Abstract
Being social with others is not the same as reading other minds. Watching seagulls space themselves on a rooftop reveals a crucial distinction: animals can coordinate socially without engaging each other as recursive beings, as significant others who model you modelling them. This article shows that interrecursivity takes on different forms, for example, relaxed being-with others is a very different experience than prolonged antagonism. Different types of interrecursivity are differently energy-demanding, ranging from the low efforts required for relaxed grooming to the high efforts required for tracking a disguised enemy’s next move. While many species show interrecursive behaviours, only humans appear to sustain prolonged, multi-year relationships, either friendly or hostile. The real cognitive load of human social life is not processing more information due to group size, but in staying constantly responsive to significant others who are responsive to you over long periods of time.
Tromsø, May 2026
In May 2026 I was invited to give a series of lectures at the University of the Arctic in Tromsø, Norway. Tromsø sits far enough north that in May the sun does not set. Daylight is continuous, and the town's ordinary rhythms, the closing of shops, the emptying of streets, the settling of birds, no longer answer to darkness, because there is none to answer to.
My hotel room looked out over a dozen houses in the centre of town, most of them with tiled V-shaped roofs built to shed snow. Sometime on the second day I noticed that one roof in particular, slightly higher than the others, was full of seagulls. The tiles below the ridge were white from the birds’ accumulated guano. They stood along its ridge, the horizontal line where the two sloping faces of the roof meet at the top, barely moving for stretches, occasionally lifting a wing or stretching a neck. The number varied, but the ridge always held between five and fifteen birds at once, arranging themselves with a peculiar and consistent regularity.
The birds kept a regular distance from each other. On this ridge, each bird held itself with at least fifty centimetres from its neighbours, a spacing that reasserted itself after any disturbance. A bird would lift off, fly in a circle, and then either return to the same ridge or move on and settle on another rooftop. Whichever happened, within a minute or two of any departure the gap between the remaining birds and their nearest neighbours had settled back into the same narrow range.
I watched this more than a dozen times at different times of the day. Because the sun never set, there was no darkness to mark a boundary between day and night activity, and the gulls showed no discernible pattern tied to the time of day at all: the same configuration, the same spacing, the same rhythm of departures and returns was visible at three in the afternoon and at three in the morning alike, with nothing in the birds' behaviour to distinguish one from the other.
What struck me most was what did not happen between the seagulls. The gulls did not interact with each other in any way I could call meaningful. They did not groom one another, did not vocalise in directed exchanges, did not orient toward one another's faces or bodies in the searching, adjustive way that signals one animal is tracking another's likely next move. They were plainly aware of each other as gulls, another type of bird landing among them would have produced an entirely different reaction than another gull landing among them, and the spacing itself is evidence of mutual registration. But registration is not engagement. They did not appear to negotiate the roof, did not appear to form or dissolve alliances on it, did not fight over position in any way, did not do anything that looked like planning together, deferring to one another, or reading one another's intentions. Each bird seemed to treat the others much as it treated the tiles, the chimney, the angle of the roof itself: an almost fixed feature of the environment to be spaced around, oriented to, and otherwise ignored.
This is, in a nutshell, the argument of what follows. The gulls on that roof socialized but they did not engage each other interrecursively. And the distance between those two types of behaviour is a distance the literature on animal cognition routinely closes without noticing it has closed it.
Introduction: The Problem Is Not Information, It Is Other Recursive Centres
The dominant account of why some animals live in large, complex groups runs, in outline, as follows: larger groups generate more social information to track, more relationships, more histories of past interaction, more contingencies to hold in mind, and tracking that information places a distinctive cognitive demand on the organisms doing the tracking. Group size becomes, on this account, a proxy for informational load, and informational load becomes the selective pressure behind enlarged brains, particularly enlarged neocortex, in primates and a handful of other lineages. This is, broadly, the social brain hypothesis, and it has organised a great deal of productive research over several decades.
I want to propose a different diagnosis of what is actually costly about social life, one that does not deny the correlation between group size and neural investment but relocates its cause. The problem large groups pose is not, in the first instance, informational. It is not that there is more to know. The problem is that some members of the group must be engaged as other recursive centres: as beings whose next action cannot be read off their current posture, their current proximity, or any regularity available from past observation alone, because their next action depends on a process of anticipation, calculation, or intention occurring inside them, inaccessible to direct inspection, and itself frequently oriented toward my likely next action. This is a different kind of problem from tracking information about a stable structure, however large that structure is. It is the problem of coordinating with something that is, in a sense that will be made precise below, coordinating back.
The thesis of this paper is that coordination of this second kind, which I will call interrecursive coordination, is rare across the living world in its sustained and escalated forms, evolutionarily late wherever it does occur at intensity, and metabolically expensive in a specific and identifiable way that has nothing to do with the sheer quantity of information involved. Most of what passes for "social cognition" in the comparative literature is not interrecursive at all. It is sophisticated, often highly organised, coordination with other bodies treated as elements of a structured but fundamentally nonrecursive environment, an environment that behaves regularly, if intricately, and does not itself have to be modelled as modelling you. The seagulls on the Tromsø roof are the clearest illustration I know of this distinction, precisely because their case is so minimal: real sociality, real mutual registration, and the near-total absence of anything one would want to call interrecursive engagement.
Living things are best understood not as possessing any fixed cognitive capacity but as capable of recursive fluidity: the ability to move up through levels of recursivity when a situation demands sustained explicit attention, and, critically, to return to seamless coordination once the demand has passed. Recursive fluidity does not only describe movement up and down levels. It also describes movement across the three types of coordination introduced below, and it is this fuller picture, fluidity across type as well as across level, that explains both why interrecursive engagement can be the most exhausting experience available to a human being and why it can, in its settled and trusted forms, be among the most restorative. Section 3 develops this in full and is the theoretical core the rest of the argument depends on.
Getting the type and level distinction right matters for reasons that go well beyond a set of Arctic seabirds. It reorganises what "social intelligence" refers to, it supplies an alternative account of why group living becomes costly, and it offers a different reading of the social brain hypothesis and of Dunbar's proposals about group size and grooming in particular. The evolution of cognition is better understood as the evolution of metabolic stakes: not what capacities did a species acquire but when did a particular form of recursive coordination become indispensable to that species' survival and reproduction. This paper takes up the human case directly. What, specifically, became the stake? The answer defended here is interrecursivity itself, in its escalated and sustained forms, not information, not culture, not language in the first instance, but the raw problem of living densely among other recursive centres whose next moves cannot be read off the world the way weather, terrain, and predictable neighbours can be read off the world.
The argument proceeds in five stages. First, I set out a threefold typology of coordination, nonrecursive, selfrecursive, interrecursive, that will do the analytic work throughout. Second, I develop the central claim: each of these three types admits its own internal range of recursivity levels, fluidity operates within and across all three simultaneously, and the three types are never engaged in isolation from one another. Third, I argue that a great deal of what the literature calls social behaviour belongs to the nonrecursive category, or to interrecursivity resting at its own lowest, cheapest level, rather than to the escalated forms that have dominated the comparative literature's imagination, and I use the Tromsø gulls, along with several harder cases, to make the boundary precise rather than merely asserted. Fourth, I explain why escalated interrecursive coordination is costly in a way that has nothing directly to do with the amount of information processed, and I show what this implies for the human case specifically. Fifth, I bring the argument to bear on Robin Dunbar's social brain hypothesis and his independent work on the neurochemistry of primate bonding, not to reject either but to show that the reframing offered here fits his own strongest evidence rather better than the informational account he built it to support.
