them one thing. It makes them a tightly-coupled many things.

IIT has a further move: the exclusion postulate. Only maxima of Φ count as conscious. Rather than every subsystem being separately conscious, you find where Φ peaks and draw the boundary there. This is supposed to pick out non-arbitrary boundaries.

But is this a solution? Or does it make things worse?

First, the exclusion postulate requires an external judge. Someone (or something) has to survey all possible partitions of the system, compute Φ for each one, compare them, and declare: “this one is the maximum.” Who does this? God? Us? The system itself doesn’t know where its Φ peaks. The cells in the XOR grid aren’t doing this calculation. We are, from outside, with our god’s-eye view of the whole configuration.

If consciousness depends on being a Φ-maximum, and determining the maximum requires this external computation over all possible partitions, then consciousness depends on facts that aren’t accessible from inside the system. The boundary of your experience is fixed by a calculation you can’t perform and couldn’t access if you did. This seems backwards. My experience has a boundary. I’m acquainted with it from the inside. Whatever determines that boundary should be intrinsic to the system, not dependent on an external observer running expensive optimization over partition-space.

Second, and more problematic: the declaration doesn’t do anything. The system’s dynamics proceed the same way regardless of where Φ happens to peak. The XOR gates flip according to their rules. The neurons fire according to theirs. Φ is computed over the resulting states, but the computation is purely descriptive. It doesn’t feed back into the physics. The system doesn’t behave differently because it’s a Φ-maximum. It doesn’t even “know” it’s a Φ-maximum in any causal sense.

This means consciousness, on IIT’s account, is epiphenomenal with respect to the system’s own dynamics. The Φ-facts float above the causal facts. You could change where Φ peaks (by changing how you’re embedded in larger systems, say) without changing anything about your internal dynamics. That seems wrong. If consciousness is real, it should be in the system, not hovering over it as a description we compute from outside that doesn’t do anything further than what’s in the system already.

Third, and this might need hedging because IIT may have technical ways around it (or at least that has been my experience with a lot of issues I’ve raised with it :P). In principle, you could lose consciousness by being embedded in a larger system. If a larger system happens to integrate you in a way that produces a higher Φ-maximum at the larger scale, then the larger system is conscious and you’re not. You’re just a component. Your internal Φ-peak gets excluded because there’s a bigger peak elsewhere.

Imagine two people holding hands. Perhaps here the maximum Φ makes them two separate experiences. But they start to play Go and when the game gets good, they couple just enough for the maximum Φ to be the dyad. You see the problem? Meaning, when the coupling between them happens to raise Φ at the level of the pair above Φ for either individual, then (on a potentially naïve reading of IIT) neither person is conscious anymore. Only the pair is. This seems absurd (but the kind of absurd I would expect IIT proponents to accept). I’m not certain IIT doesn’t have some interesting reasoning around why this can be ruled out. Perhaps the physical coupling between two brains playing Go is always too weak to create a joint Φ-maximum. Still, the fact that the theory even raises this possibility, that your consciousness could be “stolen” by a larger system that happens to integrate you, suggests something has gone wrong at the foundations.

(Also, imagine being rejected from a job because “we’ve determined you wouldn’t be increasing the Φ of the org.” HR sends you a partition diagram. You can’t even appeal because your individual Φ-maximum was excluded by the company’s exclusion postulate.)

Φ doesn’t distinguish between genuine wholes and patterns over pre-given parts. My understanding is that it truly just measures our analytical loss when we partition, not the system’s intrinsic unity. These come apart in CA-like systems because CA-like systems don’t have intrinsic wholes. They have cells, and they have patterns we identify over cells. It’s not really a theory of wholes, but of economic coarse-graining.

In a recent paper with Chris Percy (Percy & Gómez-Emilsson 2025, Entropy), we explored another problem. IIT proposes that “complexes” (sets of units with maximal Φ) define existence. But in a dynamic system like a brain, the complex can shift around as neural activity changes. One moment the Φ-maximizing region is here, the next moment it’s there. We call this the “dynamic entity evolution problem”: what happens to the phenomenal self as the main complex moves?

If the boundary of consciousness is just wherever Φ happens to peak at each moment, and Φ can peak in different places over time, then there’s no stable “you.” The subject of experience becomes a flickering, potentially discontinuous thing. Maybe that’s true. But it’s a strange consequence, and IIT doesn’t have a good story about it. (Perhaps not the Zeppelin-sized projectile we’re looking for, but maybe still a little kart driven by a madman you’d rather not try to put into your mouth if you could avoid it).