Three Situations of Coordination
Before the central distinction can be defended, it needs precision. I propose that all coordination between a living organism and something outside it falls into one of three situations, distinguished not by the complexity of the behaviour involved but by the kind of thing being coordinated with.
nonrecursive coordination is coordination with a world that does not itself model, anticipate, or respond to the organism's own modelling. Gravity does not adjust its pull because an animal has learned to compensate for it. A river's current does not change because a fish has learned to swim against it. The seasonal return of cold does not accelerate because a bird has begun preparing for it. This is the largest category of coordination in the living world by an enormous margin, and it is also, on the whole, the most tractable category, because nonrecursive regularities are learnable. However intricate the terrain, however variable the weather, however unpredictable a given storm may be in its particulars, the kind of unpredictability involved is bounded: it does not include the world trying to out-anticipate the organism's anticipation of it. A sufficiently good model of a river, built up over a lifetime or across many generations, converges on the river's actual behaviour and stays converged. The river is not adversarially, or cooperatively, or in any other way recursively engaged with the fish's model of it.
selfrecursive coordination is coordination the organism performs on or with itself: regulation, anticipation of its own future states, learning from its own past, repair, adjustment of its own behaviour in light of its own prior outcomes. This is also extremely widespread, and it varies enormously in sophistication across lineages, a bacterium's chemotactic adjustment and a corvid's caching and recovery behaviour both belong here, however far apart they sit on any plausible scale of complexity. What unites them is that the process being modelled, anticipated, or adjusted to is the organism's own trajectory through a largely nonrecursive world, even when that trajectory is highly elaborate. A great deal of what gets called "cognition" in the ordinary sense, memory, planning, learning, even fairly sophisticated forms of tool use practised alone, is selfrecursive in this sense. It does not, by itself, require engaging another organism as a recursive centre at all.
Interrecursive coordination is different in kind from both. It occurs when another organism must be engaged as another recursive centre: as something whose next action is not simply a regularity to be learned, because that action is itself shaped by an internal process, anticipation, assessment, intention, deception, alliance calculation, that is not directly observable and that may, crucially, be oriented toward my anticipated action in turn. The defining feature is not merely that another organism is present, and not merely that its behaviour is complex or hard to predict from limited data. Weather is also hard to predict from limited data, and weather is not interrecursive. The defining feature is that the other's future action is irreducible to a fixed regularity discoverable from past observation of it alone, because that action depends on a process running inside the other that is itself sensitive to what it expects from me.
It is worth distinguishing this kind of uncertainty from uncertainty in the ordinary, epistemic sense, since the two are easily run together. Epistemic uncertainty exists wherever a fact is simply unknown: how many fish are in a lake, what the weather will do next week, whether a particular structure will bear a given load. This kind of uncertainty can be reduced, in principle, by gathering more information, and it does not change in kind as more information arrives. Interrecursive uncertainty is different in structure, not merely in degree. What is uncertain is not a fact waiting to be discovered but the state of another recursive centre: its intentions, its commitments, its loyalties, its likely future actions, its interpretation of the situation, and, at a further remove, its own modelling of my modelling of it. Gathering more information does not straightforwardly reduce this kind of uncertainty, because the object of uncertainty can itself change in response to the information-gathering, and because part of what is uncertain is a process rather than a fact. This distinction, epistemic uncertainty against interrecursive uncertainty, is what makes interrecursive coordination a different ontological situation from coordination with a merely complicated but nonrecursive world, and it does real work throughout what follows.
It is worth stating the distribution of these three situations across the living world plainly and cautiously, because the stronger claims later in this paper depend on getting the weaker claim right first. nonrecursive coordination, and some minimal form of selfrecursive coordination, regulation, simple learning, basic anticipation of one's own bodily states, can be found in essentially any living being, from the simplest single-celled organism upward; these are not late achievements requiring special explanation, they are close to definitional of what it is to be a living, self-maintaining system at all. Interrecursive coordination, by contrast, is a considerably later evolutionary achievement, and it is specifically the sustained and intense forms of interrecursivity that are rare and late, most pronounced in the human case, rather than interrecursivity as such being simply absent elsewhere. This is a narrower and more defensible claim than an unqualified assertion of rarity, and the next section explains why the qualification is not a retreat but the discovery that gives the whole argument its sharpest form.
Three distinct claims are worth separating here, because collapsing them produces exactly the kind of overstatement this paper wants to avoid. The structural possibility of interrecursivity, that a lineage is capable of engaging another as a recursive centre at all, is old and widespread, present wherever the capacities described above have evolved. Ordinary interpersonal interrecursivity, in which that capacity is exercised and typically settles quickly, at L1 or after a brief resolution at L2, is also common among social species and is not itself rare or especially costly. What is rare, and what the remainder of this paper is concerned with, is chronic antagonistic interrecursivity: engagement that escalates to L3 and fails to reach closure. It is this third, narrowest category, not interrecursivity in general and not even escalated interrecursivity in general, that the human case appears to develop and sustain to an unusual degree.
This typology also cuts across, rather than tracks, familiar distinctions like solitary versus social, or simple versus complex behaviour. A solitary organism can face intensely interrecursive episodes: a single, brief predator–prey encounter in which each party is actively modelling and adjusting to the other's anticipated next move is interrecursive in exactly the sense defined here, however solitary the species involved otherwise is, and however short-lived the episode. Conversely, a highly social organism embedded in a large, stable group can spend the overwhelming majority of its time in nonrecursive or selfrecursive coordination with that group, treating its fellow group members largely as a structured, learnable, and in that sense nonrecursive backdrop against which its own selfrecursive projects, feeding, resting, moving, unfold. Sociality, in other words, is not a reliable proxy for interrecursivity. It is a separate variable, and confusing the two is one of the more consequential errors in the comparative literature on social cognition, as the following sections argue in detail.
Recursive Fluidity Across Types
3.1 What recursive fluidity means
Recursive fluidity is the central positive definition of mental health and effective functioning proposed here: not the possession of some fixed cognitive capacity, but the ability to move, as circumstances require, from the seamless, absorbed, non-deliberative coordination named L1, skilled coping, habitual action, the driving of a familiar road while thinking about something else entirely, up through L2, a brief punctuating moment of noticing and adjustment that resolves quickly and returns the organism to L1, and, when a difficulty does not resolve quickly, into L3, a level of sustained, explicit, effortful engagement that cannot simply be delegated back to habit. Further, more abstracted levels, L4 and L5, involve increasingly reflective and symbolically mediated forms of engagement with one's own situation; they matter for the fuller architecture of this framework but do comparatively little work in the present paper, which is concerned above all with the dynamics of L1 through L3.
The general finding is that the hallmark of accomplished human functioning is not constant reflection or constant deliberate effort. It is the opposite: the continual, successful return of recursive organisation to L1. A skill is mastered not when it can be performed with maximal conscious control but when conscious control is no longer required. A relationship is healthy not when it demands constant vigilant negotiation but when trust has made much of that negotiation unnecessary. Distress, on this account, is substantially a matter of coordination becoming stuck at L2 or L3, unable to resolve, unable to return to the ease of L1, rather than simply a matter of facing a difficult situation as such.
Readers will recognise a family resemblance here to Daniel Kahneman's distinction between a fast, automatic System 1 and a slow, effortful System 2, and to the broader tradition of dual-process theorising in cognitive science that Kahneman's work popularised so successfully. The resemblance is real and worth naming rather than disguising. Kahneman's own framework, for all its influence, has been substantially contested within cognitive science: critics have long argued that a strict two-system dichotomy oversimplifies what is, on closer inspection, a graded continuum rather than two separable mechanisms, that the boundary between the systems is far fuzzier in practice than the metaphor suggests, and that some of the heuristics-and-biases findings originally used to motivate the distinction have not survived subsequent replication attempts as cleanly as once assumed. None of this is offered to dismiss Kahneman's contribution, which remains genuinely foundational; it is offered because a graded, multi-level architecture, L1 through L5, admitting continuous movement rather than a binary switch, is precisely the kind of refinement that critics of a strict two-system picture have been asking for. What follows extends that refinement into a domain dual-process theory has not systematically addressed: the difference between the type of thing being coordinated with, not only the level of engagement required to coordinate with it.
3.2 Each type of coordination has its own range of levels
The claim that organises everything which follows is this: nonrecursive, selfrecursive, and interrecursive coordination are not simply three boxes an organism sits in one at a time. Each of the three admits its own internal range of recursivity, from an absorbed, seamless L1 through a briefly punctuated L2 to a sustained, effortful L3, and an organism's overall state at any moment is a composite of where it currently sits, simultaneously, within all three tracks at once. Fluidity, properly understood, is not one dial. It is the coordinated, largely automatic management of three dials at once, together with a standing tendency, in each of the three, to seek the return to L1.
nonrecursive coordination at its own levels. At L1, nonrecursive coordination is coordination that no longer registers as coordination at all: walking familiar terrain while attending to something else, breathing in a stable climate, moving through a well-known kitchen in the dark. It can escalate. Picking one's way across genuinely treacherous, unfamiliar terrain, pack ice, a storm, an unmapped slope, demands sustained, effortful, L3-level attention even though the terrain itself remains nonrecursive throughout: it is not modelling the climber, not adjusting its difficulty in response to being watched, not strategically defeating the climber's plan. This is a crucial point of contrast with what follows. nonrecursive coordination can become difficult, even severely difficult, without ever acquiring the property that makes interrecursive coordination distinctively costly, because the difficulty here is a matter of objective complexity and unfamiliarity, not of a target actively responsive to being modelled.
selfrecursive coordination at its own levels. At L1, selfrecursive coordination is a well practised skill running on its own, a habitual routine, ordinary bodily self-regulation proceeding beneath notice. This is the condition of most of an organism's own self-maintenance most of the time. It escalates when something in that self-regulation does not resolve quickly: an error in an otherwise practised skill, an unfamiliar bodily state, a point in one's own planning that will not settle. This punctuates first as L2, a brief noticing, a quick correction, a return to L1 within moments, and, when it fails to resolve at L2, escalates into L3: sustained, effortful, often uncomfortable self-monitoring, of the kind ordinary experience calls worry, rumination, or deliberate problem-solving about one's own situation. The cost of selfrecursive coordination, in other words, tracks almost entirely how quickly it resolves back down to L1. Practised, resolved self-regulation is cheap. Self-regulation stuck at L3 is not, and this is a large part of what everyday exhaustion, in the purely self-directed sense, actually consists in.
Interrecursive coordination at its own levels is the central claim of this section. Interrecursive coordination has, in exactly the same way, its own full range from L1 to L3 and beyond, and recognising this resolves what might otherwise look like a tension in the argument. At its own L1, interrecursive engagement is seamless, established, and trust-based: two beings, each recognised by the other as a recursive centre, coordinating with one another so reliably, on the basis of such an extensively confirmed shared history, that active modelling is no longer required in any effortful sense. The clearest biological instance of this is primate social grooming. Grooming is not merely a pleasant pastime layered on top of costly social cognition; it is, on the best current evidence, mediated by the brain's own endorphin system, activated through specialised C-tactile afferent fibres in the skin that respond to slow, light stroking and project to the brain's reward and pain-management circuitry. Grooming between primates who know and trust one another does not require the sustained, uncertain modelling that characterises a first encounter with a stranger or a tense negotiation with a rival; it runs largely on established expectation, and it is, distinctively, not merely low-cost in the way a habitual skill is low-cost, but actively rewarding: self-sustaining, sought out, and physiologically restorative rather than merely neutral. L1 interrecursivity is not simply cheap coordination with another mind. It is coordination with another mind that has become cheap and pleasurable precisely because the relationship's reliability has been established, and this combination, low metabolic cost alongside strong intrinsic reward, gives every organism capable of it a standing incentive to convert costly, uncertain interrecursive relationships into settled, L1 ones wherever this can be achieved. Sections 6 and 7 return to this at length in connection with Robin Dunbar's own work.
Interrecursive coordination escalates in exactly the pattern already described for selfrecursive coordination, but from a costlier baseline and with a further twist. L2 interrecursivity is brief, resolving negotiation: a glance exchanged to confirm joint attention, a short vocal exchange settling an ambiguity, a quick check-in that restores confidence and permits a return to L1. L3 interrecursivity is what happens when this does not resolve quickly: sustained, effortful, explicit modelling of another recursive centre whose intentions remain genuinely uncertain, active negotiation, assessment of a stranger's likely disposition, ongoing monitoring of a rival, detection of possible deception, the management of a coalition whose loyalties are not fully settled. This is, on the account defended in Section 5 below, the single most metabolically demanding form of coordination available to a social organism, and it is at its most demanding of all when the relationship is not merely uncertain but actively adversarial, when the other recursive centre may specifically benefit from defeating one's model of it, and one may specifically benefit from defeating theirs.
It is worth naming explicitly what happens when a track resolves, because the concept does real work in what follows. Call it recursive closure: the point at which recursive modelling of another centre no longer requires continual revision, not because agreement has been reached, and not because the relationship has become simple, but because a stable enough model is now available that further encounters confirm it more often than they overturn it. Closure is what allows a track to return to L1. It is not the same thing as resolution in any conflict-ending sense; two rivals can achieve closure about each other by arriving at a stable, mutually confirmed understanding of where each stands, without the rivalry itself ending. What closure requires is only that the model stop needing to be rebuilt.
Chronic antagonistic interrecursivity, on this account, is not simply prolonged conflict. Prolonged conflict can still achieve closure; two parties can remain opposed for a long time while each holds a stable, sufficiently accurate model of the other, and the relationship, though unpleasant, does not generate continuing recursive labour beyond what the underlying conflict itself demands. What distinguishes the chronic case is the failure of closure itself: the participants cannot arrive at a model of one another, or of the situation, that stops requiring revision. Every new encounter reopens rather than confirms. The recursive labour involved is therefore not merely sustained, in the sense of lasting a long time, but genuinely unresolved, in the sense of never reaching the point at which it could, in principle, stop.
3.3 Asymmetrical legibility and recursive asymmetry
Interrecursivity varies not only in intensity, how far up the levels a given engagement has escalated, but in the symmetry of mutual legibility between the parties involved. Some interrecursive relationships allow approximately symmetrical modelling: each party has roughly comparable access to the other's signals, history, and likely reasoning, and each can in principle be read by the other about as well as it can read in turn. Other interrecursive relationships distribute this access unequally. One party may be considerably more legible to the other than the other is to it, and this asymmetry is not merely a matter of degree; it changes what reciprocal modelling can accomplish, because a model built from an asymmetrical position cannot be corrected, tested, or confirmed at the same rate as the model held of it.