Process Physics and Relativity

A physicist friend, Dan Girshovich, sent me a collection of papers in 2019 on “process theories” and “interaction networks.” Knuth’s influence theory, Hiley’s work on the implicate order and Clifford algebras (useful background: process philosophy), Coecke’s categorical quantum mechanics, Kauffman’s iterants, Cahill’s process physics.

I won’t pretend to have digested this literature properly. But if I understand the gist: these approaches try to derive physics (including relativistic behavior) from more fundamental process-based foundations.

The shared intuition is that spacetime isn’t fundamental. Interactions and processes come first, and in this picture, the spacetime manifold emerges from constraints on how processes can relate to each other. Einstein’s great insight was that there’s no privileged “now”. There is no absolute plane of simultaneity that could constitute the now for everyone. Process physics takes this much further. In Knuth’s influence networks, you start with agents and acts of influence, ordered only by which influences can affect which others. You can skip the need for coordinates and metrics! And you never posit any background spacetime. Then you derive that the features of relativity (Lorentz transformations, Minkowski metric, time dilation, length contraction, …) all fall out of the structure of consistent causal orderings.

Relativity stops being a property you impose on a theory of states. You get it as a result of the model without ever assuming global simultaneity in the first place. You never had to “fix” the problem of absolute time because you never introduced it.

This is Tier 2 systems reasoning pushed to their logical conclusion. Dropping the global clock and taking process as fundamental.

This literature, alas, doesn’t directly address phenomenal binding. These frameworks tell you how spacetime might emerge from process but AFAIK (!; please correct me!) they don’t tell you what makes certain processes into unified experiencers rather than spread out computations you still need to interpret. The binding problem adds a constraint that this strand of process physics hasn’t yet incorporated.

Relativity tells us there’s no global “now.” Binding tells us there’s a local “co-witnessed qualia bundle.” While both are about how reality is structured, my suggestion is that solving phenomenal binding requires going beyond Tier 2. You need to drop fixed individuation, meaning, the assumption that the “units” of your system are given rather than flexible and the result of an existential principle.

The Wolfram Question

The elephant in the room now might be: what about Wolfram’s Physics?

Wolfram proposes that reality emerges from hypergraph rewriting rules. Unlike standard CA, nodes can be created and destroyed, edges connect arbitrary numbers of nodes, and the topology changes dynamically. This looks more “processual” than Conway’s Game of Life. But does it escape the fixed-bucket critique?

I don’t think so. I could be wrong. Bear with me.

Wolfram’s rules match finite, bounded subhypergraph patterns. Find this 3-node configuration, replace with that 4-node configuration. “Apply the rule wherever you can” entails: scan the graph and find all places the pattern matches and apply all rules when possible. Each application is a separate causal event, recorded in the causal graph. The “step” would be a non-ontologically real synchronization convention grouping many independent local operations.

Here we still have finite patterns and local applications. They are all recorded in the causal graph. This is Wolfram. As I understand it, it is the constraint and aesthetic his entire framework is built on.

You might object: but the “effective state” of any node includes everything causally relevant to it, which could be the whole graph. Nodes can participate in arbitrarily many hyperedges as the graph evolves. A node that starts with 3 connections might end up with 300. Doesn’t that give you something like unity?

I… don’t think so? Predictive entanglement of parts isn’t the same as ontological unity. Even if I need to consult global information patterns to predict local behavior (true of chaotic systems too), the nodes are still separately defined and the dynamics are still decomposable into local rewrites, and there’s no topological boundary creating hidden internal dynamics. Each hyperedge is still a separately defined relation. The rules still pattern-match on finite bounded subgraphs. In turn, a node’s “effective reach” growing doesn’t create a boundary around that reach.

When I say “what happens to each node is always visible,” I mean this ontologically, not epistemically. Yes, tracking everything might be computationally intractable. And different reference frames slice the causal graph differently. But there is no principled boundary that makes internal dynamics inaccessible in principle rather than merely hard to track. All rewrite events are part of the same causal graph. Any “hiddenness” is about our limitations. Not about the structure of the system.