This asymmetry generalises beyond legibility narrowly construed. Interrecursivity can become asymmetric through unequal information, unequal authority, unequal communicative access, unequal opportunities for correction, and unequal opportunities for mutual modelling more generally. Wherever several of these are asymmetric in the same direction at once, closure becomes correspondingly harder to reach for the less advantaged party, because the very means by which a model would ordinarily be tested and revised are among the resources distributed unequally.
A further dynamic is worth naming separately. Some interrecursive situations remain permanently open not because information is scarce but because new information generates additional competing interpretations rather than eliminating them. Call this recursive incompletion. Where an environment is rich enough in ambiguous or multiply interpretable signals, each new piece of evidence can be read in more than one way consistent with what came before, so that the model, rather than converging, continues to branch. Recursive incompletion and asymmetrical legibility are independent dynamics and can compound each other: an already asymmetric position becomes still harder to close when the information that does arrive is itself ambiguous.
Complex organisations introduce additional recursive centres whose relationships may substantially alter the dynamics of interrecursivity, a topic requiring separate treatment.
3.4 No hard boundaries, and no isolation
None of the three types, and none of their internal levels, operates in isolation from the other two. An organism engaged in the most intense, sustained, antagonistic L3 interrecursive encounter imaginable, assessing a genuine rival, tracking a real threat, does not thereby stop monitoring its own bodily state, and does not thereby stop attending, at some level, to the nonrecursive environment around it. It cannot afford to; an organism that became so absorbed in modelling a rival that it walked off a ledge or failed to notice an approaching predator would not survive the encounter it was so carefully managing. Equally, an organism resting in the most settled, trust-filled L1 interrecursive state, grooming, or its human equivalents of easy company and physical affection, continues, in the background, both selfrecursive regulation (the physiological changes of relaxation and bonding themselves require ongoing internal coordination) and nonrecursive environmental attunement.
What varies, then, is not whether all three types are engaged, they always are, simultaneously, as three parallel and continuously running tracks, but which of the three is currently occupying the greatest share of the organism's limited attentional and metabolic resources, and at what level within its own range. Recursive fluidity, in its fullest sense, names the organism's capacity to manage this three-track composite state as a whole: to let nonrecursive and selfrecursive coordination run largely at L1 by default, to allow interrecursive coordination to rest at its own rewarding L1 wherever trust permits, and, when escalation in any one track becomes unavoidable, to sustain the effortful L2 or L3 engagement that track demands without losing the other two tracks in the process, and, above all, to return every track that has escalated back down to L1 once the demand that raised it has actually passed. Difficulty in life, on this account, is very often not difficulty with any single track in isolation. It is difficulty releasing a track, most often the interrecursive one, and most often its antagonistic variant, in its most severe cases a variant in which recursive closure repeatedly fails to be reached, that has become stuck at L3 and will not come back down.
The Correction: Sociality Is Not Interrecursivity
Comparative psychology and behavioural ecology have, for good historical reasons, treated almost any behaviour occurring in the presence of conspecifics as a candidate instance of "social cognition." Flocking, schooling, colonial nesting, cooperative vigilance, group foraging, dominance hierarchies, even simple aggregation around a shared resource have all, at various points, been folded into a broad category whose implicit organising assumption is that being around others and coordinating with others are more or less the same achievement, differing only in degree of sophistication. I want to argue that this assumption is false, that it has obscured an important discontinuity in the living world, and that correcting it, now armed with the fluidity framework developed in Section 3, changes what counts as evidence for social cognition in the strong sense, and considerably sharpens the earlier claim about rarity.
A great deal of what looks social is nonrecursive coordination with other bodies treated as elements of a structured environment, not interrecursive engagement with those bodies as other recursive centres, and a further, separately important portion of what looks social is interrecursive engagement resting comfortably at its own L1, rather than the sustained, escalated interrecursivity that has dominated the comparative literature's imagination. The seagulls on the Tromsø roof are the clean case for the first half of this claim. Their spacing behaviour is neither trivial nor stimulus-bound in the crudest sense; it is a real, actively maintained regularity, re-established after disturbance, sensitive to the presence and rough position of every other bird on the roof. It requires each bird to register the others, to compute something like a minimum comfortable distance, and to adjust its own position when that distance is violated. This is genuine coordination, and it would be a mistake to call it merely mechanical or to deny it any cognitive content whatsoever.
But notice what this coordination does not require. It does not require any bird to model what another bird is about to do based on an assessment of that bird's internal state, intentions, or likely response to the first bird's own anticipated action. Each bird can maintain its spacing by treating every other bird much as it treats the ridge of the roof or the angle of a chimney: as a located obstacle with an approximate boundary, to be kept at a certain distance, whose position may shift but whose shifting does not need to be understood as motivated, responsive, or strategic in order for the spacing behaviour to work. The gull does not need to ask what its neighbour intends. It needs only to register where its neighbour currently is, and to keep a rough margin. This is coordination with a structured, multi-body, but nonrecursive field, resting throughout at that field's own L1, precisely the situation described in Section 3.2 under the first category, only now the field happens to be made up of other living organisms rather than tiles and chimneys.
The evidence for this reading, beyond the sheer absence of directed interaction, is what the gulls do not do across the observed hours. They do not groom. They do not vocalise toward specific neighbours in the turn-taking, response-contingent way that would indicate one bird tracking and responding to another's communicative act. They do not form or dissolve sub-groupings on the roof, no coalitions form against a bird that lands too close, no pairs consistently reposition near each other across repeated landings and takeoffs. Position on the roof, so far as an hour or more of observation could establish, was close to interchangeable: any gull could occupy any slot, provided the spacing rule was respected, and which particular gull occupied which slot did not appear to matter to the others. This interchangeability is itself diagnostic. Genuinely interrecursive relationships, even settled L1 ones, are typically not interchangeable in this way, a chimpanzee's grooming partner, a wolf's pack-mate, a primate's specific long-term ally is not a fungible occupant of a slot but a specific other whose particular history with the focal animal shapes the interaction, and whose C-tactile-mediated bonding effect, on the evidence surveyed in Section 3.2, does not transfer automatically to an arbitrary substitute. The gulls' indifference to which neighbour occupies the adjacent stretch of ridge is evidence that the relevant computation is spatial and structural, not individuated and dispositional, and it is evidence, too, that this particular behaviour is not merely low-cost interrecursivity but nonrecursive coordination proper: it lacks not only the cost but also the individuation and the reward that even minimal interrecursivity, at its own L1, characteristically carries.
This does not mean gulls are incapable of interrecursivity under any circumstances. Herring gulls and related species show genuinely sophisticated behaviour in other contexts, kleptoparasitism, in which one gull actively tracks another's foraging success and success-dependent likelihood of yielding a stolen fish, plausibly does require something closer to a model of the other bird's current state and probable next move, and, being brief, contested, and quickly resolving, sits closer to interrecursive L2 than to the sustained L3 engagement discussed later in this paper. The claim is not that gulls, as a taxon, are incapable of interrecursive coordination at any level. The claim is that this particular, extremely common behaviour, roof-perching in loosely spaced aggregations, is not evidence of it at any level, however social it looks to a casual observer, and however readily an observer primed by the "social cognition" literature might be tempted to read intention, negotiation, or planning into it.
Generalising the point: a flock of starlings in a murmuration, a school of fish executing a coordinated evasive manoeuvre, a colony of ants maintaining foraging trails, a herd of ungulates grazing at consistent inter-individual spacing are, in the great majority of documented cases, executing nonrecursive coordination with a structured field of conspecific bodies, achieved through simple, local, non-modelling rules, maintain distance from nearest neighbours, align direction with nearby individuals, follow a pheromone gradient, avoid gaps in visual coverage, that require no representation of another individual's internal state at all. These are remarkable achievements of self-organisation, and nothing in this argument diminishes them as behavioural or even as (self-recursively) cognitive phenomena. But they are not instances of interrecursive coordination at any level, and treating them as if they were, treating "these animals coordinate elaborately with each other" as sufficient grounds for attributing something like social cognition in the strong, other-minds-tracking sense, collapses a distinction the living world itself does not collapse.
It is not interrecursivity as such that is rare across the living world. It is sustained, escalated interrecursivity, engagement that does not, or cannot, quickly resolve back down to its own L1, that is rare, late, and, on the evidence assembled in Section 6, concentrated to an unusual degree in the human case. Low-level, settled, trust-based interrecursivity, exemplified by grooming and its functional equivalents, is genuinely widespread among highly social species and is neither rare nor, on the account developed here, especially costly. What is rare is the sustained management of interrecursive uncertainty that has not yet been, or cannot be, settled, and it is to the cost of exactly that condition that the paper now turns.
The corrective this section proposes is a criterion, not merely an intuition, for distinguishing nonrecursive coordination from interrecursive coordination at any level. Interrecursive coordination, even resting at its own L1, should show at least the following features, none of which nonrecursive social coordination reliably shows: differential, non-interchangeable engagement with particular others rather than uniform treatment of any conspecific occupying a given spatial or structural role; behavioural adjustment that tracks an inferred internal state of the other, however lightly, rather than only the other's current observable position or trajectory; and, where the relationship is escalated rather than settled, sensitivity to the other's anticipated response to one's own action, and flexible, context-dependent recalibration of behaviour toward that specific individual based on a history of prior interaction with them. Roof-perching spacing behaviour satisfies none of these criteria, at any level. Coalition formation in chimpanzees, individually differentiated long-term social bonds in dolphins and elephants, targeted deception in corvids caching food, and grooming across the primate order all plausibly satisfy several of them, whether resting comfortably at L1 or, in the case of coalition management and deception, escalated toward L2 or L3. The two situations, nonrecursive coordination, and interrecursive coordination at any level of its own range, are not points on a single continuum of "social complexity." They are different situations, requiring different computations, very possibly recruiting different neural and evolutionary machinery, and the evidence reviewed in Section 5 gives some direct support for exactly that last claim.
Why Escalated Interrecursivity Is Metabolically Expensive
If interrecursivity, even at its own L1, were simply a more elaborate version of nonrecursive or selfrecursive coordination, its escalated forms' cost would be puzzling; one would expect the cost to scale smoothly with complexity, in the way ordinary informational load scales. The actual pattern the fluidity framework predicts, and that the available evidence supports, is different: a cost curve within interrecursivity that is nearly flat and even rewarding at L1, and steeply rising from L2 into L3, at its highest specifically when the relationship is antagonistic or genuinely uncertain rather than settled, and, as Section 3.3 has argued, highest of all when the antagonism is compounded by asymmetrical legibility or recursive incompletion, either of which can prevent closure from being reached at all. This section sets out why, and grounds the claim in evidence rather than assertion alone, while being honest throughout about where the evidence is convergent and adjacent rather than a direct, purpose-built test of the claim.
The nonrecursive world, for all its variability, is learnable in a strong sense, as Section 3.2 established. However complex a river's flow, however unpredictable a given storm, however intricate a terrain, the regularities governing these things do not adjust themselves in response to an organism's growing model of them. A sufficiently accurate internal model of a river, built up through repeated exposure, converges on the river's actual behaviour and, once converged, stays converged; the river does not notice it has been modelled and begin behaving differently to defeat the model. This is equally true, with appropriate qualification, of much selfrecursive coordination once it has resolved back to L1: an organism's model of its own hunger cycles, its own healing processes, its own developmental trajectory is a model of a system that does not adversarially or strategically resist being modelled, even on the occasions when that system is difficult to predict.
Another recursive centre engaged at L2 or, especially, L3 is different in exactly this respect, and only in this respect, not in complexity, but in responsiveness to being modelled. If I build a model of another organism's likely next action, and that organism is itself modelling my likely next action, then my model is a model of a moving target, one that can shift in response to my modelling of it, including shifting specifically in order to defeat my model, whether through concealment, feint, or genuine unpredictability cultivated as a strategy. This is what makes escalated interrecursive coordination categorically different from even highly complex nonrecursive coordination: it is not simply harder to predict because more variables are involved, but harder to predict in principle, because prediction itself becomes an input to the thing being predicted. A river does not care that I have modelled it. Another recursive agent, under the right conditions, may specifically benefit from defeating my model of it, and I from defeating its model of me. This is a claim about the kind of uncertainty involved, and it can be, and should be, defended on structural grounds independently of any survey of how common or costly interrecursivity turns out to be empirically; the empirical evidence that follows is offered as convergent support for an independently motivated claim, not as the basis from which the claim is inferred.
Two bodies of independent evidence bear on this claim.
The first concerns whether modelling another mind recruits distinct machinery from modelling equivalent amounts of non-social information, which is the minimal claim needed to block the objection that "interrecursive cost" is simply a relabelling of ordinary informational load. Neuroimaging research on social working memory has found a clear dissociation here: when participants are asked to hold several people's mental states in mind at once, activity in the brain's dorsomedial default-network and mentalizing regions, including the medial prefrontal cortex and temporoparietal junction, rises with the number of mental states being tracked, while the same regions show the opposite pattern, disengaging, when participants hold an equivalent amount of non-mental information about the same people in mind, such as alphabetising their names. The stimuli were identical in these studies; only the kind of information being held, mental states of another recursive centre versus ordinary facts, determined which system engaged. This is real, specific, and directly relevant evidence that modelling another mind is not "more of the same" as domain-general information load; it recruits a different system with its own, separately scaling cost curve, exactly as the fluidity framework requires.
The second concerns whether that different system carries a different, and specifically a worse, cost profile under conditions of unresolved uncertainty, which is the claim needed to explain why escalated interrecursivity, L3, above all antagonistic L3, appears capable of generating an unusually persistent form of recursive labour rather than merely a different one. The physiological stress literature has long established that unpredictable and uncontrollable stressors produce different, and frequently more severe and more sustained, neuroendocrine responses than predictable stressors of equal or even greater objective intensity: cortisol dynamics that fail to resolve the way they do under predictable conditions, elevated allostatic load, and, in chronic-unpredictability animal models, measurable downstream costs including reduced neurogenesis in regions such as the prefrontal cortex and hippocampus. This literature is not, on the whole, purpose-built to test interrecursive versus nonrecursive uncertainty specifically, a great deal of it concerns unpredictability in general, including entirely non-social stressors such as unsignalled shock or an uncertain job situation. It should therefore be presented as adjacent, convergent evidence that unresolved unpredictability of any kind carries a distinctive and measurable physiological cost beyond what raw complexity would predict, rather than as a direct demonstration that interrecursive unpredictability specifically outweighs nonrecursive unpredictability of matched statistical variance. That more direct comparison, holding objective complexity constant while varying only whether the source of unpredictability is another recursive centre or an indifferent process, is an open empirical question this paper does not close. It is, however, precisely the question the fluidity framework developed in Section 3 makes it possible to state with enough precision to test.