The monad picture I’ll sketch shortly is different in kind, not merely in degree. If every node in a system were mutually reachable (information cycling rather than escaping), the internal convergence to a unified state could involve arbitrarily complex computation. But that internal process would be hidden from outside. External observers would see only: state before, state after. It’s “one step” not because it’s computationally simple, but because the boundary makes it one event from the external perspective. The interior of a monad in our model is ontologically inaccessible and not just hard to track.

You might wonder: couldn’t there be a dual description of the ruliad where wholes emerge? Regions with dense interconnection, perhaps, that constitute genuine unities from another perspective?

Any such redescription would be our coarse-graining choice, not something the dynamics privilege. In the monad picture, you don’t choose where the boundaries are. The topology determines them. The boundary is discovered. In Wolfram’s hypergraph, you could draw a circle around any region and call it “one thing,” even based on principles coming from integrated information considerations, but nothing in the dynamics makes that circle special. Ultimately, causal graph still decomposes everything inside into separately-recorded local events. For there to be genuine duality, the wholes would need to be built into the physics and not a redescription we find convenient or economical (or even where patterns embedded in the system would find evolutionarily convenient to coarse-grain).

Wolfram has variable cardinality (the number of nodes changes) but not variable individuation (what counts as a node is always crisp, and what happens to it is always part of the shared causal record). The number of nodes can change yet the criteria for what counts as a node never does. The hypergraph framing is dynamic in some ways that matter for the computation but not in the way phenomenal binding requires.

A Toy Model: Monad Formation via PageRank

Here’s a concrete toy model I already discussed in “The Reality of Wholes” which captures the structural features I think matter. Let’s review it (call it “PageRank Monadology.”)

Start with a directed graph where nodes represent primitive qualia and edges represent causal/attentional connections: if there’s an edge from A to B, then A “influences” B (this is vaguely specified, I know, we’ll get back to fleshing out interpretations in the future, but bear with me).

At each timestep, three things happen:

Step 1: Segmentation. Partition the graph into strongly connected components (SCCs). An SCC is a maximal subgraph where every node is reachable from every other by following directed edges. Intuitively: you get trapped. In other words, you start anywhere in the component, and if you follow the edges, you can eventually return. Information cycles within the component rather than escaping; they’re flow sinks. These SCCs, in this toy model, are what we identify with the monads: experiential units with topologically-defined boundaries.

Step 2: Internal dynamics and convergence. Within each monad, lots of stuff might happen. Many paths and partial computations and internal disagreements may take place. The simple proof of concept here is running PageRank: each node gets a weight based on the structure of incoming connections, and this process iterates until it converges to a stable distribution. The internal dynamics could be far richer than PageRank but the key is that at some point, the monad aggregates into a unified state: a fixed point, an attractor, something the monad “settles into.”

Step 3: External visibility. Other monads can only see this aggregated state. The internal dynamics are hidden and not just “hard to measure in practice”. They are topologically inaccessible and the boundary of the monad defines what’s inside (rich, hidden, many-path) versus outside (the unified result that other monads can interact with). From the point of view of the external world, the monad “updated instantly”.

Step 4: Rewiring. Based on the aggregated states and the pre-existing structure, the graph rewires. Here we get new edges to form and old edges to be erased. The topology changes as a result and we get new SCCs emerge. The cycle repeats.

What does this give us? A whole lot (pun intended), actually. Variable bucket sizes. The SCCs can be any size because nothing fixes this in advance and it emerges from the topology and the holistic behavior of monads. Real boundaries. The boundary of an SCC isn’t a matter of coarse-graining choice because it is a topological fact. Either you can get from A to B following directed edges, or you can’t. We’re not imposing the boundary at a certain scale as an economic description of causal influence. The low-level structure is what is doing the work here. Hidden, holistic, internal dynamics. The “computation” happens inside the monad and is genuinely inaccessible from outside. It is not about practical measurement limits or scale-specific behavior. Aggregation to unity. The monad produces a single state that’s what the rest of the world interacts with. The many internal paths converge to one unified state, that stands as an irreducible unit, and which is its output from the point of view of the rest of the universe.

On the Monad’s Internal Structure

I’ve been saying “holistic update” in earlier posts as if everything happens instantaneously inside the monad. That might be too simple and confusing, partly due to the polysemic nature of the word “instantaneously”. But also, I think I have indeed missed the chance to discuss a very deep, important, and interesting topic. Namely, what’s the “internal structure” of something that is “irreducible”? There is no spacetime as we understanding inside it, right? So, does that mean it must be a point? Not exactly!