Taken together, these two literatures support a specific, graded, and falsifiable version of the paper's central cost claim, in place of the flatter and less defensible claim that "interrecursivity is metabolically expensive" tout court. nonrecursive coordination is generally the cheapest of the three, though it can become effortful under genuine novelty or hazard without thereby acquiring the strategic-responsiveness property that drives interrecursive cost specifically. selfrecursive coordination is cheap when it runs at its own L1 and becomes costly in direct proportion to how long and how completely it becomes stuck, unresolved, at L2 or L3. Interrecursive coordination, uniquely among the three, is not simply cheap-at-L1-costly-at-L3 in the same way; it is cheap and actively rewarding at its own L1, for the reasons given in Section 3.2, and it is the single most costly condition available to a social organism when escalated to a sustained, unresolved L3, most of all when the relationship in question is genuinely adversarial and each party has reason to actively defeat the other's model, and most of all again when, as Section 3.3 argued, the antagonist's own position cannot even be legibly established. It is this last condition, sustained, unresolved, often antagonistic L3 interrecursivity, and not interrecursivity in general, that the human evolutionary trajectory needs to explain, and it is to that explanation that the paper now turns.
Interrecursivity Only Became a Dominant Stake in Humans
A metabolic stake exists when failure to stabilise a particular recursive coordination reliably reduces an organism's survival, reproduction, or the long-term viability of its mesocosm. Applying that definition here, together with the fluidity framework just developed, yields the paper's central empirical claim. At some point in the evolutionary history of the human lineage, sustained, frequently escalated interrecursivity, engagement with conspecifics that could not reliably be settled at interrecursive L1, and that therefore had to be conducted, across a very large proportion of ordinary daily life, at L2 or L3, became a dominant stake, in a way it does not appear to have become for the overwhelming majority of other social species, including highly social ones with clear interrecursive capacities of their own.
I want to state this claim explicitly as a hypothesis, supported by convergent indirect indicators rather than by the kind of systematic, cross-species application of the criteria given in Section 4 that would be needed to establish it as a demonstrated result. Establishing the latter is a substantial comparative research programme in its own right, well beyond the scope of a single paper, and the honest presentation of the argument is stronger, not weaker, for saying so plainly. What can be offered here is the shape of the case and the specific indicators that motivate it: unusually extended and cooperative juvenile dependency, requiring sustained, layered relationships with non-kin as well as kin; group compositions large enough, and residentially mixed enough, that a very large proportion of conspecifics encountered on a given day cannot be reduced to a small, stable, already-settled set of L1 relationships; and the simultaneous, overlapping presence of multiple, only partially compatible categories of relationship, kin, allies, rivals, potential mates, strangers of unknown disposition, within a single social field, such that the same individual may need to be modelled differently, and re-modelled, across different contexts and different days.
Human beings are not distinctive because they possess a generically larger quantity of "social cognition," as though intelligence were a single dial turned further up in our lineage than in others. They are distinctive because the proportion of ordinary daily coordination that cannot be settled at interrecursive L1, that must instead be conducted at L2, or sustained at L3, appears, on the indicators just given, to vastly exceed that of almost any other species, including species that show clear and sophisticated interrecursive capacities of their own at their own L1. The relevant comparison is not "do humans have more of capacity X than a chimpanzee." It is "what proportion of an individual's daily coordination, across an entire lifetime, must be conducted with entities that cannot simply be treated, in the manner of a well-groomed ally or a Tromsø gull's roof-mate, as a settled or nonrecursive element of a learnable field." I am not arguing that interrecursivity as capacity is distinctly human. I am arguing that humans spend more time interrecursively (which can include relations with nonhumans like animals), than any other species, and that only humans have prolonged, unbroken periods of interrecursive behaviours.
It follows that the traditional evolutionary puzzle, why did human cognition become so elaborate, is not quite the right question, or at least not the first question. The prior question is: why did the proportion of ordinary life conducted at escalated interrecursive levels become so large in the human case specifically, when for most social species, including highly social ones, the great majority of conspecific coordination appears to settle, and stay settled, at interrecursive L1? A full answer to that question belongs to a longer evolutionary and ecological account than can be given here, one that would need to address group size, cooperative breeding and extended juvenile dependency, the layering of kin-based and non-kin cooperative relationships, resource sharing under variance, and the specific ecological pressures of the Pleistocene African and Eurasian environments our lineage occupied. This paper's contribution is narrower but foundational to any such account: it establishes the variable that needs explaining, and it locates the human distinctiveness specifically in the escalation and non-resolution of interrecursivity, not in interrecursivity's mere presence, which the fluidity framework shows is neither rare nor especially costly at its own settled level.
A species for which a large proportion of ordinary social coordination is conducted at unresolved L2 or L3, rather than settling at the cheap and rewarding L1 that grooming and its equivalents make available among smaller-scale primate societies, faces an acute problem this paper's own cost analysis makes visible: the accumulated cost, across a lifetime, of sustaining continuously revisable models of a dense field of strategically responsive others who cannot all be brought down to L1 through grooming alone, because grooming itself, as the next section shows, does not scale. That something had to absorb this cost, that a further mechanism was needed to do, for larger and more loosely bonded groups, what grooming does for smaller and more intimate ones, is a question this paper leaves open. For now, the point to hold onto is narrower: the human evolutionary trajectory is best understood as beginning from the crossing of a threshold in the proportion of daily life conducted at escalated interrecursive levels, not from an increase in raw cognitive horsepower, and the seagulls on the Tromsø roof mark, by clean contrast, a case in which even the settled L1 form of interrecursivity is largely absent, let alone its costly escalated forms.
The Dunbar Rebuttal
Robin Dunbar's social brain hypothesis proposes that primate neocortex size correlates with typical group size because larger groups impose greater cognitive demands on their members, and that this relationship can be used to predict a species-typical upper limit on stable group size from neocortical ratio alone, famously yielding, for modern humans, a figure in the region of 150 individuals as the approximate ceiling on relationships an individual can maintain with the kind of knowledge and trust that sustains reciprocal obligation. This is among the most productive and widely engaged proposals in the evolutionary study of sociality, and nothing in what follows is intended as a wholesale rejection of it. The empirical correlation between group size and relative neocortical investment across primate taxa is real and well documented. What I want to contest is the account of why larger groups are costly, the implicit explanatory variable behind the correlation, and to propose that interrecursive density and escalation, rather than informational complexity as such, are doing the actual explanatory work.
On the standard framing, a larger group is costly to navigate because there is more to know: more individuals, more relationships between those individuals, more histories of past interaction, more permutations of possible alliance and conflict to hold in mind. This is, in essence, an informational account, the brain scales with group size because the quantity of social data to be tracked scales with group size, in something like the way the number of pairwise relationships in a group scales with the square of its membership.