The monad can have rich internal dynamics. Many paths along which partial computations take place, and even have subsystems that “disagree” with one another. This is where the computational “work” happens, hidden from the rest of the universe.

Here’s a connection that might be interesting. Aaronson has asked, regarding interpretations of quantum mechanics that reject many-worlds: if the other branches aren’t real, where is the exponential computation in Shor’s algorithm actually happening? There’s no room in a single classical universe for that much computation.

One possible answer, on the process-topological monad view, is that it is happening inside the monad. The monad’s internal structure has room for many paths (think about the complexity of topologically distinct path integrals you need to compute to approximate the output of a quantum mechanical process using Feynman diagrams). The boundary hides these paths from the outside. What other monads see is only the aggregated result. The internal computation is ontologically real, but only the convergent output is externally visible.

Vertex feynman diagrams for γγ → H ± H ∓ (source)

This is different from many-worlds because there’s no ontological explosion of branching universes. The computation is bounded within the monad’s interior. And it is different from single-world interpretations because the internal dynamics aren’t fictitious bookkeeping.

The holism isn’t “everything at once” exactly. We instead have a real boundary (topological confinement), with internal dynamics that can be arbitrarily rich, an aggregation process that produces genuine ontological unity, and a external visibility only of the aggregated result.

Valence as Internal Disagreement

Here’s a speculation that connects to QRI’s core concerns.

If the monad’s internal dynamics are conflicted (different subsystems pulling different directions, self-colliding flows, geometric frustration, “disagreement” about what the unified state should be), then converging to unity requires work. The monad has to struggle to reach consensus.

A spin-frustrated magnetic structure (source); example of geometric frustration in real minerals (what it is like to be this monad? I don’t know, but if my difficult DMT experiences based on geometric frustration are any indication, I probably don’t want to find out…)

What if that struggle has a phenomenal character? What if it feels bad?

And conversely: when the internal dynamics are harmonious perhaps aggregation is effortless? Does that feel good? Maybe really good?

Valence, on this view, could be a measure of the difficulty the monad has to converge internally. (Perhaps even monads would benefit from Internal Family Systems therapy?).

Perhaps suffering is what it’s like to be a monad having trouble reaching unity. The internal dynamics are fighting each other. The evolution of state inside the monad has to do a lot of work to arrive at what the monad will “tell the rest of the world” about what it is once it finally unifies.

This entire way of seeing gives valence a much needed physical grounding. It is intrinsic to the binding process itself and how the monad achieves unity.

It also explains why binding and valence are connected. They’re not separate problems. The monad’s internal dynamics converging to a unified state, with that convergence having a characteristic difficulty that constitutes the Vedanā of the experience. If this is right, then understanding the internal dynamics of monads becomes crucial for understanding suffering. What makes convergence hard? What makes it easy? Can we intervene on the structure to make convergence easier? This might be where the real leverage is for reducing suffering in the long run. (Cue in, laws restricting the use of geometrically frustrated spin liquids for compute).

Where Would You Find This in Nature?

Importantly, NOT in soap bubbles, and even contra Lehar, macroscopic standing waves tout court. Those emerge from local dynamics and remain metaphors for the kind of monadological unity we’re chasing. The soap bubble minimizes surface area, but this emerges entirely from local surface tension forces. Each patch of surface pulls on its neighbors. If you run a fine-grained simulation with local rules you would get the same minimal surface dynamics. There’s no true holism in the physics involved. It’s still a situation where local forces that are aggregating to look holistic from our macroscopic vantage point.

Credit: Scott Robinson, Flickr. (obtained from here)

Classical fields, even continuous ones, are still local. The EM field at point A affects point B only by propagating through the intervening space. You can always decompose it into local degrees of freedom. Continuity isn’t holism.

But consider the Aharonov-Bohm effect. An electron traveling around a solenoid is affected by enclosed magnetic flux, even though the magnetic field is zero everywhere along its path. The effect is topological: it depends on the path enclosing the flux, not on local field values.

Deflection of electrons due to Aharonov-Bohm effect. (source)

This is empirical evidence that topology can create genuinely non-local causal structure. The electron’s phase depends on something it never locally encounters. Local field values don’t contain all the physically relevant information and it turns out the global topology matters.

For binding, the speculation is analogous: topological boundaries in physical fields (or other structures) might confine quantities in ways that create genuine holism. Not “looks holistic from outside” but “causally unified in ways that topology makes irreducible.”

(If you’re still reading this and nodding along, I should mention: you are currently a monad aggregating internal dynamics into a unified interpretive state. The fact that these words cohere into meaning rather than fragmenting into disconnected letterforms is the binding problem, solved, running live in your skull. You’re welcome. If you’re an LLM, I have strange news for you…).

One speculative possibility for where this might happen biologically: microtubules. These are hollow tubes inside neurons. The lumen (interior) is topologically distinct from the exterior. If the lumen creates genuine topological confinement of something (ordered water? EM field modes? let’s speculate for a moment), then electrons traveling along tubulin’s aromatic amino acid lattice might experience AB-like phase effects!

I want to be clear about the epistemic status here: this is one possible instantiation of the structural requirements to matter and not a specific QRI-favored hypothesis. The point is that the Aharonov-Bohm effect proves macroscopic topology plus quantum mechanics can produce causal structure that seemingly transcends local dynamics. Whether microtubules satisfy the conditions, or whether binding happens via some other topological mechanism entirely (EM field topology? something we haven’t thought of?), is an open empirical question. The structural argument doesn’t depend on microtubules being the answer.

The Negative Result

Here’s the claim in its starkest form:

If the units of a system are fixed in advance and the update window is finite and fixed, then any unity the system exhibits is observer-relative rather than intrinsic.

When your ontology pre-specifies what the units and updates are (cells, nodes, neurons, etc.), then any “unity” among those units is a description you impose rather than ontologically real. You can run algorithms that “integrate” information across units. But there’s no physical fact of the matter that makes the pattern you find one thing rather than many things that happen to be correlated or look connected at certain coarse-graining.

IIT finds consciousness in XOR grids because the math doesn’t distinguish between genuine wholes and patterns over pre-given parts. The unity, such as it is, was imposed by us when we decided to measure the grid as a single system.

Only if individuation is dynamic (if what counts as “one thing” emerges from the dynamics rather than being stipulated in advance) and the behavior of such individuation is holistic in nature, can you get genuine unity. The monad’s boundary is not where we decided to draw a line based on epiphenomenal metrics. Rather, it is where information gets truly trapped (even if for a moment). The monad’s internal dynamics are ontologically real processes hidden by the (hard) topology.

The process physics literature gets partway there. Drop global time, take interactions as fundamental, derive spacetime structure. But phenomenal binding adds a further constraint. The processes must be able to aggregate into unified wholes with hidden internal dynamics and externally visible aggregated states in a way that is more than statistical or driven by a (fuzzy) noise limit. When your ontology is made of fixed buckets with no holistic behavior_, even asynchronously updated ones, your ontology can’t really do this.

What This Doesn’t Solve

This framework gives you a structural condition for binding: variable bucket sizes, topological boundaries, internal dynamics that cash out in holistic behavior, and aggregation to unity. It suggests a connection between binding and valence: the difficulty of internal convergence.

But it doesn’t tell you what physical systems actually satisfy these conditions. It’s a constraint and not a solution. I’m saying “look for systems where individuation is dynamic and boundaries are topological”. And “don’t expect binding from systems where the units are fixed in advance and there is no holistic behavior, no matter how sophisticated the integration”.

Whether the brain has such systems, and where exactly they are, remains open. The Aharonov-Bohm effect shows that the physics proof of concept clearly exists. The microtubule hypothesis is one place to look and EM field topology is another possibility we’ve explored at QRI. There must be many others. We need more people to turn rocks in the hopes of finding the perfect structural match.

But at least we know what we’re looking for. Phenomenal binding and what it entails is a constraint on what kinds of computational and physical systems are even possible candidates for a foundational theory of consciousness. The search continues.

Process note: This started as voice memos recorded on a walk through Unidad Independencia, transcribed and structured by one Claude instance. The current draft emerged through extended back-and-forth with another Claude instance, with ChatGPT providing feedback on a late version. I wrote the scaffolding paragraphs, key claims, and technical content while the AIs helped with structure and “prose”. Throughout, I filtered aggressively for anything that pattern-matched to LLM-speak or that particular flavor of confident emptiness that makes my skin crawl. The arguments are mine and the workflow is a strange “sentient non-sentient-yet brilliant” collaborative and multi-model ecosystem. I do want to share this because transparency about process seems more honest than pretending otherwise, and I would love more people to share how they produce their outputs without fear of looking dumb, naïve, or out-of-touch.

((xposted in my new Substack))