The reframing proposed here does not deny that larger groups contain more relationships in this combinatorial sense. It denies that sheer quantity of relational data is the operative cost. Consider, by way of contrast, a large non-recursively coordinated aggregation: a colony of ten thousand nesting seabirds, or, scaled up from the Tromsø case, a much larger roof or cliff face holding hundreds of gulls rather than a dozen. The combinatorial quantity of "social information" in such an aggregation, in the crude sense of the number of pairwise spatial relationships that could in principle be tracked, is enormous, far larger than the roughly 150-strong human social network Dunbar's figure describes. Yet nothing about this aggregation requires, or plausibly selects for, anything like the cognitive investment associated with the human case, because the relevant coordination remains nonrecursive throughout: each bird tracks its immediate neighbours' positions using simple, local, non-modelling rules, and the aggregate's size does not by itself convert this into an interrecursive problem, let alone an escalated one. Quantity of social data, in other words, does not reliably predict cognitive cost. What predicts cost, on the account developed here, is not how many others are present but how many of those others must be engaged at interrecursive L2 or L3, modelled, and modelled as modelling you back, without the relief of a settled, trust-based L1.
Dunbar's own independent body of research on the physiological mechanism of primate bonding turns out to describe the L1 half of this picture in exquisite and directly usable detail, in a way his informational framing of group size does not naturally anticipate. Dunbar has shown, across a substantial body of work, that primate social bonds are formed and maintained not primarily through information exchange but through social grooming, acting on the brain's endorphin system by way of specialised C-tactile afferent fibres that respond specifically to slow, light stroking. This mechanism is, in the vocabulary developed here, the biological technology for holding a specific relationship at interrecursive L1: cheap, because it does not require active, uncertain modelling of a partner whose reliability has already been established through repeated grooming; and rewarding, because it directly engages the brain's endorphin-based reward circuitry, rather than merely being the absence of cost.
Dunbar has further shown that this mechanism does not scale. The time available for grooming is finite, and as group size grows beyond what direct one-to-one grooming time can bond, primate and hominin lineages appear to have needed successive additional mechanisms that trigger the same endorphin system without requiring the same intensive, dyadic, skin-to-skin time: Dunbar has argued that laughter, and after it music, singing, dancing, and eventually the collective rituals of religion, each served in turn as a way of activating the same bonding chemistry across increasingly large numbers of people simultaneously, precisely because manual grooming alone could no longer keep pace with the group sizes hominin social life increasingly required. This is, read through the present framework, a direct empirical demonstration of the paper's central claim in miniature: the evolutionary problem was never simply more information to process. It was the problem of keeping enough relationships resting at interrecursive L1, cheap and rewarding rather than costly and uncertain, as group size outgrew the capacity of any single bonding technology to hold it there, and each successive mechanism Dunbar identifies is best understood as a technology for doing exactly that at greater and greater scale.
This reframing does not compete with Dunbar's correlational finding or with his grooming research; it proposes that his own strongest and most specific evidence supports the interrecursive-density account rather better than the informational-load account he originally built to explain it, since an informational account gives no obvious reason why touch, laughter, or music, none of which straightforwardly increases the quantity of social information exchanged, should be the mechanisms actually recruited for group bonding, whereas an account centred on holding relationships at a cheap, rewarding L1 predicts exactly this. I want to be equally clear about what remains untested. The prediction that the neocortical correlation should hold specifically for taxa whose group living requires genuine, escalated interrecursive engagement, and should not hold, or should hold only weakly, for large aggregations achieved through nonrecursive coordination of the Tromsø-gull type, is a testable prediction this paper states but does not itself test against a systematic cross-taxa survey. That remains further work, and a more developed version of this argument would need to undertake it directly rather than resting on the strong but partial fit with Dunbar's own grooming and bonding-gap research presented here.
Predictability as the Hidden Variable
One further thread sets the direction for a further step in this argument. The nonrecursive world, as Section 5 established, is predictable in a way the escalated interrecursive world structurally is not: rivers do not adjust to being modelled, but other recursive centres, under the right conditions, both can and do. Section 3 has added a further piece: predictability, within interrecursive relationships specifically, is not simply given or absent, it is achieved, relationship by relationship, through the same kind of settling toward L1 that grooming accomplishes at small scale, and Dunbar's own research names several further, larger-scale mechanisms, laughter, music, collective ritual, that appear to do the same work for larger and less intimately co-present groups.
This suggests a hypothesis about the shape of a very large portion of subsequent human evolutionary and cultural history, one this paper can only state rather than defend. If sustained, unresolved interrecursivity generates the distinctive and otherwise irreducible cost identified in Section 5, and if that cost became, as argued in Section 6, a dominant and load-bearing feature of ordinary human life once group scale and social complexity outran what grooming, and even laughter and music, could settle into L1 for every relationship that needed it, then a very great deal of what humans subsequently do, not only in explicit institutions, but in the informal fabric of promise-keeping, reputation, ritual, and shared expectation, can be read as the ongoing, never-finished work of converting portions of that interrecursive uncertainty back into something closer to the predictability of settled L1: not by eliminating the other's status as a recursive centre, which cannot be done, but by locally and provisionally stabilising enough of what can be expected from them that daily coordination becomes survivable, and, where possible, restored to something like the ease and reward that grooming provides at smaller scale. This is a claim about stabilisation, and how such stabilisation actually works once bodies alone can no longer accomplish it, what its principal technologies are, and why it never fully succeeds, is an open question this paper does not pursue further. What can be said here is only that the cost identified in Section 5 does not simply sit unaddressed across human evolutionary history; something absorbs it, and grooming and its immediate evolutionary successors already show what the earliest and smallest-scale version of that absorption looked like.
Objections and Limits
9.1 Is this simply the rich-versus-lean interpretation debate in disguise?
Comparative cognition has a long-standing methodological debate about how liberally to attribute mental states to animals on the basis of observed behaviour, so-called rich interpretations, which posit sophisticated internal representations, against lean interpretations, which favour the simplest mechanism adequate to the observed behaviour, typically associated with the tradition running through Morgan's Canon. It might be objected that the argument of this paper is simply a restatement of lean interpretive caution applied to seagulls: rather than making a substantive claim about the ontology of coordination, it is merely counselling interpretive parsimony.
This objection misreads the paper's target, though addressing it requires an honest concession. The rich-versus-lean debate is epistemic: given ambiguous behavioural evidence, which explanation should we favour on grounds of parsimony, prior to further evidence? The distinction proposed here is ontological in its target, it claims that nonrecursive and interrecursive coordination are, as a matter of fact, different kinds of process, distinguishable in principle by the empirical criteria offered in Section 4. But determining which category applies in any given observed case is, and can only be, an ordinary, fallible, revisable empirical matter, no different in this respect from diagnosing a growth as malignant or benign: the underlying distinction is real and does not depend on our current ability to detect it correctly in every instance, but our access to it in practice always runs through evidence that could, in principle, mislead us. The paper's claim about the Tromsø gulls is not "we should, out of caution, refrain from attributing rich cognition to them." It is "the available evidence, interchangeability of roof position, absence of directed interaction, absence of individuated relationship-tracking, actively supports the nonrecursive reading over the interrecursive one, at any level." Where the relevant evidence is genuinely ambiguous, as it plausibly is for a range of intermediate cases, the honest response is to say so, not to resolve the ambiguity by fiat in either direction; but the existence of ambiguous cases, and the fallibility of the criteria used to resolve them, does not collapse the ontological distinction itself, any more than diagnostic uncertainty collapses the distinction between disease states it is trying, fallibly, to track.
9.2 Surely great apes, corvids, and cetaceans are genuinely interrecursive; doesn't this undermine the paper's claim about human distinctiveness?
Not only does this not undermine the argument, it is a claim the paper explicitly makes and depends upon, and the fluidity framework developed in Section 3 makes the concession possible to state cleanly. Section 6 was careful to locate human distinctiveness not in the mere presence of interrecursive capacity, which the evidence suggests is real, and often rewarding at its own L1, across a range of lineages, but in the proportion of ordinary life conducted at escalated, unresolved interrecursive levels, at a scale that appears, on current comparative evidence, to have no close analogue elsewhere. A chimpanzee engages a small number of grooming partners and coalition allies at a settled, rewarding interrecursive L1, and a smaller number of rivals at escalated L2 or L3, against a backdrop of otherwise largely nonrecursive group coordination with the remainder of its troop; a human, by contrast, appears to conduct an unusually large proportion of total daily social coordination at L2 or L3 precisely because the sheer number and layering of relationships involved outstrips what grooming-scale bonding can settle for everyone who needs it settled. Naming plausible non-human cases of genuine interrecursivity, at both its settled and escalated levels, does not weaken this claim; if anything, it strengthens the paper's credibility, since a version of the argument that denied interrecursivity to all non-human animals would be making a far stronger and less defensible claim than the one actually advanced here.
9.3 Is there a circularity in claiming interrecursivity is rare or costly because it is expensive, and expensive because it is rare?
This is a fair methodological concern and deserves a direct answer rather than a dismissal. The argument would indeed be circular if the cost of escalated interrecursive coordination were inferred from its observed rarity or from its observed difficulty, reasoning, in effect, "it must be expensive, since so few relationships stay there for long." That is not the structure of the argument offered here. Section 5 grounds the cost of escalated interrecursive coordination independently of its distribution across species or relationships, in the structural asymmetry between modelling a non-adversarially responsive system and modelling a system that can strategically respond to being modelled, and supports that independently grounded claim with two convergent, honestly hedged bodies of evidence, the mentalizing-network dissociation and the unpredictability-and-stress literature, neither of which was constructed by, or dependent on, the paper's own claims about rarity. The observed pattern, that relationships tend, when they can, to settle toward the cheap and rewarding L1 that grooming exemplifies, and that sustained L3 is comparatively rare and specifically associated with unresolved uncertainty or antagonism, is then explained by this independently grounded cost, not used as evidence for it.
9.4 Doesn't the paper's own reasoning risk over-attributing interrecursivity to the human and other cases it does endorse?
There is a warning worth applying reflexively here: similar observed behaviour across species does not establish an identical underlying process. The present paper has argued, at some length, against over-attributing interrecursive engagement to cases, flocking, schooling, roof-perching, where nonrecursive mechanisms plausibly suffice. It is only fair to submit its own positive attributions to the same discipline. The claim that chimpanzee coalition formation, corvid caching, cetacean long-term bonds, and primate grooming involve genuine interrecursive engagement, whether settled or escalated, rests, in this paper, on plausibility and on Dunbar's own extensively documented grooming research rather than on exhaustive application of the criteria offered in Section 4 to each case, and a fuller treatment would need to do that work case by case rather than gesture toward it, as the present discussion has done for reasons of scope. The same caution applies, with even greater force, to the central claim of Section 6: that human ordinary life is unusually dominated by escalated interrecursivity is a strong empirical claim, and while it is, I think, well supported by the sheer density and layering of human cooperative and competitive relationships relative to other species, and by the specific fit with Dunbar's bonding-gap sequence developed in Section 7, it deserves the same evidential scrutiny this paper has applied to the seagulls, not exemption from it merely because it is the paper's preferred conclusion.
Conclusion
The seagulls on that Tromsø roof gave me, without meaning to, the cleanest illustration available of a distinction the comparative literature on animal social cognition has too often collapsed. They were unmistakably social, mutually registering, actively spaced, responsive to disturbance in a coordinated way. They were not, so far as an extended period of direct observation could establish, interrecursive at any level, not even the settled, low-cost, rewarding level that grooming exemplifies elsewhere in the primate order. They did not engage one another as other recursive centres whose intentions had to be tracked, whose future actions depended on an internal process oriented toward the observing bird's own anticipated behaviour, and they did not, so far as observation could establish, derive from one another's proximity anything resembling the reward that a settled interrecursive bond provides. They solved a real coordination problem, how to share a crowded roof without constant low-grade conflict, using resources that stayed entirely within the nonrecursive category defined in Section 2, and they solved it well, cheaply, and, to a human observer on a sleepless Arctic night, beautifully.
This paper has argued that the gap between sociality and interrecursivity, made vivid by that minimal and unremarkable case, is not a curiosity about seagulls but a correction the field needs to make more generally, and that the correction is best made not by declaring interrecursivity simply rare, but by recognising that it has, like the selfrecursive coordination it sits alongside, its own internal range of recursivity levels, a cheap and rewarding L1, exemplified biologically by the endorphin-mediated mechanism of primate grooming, and a costly, sometimes gravely costly, escalated form at L2 and above, most costly of all when sustained and antagonistic, and most costly of all again when closure fails to be reached because of asymmetrical legibility or recursive incompletion. Interrecursive coordination in this fuller sense is a distinct evolutionary achievement, structurally costly at its escalated levels for reasons independent of mere informational load and supported by convergent evidence from social neuroimaging and from the physiology of unpredictable stress, genuinely widespread at its settled L1 across highly social species, and, on the evidence assembled here, escalated and sustained across an unusually large proportion of ordinary life specifically and perhaps distinctively in the human case. The evolutionary question this reframing poses is not how human beings came to process more social information than other species. It is when, and under what pressures, the proportion of daily conspecific coordination that could be settled at the cheap and rewarding L1 of grooming and its equivalents began to fall short of what human group life actually required, the threshold named in Section 6, and the specific metabolic stake this paper identifies as central to the human case.
Two consequences follow, one methodological and one substantive, and I close with each in turn. Methodologically, the criteria offered in Section 4, now read alongside the levels internal to interrecursivity itself, give comparative researchers a way of asking, of any given social behaviour in any given species, not only whether it belongs to the nonrecursive or the interrecursive category, but, if interrecursive, whether it is resting at a settled and rewarding L1 or straining at an unresolved and costly L2 or L3, a considerably more precise question than "occurs among conspecifics," and one that Dunbar's own grooming research already shows can be answered with real physiological evidence rather than behavioural inference alone.
Substantively, the reframing offered here relocates the central puzzle of human social evolution. It is not why our species became more intelligent in some generic sense. It is why, uniquely or near-uniquely among social species, so much of ordinary conspecific life came to be conducted beyond the reach of the settled, cheap, rewarding L1 that grooming and its close relatives provide. How a lineage facing that level of continuous, structurally irreducible uncertainty about its own conspecifics managed, across the following stretch of evolutionary and cultural history, to build further mechanisms, beyond the body's own endorphin system, capable of doing at scale what grooming alone no longer could, is not a question this paper attempts to answer.
What this paper has offered is a conceptual framework, not a completed account. Recursive closure, asymmetrical legibility, recursive incompletion, and the distinction between epistemic and interrecursive uncertainty are general properties of interrecursive coordination, developed here at the level of the organism and the species. Their implications for particular institutional and historical settings, education, healthcare, formal organisations, legal systems, politics, remain to be explored, and each is likely to reveal further, more specific dynamics that a general treatment of this kind cannot anticipate.